(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.2' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    352706,       8502]
NotebookOptionsPosition[    309880,       7682]
NotebookOutlinePosition[    310343,       7700]
CellTagsIndexPosition[    310300,       7697]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[StyleBox["Help sheet and Command sheet for Exam\n",
 FontWeight->"Bold"]], "Title",
 CellChangeTimes->{{3.719635745443804*^9, 3.7196358000954056`*^9}, {
   3.7196358304125524`*^9, 3.7196358486595926`*^9}, {3.719635898132081*^9, 
   3.719635904500785*^9}, {3.737348124783411*^9, 3.737348128566285*^9}, 
   3.737356735545039*^9, {3.737356847711321*^9, 3.73735686381159*^9}},
 TextAlignment->Center,ExpressionUUID->"b0ef0f06-84a0-46fa-a12c-6d805de792a5"],

Cell[TextData[StyleBox["Shortcuts to Mathematica (Mac based)",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737363156552958*^9, 
  3.737363172801181*^9}},ExpressionUUID->"16450fb1-7f6a-40ca-bfb3-\
4637e33b6a6f"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Command shortcuts --> Control key for Mac",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737363290100872*^9, 
  3.737363317962183*^9}},ExpressionUUID->"fde2863a-706e-43aa-84e4-\
bdca58946f69"],

Cell[CellGroupData[{

Cell["For Powers", "Subsection",
 CellChangeTimes->{{3.737363336410222*^9, 3.7373633453384132`*^9}, {
  3.737363384390169*^9, 
  3.737363386714859*^9}},ExpressionUUID->"0c3499a5-6151-4698-aa2b-\
41835b94fbd0"],

Cell["Control key and 6", "Text",
 CellChangeTimes->{{3.737363351444549*^9, 
  3.737363366114729*^9}},ExpressionUUID->"fd26895d-66f3-478c-84f8-\
a6f9c6bab878"]
}, Open  ]],

Cell[CellGroupData[{

Cell["For Fractions", "Subsection",
 CellChangeTimes->{{3.737363373359593*^9, 
  3.737363382284421*^9}},ExpressionUUID->"5bfe5877-f6cc-4be1-bbcc-\
dc431bf0c1ca"],

Cell["Control key and /", "Text",
 CellChangeTimes->{{3.7373633911683083`*^9, 
  3.737363406268409*^9}},ExpressionUUID->"4da526b5-bcae-4eeb-8748-\
e2f1c4499c6e"]
}, Open  ]],

Cell[CellGroupData[{

Cell["For Square Root", "Subsection",
 CellChangeTimes->{{3.737363414848255*^9, 
  3.737363422664094*^9}},ExpressionUUID->"2db884f4-d02f-4e03-af07-\
9b477da89d8a"],

Cell["Control key and 2", "Text",
 CellChangeTimes->{{3.737363427515476*^9, 
  3.7373634413236437`*^9}},ExpressionUUID->"46627abb-ce3a-4570-bedd-\
6e1858a66aaa"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Escape Key shortcuts --> Applicable to all computers ",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737363472948635*^9, 
  3.737363509825569*^9}},ExpressionUUID->"06afeb0b-3922-47bc-9d98-\
e6ef21fbdfb7"],

Cell[CellGroupData[{

Cell["Degree --> \[Degree]", "Subsection",
 CellChangeTimes->{{3.737363538217494*^9, 3.737363560813157*^9}, {
  3.737363793262885*^9, 
  3.737363796225012*^9}},ExpressionUUID->"9f666182-37a0-48d9-8d3b-\
7fa326dcdd33"],

Cell["(Esc) deg (Esc)", "Text",
 CellChangeTimes->{{3.737364122413641*^9, 
  3.737364178573958*^9}},ExpressionUUID->"640a3026-c480-4beb-9084-\
5839a1d42079"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Pi --> \[Pi]", "Subsection",
 CellChangeTimes->{{3.737363576394322*^9, 3.737363576729415*^9}, {
  3.737363800750751*^9, 
  3.7373638098653097`*^9}},ExpressionUUID->"1301e941-0574-40c8-9472-\
214749288cd3"],

Cell["(Esc) pi (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.737363580215559*^9, 3.737363581277732*^9}, {
  3.7373641551064177`*^9, 
  3.737364171228292*^9}},ExpressionUUID->"4847bccc-6eab-48b9-903a-\
61a4aaddbe8e"]
}, Open  ]],

Cell[CellGroupData[{

Cell["e --> \[ExponentialE]", "Subsection",
 CellChangeTimes->{{3.7373635899800587`*^9, 3.7373635921883287`*^9}, {
  3.737363812547923*^9, 
  3.7373638224197397`*^9}},ExpressionUUID->"916df522-938e-46af-ba79-\
a6767050fc2d"],

Cell["(Esc) ee (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.737363599356345*^9, 3.7373635995920763`*^9}, {
  3.7373641846218367`*^9, 
  3.73736418918252*^9}},ExpressionUUID->"76d6449d-53a2-4679-b83b-\
cdf059aad0a2"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Distribution --> \[Distributed]", "Subsection",
 CellChangeTimes->{{3.73736360653302*^9, 3.737363626741519*^9}, {
  3.737363825367827*^9, 
  3.7373638348193283`*^9}},ExpressionUUID->"5a9b799b-66f3-49a3-8a81-\
6e8cd83c58d6"],

Cell["(Esc) dist (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.737363613504922*^9, 3.7373636137085037`*^9}, {
  3.737364194507607*^9, 
  3.737364201110005*^9}},ExpressionUUID->"fcd996d8-7792-4940-a82a-\
f6cdb06f1ca7"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Theta --> \[Theta]", "Subsection",
 CellChangeTimes->{{3.737363723273841*^9, 3.737363724503539*^9}, {
  3.73736383997001*^9, 
  3.7373638608381577`*^9}},ExpressionUUID->"6a6c4df8-fcc1-4bc2-96ad-\
6811e542206f"],

Cell["(Esc) theta (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.737363728092826*^9, 3.737363728309675*^9}, {
  3.7373642060635777`*^9, 
  3.737364217003603*^9}},ExpressionUUID->"4c5c6773-8ebd-4b32-997d-\
542d48ef0685"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Sum (Sigma) -->  \[Sum]", "Subsection",
 CellChangeTimes->{{3.737363734463451*^9, 3.737363741632893*^9}, {
  3.7373638506078463`*^9, 
  3.737363854402405*^9}},ExpressionUUID->"ac4c80b8-1f9e-4fd9-b9ed-\
984b7be19683"],

Cell["(Esc) sum (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.737363745009863*^9, 3.737363745280245*^9}, {
  3.737364222824779*^9, 
  3.7373642329346733`*^9}},ExpressionUUID->"ddf7d5ef-daae-46ab-b999-\
290eaf34f793"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Union --> \[Union]", "Subsection",
 CellChangeTimes->{{3.73736375313166*^9, 3.737363755335288*^9}, {
  3.7373638650899153`*^9, 
  3.737363876496409*^9}},ExpressionUUID->"5effcf03-c572-4b8b-8e22-\
bcd5a7d08019"],

Cell["(Esc) un (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.7373637593699503`*^9, 3.737363759611421*^9}, {
  3.7373642491516867`*^9, 
  3.737364267154355*^9}},ExpressionUUID->"36ff7dc9-6241-4a9d-9b60-\
7d943971be24"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Intersection --> \[Intersection]", "Subsection",
 CellChangeTimes->{{3.737363900945931*^9, 
  3.737363912296002*^9}},ExpressionUUID->"f5b4aba1-db65-46a6-ac1f-\
c5949c89a40d"],

Cell["(Esc) inter (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.73736391464677*^9, 3.737363914886395*^9}, {
  3.737364271929288*^9, 
  3.737364279111073*^9}},ExpressionUUID->"7b9ee778-f66c-47f7-88a6-\
fa3165ac5779"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Infinity --> \[Infinity]", "Subsection",
 CellChangeTimes->{{3.737363935867867*^9, 
  3.737363951444437*^9}},ExpressionUUID->"d55ff143-92dd-4ad4-b343-\
174bf07ff468"],

Cell["(Esc) inf (Esc)", "Text",
 CellGroupingRules->"NormalGrouping",
 CellChangeTimes->{{3.737363954053259*^9, 3.7373639542871437`*^9}, {
  3.737364284044099*^9, 
  3.737364289328579*^9}},ExpressionUUID->"afc9e6dc-7510-4b37-b4ab-\
d6456d82b5ec"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Stuff I don\[CloseCurlyQuote]t know the name for", "Subsection",
 CellChangeTimes->{{3.7373639676264763`*^9, 
  3.7373639916961412`*^9}},ExpressionUUID->"ab97e1ec-5bca-47d6-b191-\
e3f7b5bef78c"],

Cell[TextData[{
 "sumt = ",
 Cell[BoxData[
  RowBox[{
   UnderoverscriptBox["\[Sum]", 
    RowBox[{"\[SelectionPlaceholder]", "=", "\[Placeholder]"}], 
    "\[Placeholder]"], "\[Placeholder]"}]],ExpressionUUID->
  "75ece7c9-0449-4bd1-9ee7-a05918df0708"],
 "\nprodt = ",
 Cell[BoxData[
  RowBox[{
   UnderoverscriptBox["\[Product]", 
    RowBox[{"\[SelectionPlaceholder]", "=", "\[Placeholder]"}], 
    "\[Placeholder]"], "\[Placeholder]"}]],ExpressionUUID->
  "78d01799-8b3d-4d23-9af6-f1eac79a40d9"],
 "\nprod = \[Product]"
}], "Text",
 CellChangeTimes->{{3.7373632460949373`*^9, 3.737363251587639*^9}, 
   3.737363322105967*^9, {3.737363445994958*^9, 3.7373634615725946`*^9}, 
   3.737363533181921*^9, {3.737364238165813*^9, 3.737364239316701*^9}, {
   3.7373642938124647`*^9, 
   3.737364299093205*^9}},ExpressionUUID->"4187de2b-ffd5-4352-87bc-\
07ae6125faa7"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nArithmetic Sequences and Series  and Mean ",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737973165442162*^9, 3.73797318329323*^9}, {
   3.737973272967794*^9, 3.737973282112844*^9}, {3.737973354814856*^9, 
   3.7379733600798073`*^9}, 3.737974143294705*^9, 
   3.737975142294503*^9},ExpressionUUID->"636e6fd5-e9e0-433a-bd2e-\
460ac08c94b8"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Arithmetic Sequences",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737973289022015*^9, 3.737973309444051*^9}, {
  3.73797336161973*^9, 3.73797336195758*^9}, {3.737973537875804*^9, 
  3.737973539913105*^9}},ExpressionUUID->"a8c89097-6ba4-475b-9152-\
992dd7d9d99b"],

Cell[CellGroupData[{

Cell["\<\
The general formula for Arithmetic Sequence is: a + d(n-1) = t(n)
a is the first term
d is difference 
n is the position or order on Sequence/Series\
\>", "Subsection",
 CellChangeTimes->{{3.737973547771943*^9, 
  3.737973674636571*^9}},ExpressionUUID->"41bfbcda-1250-406b-9411-\
9badbce2f065"],

Cell[CellGroupData[{

Cell[TextData[{
 "Example 1: ",
 StyleBox["Here is a formula for calculating the nth term of an arithmetic \
sequence with first term a = 3 and common difference d = 2. \na) Find the 5th \
term  ",
  FontSize->18]
}], "Subsubsection",
 CellChangeTimes->{{3.737973691815447*^9, 3.737973750831978*^9}, 
   3.737973787219952*^9, {3.737973847095542*^9, 
   3.7379738780615387`*^9}},ExpressionUUID->"c8a98c55-81b5-4605-81f4-\
6e6fd8dbddbb"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "t", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"t", "[", 
   RowBox[{"n_", ",", "a_", ",", "d_"}], "]"}], ":=", 
  RowBox[{"a", "+", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"n", "-", "1"}], ")"}], "d"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"t", "[", 
  RowBox[{"5", ",", "3", ",", "2"}], "]"}]}], "Input",
 CellChangeTimes->{{3.737973682786469*^9, 3.737973683016202*^9}, 
   3.7379739617215233`*^9, {3.737973993401732*^9, 3.737974012552895*^9}},
 CellLabel->"In[76]:=",ExpressionUUID->"4ae42663-5978-4477-9861-64f41d7c45a7"],

Cell[BoxData["11"], "Output",
 CellChangeTimes->{3.737973962711664*^9, 3.737974013431983*^9},
 CellLabel->"Out[78]=",ExpressionUUID->"d89fc5fe-3b3c-4745-9710-d67d17e01fbe"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["b) used to find which numbered term is equal to 101. ",
 FontSize->18]], "Subsubsection",
 CellChangeTimes->{
  3.737973891310976*^9},ExpressionUUID->"778c1618-3356-4f76-98ed-\
47fa56455355"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "t", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"t", "[", "n_", "]"}], ":=", 
  RowBox[{"3", "+", 
   RowBox[{"2", 
    RowBox[{"(", 
     RowBox[{"n", "-", "1"}], ")"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"t", "[", "n", "]"}], "\[Equal]", "101"}], ",", "n"}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.737973894705971*^9, 3.737973894905282*^9}, 
   3.737973929780497*^9, {3.737974022818391*^9, 3.737974023854951*^9}},
 CellLabel->"In[79]:=",ExpressionUUID->"e56277e9-83eb-4f7e-b174-2df1392490c8"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"n", "\[Rule]", "50"}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.73797393110798*^9, 3.737974030413872*^9},
 CellLabel->"Out[81]=",ExpressionUUID->"86801a85-9e21-4822-a9ab-53c8b00e9b08"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Arithmetic Series",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737974160379003*^9, 
  3.737974187166888*^9}},ExpressionUUID->"fb7a770a-cf17-4fa4-be42-\
4bfc3a91ea21"],

Cell[CellGroupData[{

Cell["Series is the sum of the terms in a sequence.", "Subsection",
 CellChangeTimes->{{3.737974196761261*^9, 
  3.7379742226256933`*^9}},ExpressionUUID->"ff1c0071-5aea-45af-a5e6-\
c347a92b5112"],

Cell[CellGroupData[{

Cell[TextData[{
 "a) ",
 StyleBox["T",
  FontSize->18],
 StyleBox["he sum of the first 100 counting numbers",
  FontFamily->"Times New Roman",
  FontSize->18,
  FontWeight->"Regular"]
}], "Subsubsection",
 CellChangeTimes->{{3.737974249344018*^9, 
  3.7379742665818*^9}},ExpressionUUID->"5b8b6dec-38ab-4622-9028-e1924e79ee1d"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"S", "[", 
   RowBox[{"n_", ",", "a_", ",", "d_"}], "]"}], ":=", 
  RowBox[{
   FractionBox["n", "2"], 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"2", "a"}], "+", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"n", "-", "1"}], ")"}], "d"}]}], 
    ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"S", "[", 
  RowBox[{"100", ",", "1", ",", "1"}], "]"}]}], "Input",
 CellChangeTimes->{{3.737974296335374*^9, 3.73797429651906*^9}, {
  3.7379743745260687`*^9, 3.737974381070504*^9}},
 CellLabel->"In[82]:=",ExpressionUUID->"132dbb1d-31d4-4188-918c-30e38418a8ba"],

Cell[BoxData["5050"], "Output",
 CellChangeTimes->{3.737974382421973*^9},
 CellLabel->"Out[83]=",ExpressionUUID->"1ee06608-2935-4df9-bdcb-80498aff673f"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "b) T",
 StyleBox["he sum of the first 100 odd numbers",
  FontFamily->"Times New Roman",
  FontSize->18,
  FontWeight->"Regular"]
}], "Subsubsection",
 CellChangeTimes->{{3.737974304340398*^9, 
  3.737974323219193*^9}},ExpressionUUID->"314877f4-109a-4672-abdf-\
d5e7dd743ef7"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"S", "[", 
  RowBox[{"100", ",", "1", ",", "2"}], "]"}]], "Input",
 CellChangeTimes->{{3.737974326947391*^9, 3.7379743271485357`*^9}, 
   3.737974388567663*^9},
 CellLabel->"In[84]:=",ExpressionUUID->"a5783735-e583-4f70-8844-a2ca8385bbe2"],

Cell[BoxData["10000"], "Output",
 CellChangeTimes->{3.737974389594537*^9},
 CellLabel->"Out[84]=",ExpressionUUID->"e162976c-9281-4422-a412-58c75f91b275"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "c) T",
 StyleBox["he sum of the first 100 even numbers",
  FontFamily->"Times New Roman",
  FontSize->18,
  FontWeight->"Regular"]
}], "Subsubsection",
 CellChangeTimes->{{3.737974346006131*^9, 
  3.737974354895629*^9}},ExpressionUUID->"2672cdc1-df09-412f-931c-\
7116aeeb2c2a"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"S", "[", 
  RowBox[{"100", ",", "2", ",", "2"}], "]"}]], "Input",
 CellChangeTimes->{{3.737974364145851*^9, 3.737974364358821*^9}, 
   3.737974396039585*^9},
 CellLabel->"In[85]:=",ExpressionUUID->"06c0b8cf-a49a-44da-adf2-580b143bf459"],

Cell[BoxData["10100"], "Output",
 CellChangeTimes->{3.73797439674536*^9},
 CellLabel->"Out[85]=",ExpressionUUID->"a829cfec-9bd2-4a24-bf51-15280c5f56ce"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Arithmetic Mean",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7379744072640543`*^9, 
  3.7379744210919313`*^9}},ExpressionUUID->"1a40cdcb-f067-4e6a-bd0e-\
39ed7e510a8a"],

Cell[CellGroupData[{

Cell["\<\
Arithmetic mean is the mean between two numbers of a sequence and they have \
to be consecutive terms.
Example 1: 8 and 15 \
\>", "Subsection",
 CellChangeTimes->{{3.737974437205924*^9, 3.737974520559904*^9}, {
  3.7379757648564787`*^9, 
  3.737975779309375*^9}},ExpressionUUID->"6c5d65ca-4b3f-4e8a-8adf-\
39d7fec7292b"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"L", "[", 
   RowBox[{"n_", ",", "a_"}], "]"}], ":=", 
  FractionBox[
   RowBox[{"n", "+", "a"}], "2"]}], "\[IndentingNewLine]", 
 RowBox[{"L", "[", 
  RowBox[{"8", ",", "15"}], "]"}]}], "Input",
 CellChangeTimes->{{3.737974427070396*^9, 3.737974427304255*^9}, {
  3.737974535820513*^9, 3.7379745932532053`*^9}},
 CellLabel->"In[86]:=",ExpressionUUID->"32bd7c35-99b9-452d-8b4e-17e7910777b1"],

Cell[BoxData[
 FractionBox["23", "2"]], "Output",
 CellChangeTimes->{3.737974593810095*^9},
 CellLabel->"Out[87]=",ExpressionUUID->"29c237e3-8d7a-4962-b2fe-7fd675568421"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nRecurrence Relations",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.7379746503388033`*^9, 
  3.737974667289215*^9}},ExpressionUUID->"0e6fe98c-5287-4dca-a206-\
e807bc9d1b41"],

Cell[CellGroupData[{

Cell[TextData[StyleBox[" Calculating Recurrence Relations",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737974677669195*^9, 
  3.737974707184534*^9}},ExpressionUUID->"e76e7b26-e519-4de6-85c1-\
aa5c6ca0b10f"],

Cell[CellGroupData[{

Cell["\<\
General command format for recurrence relations:
RecurrenceTable[{U[n+1]\[Equal]a*U[n],t[1]\[Equal]1},U,{n,min value, max \
value,}]\
\>", "Subsection",
 CellChangeTimes->{{3.7380032273122177`*^9, 
  3.738003253141521*^9}},ExpressionUUID->"fa17f597-5dd1-4ccc-a33a-\
a27579043e60"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", "U", "]"}], "\[IndentingNewLine]", 
 RowBox[{"RecurrenceTable", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"U", "[", 
       RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", 
      RowBox[{"2", "*", 
       RowBox[{"U", "[", "n", "]"}]}]}], ",", 
     RowBox[{
      RowBox[{"U", "[", "1", "]"}], "\[Equal]", "1"}]}], "}"}], ",", "U", ",", 
   RowBox[{"{", 
    RowBox[{"n", ",", "1", ",", "3"}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.737974709297064*^9, 3.737974822597006*^9}, {
  3.7379759677368383`*^9, 3.73797597336537*^9}, {3.738003094403016*^9, 
  3.738003105264488*^9}, {3.738003136324511*^9, 3.738003209330641*^9}, {
  3.738003259219293*^9, 
  3.73800335171472*^9}},ExpressionUUID->"f5076070-ab5e-4ae2-a254-\
3ad65114f2af"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1", ",", "2", ",", "4"}], "}"}]], "Output",
 CellChangeTimes->{{3.738003278426553*^9, 
  3.738003357400775*^9}},ExpressionUUID->"b7f3519d-5bd8-461f-9c3b-\
19078e5ca198"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "\n",
 StyleBox["Geometric Sequences, Series and Mean",
  FontSize->48]
}], "Subtitle",
 CellChangeTimes->{{3.737974879105538*^9, 
  3.73797489850581*^9}},ExpressionUUID->"1f479103-3305-4378-a488-\
13dd7f574b1a"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Geometric Sequence",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737975244395447*^9, 
  3.737975284409531*^9}},ExpressionUUID->"a298839f-c4ab-488a-82e0-\
e2ac9e865fc1"],

Cell[CellGroupData[{

Cell["\<\
Example 1: Find the Geometric Sequence of when a = 4, r = 1/3 and n = 5\
\>", "Subsection",
 CellChangeTimes->{{3.737975369996258*^9, 
  3.737975433675457*^9}},ExpressionUUID->"bfcead0b-efbd-4717-ad25-\
479e9fec5b25"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"G", "[", 
   RowBox[{"n_", ",", "a_", ",", "r_"}], "]"}], ":=", 
  RowBox[{"a", "*", 
   SuperscriptBox["r", 
    RowBox[{"n", "-", "1"}]]}]}], "\[IndentingNewLine]", 
 RowBox[{"G", "[", 
  RowBox[{"5", ",", "4", ",", 
   FractionBox["1", "3"]}], "]"}]}], "Input",
 CellChangeTimes->{{3.737975286294882*^9, 3.737975351952317*^9}, {
  3.737975435906103*^9, 
  3.73797545309234*^9}},ExpressionUUID->"f93960a7-9e48-41a7-a230-\
a81917b0bc46"],

Cell[BoxData[
 FractionBox["4", "81"]], "Output",
 CellChangeTimes->{
  3.7379754535718727`*^9},ExpressionUUID->"5ed712aa-b86f-4d32-9472-\
ccc3647ccbbd"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Geometric Series",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737975484027669*^9, 
  3.7379754976693687`*^9}},ExpressionUUID->"bd6776b3-e9bc-49ad-b6a8-\
60bc7a197c78"],

Cell[CellGroupData[{

Cell["\<\
Example 1: Find the Geometric series of 5 + 10 + 20 ... S[10]\
\>", "Subsection",
 CellChangeTimes->{{3.737975504435948*^9, 3.737975518434938*^9}, {
  3.737975563817555*^9, 
  3.737975590070922*^9}},ExpressionUUID->"905f2d34-8012-4504-a12f-\
6baef1467562"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"S", "[", 
   RowBox[{"n_", ",", "a_", ",", "r_"}], "]"}], ":=", 
  FractionBox[
   RowBox[{"a", 
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["r", "n"], "-", "1"}], ")"}]}], 
   RowBox[{"r", "-", "1"}]]}], "\[IndentingNewLine]", 
 RowBox[{"S", "[", 
  RowBox[{"10", ",", "5", ",", "2"}], "]"}]}], "Input",
 CellChangeTimes->{{3.737975593315136*^9, 
  3.737975676696968*^9}},ExpressionUUID->"bff0e671-8282-4083-8157-\
dd77c72771b8"],

Cell[BoxData["5115"], "Output",
 CellChangeTimes->{{3.7379756737119713`*^9, 
  3.737975677476966*^9}},ExpressionUUID->"3ea4acde-7332-41dd-943e-\
2b1860051a6d"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Geometric Mean",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737975707058641*^9, 
  3.737975715774829*^9}},ExpressionUUID->"3a215b5a-572a-4df8-9650-\
84e238ce54d3"],

Cell[CellGroupData[{

Cell["\<\
They have to be consecutive terms.
Find the Geometric Mean of 8 and 24\
\>", "Subsection",
 CellChangeTimes->{{3.7379757436839933`*^9, 3.73797575142819*^9}, {
  3.7379757835318193`*^9, 3.737975799900832*^9}, {3.7379758412582817`*^9, 
  3.737975848827133*^9}},ExpressionUUID->"d856b67c-1864-4082-aae2-\
8d4885463ebf"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"d", "[", 
   RowBox[{"a_", ",", "b_"}], "]"}], ":=", 
  SqrtBox[
   RowBox[{"a", "*", "b"}]]}], "\[IndentingNewLine]", 
 RowBox[{"d", "[", 
  RowBox[{"8", ",", "24"}], "]"}]}], "Input",
 CellChangeTimes->{{3.7379757179600782`*^9, 3.737975718160151*^9}, {
  3.7379758555545473`*^9, 
  3.7379759507793503`*^9}},ExpressionUUID->"57f4c99c-8ace-4e32-afa0-\
344f6916daa0"],

Cell[BoxData[
 RowBox[{"8", " ", 
  SqrtBox["3"]}]], "Output",
 CellChangeTimes->{
  3.7379759520345984`*^9},ExpressionUUID->"3de0cd78-0672-4f09-a193-\
15a7010509b4"]
}, Open  ]]
}, Open  ]],

Cell["", "Subsection",ExpressionUUID->"8fbe765c-7608-4deb-a7e2-bf57c4e1a78c"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "\n",
 StyleBox["Zeno\[CloseCurlyQuote]s paradox and Infinite Geometric Series",
  FontSize->48]
}], "Subtitle",
 CellChangeTimes->{{3.737975997790352*^9, 3.737976025272807*^9}, 
   3.737976571576777*^9},ExpressionUUID->"c1d6440a-a585-45f5-ba4f-\
7d9cf40fd79d"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Calculating the Infinite Geometric Series",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737976038681799*^9, 
  3.737976083317996*^9}},ExpressionUUID->"a2b4b697-ea49-4a34-a521-\
04cc40b18c26"],

Cell[CellGroupData[{

Cell["\<\
If r is -1 > r > 1, then its convergent
Example 1: Find the sum to infinity to the series 1/2 + 1/4 + 1/8 ...\
\>", "Subsection",
 CellChangeTimes->{{3.7379761063868237`*^9, 3.7379761239327383`*^9}, {
  3.737976169069538*^9, 3.737976178553363*^9}, {3.737976230793324*^9, 
  3.737976287586494*^9}},ExpressionUUID->"f10a8f2e-3de0-4729-953d-\
0fa7e6c011fd"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"K", "[", 
   RowBox[{"a_", ",", "r_"}], "]"}], ":=", 
  FractionBox["a", 
   RowBox[{"1", "-", "r"}]]}], "\[IndentingNewLine]", 
 RowBox[{"K", "[", 
  RowBox[{
   FractionBox["1", "2"], ",", 
   FractionBox["1", "2"]}], "]"}]}], "Input",
 CellChangeTimes->{{3.737976086645933*^9, 3.737976100690749*^9}, {
  3.737976132189475*^9, 3.737976132574522*^9}, {3.737976186711275*^9, 
  3.7379761993576937`*^9}, {3.737976291989601*^9, 
  3.737976330401556*^9}},ExpressionUUID->"73388cf3-3ecd-4075-9fd4-\
0ba869ed8e2a"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{{3.737976314192606*^9, 
  3.737976331169361*^9}},ExpressionUUID->"a28d020d-6005-4356-9e45-\
bcd708f1a090"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Example 2: Express the recurring decimal 0.3*2* as the ratio of two integers\
\>", "Subsection",
 CellChangeTimes->{{3.73797638183*^9, 
  3.737976498384041*^9}},ExpressionUUID->"51fcff16-d501-487a-ae9f-\
f34c8cfcf6bc"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"K", "[", 
   RowBox[{"a_", ",", "r_"}], "]"}], ":=", 
  FractionBox["a", 
   RowBox[{"1", "-", "r"}]]}], "\[IndentingNewLine]", 
 RowBox[{"K", "[", 
  RowBox[{
   FractionBox["32", "100"], ",", 
   FractionBox["1", "100"]}], "]"}]}], "Input",
 CellChangeTimes->{{3.737976342051303*^9, 3.737976342399193*^9}, {
  3.7379765044255247`*^9, 
  3.7379765557296343`*^9}},ExpressionUUID->"a23c4c14-1f1f-479b-a7df-\
99fd61d3a5d5"],

Cell[BoxData[
 FractionBox["32", "99"]], "Output",
 CellChangeTimes->{{3.737976530257094*^9, 
  3.7379765564449673`*^9}},ExpressionUUID->"2fcd3aa7-cdac-477f-8e15-\
8610caae74e6"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nBinomial distribution and Hypergeometric \
Distribution \[LongRightArrow] Probability",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737953407693619*^9, 3.737953443572145*^9}, {
   3.7379535417083693`*^9, 3.737953566533063*^9}, 
   3.7379731563531713`*^9},ExpressionUUID->"2a27004c-4bda-449b-b510-\
36505e4fd01b"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Binomial Distribution",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7379534667622213`*^9, 3.7379534782792387`*^9}, {
  3.737953569608287*^9, 3.7379535810039873`*^9}, {3.7820730511318913`*^9, 
  3.782073053580937*^9}},ExpressionUUID->"aecc5405-4ef2-44a8-abcf-\
13ef02d2281c"],

Cell[CellGroupData[{

Cell["\<\
For binomial distribution to be possible, it needs to have 
1) A set number of trials
2) A set number of samples (also seen as \[OpenCurlyQuote] with replacement\
\[CloseCurlyQuote])
3) Only two results: Success or Failure
Representation of the Binomial form in Mathematica\
\>", "Subsection",
 CellChangeTimes->{{3.737953588011574*^9, 3.737953588341549*^9}, {
  3.737955293812372*^9, 3.73795537647653*^9}, {3.7379628694227877`*^9, 
  3.7379628943470097`*^9}, {3.737966089998658*^9, 3.737966115708057*^9}, {
  3.737971216376068*^9, 
  3.73797123430508*^9}},ExpressionUUID->"7f858c78-3f24-48d5-a645-\
6abcb45594d1"],

Cell[CellGroupData[{

Cell["\<\
 Example 1: Suppose 10 males are selected at random. Find the probability, \
correct to four decimals \
\>", "Subsubsection",
 CellChangeTimes->{
  3.737963107202821*^9, {3.737963679047431*^9, 
   3.737963682449471*^9}},ExpressionUUID->"4cf4dd62-456d-4810-88c8-\
4f4ecc134cf7"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Probability", "[", 
  RowBox[{
   RowBox[{"x", "\[GreaterEqual]", "2"}], ",", 
   RowBox[{"x", "\[Distributed]", 
    RowBox[{"BinomialDistribution", "[", 
     RowBox[{"10", ",", "0.0993"}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737953590780734*^9, 3.7379535910014277`*^9}, 
   3.737963139733388*^9},ExpressionUUID->"b1241c13-a32e-403c-8ff5-\
efb1565cf157"],

Cell[BoxData["0.2611902062457971`"], "Output",
 CellChangeTimes->{
  3.7379631410784607`*^9},ExpressionUUID->"366ef63f-8e0f-49d2-85cd-\
245c03186381"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Example 2: Suppose that the probability that a person selected at random is \
left-handed is always 0.2 . If 11 people are selected at random for the \
cricket team: \
\>", "Subsubsection",
 CellChangeTimes->{{3.737963692043007*^9, 3.7379637519557543`*^9}, {
  3.737963864667583*^9, 
  3.737963873556452*^9}},ExpressionUUID->"161afa52-f35f-438f-91fb-\
6bd28172b5e6"],

Cell[CellGroupData[{

Cell["\<\
a) Find the probability of selecting exactly two left-handed.\
\>", "Subsubsubsection",
 CellChangeTimes->{{3.73796388832302*^9, 3.737963919573493*^9}, {
  3.737966021107958*^9, 
  3.73796602191053*^9}},ExpressionUUID->"bdecef72-3317-4066-a9fe-\
76c0c3d6455d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Probability", "[", 
  RowBox[{
   RowBox[{"x", "\[Equal]", "2"}], ",", 
   RowBox[{"x", "\[Distributed]", 
    RowBox[{"BinomialDistribution", "[", 
     RowBox[{"11", ",", "0.2"}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737965099378373*^9, 
  3.737965123338533*^9}},ExpressionUUID->"c2882756-0bc0-46f1-a672-\
4cb6bd17a9ad"],

Cell[BoxData["0.29527900160000004`"], "Output",
 CellChangeTimes->{
  3.737965124459569*^9},ExpressionUUID->"2b1d7a35-ad70-47cd-9e0c-\
3c5560e754f7"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
b) Find the probability of selecting at least four left-handed.\
\>", "Subsubsubsection",
 CellChangeTimes->{{3.7379652708995132`*^9, 3.7379652857660007`*^9}, {
  3.737965478692932*^9, 3.7379654969541187`*^9}, {3.737966017373228*^9, 
  3.7379660183719463`*^9}},ExpressionUUID->"1849d6f3-ecde-4bb8-8c59-\
16733c8f4c1c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Probability", "[", 
  RowBox[{
   RowBox[{"x", "\[GreaterEqual]", "4"}], ",", 
   RowBox[{"x", "\[Distributed]", 
    RowBox[{"BinomialDistribution", "[", 
     RowBox[{"11", ",", "0.2"}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7379660249989157`*^9, 
  3.737966064886698*^9}},ExpressionUUID->"523f479b-0546-4f3c-8545-\
b58ac6d3691e"],

Cell[BoxData["0.16113920000000015`"], "Output",
 CellChangeTimes->{
  3.737966065662746*^9},ExpressionUUID->"b7bc236e-3bb4-43ab-bb88-\
9ff412dd71cd"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Example 3: Monique is practising goaling for netball. She knows from past \
experience that
her chance of making any one shot is about 70%. Her coach has asked her to keep
practising until she scores 50 goals. How many shots would she need to \
attempt to
ensure that the probability of scoring at least 50 goals is more than 0.99?\
\>", "Subsubsection",
 CellChangeTimes->{{3.782072469827057*^9, 
  3.782072477280414*^9}},ExpressionUUID->"0b4d06c9-e0b5-4893-ac69-\
25dd3128d516"],

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "[", "n_", "]"}], ":=", 
  RowBox[{"Probability", "[", 
   RowBox[{
    RowBox[{"x", "\[GreaterEqual]", " ", "50"}], ",", 
    RowBox[{"x", "\[Distributed]", 
     RowBox[{"BinomialDistribution", "[", 
      RowBox[{"n", ",", 
       RowBox[{"7", "/", "10"}]}], "]"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.782072165325266*^9, 3.782072165725708*^9}, {
  3.782072561011898*^9, 
  3.782072761221993*^9}},ExpressionUUID->"8e5e5819-4042-4080-8285-\
83e8164b169d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"f", "[", "n", "]"}], ">", " ", 
    RowBox[{"99", "/", "100"}]}], ",", "n"}], "]"}]], "Input",
 CellChangeTimes->{{3.7820728808413258`*^9, 3.782072892871014*^9}, {
  3.7820729378598003`*^9, 
  3.782072949154004*^9}},ExpressionUUID->"065c002b-d3cd-4d6a-a5f5-\
74fa2e7b299c"],

Cell[BoxData[
 TemplateBox[{
  "Reduce","ivar",
   "\"\\!\\(\\*RowBox[{\\\"0\\\"}]\\) is not a valid variable.\"",2,358,38,
   33101119956967447138,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{
  3.782072764481834*^9, {3.782072887096613*^9, 
   3.782072893477229*^9}},ExpressionUUID->"868a32cc-6846-45ee-9998-\
5dac8c6c1e23"],

Cell[BoxData[
 RowBox[{"Reduce", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     TagBox[GridBox[{
        {"\[Piecewise]", GridBox[{
           {
            RowBox[{"BetaRegularized", "[", 
             RowBox[{
              FractionBox["7", "10"], ",", "50", ",", 
              RowBox[{
               RowBox[{"-", "49"}], "+", "n"}]}], "]"}], 
            RowBox[{"49", "<", "n"}]},
           {"0", 
            TagBox["True",
             "PiecewiseDefault",
             AutoDelete->True]}
          },
          AllowedDimensions->{2, Automatic},
          Editable->True,
          
          GridBoxAlignment->{
           "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
          
          GridBoxItemSize->{
           "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{1.}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.84]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}},
          Selectable->True]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
          "RowsIndexed" -> {}},
       GridBoxItemSize->{
        "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
         "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.35]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      "Piecewise",
      DeleteWithContents->True,
      Editable->False,
      SelectWithContents->True,
      Selectable->False], ")"}], "\[Equal]", 
    FractionBox["99", "100"]}], ",", 
   RowBox[{"{", 
    RowBox[{"n", ",", "0"}], "}"}]}], "]"}]], "Output",
 CellChangeTimes->{
  3.782072764489275*^9, {3.782072887117634*^9, 
   3.782072893499405*^9}},ExpressionUUID->"ec811c7b-520e-4ce3-bd0e-\
f0d5aa99355d"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"As", " ", "evident", " ", "above"}], ",", " ", 
   RowBox[{
    RowBox[{"solve", "/", "reduce"}], " ", 
    RowBox[{"doesn", "'"}], "t", " ", "work", " ", "sometimes", " ", 
    "therefore", " ", "USE", " ", "TABLE"}]}], "*)"}]], "Input",
 CellChangeTimes->{{3.782072769347487*^9, 
  3.782072813807313*^9}},ExpressionUUID->"8a86ef30-c06d-4db1-b332-\
67b19f23482d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"n", ",", 
       RowBox[{"f", "[", "n", "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"n", ",", "80", ",", "90"}], "}"}]}], "]"}], "//", 
   "TableForm"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.7820728179487047`*^9, 3.78207285482097*^9}, {
  3.7820729653054857`*^9, 
  3.782072982804681*^9}},ExpressionUUID->"a9ca5e43-f88b-4539-8a5f-\
6d95e7cddda8"],

Cell[BoxData[
 TagBox[GridBox[{
    {"80.`", "0.9412518864088272`"},
    {"81.`", "0.9571469394920525`"},
    {"82.`", "0.9692172454271266`"},
    {"83.`", "0.9782151098514547`"},
    {"84.`", "0.9848047223269184`"},
    {"85.`", "0.9895492433092523`"},
    {"86.`", "0.9929099456717388`"},
    {"87.`", "0.9952533543461213`"},
    {"88.`", "0.9968629060935261`"},
    {"89.`", "0.9979524488148465`"},
    {"90.`", "0.9986797185813274`"}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[2.0999999999999996`]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  Function[BoxForm`e$, 
   TableForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{
  3.782072983486783*^9},ExpressionUUID->"d21b826e-d659-41c4-9ba7-\
5ea7395ab088"]
}, Open  ]],

Cell["Therefore n = 86", "Text",
 CellChangeTimes->{{3.782073025316183*^9, 
  3.782073033176919*^9}},ExpressionUUID->"2339955c-ad04-4c78-bcf8-\
9eb4f3d56cb5"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Graphing a Binomial Probability Distribution",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737972793533827*^9, 
  3.737972823378132*^9}},ExpressionUUID->"1b89bcc7-b79e-4164-b357-\
0777053a83ee"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiscretePlot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"PDF", "[", 
       RowBox[{
        RowBox[{"BinomialDistribution", "[", 
         RowBox[{"40", ",", "p"}], "]"}], ",", "k"}], "]"}], ",", 
      RowBox[{"{", 
       RowBox[{"p", ",", 
        RowBox[{"{", 
         RowBox[{"0.1", ",", "0.5", ",", "0.7"}], "}"}]}], "}"}]}], "]"}], "//",
     "Evaluate"}], ",", 
   RowBox[{"{", 
    RowBox[{"k", ",", "36"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}], ",", 
   RowBox[{"PlotMarkers", "\[Rule]", "Automatic"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972862513475*^9, 3.737973009833206*^9}},
 CellLabel->"In[62]:=",ExpressionUUID->"f1997178-d379-4a47-bc35-83f2a0b45d0a"],

Cell[BoxData[
 GraphicsBox[{{
    {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.011000000000000001`],
      AbsoluteThickness[1.6], {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6], Opacity[0.2], 
       LineBox[{{{36., 5.996097900000023*^-32}, {36., 
        5.996097900000023*^-32}}},
        VertexColors->None]}, 
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6], Opacity[0.2], 
       LineBox[CompressedData["
1:eJxVy11IU3EYx/GlglMIxTKlDT1rFW1F21FbO9s5///P6IXAXRTCYhjYixdB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        "],
        VertexColors->None]}}}, 
    {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.011000000000000001`],
      AbsoluteThickness[1.6], {
      {RGBColor[0.880722, 0.611041, 0.142051], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6], Opacity[0.2], 
       LineBox[{},
        VertexColors->None]}, 
      {RGBColor[0.880722, 0.611041, 0.142051], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6], Opacity[0.2], 
       LineBox[CompressedData["
1:eJxd0ztIw1AUgOGgSxUHkQ4OHbREERGpjz7SJvekraBCQBBEBwcVOnRy8LE2
k1sHER3EQURKF6FDcVCQDoKT0MnJQSg4OegiLgXvTXranBNIws+XS173ju/t
rxf6NU3T5d7X2f3tG/zzs4Wd2Lxvbx8dGJ0LbO+4ExLY1EO+O3mBTX3Y84+1
Y4FNPex5LXwrsKmPev628iqwqUeUu5WXH4FNfUx5vbUxAtjUo8qvt5wYYFPX
lf9F86uATX1SuVM0dgGb+pR093OgeQjY1KfV+OVW8QSwqc9Ib1z8Xp0DNvVZ
6XbEfLwBbOox6fpXeekOsKnPSa9V3qt1wKY+L71aahceAJv6gvTm2eDpE2BT
X5R+WZ4YagA29TgbH2eeYPdPME+y508yT7H3TzE32PczmKfZ908zz7D/l2Fu
2vT/m8wtNT4wfyzmQnlg/gnmoDwwf4G5rTww/23qrue99eMy17LKA+svy8b7
3l2/LnMt53lv/ee6/g/GwQDN
        "],
        VertexColors->None]}}}, 
    {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.011000000000000001`],
      AbsoluteThickness[1.6], {
      {RGBColor[0.560181, 0.691569, 0.194885], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6], Opacity[0.2], 
       LineBox[{},
        VertexColors->None]}, 
      {RGBColor[0.560181, 0.691569, 0.194885], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6], Opacity[0.2], 
       LineBox[CompressedData["
1:eJxd0F1Ik3EUx/GHDGYIQ8ewAoul01bYrNY2Z8/znJ9b0IXUhV2soAt7GZgS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        "],
        VertexColors->None]}}}}, {
    {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.011000000000000001`],
      AbsoluteThickness[1.6], {}, GeometricTransformationBox[InsetBox[
       StyleBox["\<\"\[FilledCircle]\"\>",
        StripOnInput->False,
        LineColor->RGBColor[0.368417, 0.506779, 0.709798],
        FrontFaceColor->RGBColor[0.368417, 0.506779, 0.709798],
        BackFaceColor->RGBColor[0.368417, 0.506779, 0.709798],
        GraphicsColor->RGBColor[0.368417, 0.506779, 0.709798],
        PointSize->0.011000000000000001`,
        Thickness->Absolute[1.6],
        FontSize->8.96,
        FontColor->RGBColor[
         0.368417, 0.506779, 0.709798]], {0, 0}], CompressedData["
1:eJxTTMoPSmVmYGBQAWJGIGZigIEP9voKu5vtLm6whwo4dPIm7GS2OATlczhM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      "]], {}}, 
    {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.011000000000000001`],
      AbsoluteThickness[1.6], {}, GeometricTransformationBox[InsetBox[
       StyleBox["\<\"\[FilledSquare]\"\>",
        StripOnInput->False,
        LineColor->RGBColor[0.880722, 0.611041, 0.142051],
        FrontFaceColor->RGBColor[0.880722, 0.611041, 0.142051],
        BackFaceColor->RGBColor[0.880722, 0.611041, 0.142051],
        GraphicsColor->RGBColor[0.880722, 0.611041, 0.142051],
        PointSize->0.011000000000000001`,
        Thickness->Absolute[1.6],
        FontSize->8.96,
        FontColor->RGBColor[
         0.880722, 0.611041, 0.142051]], {0, 0}], CompressedData["
1:eJxTTMoPSmVmYGBQAWJGIGZigIEP9hD6iC1UwAFMJnDYQbgcEL6PM5QvAOY/
8C+D8kXA/A0iS6B8CTD/msdZKF8GxG9YdvwjlK8A4m95HCoEtVcJxF8Q4WMA
5auA+D+UnD2hfDUQ3yfTMhHK1wDyG55xXiiB8rVA8u6PM9ugfB0g/8C0b3Om
Qvl6QL6DjM3uRVC+AZCv8qbXZS2Ubwjkb1h2Z8UWKN8IyF9R/zd1F5RvDORf
mMw1cR+UbwLkz+pV5TkA5ZuiyZuh6TdHM98CzX5LNPdZobnfGs1/Nmj+t0UL
Hzu08LNHC18HEB8R/g1gPlL8OIL4iPhrgPAR8esE5oPiHwAAamjm
      "]], {}}, 
    {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.011000000000000001`],
      AbsoluteThickness[1.6], {}, GeometricTransformationBox[InsetBox[
       StyleBox["\<\"\[FilledDiamond]\"\>",
        StripOnInput->False,
        LineColor->RGBColor[0.560181, 0.691569, 0.194885],
        FrontFaceColor->RGBColor[0.560181, 0.691569, 0.194885],
        BackFaceColor->RGBColor[0.560181, 0.691569, 0.194885],
        GraphicsColor->RGBColor[0.560181, 0.691569, 0.194885],
        PointSize->0.011000000000000001`,
        Thickness->Absolute[1.6],
        FontSize->10.88,
        FontColor->RGBColor[
         0.560181, 0.691569, 0.194885]], {0, 0}], CompressedData["
1:eJxTTMoPSmVmYGBQAWJGIGZigIEP9uZ9v/Kv7mOwgQo4mDlZVIefD4fyORwc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      "]], {}}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{1., 5.996097900000023*^-32},
  BaseStyle->{FontFamily -> "Arial"},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "MessagesHead" -> DiscretePlot, "AxisPadding" -> Scaled[0.02], 
    "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "DefaultPlotStyle" -> {
      Directive[
       RGBColor[0.368417, 0.506779, 0.709798], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.880722, 0.611041, 0.142051], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.560181, 0.691569, 0.194885], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.922526, 0.385626, 0.209179], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.528488, 0.470624, 0.701351], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.772079, 0.431554, 0.102387], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.363898, 0.618501, 0.782349], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[1, 0.75, 0], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.647624, 0.37816, 0.614037], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.571589, 0.586483, 0.], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.915, 0.3325, 0.2125], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.40082222609352647`, 0.5220066643438841, 0.85], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.9728288904374106, 0.621644452187053, 0.07336199581899142], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.736782672705901, 0.358, 0.5030266573755369], 
       AbsoluteThickness[1.6]], 
      Directive[
       RGBColor[0.28026441037696703`, 0.715, 0.4292089322474965], 
       AbsoluteThickness[1.6]]}, "DomainPadding" -> Scaled[0.02], 
    "PointSizeFunction" -> "SmallPointSize", "RangePadding" -> Scaled[0.05]},
  PlotRange->{{1., 36.}, {5.996097900000023*^-32, 0.20588704344119954`}},
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.02]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.737973011739141*^9},
 CellLabel->"Out[62]=",ExpressionUUID->"ec5ee9a2-a17b-4874-8d87-7eed4b12367c"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Hypergeometric Distribution",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7379710841812572`*^9, 
  3.7379710930964317`*^9}},ExpressionUUID->"4a6a48c0-a20a-4100-a754-\
acc2d1fbdb51"],

Cell["\<\
Hypergeometric distribution is only use when it is without replacement, which \
means it decreases in the sample size.
Hypergeometric Distribution command format: \
HypergeometricDistribution[n,n(success),n(total)]
\[OpenCurlyQuote]n\[CloseCurlyQuote] is the number in sample
\[OpenCurlyQuote]n(success)\[CloseCurlyQuote] is the number of success states
\[OpenCurlyQuote]n(total)\[CloseCurlyQuote] is the total number in population\
\>", "Subsection",
 CellChangeTimes->{{3.737971172370755*^9, 3.737971208703436*^9}, {
  3.737971245258328*^9, 
  3.737971406211658*^9}},ExpressionUUID->"25d6b4cc-71e9-4e06-9afc-\
b907d3a131c5"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Example 1: A deck of cards contain 20 cards: 6 red \
cards and 14 black cards. 5 cards are drawn randomly without replacement.",
 FontColor->RGBColor[1, 0, 0]]], "Subsection",
 CellChangeTimes->{{3.737971436087119*^9, 3.737971489753805*^9}, {
  3.737971535342671*^9, 
  3.737971538467436*^9}},ExpressionUUID->"a36dfe7b-8d67-46d5-bb6b-\
867d6be4e6af"],

Cell[CellGroupData[{

Cell["a) What is the probability that exactly 4 red cars are drawn", \
"Subsubsubsection",
 CellChangeTimes->{{3.737971555158104*^9, 3.737971576693726*^9}, {
  3.737971649691699*^9, 
  3.737971650797433*^9}},ExpressionUUID->"828888a5-69ed-4b78-bdc3-\
4efbadd8e46f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Probability", "[", 
  RowBox[{
   RowBox[{"x", "\[Equal]", "4"}], ",", 
   RowBox[{"x", "\[Distributed]", 
    RowBox[{"HypergeometricDistribution", "[", 
     RowBox[{"5", ",", "6", ",", "20"}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737971541227098*^9, 3.7379715457252913`*^9}, {
  3.737971582120594*^9, 3.7379716238727093`*^9}},
 CellLabel->"In[27]:=",ExpressionUUID->"f8352939-bc20-4ef4-9992-b279429c0086"],

Cell[BoxData[
 FractionBox["35", "2584"]], "Output",
 CellChangeTimes->{3.737971624301778*^9},
 CellLabel->"Out[27]=",ExpressionUUID->"fc5cc479-2c01-4e70-b714-4ad6b5b4ab4d"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["b) What is the probability that more than 4 cards are drawn?", \
"Subsubsubsection",
 CellChangeTimes->{{3.73797168008454*^9, 
  3.7379717072634706`*^9}},ExpressionUUID->"88c8f347-80fc-440e-8357-\
a419f6d94356"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Probability", "[", 
  RowBox[{
   RowBox[{"x", ">", "4"}], ",", 
   RowBox[{"x", "\[Distributed]", 
    RowBox[{"HypergeometricDistribution", "[", 
     RowBox[{"5", ",", "6", ",", "20"}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7379717096059313`*^9, 3.737971735151229*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"4632b873-cdeb-49b7-9cba-d7e07e80a9f0"],

Cell[BoxData[
 FractionBox["1", "2584"]], "Output",
 CellChangeTimes->{3.737971735631069*^9},
 CellLabel->"Out[28]=",ExpressionUUID->"5c16cdd9-247f-4ea7-9bb8-3bd6b1f880fd"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nNormal and Standard Normal Distribution",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737950685620327*^9, 3.737950725554716*^9}, 
   3.737953395406371*^9, {3.737970152025918*^9, 3.737970158010726*^9}, {
   3.737970581295854*^9, 
   3.737970583233407*^9}},ExpressionUUID->"9a06586b-9805-4db0-8d4b-\
f55b319382f7"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Normal Deviation",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737950745246895*^9, {3.737950783782189*^9, 3.737950789671053*^9}, 
   3.737953469749559*^9},ExpressionUUID->"75c21fc3-7c32-4fa9-8029-\
282be88f4ee3"],

Cell[CellGroupData[{

Cell[TextData[{
 "Normal distribution command format: NormalDistribution[\[Micro], \[Sigma] ]\
\n\[Micro]  is the mean\n\[Sigma]  is the standard deviation\n",
 StyleBox["Example 1: The results of a maths exam are normally distributed \
with \[Micro] = 50, and \[Sigma] =7",
  FontColor->RGBColor[0.5, 0, 0.5]]
}], "Subsection",
 CellChangeTimes->{{3.737952082699656*^9, 3.737952141696162*^9}, {
  3.737952249657895*^9, 3.737952273739698*^9}, {3.737952379039804*^9, 
  3.7379524021376143`*^9}, {3.737971767371607*^9, 
  3.737971881106937*^9}},ExpressionUUID->"86cbef4a-e462-4f82-aa63-\
87e60e705179"],

Cell[CellGroupData[{

Cell["\<\
a) What is the probability a student has an exam mark greater than 60.\
\>", "Subsubsection",
 CellChangeTimes->{
  3.7379523143961287`*^9},ExpressionUUID->"0c937a80-ffe0-4a61-ae2d-\
2ac71be050cd"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Probability", "[", 
   RowBox[{
    RowBox[{"x", ">", "60"}], ",", 
    RowBox[{"x", "\[Distributed]", 
     RowBox[{"NormalDistribution", "[", 
      RowBox[{"50", ",", "7"}], "]"}]}]}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.737952296144755*^9, 3.737952323500965*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"fe9e2464-8af0-4765-90cc-834d05d4628e"],

Cell[BoxData["0.07656372550983476`"], "Output",
 CellChangeTimes->{3.737952324872837*^9},
 CellLabel->"Out[7]=",ExpressionUUID->"61cdd3da-8891-4e06-9fea-3ad3a1c47ad2"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
b) If 25 students are selected, what is the probability at least 10 have a \
greater score than 60.\
\>", "Subsubsection",
 CellChangeTimes->{
  3.737952459819214*^9},ExpressionUUID->"a19d447f-05d2-4fe1-a6d4-\
d80e92650900"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Probability", "[", 
   RowBox[{
    RowBox[{"x", "\[GreaterEqual]", "10"}], ",", 
    RowBox[{"x", "\[Distributed]", 
     RowBox[{"BinomialDistribution", "[", 
      RowBox[{"25", ",", "0.0766"}], "]"}]}]}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.737952467396145*^9, 3.737952476091692*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"db7823df-f9b9-42ab-8f45-49b65030336c"],

Cell[BoxData["7.7390619497788`*^-6"], "Output",
 CellChangeTimes->{3.737952477169477*^9},
 CellLabel->"Out[8]=",ExpressionUUID->"acaf1d9e-8eab-490b-b9cb-81a8f49723c7"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
c) The top 15% are awarded a distinction. What minimum mark guarantees a \
distinction?\
\>", "Subsubsection",
 CellChangeTimes->{
  3.737952490561893*^9},ExpressionUUID->"eb505847-2ae2-4f53-a67e-\
8a47ed456bf4"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Quantile", "[", 
  RowBox[{
   RowBox[{"NormalDistribution", "[", 
    RowBox[{"50", ",", "7"}], "]"}], ",", "0.85"}], "]"}]], "Input",
 CellChangeTimes->{{3.737952497610569*^9, 3.73795250484175*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"1dc5fff6-ed96-4c66-97f3-cb52476afbd6"],

Cell[BoxData["57.255033726456524`"], "Output",
 CellChangeTimes->{3.737952505918744*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"3325c4f4-66e2-49da-87a4-d3e5013162ca"]
}, Open  ]],

Cell["\<\
Quantile is function used to find the point on the x-axis, when the success \
probability or the space it covers is given in percentage covered by the \
graph. Key words to look for --> minimum and maximum \
\>", "Text",
 CellChangeTimes->{{3.737952921338146*^9, 3.737952932518478*^9}, {
  3.7379533312848663`*^9, 3.737953379223424*^9}, {3.737966448814187*^9, 
  3.737966461784892*^9}, {3.737966492858951*^9, 3.737966529218351*^9}, {
  3.737966597691884*^9, 
  3.737966653799399*^9}},ExpressionUUID->"40291466-e0c0-4f74-9bc1-\
9529f8fb5936"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Standard Normal Distribution",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737964424665765*^9, 3.737964426298418*^9}, {
  3.7379644702012978`*^9, 3.737964483468678*^9}, {3.737970161740251*^9, 
  3.7379701682242804`*^9}, {3.7379705749638577`*^9, 
  3.737970577030295*^9}},ExpressionUUID->"70fe83a7-e0bd-45f9-85a7-\
23161200852a"],

Cell["\<\
Note: The Normal distribution with a constant mean of 0 and standard \
deviation of 1 is known as a standard normal distribution.\
\>", "Subsection",
 CellChangeTimes->{
  3.7379706072162247`*^9},ExpressionUUID->"6df0be3e-5e0f-4e4b-87d9-\
85f051f2575a"],

Cell[CellGroupData[{

Cell["\<\
A taxi company determined that on an annual basis the distance travelled per \
taxi is normally distributed with a mean of 92,000 kilometres and a standard \
deviation of 23,500 kilometres.\
\>", "Subsection",
 CellChangeTimes->{{3.7379701218689947`*^9, 3.7379701260410967`*^9}, {
  3.73797016976*^9, 3.7379701881798*^9}, {3.737970293498212*^9, 
  3.737970327782881*^9}},ExpressionUUID->"20588c9b-707a-4c65-a25f-\
9c9b8f86b75e"],

Cell[CellGroupData[{

Cell["\<\
a. What is the probability, correct to four decimal places, that a taxi \
travels less than 75 000 kilometres per year?\
\>", "Subsubsection",
 CellChangeTimes->{
  3.7379704608758497`*^9},ExpressionUUID->"6b49a7db-2ee7-4e6e-bab7-\
9c7aec7b319f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Probability", "[", 
   RowBox[{
    RowBox[{"x", "<", "75000"}], ",", 
    RowBox[{"x", "\[Distributed]", 
     RowBox[{"NormalDistribution", "[", 
      RowBox[{"92000", ",", "23500"}], "]"}]}]}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.737970111722909*^9, 3.737970112624995*^9}, {
  3.737970478948126*^9, 3.7379705090087147`*^9}},
 CellLabel->"In[23]:=",ExpressionUUID->"4022dc82-58e7-43eb-81c2-f273adea00df"],

Cell[BoxData["0.23471577882277778`"], "Output",
 CellChangeTimes->{3.7379705130865507`*^9},
 CellLabel->"Out[23]=",ExpressionUUID->"b2640796-9321-40aa-a178-b229e0705de4"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
b. What is the probability, correct to four decimal places, that a taxi \
travels more than 80,00 kilometers per year?\
\>", "Subsubsection",
 CellChangeTimes->{{3.737970671330208*^9, 
  3.7379707274385223`*^9}},ExpressionUUID->"ab12e1e5-ce60-4b0a-8091-\
20c89c56aab6"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Probability", "[", 
   RowBox[{
    RowBox[{"x", ">", "80000"}], ",", 
    RowBox[{"x", "\[Distributed]", 
     RowBox[{"NormalDistribution", "[", 
      RowBox[{"92000", ",", "23500"}], "]"}]}]}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.737970650262258*^9, 3.737970651130116*^9}, 
   3.737970737142376*^9},
 CellLabel->"In[24]:=",ExpressionUUID->"a6e36c50-aba2-4843-872e-1cbac4f68851"],

Cell[BoxData["0.6951978232591206`"], "Output",
 CellChangeTimes->{3.737970737841722*^9},
 CellLabel->"Out[24]=",ExpressionUUID->"848f6fbf-2cde-4fd3-91fd-2f8580bc80be"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
c. What is the probability, correct to four decimal places, that a taxi \
travels between 60,00 and 100,000 kilometers per year\
\>", "Subsubsection",
 CellChangeTimes->{{3.7379707437969847`*^9, 
  3.737970800772764*^9}},ExpressionUUID->"752caf8f-db60-43ad-bbec-\
9e9682d9c1ea"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Probability", "[", 
   RowBox[{
    RowBox[{"60000", "<", "x", "<", "100000"}], ",", 
    RowBox[{"x", "\[Distributed]", 
     RowBox[{"NormalDistribution", "[", 
      RowBox[{"92000", ",", "23500"}], "]"}]}]}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.7379708033689423`*^9, 3.737970810963896*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"e2fee661-80c7-4d3c-b8e5-50742bf8c882"],

Cell[BoxData["0.5465859982536845`"], "Output",
 CellChangeTimes->{3.7379708116353083`*^9},
 CellLabel->"Out[25]=",ExpressionUUID->"d718b02e-5c64-4d41-8aaa-cdf02ebc75d5"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
d. Find the minimum mileage that could be expected by 95% of taxis, to the \
nearest km. (Hint: Quantile function can only deal with probabilities that \
exist in the left tail of the normal distribution)\
\>", "Subsubsection",
 CellChangeTimes->{{3.737970836700658*^9, 
  3.7379709509568644`*^9}},ExpressionUUID->"d89f0a17-f2f8-4e33-9f60-\
c2dcf7f2f790"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Quantile", "[", 
   RowBox[{
    RowBox[{"NormalDistribution", "[", 
     RowBox[{"92000", ",", "23500"}], "]"}], ",", "0.05"}], "]"}], "//", 
  "N"}]], "Input",
 CellChangeTimes->{{3.737970955495329*^9, 3.7379709640132103`*^9}},
 CellLabel->"In[26]:=",ExpressionUUID->"a1201dd2-de65-44d4-8462-a40399e95a7f"],

Cell[BoxData["53345.93976664039`"], "Output",
 CellChangeTimes->{3.737970965054008*^9},
 CellLabel->"Out[26]=",ExpressionUUID->"95471f8a-3a5b-486d-a354-1dd11bdb5225"]
}, Open  ]],

Cell["\<\
Quantile command format is : Quantile[distribution, Percentage]\
\>", "Text",
 CellChangeTimes->{{3.737970980524639*^9, 
  3.73797102907386*^9}},ExpressionUUID->"f151956a-bb99-45ac-9dd6-\
93a7f1f9d877"]
}, Open  ]]
}, Open  ]],

Cell["", "Subsection",ExpressionUUID->"156ffc83-4934-40d5-941d-fecdfd61ce10"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Modulus (Absolute value) Function",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.7379648440259123`*^9, 
  3.737964871341671*^9}},ExpressionUUID->"2f13d95b-948b-4e15-9ae9-\
b47f11fa88f9"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Calculating Absolute values of numbers",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7379719719166317`*^9, 
  3.737972007115679*^9}},ExpressionUUID->"0c87da2e-4069-4556-9112-\
0f9019837b1a"],

Cell[CellGroupData[{

Cell["Command for Absolute value: Abs[_]", "Subsection",
 CellChangeTimes->{{3.737972042596179*^9, 
  3.7379720638483763`*^9}},ExpressionUUID->"462adcbf-bc58-4353-a343-\
af0d8de3fea7"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Abs", "[", 
  RowBox[{"-", "5"}], "]"}]], "Input",
 CellChangeTimes->{{3.737972016932705*^9, 3.737972029715077*^9}},
 CellLabel->"In[29]:=",ExpressionUUID->"be8a354e-2f4b-4795-9282-de7c6be7cad6"],

Cell[BoxData["5"], "Output",
 CellChangeTimes->{3.73797203058988*^9},
 CellLabel->"Out[29]=",ExpressionUUID->"767c1d5a-9778-4702-8e28-83257670eef4"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Abs", "[", 
  RowBox[{"-", "123"}], "]"}]], "Input",
 CellChangeTimes->{{3.73797206864974*^9, 3.737972077591976*^9}},
 CellLabel->"In[30]:=",ExpressionUUID->"01ae0173-d38d-470e-bd15-463b3f76acb7"],

Cell[BoxData["123"], "Output",
 CellChangeTimes->{3.737972078029244*^9},
 CellLabel->"Out[30]=",ExpressionUUID->"e9e662fd-24e7-404c-9377-d95b7808213d"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Graphing Absolute values of algebraic functions",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7379720860049067`*^9, 3.737972122341536*^9}, {
  3.737972229633326*^9, 
  3.737972233471858*^9}},ExpressionUUID->"8e035bc5-e846-4de8-a7ac-\
94e4e7e5a699"],

Cell[CellGroupData[{

Cell["Hyperbolic function", "Subsection",
 CellChangeTimes->{{3.737972251572761*^9, 
  3.737972256385639*^9}},ExpressionUUID->"c2d166c2-70f8-464c-bfca-\
9b07aed8078a"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    FractionBox["1", 
     RowBox[{"Abs", "[", 
      RowBox[{"x", "+", "5"}], "]"}]], "-", "2"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972126345312*^9, 3.737972209824704*^9}, 
   3.737972263526409*^9, {3.7379726604389467`*^9, 3.7379726848531218`*^9}},
 CellLabel->"In[61]:=",ExpressionUUID->"1e315af4-1417-4e07-b3ec-466bd4b4642c"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwVjms41Akfhkc5pCSHMmMY85+ZrXaISDnNkl1tqMhaRcohOS1yCimUKCE6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        "]], LineBox[CompressedData["
1:eJwV0Xk41PsXB/CxLzPGUGQr9C1XsidlqflWthYpMVouQkpyVbrURanIRVoQ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        "]]},
      Annotation[#, "Charting`Private`Tag$6472#1"]& ]}, {{}, {}, {}}}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, -1.9333333315192744`},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {-1.9333333315192744`, -0.6897300667801534}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.737972264356827*^9, {3.737972665085845*^9, 3.737972686670815*^9}},
 CellLabel->"Out[61]=",ExpressionUUID->"d1d7ce08-c1e9-443e-830d-899479b0698e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    FractionBox["1", 
     RowBox[{"Abs", "[", 
      RowBox[{
       RowBox[{"-", "x"}], "+", "5"}], "]"}]], "-", "2"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972268725815*^9, 3.737972291231222*^9}},
 CellLabel->"In[35]:=",ExpressionUUID->"6a382e3e-4e9a-4111-b26c-e49ca9646fec"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwVkHk41PsXx4eZsQ4zIhJlGUWSCpFK30+LdJPSLbIksrVJUolsV1lSImuL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        "]], LineBox[CompressedData["
1:eJwVjnk81Akfxz2T7VpUqLkwM34khSJPW458S5JiO5FCiyFXp6JNCatoQ2Ed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        "]]},
      Annotation[#, "Charting`Private`Tag$5371#1"]& ]}, {{}, {}, {}}}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, -1.9333333315192744`},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {-1.9333333315192744`, -0.7014234186708168}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.7379722819500427`*^9, 3.737972292237048*^9}},
 CellLabel->"Out[35]=",ExpressionUUID->"7bd6f152-90a5-43ef-bf24-8ba8837e958a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    FractionBox["3", 
     RowBox[{"Abs", "[", 
      RowBox[{
       RowBox[{"-", "x"}], "-", "2"}], "]"}]], "-", "2"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972300127018*^9, 3.737972320030623*^9}},
 CellLabel->"In[37]:=",ExpressionUUID->"abab4e91-f189-41f9-9dc9-dfb235128311"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwVjHlUzAsfh5Nm2vemmijTRrIU0iZ+LURJzYuEVkLrW6mkSzdFJUTaqNRF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        "]], LineBox[CompressedData["
1:eJwV1Hk41XkXAPDbDV1RCY0tkZ9khKmUidT3WxItSsJIyCBhZM97ZS032SaV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        "]]},
      Annotation[#, "Charting`Private`Tag$5465#1"]& ]}, {{}, {}, {}}}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {-1.7499999914965985`, 1.6978306030646526`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.737972313342588*^9, 3.7379723203605967`*^9}},
 CellLabel->"Out[37]=",ExpressionUUID->"302a2b6e-b386-42ff-9f36-2c7fe2ebd049"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Quadratic functions", "Subsection",
 CellChangeTimes->{{3.7379723278223457`*^9, 
  3.7379723333512373`*^9}},ExpressionUUID->"e3eea411-63e6-4b9c-90d7-\
b36ca922f7ea"],

Cell[BoxData[
 RowBox[{
  RowBox[{"n", "[", "x_", "]"}], ":=", 
  RowBox[{
   SuperscriptBox["x", "2"], "+", 
   RowBox[{"6", "x"}], "-", "9"}]}]], "Input",
 CellChangeTimes->{{3.737972424461794*^9, 3.7379724409655323`*^9}, {
  3.7379725343393793`*^9, 3.737972564802105*^9}},
 CellLabel->"In[49]:=",ExpressionUUID->"ef608d02-6c60-4ba9-82d3-81add1c77019"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Abs", "[", 
    RowBox[{"n", "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.73797234984433*^9, 3.737972378523221*^9}, {
  3.737972445822568*^9, 3.73797245839108*^9}},
 CellLabel->"In[50]:=",ExpressionUUID->"20c62965-b8ba-41ab-aa87-843785c26c8f"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwt2Hk0lO37APCxzQzGOnZlm1SWxjyyJNVzWUIlydZqmyxZkhBeCW2W8vYm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       "]]},
     Annotation[#, "Charting`Private`Tag$5953#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {0., 150.99998938775528`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.737972379570135*^9, 3.737972459113551*^9, {3.737972552825362*^9, 
   3.7379725681501007`*^9}},
 CellLabel->"Out[50]=",ExpressionUUID->"52df9e78-7ae8-4d12-b793-a7c37eee9259"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"n", "[", 
    RowBox[{"Abs", "[", "x", "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972385174571*^9, 3.737972408021977*^9}, {
  3.737972464366805*^9, 3.7379724939810038`*^9}},
 CellLabel->"In[51]:=",ExpressionUUID->"1d51226d-7226-4c97-a8ce-2de5d63f075a"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJw11fs/VPkfwPEhtRM2txEzYeY4bblrEyI676kGlYZcRtZDOCiVRSOlKLWI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       "]]},
     Annotation[#, "Charting`Private`Tag$6000#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {-8.990761853018759, 150.99998938775528`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.7379724744644938`*^9, 3.737972494747942*^9}, {
  3.7379725547658043`*^9, 3.7379725705427523`*^9}},
 CellLabel->"Out[51]=",ExpressionUUID->"a71e60ad-3d7d-41bb-8c05-484c4868c0af"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Abs", "[", 
    RowBox[{"n", "[", 
     RowBox[{"Abs", "[", "x", "]"}], "]"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972505411669*^9, 3.737972522182886*^9}},
 CellLabel->"In[52]:=",ExpressionUUID->"3f232a2b-c697-4d4b-9e9f-4da11fef75b0"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJw112k4lWvbB/BFtMXaEcpUWN3tkrmEUF2nZKgkmQqPcFM7JUTKVBKVaGsw
k0KSKRkKSa5bhkwpERlCikzbsKxlyvCs9zje58N1nMfv+J/np+vTn0G6m53i
ptFoLZz3f/PKryPMlRWC2hFXPrzSS8Kg/wZ21yJB5SmpvB3oJMFEqHe2eJ6g
3LPdlRu/kCCr5bHkPk1QJfYOIwkNJLwLe8DXN0hQDtm0WlRMAp9yuzT1gaCk
P+6RfBZBQtRFh8PXEgnKwOiJ5NheErK5vNJomgS1j2t7+NFHjsB7ynCnhN1m
ilSafvrS2AFEvla7pt5nUDmKm+72aZ4Es8oEp+31slT987+3jbFtwX9ir+u9
HzLUzNxuzek4ayi5nHD2xVFpSq6o03Pe5ziYPLCUXY7fSJUln1aZ1LUEw6S3
JkZjklTJAzG1ZQVzSH/v2+ZlK0GVkbsfgckxOBkStf5jhhi1J67lOi4zgasO
q3IFRDZQpGjWthCjw0BTksF6N0SpcV+mbwHdCDrD429lfxGmam5YWO4qOgAb
+c9ksvavozwWosN/VejCOXV53q6NgpR4nKfXU++94KTZk1FZKUAp21U/serR
BHkf7RW3ND5KW/finPHcTkj5Zl7lq8tL+XzI8MihKcKvoPV7DMW5KVO5HS4f
7AkojZbTH7JawnT/8eEo7/XAZ/vLiWvPEr5HpyUm7loPVrLp1yUZS9j0YsVw
ybQoMLMIynh0EYfUmDtoeorCdkpaJz9wEad5F+XreYhA3IjoDr+M33hk2Wsg
3mMdeCOuTfSFedzn95jhyyMA73gonb9653GUYsmEUig/CNVftdlXNY+pMNV5
QTo/5FgsxnpEzGMfYyi3FV0DP11mhb9snsdnBrqEhLf9AWZR//I9OjyHjc6v
+jpvsQpUhztYKkkzmC9rW/e5p7Po4qTSdrGQGVzLStj6Z+0MKpkNsls+O4OT
6RaKSyNspLtavqZx9wzOexLrUreDhcwIv1iXVjYWcnfOFq6cRDHyTQ2mb9gY
9OnJ5p8mUNeOzbTdqWxMGXTZy0iNI2eoP7Pag41NxTfq3S0YQd52ktpPBNiY
NiMX92noByp1dnMLY7IwTaUuekSzHy2fe5d6oYOFZbnZa1Jv9aGbfmcF4BkL
w3hP9udjnag+qBxti2BhakeALZPVhgRvC19c6825z1KdM45vQXGxpd3d+zl2
L5861VCHuh+tXVe1nbMfX/A6QKoSyaaT+tlCLHzNJqtYuLsEOT8v8n0wO41p
6XEOKvRnKPMlf65vD8fiJgp+LwLQ+JuT/Q7VHIcVXNdQzkU7Kws2GOVw3J6s
YH6yDJU22wRu8OO48s7UilsDWv6aW7jkMI2TM4QVk3ib0f4+7qGfhtPY4Y2h
Z6BZK2oYzzItXD+Nr+m5akYOdaJugd8M03wmdnA/+vk390+0op9YdXtoCvPd
y+I+HzSJDpR2rVmymsQ8rlYV+wyWUG7WU633OpN4seNr16DsMhJPdHe5LzuJ
xXsLXXb+XkZts6sfHG6dwCfaX09YH6fBX/5WQkkL4zhjxz8SeXzc8C6ITQfD
f/G+ddf3viB5YTFCbfXNvmGsHZBWMzctAB6ZL+bWifzApbRBt259UVBd6xa8
v68flxX4mVzzEoUpT8W1Xs/7cXN4NrdQiih47skkWg37sUbh9yHmb1Hw/phq
EhPwHfe3Pc6pyVsP0yMKB9Ube3HrBad16RvEYHXwXLKBZwfmm/nD9ECLBNwy
9i56Ru/AbmGMSnJZAvg2MBv4nn3Fg/rt/Oe3SwJ/5uhMfVc7FtopJq4fKAmC
H3uMj+q3YePeoe2r5KVAXKp67rh4C7b6p0W+2H8jWJ0mUj4H1GGsWZOyLCgD
YRe8Qh+8qsUqXkbvGjRl4G1ApbvZ+Hvc36d27Ya9DGyJdNr32b4GC5kbtJbn
ygATP+lq3l+JDety3LZslQVpNSPF1HWlWAA/1PpWIQs3Dg4tMIJLcIfbtldy
X2RhzD60LoVVhOuLTweeHZKF0ju1p1PaC7Hg+lW05rUMeN54f7+uTjaWXyrI
327LAP/55l6QzsC8l/pTt7kx4OBW4SvA9RRzhdb0SwUxoGFli3tgRBK2u5xj
8iudAWesn2ZetYjFby1y/cpfM4Cn8K+fVyTvY9TgzA5vZABIGO9doG7g/s6P
5Ud7GTAZF+88Fe+J04Mn2tYwGRDAHVVtsNsaCeRqEfq/GaCc4PReVCMQKYUz
Wu8OMaBHIn9cQPAOcucqb/n0hQHmal/LbupGoRYhwc18lQwo6jh+/ZZ/Ajrx
WhSr5zHgT2qUqLJJRisLTVnWSQy4cPrccFVUOso/6OgWcpkBqVoKxtX5majM
Sssg3JkBrfTR3OqmHDS8WO0aeowBD63VtZ1C8tEz0aWnpxQYQKO9WnEqL0aF
F/prs3tk4X1jR5iaeS2KVX/Bf+6wDJzx6Xxvq1CHVklrthnIygDfli6ekFX1
6JedbrMAWxoO+XdfbS1sQGI/uy2PPZKGxu29nt6iH5EYv2p8/cQmOKPn+bxr
5DOKKjPguxSxEVyTL0dvyulAN96oh+aVSoC2UkWBaewPpM+QFHzZJALqrW0x
5XU/ENZJey+TIgKq/mN+ios/0IEP7JTLXiKwtU5Mj8/xJ3K1nHgzKiYCIqfc
WrD8ANJY0LkxYC8MYw+lWMrlg6g4Wue8zJgQPKZfUv9zYBg1ymX8ZT0qAAmF
4RL+YiPIVDaBTytcAGJsUpaGDo6gIV4plSl5AbiT0VhdlTuCrBLrDEZc+MHn
AGEV4DOK5Cc6klcG+MAs4NOlUYF/Ubr2+5WiNl7gvrS+21liEtHeZTTn7VpB
Ng5Zn0t2TaK4/MW8cOtlVHAI1dFNJ1HVvLTGmqtLiJRxKXp5k+PIph1j1b/R
u9qyezysSRQ63jF+7NgcCpZy1k9rmkI8KCXwodUU6uad15kbnkL3ijvfpHhP
ol2T/+w05mUij3XVOpFyE+hnVbEMS4djl9J07pRRdMBNYEEvk4n6Ti/9wbj9
Ez08kTwZW8VEQt8tv1lW9CPWfvVfo71M5EA/vPxxrg+lidm3Rm6YRsljGwzk
GjrRIher/teOaUQ7+/xImXo7shgLrdA5wskPXhnrfNSCeCoKcn8Ec3L7B73u
HbXoP9mGTzUfTyPqXFjGWGoFehndnRheysn9RtDS55eIfu3Cg94vHEfFKCu7
xCPns6tvq01xfMQr9rJRMiqzSAy8RWchmotaTVxGERJFqpe6trHQteYf+afi
36FqERun4JOcvFeQVIz5hKSXx63bfVmIqqnVk9jbii4NBZsqRLMQGBtF+A+0
o61vn+9taWAhB9VEu2TtXnTzNJc4ocVGn5RrPdV/D6Ie05i1ly3YKE8C3wxq
HUIaOgq8De5s5GAucTSU8++DgpZMz3Q28iicXax2HkcGrzMa34nMICGR3EHa
v0z0B900iByfQbUjjslvvRbQiW02lMaaWUTr8dJqcPyNsvY7r/Bv4ThVunGn
6SIy8fW5Umg9i8Qf7usRVF5GMYPJvjzVsyhEsbWTNkuDrRVTF9IT59CQ331x
EvOA/qVIcsRoAXnY2Sj1X6BDcF+bnueTJVTyUPjkmPIGyEu8aXqVyQWtVz4Y
3F/cDO6pzkI/rXjB+a7xySN7FeHk2YRNt4L4YEFj12fTyp1w+9glLbWHAhBa
4P3N7ZEm8IhGDwYurIXPcRZH7mjvhfaGG5MhguvggEGZn5yzLlj6kxoJlcJw
9IlVrWvkAXAVGN3cZCMKeWQYM6nIEGSya2JWj6yHWvUTYnZTh8C/RM9cMFEM
rkmm9ss+MgGPdNciDRUJGLT0ESuVPAZ0bk1SeUASOuvyq2wJc9A/bxEtH7kR
ajucUg21LEH89SZ3/S3SUHIC5b1Ax+GBZ+h91XYZMOFe3bR4yxrMbh5VSiqS
hUN3XPwsym1B3jbEMu0KA+jRiqIiS3bQNrgmNdJyMzTU85js13WAJnJAV1iG
AP8gh4IsH0f4zvNsLnozAVnqrFcqVx2BlX7mhcRWAtAbucBXwY4gMTq6kaFE
QJL2RbIywhGcvZizKjoEqPBHuw6lOcJC8MrzI8cJSBtbijje7Ahbn0pI3r5L
wKdyV3q9PAlahl2f6JEE9D6WrPpblQTj4Ye37sUQYGnmortag4QLSrLs2CQC
LioM39HXJaHs1dZP6dkEhOZ6/v3hOAlmNWo3q94TQJvLkee+QcKpM+w9Rg0E
BE78vScnjAQf/uLphiYCTpVUihy/R0KSibZjyxcCnMvtRF4kkjDUBnv6fxCg
lShldaaAhAUf7ulTvwgY3/QtSryEhD+lqjKHRwige6L4urck7LQ3FJuaIiAg
YpCpVEeCPteapotsAj5aKRh9byLhxJP6kLk5AsImhZyiW0k4q39HJ2CRgEzb
WL1DnP7z//0I/teP/gtPM2Wd
       "]]},
     Annotation[#, "Charting`Private`Tag$6047#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {0., 150.99998938775528`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.737972523208555*^9, {3.737972557214314*^9, 3.737972572852627*^9}},
 CellLabel->"Out[52]=",ExpressionUUID->"dc7f1c8a-91d8-4256-9b3b-b6b995eb06bd"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Linear", "Subsection",
 CellChangeTimes->{{3.737972603461803*^9, 
  3.7379726043705273`*^9}},ExpressionUUID->"9741036b-707b-462d-8b2c-\
d9975aa44fb9"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Abs", "[", 
    RowBox[{
     RowBox[{"2", "x"}], "-", "3"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737972588155011*^9, 3.73797262586692*^9}},
 CellLabel->"In[54]:=",ExpressionUUID->"f9e33a13-3002-478f-9759-3ccb6f36e036"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwt1X041OkaB3BES2zkJZEMfg5hh99GI1T3vdUcri3WIXYPrbUTrdUwJSuO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       "]]},
     Annotation[#, "Charting`Private`Tag$6143#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {0., 22.99999918367347}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.7379726203589497`*^9, 3.737972626492588*^9}},
 CellLabel->"Out[54]=",ExpressionUUID->"47ab987c-3cb6-4e5a-8617-644733ba141f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Abs", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "2"}], "x"}], "-", "3"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.73797263106637*^9, 3.737972648520316*^9}},
 CellLabel->"In[56]:=",ExpressionUUID->"698412c6-d8fb-4bad-a21a-bcfad8596f22"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwt1XdUVMceB/DdfYC0CNKX5sKVGheWdhUlzk+RAGLoEAIxkeYxiEAAsdKU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       "]]},
     Annotation[#, "Charting`Private`Tag$6237#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-10, 10}, {0., 22.99999918367347}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.737972644895319*^9, 3.737972649246299*^9}},
 CellLabel->"Out[56]=",ExpressionUUID->"df598669-dcfe-4b00-bce1-56f63e96b5b5"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nPartial Fractions and Algebraic function",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737787132776928*^9, 3.737787145055173*^9}, 
   3.737787192913722*^9, {3.7379522341847773`*^9, 
   3.737952238713409*^9}},ExpressionUUID->"a60a4d30-7e71-443b-ad2e-\
fae84455a656"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Splitting into Partial Fraction",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737787204467952*^9, 
  3.7377872427222137`*^9}},ExpressionUUID->"6d5991f4-5cec-47fa-9666-\
cda6ee5d2d54"],

Cell[CellGroupData[{

Cell[TextData[{
 "Split the Partial fraction ",
 Cell[BoxData[
  FormBox[
   FractionBox[
    RowBox[{"1", "+", 
     SuperscriptBox["x", "2"]}], 
    RowBox[{"1", "+", "x"}]], TraditionalForm]],
  FormatType->"TraditionalForm",ExpressionUUID->
  "a89bc182-5dae-4add-9ad2-2a1e4d6d7fb9"]
}], "Subsection",
 CellChangeTimes->{{3.73778726648422*^9, 
  3.737787343145667*^9}},ExpressionUUID->"a699304a-b994-4a23-82d5-\
6e43d4560a44"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Apart", "[", 
   FractionBox[
    RowBox[{"1", "+", 
     SuperscriptBox["x", "2"]}], 
    RowBox[{"1", "+", "x"}]], "]"}], "//", "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.737787257232647*^9, 3.7377872582395773`*^9}, {
  3.737787352108225*^9, 3.737787355353717*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"d7c47b23-47ad-4101-9435-1b05e4d73e72"],

Cell[BoxData[
 FormBox[
  RowBox[{"x", "+", 
   FractionBox["2", 
    RowBox[{"x", "+", "1"}]], "-", "1"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.737787355905343*^9},
 CellLabel->
  "Out[1]//TraditionalForm=",ExpressionUUID->"7e1b4ece-69fb-4f11-8bba-\
434148e3d652"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nTransformations and Matrices",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.7373619477678423`*^9, 3.737361959716154*^9}, {
   3.737362629050335*^9, 3.737362630233316*^9}, {3.737362961571636*^9, 
   3.737362966796749*^9}, 
   3.737364312453195*^9},ExpressionUUID->"245d058a-40cc-40ed-8f5a-\
2c56801512b4"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Converting Coordinates into Matrices",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737362041593523*^9, 3.737362042918879*^9}, {
  3.737362073952798*^9, 
  3.7373620932372627`*^9}},ExpressionUUID->"42684e1d-8400-422b-98ec-\
82879fb98a03"],

Cell["Points (a , b) and (c , d) are coordinates. ", "Text",
 CellChangeTimes->{{3.737362114549193*^9, 3.737362158630185*^9}, 
   3.7373623814518023`*^9},ExpressionUUID->"86c728c4-0403-4519-ada0-\
9a7bda2d6a5b"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"a", ",", "b"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"c", ",", "d"}], "}"}]}], "}"}], "//", "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.737361974358478*^9, 3.737361975827875*^9}, {
  3.737362103790534*^9, 3.7373621075024147`*^9}},
 CellLabel->"In[57]:=",ExpressionUUID->"5086749f-66ab-4b07-a35b-e87a196c85aa"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"a", "b"},
     {"c", "d"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.737362108857366*^9},
 CellLabel->
  "Out[57]//MatrixForm=",ExpressionUUID->"7d13e075-f5f7-49b2-bd88-\
608d9db29973"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"{", 
   RowBox[{"a", ",", "b"}], "}"}], "//", "MatrixForm"}]], "Input",
 CellLabel->"In[58]:=",ExpressionUUID->"4aad1002-124b-4a4a-9eb5-1c93600eb66c"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", 
   TagBox[GridBox[{
      {"a"},
      {"b"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
        "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    Column], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7373624112610207`*^9},
 CellLabel->
  "Out[58]//MatrixForm=",ExpressionUUID->"30c6710d-c936-4e7a-9487-\
1f9eb5558bb4"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Matrix addition and subtraction",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737362430701556*^9, 
  3.737362451697418*^9}},ExpressionUUID->"6f72b227-baa5-4b18-9bf8-\
3d94bba78be4"],

Cell[CellGroupData[{

Cell["Addition", "Subsection",
 CellChangeTimes->{{3.737362488981915*^9, 
  3.737362490885727*^9}},ExpressionUUID->"7a280568-9133-4feb-af2a-\
2ac524b8977f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"2", ",", "1", ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "4", ",", "6"}], "}"}]}], "}"}], "+", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"7", ",", "1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"9", ",", "1", ",", "2"}], "}"}]}], "}"}]}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.7373619807662497`*^9, 3.737361981689616*^9}, 
   3.737362470062647*^9},
 CellLabel->"In[59]:=",ExpressionUUID->"a69e315e-99f4-42a9-bad0-2e8387509654"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"9", "2", "4"},
     {"10", "5", "8"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.737362471579218*^9},
 CellLabel->
  "Out[59]//MatrixForm=",ExpressionUUID->"5284fad4-cdd9-416c-8e88-\
fe81bcb0379f"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Subtraction", "Subsection",
 CellChangeTimes->{{3.737362502917066*^9, 
  3.73736250617731*^9}},ExpressionUUID->"59b965f0-3264-4149-bd7f-\
be57bf15124d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"2", ",", "1", ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "4", ",", "6"}], "}"}]}], "}"}], "-", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"7", ",", "1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"9", ",", "1", ",", "2"}], "}"}]}], "}"}]}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.737362475392828*^9, 3.73736247966115*^9}},
 CellLabel->"In[60]:=",ExpressionUUID->"d0f5ecac-3a35-44a8-9d4b-23b022dc162e"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{"-", "5"}], "0", "4"},
     {
      RowBox[{"-", "8"}], "3", "4"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.737362480529381*^9},
 CellLabel->
  "Out[60]//MatrixForm=",ExpressionUUID->"e523d36c-4736-41b8-8e92-\
829e5fe9c396"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Matrix Multiplication and Division",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737362581754198*^9, 3.737362585434492*^9}, {
  3.737362755424346*^9, 
  3.7373627664859743`*^9}},ExpressionUUID->"de0ade0b-890a-4bbb-b84e-\
e7afb39c97d3"],

Cell[CellGroupData[{

Cell["Multiplication", "Subsection",
 CellChangeTimes->{{3.737362776218589*^9, 
  3.737362781672127*^9}},ExpressionUUID->"03b9db56-1ff7-40a4-9a3b-\
9f2135b397f4"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"2", ",", "1", ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "4", ",", "6"}], "}"}]}], "}"}], "*", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"7", ",", "1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"9", ",", "1", ",", "2"}], "}"}]}], "}"}]}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.7373627872071466`*^9, 3.73736278747841*^9}, {
  3.7373628437991323`*^9, 3.737362847539029*^9}},
 CellLabel->"In[61]:=",ExpressionUUID->"10bed3f8-0233-48b0-bf76-a63cdc1b3313"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"14", "1", "0"},
     {"9", "4", "12"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.737362848724297*^9},
 CellLabel->
  "Out[61]//MatrixForm=",ExpressionUUID->"ba312895-1e97-465d-b185-\
0ac65636f4c0"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Division", "Subsection",
 CellChangeTimes->{{3.737362857321328*^9, 
  3.737362859475072*^9}},ExpressionUUID->"caa52839-2df8-4b8b-9a97-\
95e6febad77c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"2", ",", "1", ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "4", ",", "6"}], "}"}]}], "}"}], "/", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"7", ",", "2", ",", "5"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"9", ",", "7", ",", "4"}], "}"}]}], "}"}]}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.737362865394701*^9, 3.7373629162809973`*^9}},
 CellLabel->"In[65]:=",ExpressionUUID->"12b27982-5105-48b3-ba69-21adc815b1b8"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      FractionBox["2", "7"], 
      FractionBox["1", "2"], 
      FractionBox["4", "5"]},
     {
      FractionBox["1", "9"], 
      FractionBox["4", "7"], 
      FractionBox["3", "2"]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.737362872611649*^9, 3.7373629173301764`*^9}},
 CellLabel->
  "Out[65]//MatrixForm=",ExpressionUUID->"9c11f731-d1a7-4e61-81ef-\
9b085d464939"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Matrices to find the transformation",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737362977568864*^9, 
  3.7373630295809593`*^9}},ExpressionUUID->"920edcda-f646-40ae-83a9-\
1ec216a3a9f2"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], ".", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"0", ",", 
       RowBox[{"-", "3"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "0"}], "}"}]}], "}"}]}], "//", 
  "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.737363035599859*^9, 
  3.73736304440169*^9}},ExpressionUUID->"d2aea1f6-35a5-489f-b641-\
43d8680f8d5b"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", 
   TagBox[GridBox[{
      {"y"},
      {
       RowBox[{
        RowBox[{"-", "3"}], " ", "x"}]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
        "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.5599999999999999]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    Column], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{
  3.73736304524673*^9},ExpressionUUID->"7f613190-18fb-4f5b-a8bf-cc7bc1738a5e"]
}, Open  ]],

Cell[CellGroupData[{

Cell["With translation", "Subsection",
 CellChangeTimes->{{3.7373630602893267`*^9, 
  3.73736306419666*^9}},ExpressionUUID->"dd1cfebc-04f3-4109-9057-\
2aa087c887a1"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "4"}], "}"}]}], "}"}], ".", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}]}], "+", 
  RowBox[{"{", 
   RowBox[{"3", ",", "5"}], "}"}]}]], "Input",
 CellChangeTimes->{{3.737363069048581*^9, 
  3.737363070080798*^9}},ExpressionUUID->"46351e68-d3e5-497b-a648-\
70de18bcea84"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"3", "-", 
    RowBox[{"2", " ", "x"}]}], ",", 
   RowBox[{"5", "+", 
    RowBox[{"4", " ", "y"}]}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.737363070883802*^9},ExpressionUUID->"88014ed0-cf60-443c-bf43-\
cfee54f0ff68"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox[" \nCubic graph plotting and other cubic commands",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.7373567690070972`*^9, 3.737356818704365*^9}, {
  3.737358909873163*^9, 3.7373589130211363`*^9}, {3.7373618738526278`*^9, 
  3.73736190081513*^9}},ExpressionUUID->"6c4100c8-1ffa-4f6b-8b25-\
934c6b73c27b"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Plotting Cubic graphs",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7373568233001633`*^9, 3.737356923304997*^9}, {
  3.73735695445153*^9, 
  3.737356956323049*^9}},ExpressionUUID->"b3a45641-7a81-43f7-aef0-\
5da0739aa497"],

Cell[CellGroupData[{

Cell["Always state the labels when drawing the graph", "Subsubsubsection",
 CellChangeTimes->{
  3.737358129427636*^9},ExpressionUUID->"ee175631-fc87-483e-89a5-\
134058e3ab21"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"x", "+", "10"}], ")"}], "2"], 
    RowBox[{"(", 
     RowBox[{"10", "-", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "20"}], ",", "20"}], "}"}], ",", " ", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737356961591086*^9, 3.7373569781420813`*^9}, {
  3.737358039113755*^9, 3.7373580644384317`*^9}, {3.737358142115676*^9, 
  3.737358178836817*^9}},
 CellLabel->"In[32]:=",ExpressionUUID->"c33fcf45-f3b1-4942-946d-a11272762ea2"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV1nc8V98fB3B7Z5O9Ph97ZiZ033aSQkUk2cmKT9kroWR/PrYSJUJERPKt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       "]]},
     Annotation[#, "Charting`Private`Tag$18243#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{
    FormBox[
     TagBox["x", HoldForm], TraditionalForm], 
    FormBox["y", TraditionalForm]},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-20, 20}, {-5021.1788507242945`, 2999.9994285714624`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.737358040826603*^9, 3.737358065464301*^9}, {
  3.73735814674921*^9, 3.737358179646552*^9}},
 CellLabel->"Out[32]=",ExpressionUUID->"e7ff2925-133a-4b6f-917e-58e4d8c132df"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"2", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "+", "10"}], ")"}], "3"]}], "+", "5"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "20"}], ",", "20"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "10"}], ",", "10"}], "}"}]}], ",", " ", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737358186899665*^9, 3.737358236512867*^9}},
 CellLabel->"In[33]:=",ExpressionUUID->"84b1ce21-da31-4b93-9a83-b015b527ee3d"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJw11nk01esaB3AzmWL/fmQq9v799t4V4pSipP1ISMqQyqkcs8qupH0qmpyI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       "]]},
     Annotation[#, "Charting`Private`Tag$18626#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{
    FormBox[
     TagBox["x", HoldForm], TraditionalForm], 
    FormBox["y", TraditionalForm]},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-19.99999918367347, 19.99999918367347}, {-10, 10}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.73735823749641*^9},
 CellLabel->"Out[33]=",ExpressionUUID->"6616951d-1dd6-4e9c-9337-a1bb37044e69"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Finding Minimum and Maximum Functions from Cubic \
Functions",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737358717389316*^9, 
  3.7373587330972223`*^9}},ExpressionUUID->"629e28e5-f6f1-4317-b95c-\
f7d865526d81"],

Cell["\<\
For cubic graphs, sometimes, they may ask the minimum or maximum after a \
certain point in a certain range. for that do it the way below by adding a \
comma after the x to state where the point  starts from or the range\
\>", "Subsubsubsection",
 CellChangeTimes->{{3.737358766694173*^9, 
  3.73735885761727*^9}},ExpressionUUID->"2c9cbce1-5e87-4114-a6b1-\
431bc1cc95f8"],

Cell[CellGroupData[{

Cell["\<\
Example: Find the maximum point after x --> 20, on the R[x] function\
\>", "Subsubsection",
 CellChangeTimes->{{3.7373618121319304`*^9, 
  3.737361850278557*^9}},ExpressionUUID->"14d19d5c-7d73-479f-a2f3-\
24b2779b4f39"],

Cell[BoxData[
 RowBox[{
  RowBox[{"R", "[", "x_", "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"-", "0.02"}], 
    SuperscriptBox["x", "3"]}], "+", 
   RowBox[{"0.76", 
    SuperscriptBox["x", "2"]}], "-", 
   RowBox[{"8.82", "x"}], "+", "32.4"}]}]], "Input",
 CellChangeTimes->{{3.737358861541759*^9, 3.737358861775044*^9}, 
   3.73736170353552*^9},
 CellLabel->"In[56]:=",ExpressionUUID->"18f4ae55-e8ea-4dec-9134-273683fe3108"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindMaximum", "[", 
  RowBox[{
   RowBox[{"R", "[", "x", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "20"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7373617063352413`*^9, 3.737361709694337*^9}, 
   3.737361786620057*^9},
 CellLabel->"In[55]:=",ExpressionUUID->"5b32e9b0-93da-44ae-bf80-c4f09fc9fe37"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"3.9437037037037044`", ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "16.333333333351614`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.737361858999156*^9},
 CellLabel->"Out[55]=",ExpressionUUID->"f8040880-a658-4e6b-80dc-3e9f26d90ae2"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nLinear ,Quadratic and Relations Plotting and other \
linear and quadratic commands",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737356243967661*^9, 3.737356246317296*^9}, {
  3.737356437665504*^9, 3.7373564408646173`*^9}, {3.737356722130163*^9, 
  3.737356763252306*^9}, {3.737358873068012*^9, 3.737358941476159*^9}, {
  3.7373625651249647`*^9, 3.7373625670246763`*^9}, {3.737398960409543*^9, 
  3.7373989829065943`*^9}},ExpressionUUID->"e811121f-46c6-4705-a3b8-\
51ccee61f12a"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Distance between two points",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.7373987934593697`*^9, 
  3.737398807284133*^9}},ExpressionUUID->"ed7b49c9-fcc8-4f92-94c5-\
43078f659908"],

Cell[CellGroupData[{

Cell["Example: Find the distance between (2,-3) and (4,-7)", "Subsection",
 CellChangeTimes->{{3.7373988424338408`*^9, 
  3.737398897494945*^9}},ExpressionUUID->"19ad7b44-af7b-415c-874b-\
8b08331ac2d4"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"EuclideanDistance", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"2", ",", 
     RowBox[{"-", "3"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"4", ",", 
     RowBox[{"-", "7"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737398812296295*^9, 3.7373988125070477`*^9}, {
  3.737398903472579*^9, 
  3.737398938012784*^9}},ExpressionUUID->"9a71d743-4918-423c-9c44-\
11a745fe7fea"],

Cell[BoxData[
 RowBox[{"2", " ", 
  SqrtBox["5"]}]], "Output",
 CellChangeTimes->{
  3.737398938892372*^9},ExpressionUUID->"9fa14039-98c0-4dff-bad1-\
f1fc6c95fc66"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Complete the Square:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737348150383625*^9},ExpressionUUID->"c7b52a9d-0ded-49e9-8bc2-\
8f97362e67e8"],

Cell[BoxData[
 RowBox[{
  RowBox[{"CompleteSQ", "[", 
   RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "]"}], " ", ":=", " ", 
  RowBox[{
   RowBox[{"a", "*", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"x", "+", 
       FractionBox["b", 
        RowBox[{"2", "a"}]]}], ")"}], "2"]}], "-", 
   FractionBox[
    SuperscriptBox["b", "2"], 
    RowBox[{"4", "a"}]], "+", "c"}]}]], "Input",
 CellChangeTimes->{{3.71963580671703*^9, 3.7196358225555754`*^9}, {
  3.719635912472605*^9, 3.7196359517330446`*^9}, {3.719636012994155*^9, 
  3.719636113154935*^9}},ExpressionUUID->"871414a5-8c4a-4ebf-b0b6-\
874de043ae40"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"CompleteSQ", "[", 
   RowBox[{"2", ",", "7", ",", "13"}], "]"}], "//", 
  "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.719636120767704*^9, 
  3.719636145907349*^9}},ExpressionUUID->"06370c14-53fa-447c-a4a9-\
3c393e40a197"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"x", "+", 
       FractionBox["7", "4"]}], ")"}], "2"]}], "+", 
   FractionBox["55", "8"]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.719636147935361*^9, 
  3.7196361516216297`*^9}},ExpressionUUID->"969b4c3b-34db-4ae5-b57c-\
76dd30aa705d"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Finding the angle between two coordinates \[Implies] \
Linear mostly",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737359044811311*^9, 
  3.7373591230343847`*^9}},ExpressionUUID->"be0542c2-414e-47e4-9fd3-\
1c39b45a95d6"],

Cell[TextData[{
 "The gradient formula of the linear graph is ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    FractionBox[
     RowBox[{"y2", "-", "y1"}], 
     RowBox[{"x2", "-", "x1"}]], "."}], TraditionalForm]],
  FormatType->"TraditionalForm",ExpressionUUID->
  "d707125f-56df-4194-9e33-125d8b364ef1"],
 " This can be turned into ",
 Cell[BoxData[
  FormBox[
   FractionBox["Sin\[Theta]", "Cos\[Theta]"], TraditionalForm]],
  FormatType->"TraditionalForm",ExpressionUUID->
  "33ca4624-c0bb-4d74-a329-817649934a3b"],
 "= Tan \[Theta].  In other words m = Tan\[Theta]."
}], "Subsubsubsection",
 CellChangeTimes->{{3.737359126180923*^9, 3.7373591500361643`*^9}, {
  3.7373592227112637`*^9, 3.7373593404110003`*^9}, {3.7373593763029833`*^9, 
  3.737359376303154*^9}, {3.737359888349409*^9, 
  3.737359932335627*^9}},ExpressionUUID->"d73030fe-474d-4150-bb22-\
9ea91c08a110"],

Cell[CellGroupData[{

Cell["Example : Find the angle of depression from (0,10) and (4,0)", \
"Subsubsection",
 CellChangeTimes->{{3.737360333315805*^9, 3.737360408128221*^9}, 
   3.737361758091011*^9},ExpressionUUID->"2a7df301-f921-4bd3-b3ba-\
c6fb7010015c"],

Cell[TextData[{
 StyleBox["First find the gradient",
  FontWeight->"Bold"],
 " ",
 StyleBox["(",
  FontWeight->"Bold"],
 StyleBox["Shortcut of fractions --> On macs, just control and / for a \
fraction",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox["), then turn it into a decimal.",
  FontWeight->"Bold"]
}], "Text",
 CellChangeTimes->{{3.737360411557541*^9, 3.737360480896737*^9}, {
  3.737361564819413*^9, 
  3.737361580434874*^9}},ExpressionUUID->"3f3536c8-bd1d-4498-91a1-\
df23f1ee90e1"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"0", "-", "10"}], 
   RowBox[{"4", "-", "0"}]], "//", "N"}]], "Input",
 CellChangeTimes->{{3.737360431859646*^9, 3.7373604332837143`*^9}, {
  3.7373605232516212`*^9, 3.73736053107752*^9}, {3.737361552417796*^9, 
  3.73736155378948*^9}},ExpressionUUID->"311d2c8a-dbe1-4a47-b46e-\
00b25b6dd246"],

Cell[BoxData[
 RowBox[{"-", "2.5`"}]], "Output",
 CellChangeTimes->{3.737360531933272*^9, 
  3.737361554629381*^9},ExpressionUUID->"cbbe2895-9fcc-4339-822b-\
e98e5b53b1cc"]
}, Open  ]],

Cell["Then find Tan inverse to find out the angle", "Text",
 CellChangeTimes->{{3.737360535031773*^9, 
  3.73736055211204*^9}},ExpressionUUID->"6e36ff0b-0379-434c-87d4-\
bf1a22d76a04"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"ArcTan", "[", 
   RowBox[{"-", "2.5"}], "]"}], "/", "Degree"}]], "Input",
 CellChangeTimes->{{3.737360554572996*^9, 3.737360665541658*^9}, {
  3.737361484992478*^9, 3.737361558974106*^9}, {3.7373987233581877`*^9, 
  3.7373987267762623`*^9}},ExpressionUUID->"4e30d7e4-3a3c-4d36-ba9e-\
952e4c082c8c"],

Cell[BoxData[
 RowBox[{"-", "68.19859051364818`"}]], "Output",
 CellChangeTimes->{
  3.737360600407826*^9, 3.7373606665531*^9, {3.7373614881626797`*^9, 
   3.737361495648985*^9}, {3.737361532960321*^9, 3.737361559431775*^9}, 
   3.737398728106983*^9},ExpressionUUID->"5c4f6e9d-143d-4197-ad61-\
3bcef4255159"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Manipulate Function:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellGroupingRules->{"SectionGrouping", Inherited},
 CellChangeTimes->{{3.7196362662036586`*^9, 3.7196362941112795`*^9}, 
   3.719637053146584*^9, {3.7373481660774384`*^9, 
   3.737348175683663*^9}},ExpressionUUID->"998460aa-17ee-41a7-9cb6-\
48f39571b576"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"f", "[", "x_", "]"}], ":=", 
  RowBox[{
   RowBox[{"a", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"x", "-", "2"}], ")"}], "2"]}], "+", 
   "3"}]}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "10"}], ",", "10"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"k", ",", 
     RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.7196362264693327`*^9, 3.7196362388309*^9}, {
  3.719636296402275*^9, 3.719636297381277*^9}, {3.719636763429422*^9, 
  3.7196367733122935`*^9}, {3.719636894719407*^9, 3.719636984512578*^9}, {
  3.737356295090624*^9, 3.737356334021508*^9}, {3.7374046396799173`*^9, 
  3.737404661407617*^9}},ExpressionUUID->"833fe1e1-c290-4220-b275-\
53e2b96da2e9"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`k$$ = -5., Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`k$$], -5, 5}}, Typeset`size$$ = {450., {142., 149.}}, 
    Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = 
    True, $CellContext`k$4900$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, "Variables" :> {$CellContext`k$$ = -5}, 
      "ControllerVariables" :> {
        Hold[$CellContext`k$$, $CellContext`k$4900$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Plot[
        $CellContext`f[$CellContext`x], {$CellContext`x, -10, 10}, 
        PlotRange -> {-10, 10}], 
      "Specifications" :> {{$CellContext`k$$, -5, 5}}, "Options" :> {}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{505., {195., 202.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.7196367762139683`*^9, {3.719636908691844*^9, 3.7196369852102165`*^9}, 
   3.737356269518217*^9, {3.737356302929412*^9, 3.7373563352990847`*^9}, 
   3.737404663369052*^9},ExpressionUUID->"d56ed259-86db-49be-bc39-\
903ccc4e02a8"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Simultaneous Equations:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737348196013487*^9},ExpressionUUID->"a24fb3da-9a23-4958-b3b4-\
1a66f605c8ee"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      TagBox[
       FrameBox[
        SubscriptBox["lhs", "1"]],
       "Placeholder"], "\[Equal]", 
      TagBox[
       FrameBox[
        SubscriptBox["rhs", "1"]],
       "Placeholder"]}], ",", 
     RowBox[{
      TagBox[
       FrameBox[
        SubscriptBox["lhs", "2"]],
       "Placeholder"], "\[Equal]", 
      TagBox[
       FrameBox[
        SubscriptBox["rhs", "2"]],
       "Placeholder"]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     TagBox[
      FrameBox[
       SubscriptBox["var", "1"]],
      "Placeholder"], ",", 
     TagBox[
      FrameBox[
       SubscriptBox["var", "2"]],
      "Placeholder"]}], "}"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"8", "\[Equal]", 
      RowBox[{
       RowBox[{"2", "x"}], "+", 
       RowBox[{"3", "y"}]}]}], ",", 
     RowBox[{"y", "\[Equal]", 
      RowBox[{
       RowBox[{"4", "x"}], "-", "3"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.7196370356580863`*^9, 3.7196370656155443`*^9}, 
   3.7196370988541403`*^9},ExpressionUUID->"818d8b80-0c00-4e5f-b352-\
e689f74a492c"],

Cell[BoxData[
 RowBox[{"{", "}"}]], "Output",
 CellChangeTimes->{
  3.7196371003109436`*^9},ExpressionUUID->"e1d81b3d-61c2-4352-a9cf-\
6772cfa427d6"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", 
     FractionBox["17", "14"]}], ",", 
    RowBox[{"y", "\[Rule]", 
     FractionBox["13", "7"]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{
  3.719637100551831*^9},ExpressionUUID->"59930920-9abf-4005-878f-\
9442347145db"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Plot Functions:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737348208552732*^9},ExpressionUUID->"a201d07e-9f69-4e71-8201-\
68325ab09ce3"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"2", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "+", "4"}], ")"}], "2"]}], "-", "5"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "20"}], ",", "20"}], "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "20"}], ",", "20"}], "}"}]}], ",", " ", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7196372809413586`*^9, 
  3.71963729756689*^9}},ExpressionUUID->"a819a227-5060-492f-adaa-\
bc86c73bca2c"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJw1lnk0lI0Xx61jGTPzzPMYa2NJlogkJZJ5KiWKpJrQQlpEhYhQokibFiVt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       "]]},
     Annotation[#, "Charting`Private`Tag$13665#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{
    FormBox[
     TagBox["x", HoldForm], TraditionalForm], 
    FormBox["y", TraditionalForm]},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-19.99999918367347, 19.99999918367347}, {-20, 20}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.7196372985186057`*^9, 
  3.7196373322908525`*^9},ExpressionUUID->"db859691-70f4-4c66-a969-\
a6d681f5109c"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", " ", 
    RowBox[{
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"x", "+", "3"}], ")"}], "2"], "-", "10"}], ",", 
     FormBox[
      RowBox[{
       RowBox[{
        FractionBox["1", "2"], 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"x", "+", "3"}], ")"}], "2"]}], "-", "10"}],
      TraditionalForm], ",", " ", 
     RowBox[{
      RowBox[{"2", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"x", "+", "3"}], ")"}], "2"]}], "-", "10"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "7"}], ",", "3"}], "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "10"}], ",", "10"}], "}"}]}], ",", " ", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7196373339450536`*^9, 
  3.719637335916149*^9}},ExpressionUUID->"1247a84c-00d5-4ef6-9c3e-\
3544dc46f09a"]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Region Required for Quadratic and Linear Functions",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737399345356927*^9, 
  3.737399369300658*^9}},ExpressionUUID->"fb7e8340-adab-4d23-93bf-\
702c87664545"],

Cell[CellGroupData[{

Cell["Quadratic", "Subsection",
 CellChangeTimes->{{3.737399376765744*^9, 
  3.7373993792998657`*^9}},ExpressionUUID->"5d463261-d258-4939-b61b-\
08ae2992e051"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"RegionPlot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       SuperscriptBox["x", "2"], "-", "6"}], "\[LessEqual]", "y"}], ",", 
     RowBox[{"y", "<", "7"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"BoundaryStyle", "\[Rule]", "Dashed"}], ",", 
   RowBox[{"Axes", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.73739938187118*^9, 3.737399509172928*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"150bd53c-8e84-4543-afd8-f15c3e78d3fe"],

Cell[BoxData[
 GraphicsBox[GraphicsComplexBox[CompressedData["
1:eJy1mnt0lEWWwGMSQ3h0CK8ADQIJiC2MoECDAyxdY8tbJLAMCmKQl+MQEMER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   "], {{
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      0.3], EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxVl3uU11UVxc9FBZ0hRMQJBGFGecVbRgYYxEEEFERIfIMCoSiBvExFMVF8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         "]], PolygonBox[CompressedData["
1:eJwtlPdvj1EUh+8xorbYFGmN2nvECIrYI9RoNWaNmjVaWqo1SmmNFrVDUELE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         "]]}]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
      0.3], EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmXfc12MXx+/7+01GIqkoGVEim+yRkSgKFVJmiKyQnT0ysp4RHjzDjlCR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         "]], PolygonBox[CompressedData["
1:eJwtkWkrxUEUh//mkCRJkiQvvPEBLFnKEm6WLLlkyRJXlmwXXWTJkiVLlg9p
33dJ4pnOefH0/M6Zc2fuzD83Eg3PuCAI8iAeKiUIquCX5hWUksvgh3wJc+R5
SIMX6gUcs5yOD2AfPqiz8S7sQZb1DvGR6NondT8egCR4oB7Cg5aTcR/0wr3T
mW7ogUTrTeIJeCKn4jEYhxTrneBjOysHT8G06OwzvVE8Ao9OfxOBYdGzfW8W
R23W37kGqkXf5g92yNvw7vSOi7Ak+hav9MK4DW7JCbgFWkGsV4tDontdQwm5
GC6cvnkFuVz07f03qSfXic7G4WZoghunezZAo+ia7xXiIvh2uucqeQ0y4I16
E29Bpt1hBS/bf/czG7Bus36mHTpE73JHrwDnw7nTM7rInbbmv9EpnIm+/Re9
fw4ITUY=
         "]]}]}, {}, {}, {}, {}, {}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJwl01VXVGEUgOEZAwtQsFsMsLsVEQSVFDGwA1tURAUDC7uwA7vu/TVemZio
2IqJ6DPLi2e9+9vnzJw1a2Zi8gpy1gUDgcBdPpBKGulkkEkWU8jmDk294DCR
HOAQB7nAHvayi1J2c55BnKMLZ4lhIAN46z2rmWyeRAnbqLKbqCkk04RNvLGf
oEkk0pBO3KYjoQ9UnzXUYy3tOckqVrOclazgBH3oSzuuU+kZvfW5fmaMeTRL
yOOZ3SgdyQiCtOEWrZlDrXtm6R+drcc4Shw9ackVnrgeq4/0I0PMg/llnqkP
9ZK24Ke5uV7kgXmq3gt9P5pFNvedy7UZXYnmJlFM44frOTqD6RyhB4/tL+tv
7aaftIJcc40O1WEM56nzVW3FX/Pc0I+IebSljAUsZD6LWcRxevHC7de0Dt35
4vySpeZljCWer3avyDfXZRwJjOe1/Q3tQBgFNGA9ndlAIwppzEZOc4piNlPE
VrZwhn70J4LthPPNc96xw7yTVNL4bveefeb9pJNBZvD/f+kfEHNefg==
       "]]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJwl0tlSzgEAxuF/HNQ91KQoFWmRrRApbRSVNhSytJclpOIrKS2WZrgE6ouk
TcxwB8zkDmpGd8CMU8+Mg2fmPX9/8U3dlV0RQRCEeWu84Qs/2OAPUVuCIIYM
Cqijg0FeE+YbP9nk8NYg2EsWmexnH7Ec5BAHyCGbbRwllyMc5xhxnCCfPE5S
QDxFFFNIKSVs5zRlnOIM5eyggkrOco4qEqihlmrqqSORC1zkPI00sJPLXOES
V2kiievc4BotNJNMG+200kkHKXRzky5uc4td9HCXO9znHrt5QB+9DNBPKo8I
8ZAhBtnDME94zCgjpDHGOE+ZZIJ0nvOCZ0zxkgz++vMXa3xlhleEaKeWfNKJ
JpLfmlnnO59Z5RMrLLPEIgt8ZJ4PzPGed8wSZobpiP9t/gNan0s7
       "]]}}}],
  AspectRatio->1,
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{Automatic, Automatic},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{True, True}, {True, True}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "ScalingFunctions" -> None, "TransparentPolygonMesh" -> True, 
    "AxesInFront" -> True},
  PlotRange->{{-10, 10}, {-10, 10}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.02]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.737399457628529*^9, 3.7373995101800632`*^9},
 CellLabel->"Out[6]=",ExpressionUUID->"25e1b52f-f41a-48ae-90e6-d796fe8e423d"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Linear", "Subsection",
 CellChangeTimes->{{3.7373995342198677`*^9, 
  3.7373995371284103`*^9}},ExpressionUUID->"e0572fde-5395-4a06-9413-\
4d1da78fb83f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"RegionPlot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"4", "x"}], "-", "6"}], "\[LessEqual]", "y"}], ",", 
     RowBox[{"y", "<", "3"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"BoundaryStyle", "\[Rule]", "Dashed"}], ",", 
   RowBox[{"Axes", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.73739953918367*^9, 3.737399570320531*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"e7506b55-738c-4328-a7e7-2eeb0b4131b5"],

Cell[BoxData[
 GraphicsBox[GraphicsComplexBox[CompressedData["
1:eJzVmntcVNUWxxERUBzloQgjIQ/TKRWf4wvvPbtGzbJ0fITv8dlDxys+0hq7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   "], {{
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      0.3], EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmHv819Mdx88JKRXdCEmlklt+FUnIfaSkuSTKJcmlkPv9slxqCk1Xl4hI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         "]], PolygonBox[CompressedData["
1:eJwt0/tPz3EUx/H3UWZYoxnGqskwjN9bw0jIpS25p4xqGVu5NUZzXyhTaLlk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         "]]}]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
      0.3], EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxNmXncl1Maxt/feUKEYcYy1rFFSrKVFtl3YzcMEpNB1GQ0GvsWM2QMo7LM
2MfYzWSmBjXKklJky1ayRKlUFEl7zf39nO/5PP64u35nu8993ec851znbese
5x/XJzU1NR0V/1SBnwb+N+yBsHcaTU2jwp4Pe1d8Iew98cWw98WXwj4QR4dN
El8OmyyOCZse9mbYW2FTwsaGvRI2LewN2z4OGxc2PuwL+74d9pF9afs07NWw
18I+C5sQ9nrY5yK+ptpO28ywiY3MaVnYDOu+0xd9v5Qn/GaL8Jsjwm+uCL+v
RPh9LX4YNk+E33yR2L8R4fet+EnYApE4ZhkjcSw0Lvh9L8JvkTjNcePNxRLz
S84W2075yljLc8POC1sub+ZZKWe4rhLh2pQywrWRMsI1pYxwrVJGuDZLGeG6
WsoI19VTRriukTLCtXnKSO7XTBnh+uP4vcK4WqTMGa5rp4xwWidlhOv68mHM
eimvK+Ufxe+lrvMOKfv9ibZSrlulPAe+N0yZM1w3EuG6sQjXn4pw3USE66Yi
XDcT4bq5CNctRLhuKa4V9jORODZIOS7i2Nq44Lpt2Lopc9pOXM88zXL9tk85
F/Bsafv6+l7o3mklf+bpEXZkyt98W7nBqY384b2bcRPvTtbRb1e50dZO/vDe
WR+Ud7GOfrvrA657pbwexNI+5TWA63FhXcP2DtvDvrR1lD+8O8sNrl1EfHWy
vaU+8L2jvsDWYfuI8NtPPvDeXyT2A0Q4HSjC4yAR3geL5OYQEX776hu/h1oH
jyPCOoTtaa47yePn1nV0HTradrTt8DtMH+3tu425ONY8wvUY+1I+Xs5wPUEk
rl+I8D5RhPdJIrx/KcL7ZBHep4jwPlWEdzcRrqeJxHt62OHyPkOE669EuJ5r
fMR1pnmB969FOJ0lwrWn3BhzTsp7hfLZth/nOrOv+Y7P0zdcL3YOfPeWM1x/
I8K1jwjX80W4/laE6wUiXH8X1l2uF4pw7SfC9fci39lFInH0Mi7iuMS44Hqp
CKfLRLi2lhPf5BXmgvxdbnvPVO9v1v4q+TPPNXKG63Vyg1N/6+B9o3ET77XW
0W+A3Gi7PqyvvP+gD/Jxg3X0+5M+4Doo5fuGWP7sGsD1trCrjesm+9J2i/zh
favc4DpQxNdfbKdtsL7xdbv+4PS4c1B3V9gfjf1OuZGD+42V+f9qHZzuMxe0
3SM3cnC3Pig/4Dg4/V28OewxY2Luf8iHeB+0nfIdxkgcD9kO14fFgfa9xFw8
ah7x+4jtg+Tcy3V9Qq74/qc84fSS/IeEjZXDU2Gvye3fYW+G3Rv2n7B35D80
7ANzNCxsipzRgp/K+emwaXJ7JmymnJ8NmyO34WEtqhzTi2EL5PC/sEVyey5s
mbkbGbZG9H8y8IWwqsrcng9b5bqOMt4BrtMoNdJE9d1UtVPRpminok0pF21K
uWhTykWbUh6jZqM8Vs1G+RU1G+VxaraP1FyfWH7V+SkXrUx8E9RsxFe0KeU3
1GaUn3QNWb+31G5FI0+330Q12wz9zrL8rvf/rEatR+c2as06u1FrzW8atX6d
06j16PxGrVmLhv1aX0Wbfiu/7yzPVGcta9TatGjVhfZboZ5DhxTN+r18Flsu
+nie3PC3VN5L7IdeQ7fga5Z+lzdqzbqyUetUtFPRqZSLTqVcdCrlolMpF51K
uehUykUHr2rUmpU2+KGr0HBFj6LV4IaOo61oVsrwQbOh4YrexdeXxl74kKei
YUHGFB3T1Ti448gFugodskuqtenGqdavG6Zad26eai27Uaq16Wap1q9Fz26i
r6JTt0i1Tt3SNUBzbS9ntFvR0VvZbwPjbiVnNMs2qdav26ZaK2/q/sBf0a0t
7dckj8K5lXOXtxn5I140W1v5ob/aGCsabDf5tLVtC+t2dX7yVzRsO33BYQ/H
w6m95Vauw15yQLMVXQZ2ML/M31oOnewHp86WN7R9R/ngr+jZLvabl/LdMCLl
b3OMZ9I1cTYeGrZule8A7j7uBHQEdwf3adEQ3CPoA+7Qohcutw0NcaVtRX9c
YuxoRfQEd8RbKd8X01M+9znzj4i5tw0bE79n2PaMfRnDnTLRMr/RI1c5X9FD
aIVexk5b0VLoCbRJf7kRK3cldyiaqbfjzpQrvro7Do1StBoapeiwosv6OUfR
dkXrgUUD9nH+S52TO3lCyncneXg57NWwf4UdEDm4NGy1Kt+h78p3nyhfGLYi
fh8UeEXYmmH7hV0U1gj7JNo+Svlu5V7lfuWunervp22fYh/qP/P3FNu4oz+3
jf5oGe5/7pF7jJm7/5CY7+qwdcJGp6wP0Aaj5QOXE6KtdZXXbYxtQxyPhkBP
HBXtLcPGO//HxvCKfdAYx0Z7q7A3zAd5GWqfcfpkX7xtPsfaRv14fz/lOlzr
PmDP3uo+KLqQMtqfvV7eCiDfAe+Bc2zjzcBeL2+InrbxDunhHilvIXR5eYew
v8objzfPUdYxpryv8Mc74zznKO8r6spbkbdTef+ckeo31cnyY624+8ubkzcY
uZtgfu4zh/e6nhPMT3lf8d3wnaADb0v12+zUVL/r4Fbead1S/caj7XB9dE/1
G4/4dncM/sobmHHoPs4B9izfENq5vC2ukxPfInoZ3cz3NsAy3yL6urw5brSt
r33R63zT6Gp0NufFINf7IusYz3kx2DbOrJsdc7U5GJzqN15v16SX69TffJOv
DuaRHOzpOlHmrD9M/uVvBKxt+RsB5b1d//J3C7C8y0H2I2c9+6a87490jvIm
Zw9x1h9tvy6Oo8xZwHd+v2v+uutOGY3OvjgpvrOdwt53TTiHOQdWj7pmVdbP
3CHcJehydPh3Kd8pc8O+Slm3z7cP9WjRNdTfaHU0O9odHY5OR69zfnBm/C1l
DY+Wf1T/I5xzjr55G6Dn0e+POw/zDRe/8fdDjqE/b4pZKd8ps/39rLEvMCbq
vrTPt/oa8YPxD9pnpmMfcezD5ukLc/W1uRguzvH3HMuM/d65mXeb4HJ4lc/N
HQKPqfLarO35yvuFfXyX+eGepo13UPMq55Y+a1W5/IL5bu56zZQT8XOXcgbc
414Y5vpzHnDP3OteGOp+eM09crf7AX58p9uF7yOrfP429y5iLt5nLXx3tQvs
VuUzvW3gyWGT4/eugadX+e5pH3hWlfO+e2CPKuexhRzhwnk+RP5tou7EsPfM
TwvzsGPg8VW+A+b9YP2beZeOMifE+IT7p5n1/AcFe7Hsp1XuyVtce/J2m23l
Xf6Y+3Og+4A9cFn4ObDK38qVYQdXeU26hl0QtiTl++Yh/Z4Wdbt4b99uXMxx
RtTtVuV7+GbnJ+d3ml9yO8C1Yh3Lmx+/6FHOlX1dx0muZb/wt2/YSusmW899
+p5rP8kx7IlB8oNb3xi3d9jS+H1+4F5V3r8XB+4flsI+dPww1+kl9yrIvc+3
jQZBV6A3TokxOzuuhesMrxvkxH7jHFie8lmw0t+cF5whi1P+dhZbLufFImNe
attzjlvh77L25Jnvb2HK3zh7oarqvw+wJ0aKDX/Ds8k9s9z4RjrPEuN5zHpi
OTf6dqzyecAdw3fGN1X+1sN5fKN1rOWZ0XePKuvfm2xnzNlR16HK51bvwM5V
Pp/2DOxZ5TO3U2CvKp99XQL7VJnb9eaSNbnDHJOD9137oc79pnn/P4ihn6M=

         "]], PolygonBox[CompressedData["
1:eJwtlPePTVEURp+zhyBG73303nsfvYw2emf0NqP3+hfpvQdRgiAIgiAIgiAI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         "]]}]}, {}, {}, {}, {}, {}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJwt0klXDQAAhuGbyrS16xwLq9bt4pIyRBLuVWkSRUpKkzLLUKQiImWM3JDQ
RKL4A36BCBna+weezrF4zvmW3+JdUVwVPhwVCARGWcD8XsoylhNPAkFSCVFA
KXU00kY3EUb4yCc+M80XvjLDN77zg1l+8ovf/GGOOCe28YheHnKPB9znHYd4
ywTjFFDOQZI5wXGOkcFd1vKBfLZym3TukMcbuunhJrfo4jVljDLGCLmUcoAk
jtJAPVu4wRqmyCGN62ymk10M08E12rnKFYYo4SWveEE2+9nHao5QRy2baCPI
JFmkcpmNtJLJIJdooYmLNPOcYp4xwFN2UsReVlFDNVVs4AIreU+Y9ZxjHecJ
8YRGznKKM5ymnz08JkIfOyhkN4nMR1lJBSmcZDt/9bGExSxiIbHEEP2/4X8s
QFeY
       "]]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJwl0tlSzwEABeBfXKdVofUfKYmUilZKtBCtovqHNtnaNyXLRb0Ddx6AR9BC
ISp6B95BV30zLr6ZM3Muzwn1jrQMRwRB8J5l4RO7/GWPQweCIINiGuhhnCXe
8ZFNTh7Uk0E9x7lOFI2c4AaZ3CSaJrK4RTbNxNDKKVrIoY1YbnOadnLpII67
nOEOZ+kknm7y6OIcYQ5zj3x6KOA+CfRyngcU0kciAxTRTzGDHGGICzzkIo84
yhNKeEwpTznGMGU8o5wRkhijglEqGSeZSS4xwWWmSGGGKqapZpZU5rjCc2qY
J40FrvKCa7wkndfU8oo63hBi1Z4feMsiY4Spp4gQkfzzjz/85hc7bLPFT36w
yXe+8ZUN1vnCZ9ZYZSXi///2AeRIQUs=
       "]]}}}],
  AspectRatio->1,
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{Automatic, Automatic},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{True, True}, {True, True}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "ScalingFunctions" -> None, "TransparentPolygonMesh" -> True, 
    "AxesInFront" -> True},
  PlotRange->{{-10, 10}, {-10, 10}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.02]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.7373995617270203`*^9, 3.7373995740185127`*^9}},
 CellLabel->"Out[9]=",ExpressionUUID->"3983e872-dc23-4b67-ab60-3f89070adacf"]
}, Open  ]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Sketching Circle relations",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737398995564744*^9, 
  3.737399011363956*^9}},ExpressionUUID->"8350f85e-3f3d-4ad4-a33c-\
5c88f6020cd9"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ContourPlot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "-", "3"}], ")"}], "2"], "+", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"y", "+", "2"}], ")"}], "2"]}], "\[Equal]", "9"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "2"}], ",", "8"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", 
     RowBox[{"-", "7"}], ",", "3"}], "}"}], ",", 
   RowBox[{"Axes", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737399014541977*^9, 3.737399133817093*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"2b2226d8-c002-4974-ba7f-f9983536d2ae"],

Cell[BoxData[
 GraphicsBox[GraphicsComplexBox[CompressedData["
1:eJxdVmtMVEcUXlBeC7jLXtyt1CJFJIWIUSEGFJlBhPBQiJUaKVIEragBMZXa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   "], {{}, {}, 
    TagBox[
     TooltipBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       StyleBox[
        LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 
         18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 
         35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 
         52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 
         69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 
         86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 
         102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115,
          116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 
         129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142,
          143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 
         156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168}],
        FontFamily->"Arial"]},
      RowBox[{
        RowBox[{
          SuperscriptBox[
           RowBox[{"(", 
             RowBox[{
               RowBox[{"-", "3"}], "+", 
               TagBox["x", HoldForm]}], ")"}], "2"], "+", 
          SuperscriptBox[
           RowBox[{"(", 
             RowBox[{"2", "+", 
               TagBox["y", HoldForm]}], ")"}], "2"]}], "\[Equal]", "9"}]],
     Annotation[#, (-3 + HoldForm[$CellContext`x])^2 + (2 + 
         HoldForm[$CellContext`y])^2 == 9, "Tooltip"]& ]}],
  AspectRatio->1,
  Axes->True,
  AxesLabel->{None, None},
  AxesOrigin->{0., 0.},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->True,
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{"DefaultBoundaryStyle" -> Automatic, "GridLinesInFront" -> True},
  PlotRange->{{-2, 8}, {-7, 3}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.02]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.737399135972622*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"caa3fdab-24b9-41ff-9185-569d5958357c"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Region required for Circle relations",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737399150663484*^9, 
  3.7373991872936068`*^9}},ExpressionUUID->"b363190d-012e-4cd7-b559-\
050193774c20"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"RegionPlot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"]}], "\[LessEqual]", "36"}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", " ", 
   RowBox[{"ColorFunction", "\[Rule]", "\"\<Rainbow\>\""}]}], "]"}]], "Input",
 CellChangeTimes->{{3.737399194916748*^9, 3.7373992898783817`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"1206d525-c786-4a80-b92b-351dd5387358"],

Cell[BoxData[
 GraphicsBox[GraphicsComplexBox[CompressedData["
1:eJyFl31o1VUYx6/Tqc1u07vt3hgR+dJali8Yl0So+5M5lcpaL6NattRK04lF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   "], {{
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1], EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
1:eJxVmHm0llUVxs9G0G6ocJlRUZB5cAARQULR8CoIxSQyyXABEUPkiijiADgg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         "]], PolygonBox[CompressedData["
1:eJwtlHnQjlUYh88tSyRm0DBMthkZ/IGGGVuEQiTbSGPrQ4iyRHYj2YmUz76W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         "]]}]}, {}, {}, {}, {}}, 
    {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
     LineBox[CompressedData["
1:eJwl02VvFUEYgNF7cS/FHYq7u0OxClbcobgWd7cWiru7u7u78zdwdz8NH06e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      "],
      VertexColors->None]}},
   VertexColors->CompressedData["
1:eJztmntUzPv6xytkSJKkokS5bSLJXXpXiF+SLsRud0FFbISdti6KFKWb2omO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    "]],
  AspectRatio->1,
  Axes->{False, False},
  AxesLabel->{None, None},
  AxesOrigin->{Automatic, Automatic},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{True, True}, {True, True}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "ScalingFunctions" -> None, "TransparentPolygonMesh" -> True, 
    "AxesInFront" -> True},
  PlotRange->{{-10, 10}, {-10, 10}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.02]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.7373992904521027`*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"0e12ea93-a942-48af-ae1d-8cb9fa8cadae"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Finding Intersection Function",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737348225644299*^9},ExpressionUUID->"967fbcb0-fe7f-40bc-8afa-\
110dfd3fc970"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"-", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"x", "+", "1"}], ")"}], "2"]}], "+", "5"}], "==", 
    RowBox[{"4", "*", 
     SuperscriptBox["2", 
      RowBox[{"2", "x"}]]}]}], ",", "x", ",", "Reals"}], "]"}]], "Input",
 CellChangeTimes->{{3.719646221439598*^9, 3.719646222222287*^9}, 
   3.719646260148348*^9, {3.737348567484828*^9, 3.7373486053458347`*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"8713ce27-99e5-46bd-8e05-82a112e16533"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"Root", "[", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"-", "4"}], "+", 
          SuperscriptBox["2", 
           RowBox[{"2", "+", 
            RowBox[{"2", " ", "#1"}]}]], "+", 
          RowBox[{"2", " ", "#1"}], "+", 
          SuperscriptBox["#1", "2"]}], "&"}], ",", 
        RowBox[{
        "-", "3.22582561264677868698465569468591249435`20.602055566432004"}]}]\
, "}"}], "]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.7196462612639723`*^9, {3.737348560768285*^9, 3.7373486063976097`*^9}},
 CellLabel->"Out[6]=",ExpressionUUID->"8de2ca51-f6b3-4d37-95de-e8dba8cca6ae"]
}, Open  ]],

Cell["Sub in x=0 in both the equations", "Text",
 CellChangeTimes->{{3.719646351427559*^9, 
  3.719646397295719*^9}},ExpressionUUID->"54c93a6a-90b6-4882-b6fc-\
49b938d503b5"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"4", "*", 
  SuperscriptBox["2", 
   RowBox[{
    RowBox[{"-", "3"}], " ", "0"}]]}], "\[IndentingNewLine]", 
 RowBox[{"5", "-", 
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{"0", "+", "1"}], ")"}], "2"]}]}], "Input",
 CellChangeTimes->{{3.7196463567643833`*^9, 
  3.7196463897114334`*^9}},ExpressionUUID->"552a3ead-cd08-4280-8b2a-\
102e7f289bee"],

Cell[BoxData["4"], "Output",
 CellChangeTimes->{
  3.719646390642728*^9},ExpressionUUID->"beda450e-7fad-49f7-a984-\
1808f916c560"],

Cell[BoxData["4"], "Output",
 CellChangeTimes->{
  3.7196463906462293`*^9},ExpressionUUID->"d33c131d-a81b-4fb1-9d13-\
8cbf22178128"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Expand functions:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.73735491478459*^9},ExpressionUUID->"b3a9a228-2da8-450b-8400-8040326b8d8f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Expand", "[", 
  RowBox[{
   RowBox[{"3", 
    RowBox[{"(", 
     RowBox[{"a", "+", "2"}], ")"}]}], "-", 
   RowBox[{"4", 
    RowBox[{"(", 
     RowBox[{"a", "-", "5"}], ")"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7196374473938565`*^9, 3.7196374488373923`*^9}, {
  3.7196374860704*^9, 
  3.7196374958493385`*^9}},ExpressionUUID->"e58ca135-9660-416b-b717-\
c62370415099"],

Cell[BoxData[
 RowBox[{"26", "-", "a"}]], "Output",
 CellChangeTimes->{
  3.719637497122861*^9},ExpressionUUID->"771e6afb-5d7d-4a83-b939-\
96bd89075628"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Expand", "[", 
   RowBox[{
    RowBox[{"4", 
     RowBox[{"(", 
      RowBox[{"x", "-", "3"}], ")"}]}], "+", 
    RowBox[{"3", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["x", "2"], "+", 
       RowBox[{"2", "x"}], "+", "1"}], ")"}]}]}], "]"}], "//", 
  "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.7196374987527566`*^9, 
  3.719637504628662*^9}},ExpressionUUID->"3ca6b87f-30c0-4296-be74-\
9e32cefa53ca"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"3", " ", 
    SuperscriptBox["x", "2"]}], "+", 
   RowBox[{"10", " ", "x"}], "-", "9"}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7196375050763197`*^9},ExpressionUUID->"31beb3b9-ab02-434b-b706-\
bdeb4abc0d23"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Expand", "[", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"2", "mn"}], "+", "1"}], ")"}], 
    RowBox[{"(", 
     RowBox[{"mn", "-", "3"}], ")"}]}], "]"}], "//", 
  "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.7196375171035414`*^9, 3.719637518441501*^9}, {
  3.7196375925614877`*^9, 
  3.719637593499464*^9}},ExpressionUUID->"4624b164-981b-412f-9300-\
29e6bc07c418"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    SuperscriptBox["mn", "2"]}], "-", 
   RowBox[{"5", " ", "mn"}], "-", "3"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.7196375192280226`*^9, 
  3.7196375953301873`*^9},ExpressionUUID->"79bdb1fa-fa8a-4551-9b8f-\
a095b405cc79"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Factor Functions:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356104412269*^9},ExpressionUUID->"2c0e32e4-05c2-4d8b-bf4f-\
a38422a1604f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Factor", "[", 
   RowBox[{
    SuperscriptBox["x", "2"], "-", "4"}], "]"}], "//", 
  "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.7196376029880323`*^9, 3.7196376040703564`*^9}, 
   3.7196376534378757`*^9},ExpressionUUID->"8550c007-e6f1-4d49-8414-\
56c7577d8a9a"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"(", 
    RowBox[{"x", "-", "2"}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{"x", "+", "2"}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.719637654432024*^9},ExpressionUUID->"d3c727b9-bfa7-4b84-a67b-\
8b3dba0d602f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Factor", "[", 
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"x", "+", 
       RowBox[{"2", "y"}]}], ")"}], "2"], "-", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"2", "x"}], "-", 
       RowBox[{"3", "y"}]}], ")"}], "2"]}], "]"}], "//", 
  "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.7196376559144845`*^9, 
  3.7196376681485934`*^9}},ExpressionUUID->"3b5c2308-366a-4656-9c52-\
27d843465a1b"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    RowBox[{"(", 
     RowBox[{"x", "-", 
      RowBox[{"5", " ", "y"}]}], ")"}]}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"3", " ", "x"}], "-", "y"}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7196376689990797`*^9},ExpressionUUID->"0c241957-a501-4fbc-badb-\
a9f6248403cf"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Factor", "[", 
   RowBox[{
    RowBox[{"2", 
     SuperscriptBox["x", "2"]}], "-", 
    RowBox[{"5", "x"}], "-", "12"}], "]"}], "//", 
  "TraditionalForm"}]], "Input",
 CellChangeTimes->{{3.719637678066615*^9, 
  3.719637679231556*^9}},ExpressionUUID->"41c03852-6302-42f9-97b5-\
98bbc4c9714b"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"(", 
    RowBox[{"x", "-", "4"}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"2", " ", "x"}], "+", "3"}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.7196376799376535`*^9},ExpressionUUID->"16322ea2-ade0-44a9-a2e2-\
4bf3a80e67e6"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Solve Functions:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356121665492*^9},ExpressionUUID->"93729601-a315-4a98-9aad-\
85223eb938d9"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     RowBox[{"4", "x"}]}], "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input",
 CellChangeTimes->{{3.7196376864052353`*^9, 
  3.7196377141660705`*^9}},ExpressionUUID->"4d10019d-8e82-48e3-ba58-\
da3ed2245848"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"-", "4"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "0"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.7196377164018526`*^9},ExpressionUUID->"a5e1c0ec-fbb9-451c-b616-\
fd52fe96a4e2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"x", "-", "3"}], ")"}], 
     RowBox[{"(", 
      RowBox[{"x", "-", "4"}], ")"}]}], "\[Equal]", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.719637717704303*^9, 
  3.7196377239250994`*^9}},ExpressionUUID->"e880e88b-5625-40f0-9133-\
fc3734689d38"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "3"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "4"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.7196377246741*^9},ExpressionUUID->"eff2628b-8367-42e5-af95-2a37cb76ad8a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "+", "25"}], "\[Equal]", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.7196377258087273`*^9, 
  3.7196377465692005`*^9}},ExpressionUUID->"5e09c9d4-95e2-41e4-8367-\
8687bcef245f"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      RowBox[{"-", "5"}], " ", "\[ImaginaryI]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{"5", " ", "\[ImaginaryI]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.7196377471383295`*^9},ExpressionUUID->"ac1fe86a-9df6-4287-8e96-\
21cbbecfd9cf"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"3", 
      SuperscriptBox["x", "2"]}], "-", 
     RowBox[{"5", "x"}], "-", "1"}], "\[Equal]", "0"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.719637748130249*^9, 
  3.7196377572521954`*^9}},ExpressionUUID->"b534451b-4999-45ba-9cb5-\
b0f036f79b9a"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      FractionBox["1", "6"], " ", 
      RowBox[{"(", 
       RowBox[{"5", "-", 
        SqrtBox["37"]}], ")"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", 
     RowBox[{
      FractionBox["1", "6"], " ", 
      RowBox[{"(", 
       RowBox[{"5", "+", 
        SqrtBox["37"]}], ")"}]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.719637757977302*^9, 
  3.7196378105562267`*^9},ExpressionUUID->"90a496ff-cd34-46e5-9aab-\
cc8950725f6f"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["To convert equation into Turning Point form command:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.73735613529811*^9},ExpressionUUID->"3befe438-a994-4c0d-b797-6e759b2edf24"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Expand", "[", 
  RowBox[{
   RowBox[{"a", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"x", "-", "h"}], ")"}], "2"]}], "+", "k"}], "]"}]], "Input",
 CellChangeTimes->{{3.7196468645147796`*^9, 3.7196468652451153`*^9}, {
  3.7196469197538376`*^9, 
  3.719646928763656*^9}},ExpressionUUID->"cb228cb0-a33d-48e6-b90f-\
45811ab8c897"],

Cell[BoxData[
 RowBox[{
  RowBox[{"a", " ", 
   SuperscriptBox["h", "2"]}], "+", "k", "-", 
  RowBox[{"2", " ", "a", " ", "h", " ", "x"}], "+", 
  RowBox[{"a", " ", 
   SuperscriptBox["x", "2"]}]}]], "Output",
 CellChangeTimes->{
  3.719646930538542*^9},ExpressionUUID->"a042d608-c758-4835-82ad-\
7d184812b87a"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Clear", "[", "h", "]"}]], "Input",
 CellChangeTimes->{{3.7196469320305967`*^9, 
  3.7196469374244018`*^9}},ExpressionUUID->"cf67ee17-4276-4042-bcc8-\
c84908a2f113"],

Cell[BoxData[
 RowBox[{"Clear", "[", "k", "]"}]], "Input",
 CellChangeTimes->{{3.719646940430173*^9, 
  3.719646946825101*^9}},ExpressionUUID->"834274ab-3a86-4535-8e42-\
b7d07af56e6e"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"a", "*", 
        SuperscriptBox["h", "2"]}], "+", "k"}], "\[Equal]", "5"}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", "2"}], "*", "a", "*", "h"}], "\[Equal]", "7"}], ",", 
     RowBox[{"a", "\[Equal]", "2"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"a", ",", "h", ",", "k"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7196469494961796`*^9, 
  3.719646956415901*^9}},ExpressionUUID->"ec146eed-3f3b-4dc7-a583-\
479019068661"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"a", "\[Rule]", "2"}], ",", 
    RowBox[{"h", "\[Rule]", 
     RowBox[{"-", 
      FractionBox["7", "4"]}]}], ",", 
    RowBox[{"k", "\[Rule]", 
     RowBox[{"-", 
      FractionBox["9", "8"]}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{
  3.719646957354896*^9},ExpressionUUID->"4a1d5a48-1046-438c-a685-\
2802fe0738b9"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Discriminant Function:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356188434902*^9},ExpressionUUID->"a4ffdef9-3ebb-4b96-a152-\
bf053f63cd70"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Discriminant", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"4", 
     SuperscriptBox["x", "2"]}], "-", 
    RowBox[{"12", "x"}], "+", "9"}], ",", "x"}], "]"}]], "Input",
 CellChangeTimes->{{3.7196380486928067`*^9, 
  3.7196380670271616`*^9}},ExpressionUUID->"09e80b31-be4c-4447-a2bc-\
af4220a57604"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{
  3.7196380683736415`*^9},ExpressionUUID->"9b5ab5e4-aab2-4dc1-95dc-\
08c0d1938aaa"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Finding Minimum and Maximum Functions:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.7373562061551037`*^9},ExpressionUUID->"d34f7950-fcf5-4d60-a9de-\
cba01d2c66ad"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindMinimum", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"5", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "-", "2"}], ")"}], "2"]}], "+", "3"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.719638492234975*^9, 3.71963849302465*^9}, {
  3.7196385346313825`*^9, 3.7196385943899727`*^9}, {3.7196386326645603`*^9, 
  3.71963867547894*^9}},ExpressionUUID->"23522bea-ed07-41a0-9d37-\
450d5764c4f8"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"3.`", ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "2.`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.719638572928463*^9, 3.719638596073318*^9}, 
   3.719638635388418*^9, 
   3.719638676747851*^9},ExpressionUUID->"a565a5dc-7221-4c66-9895-\
eb99db7a0e9d"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindMaximum", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"-", "4"}], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "-", "6"}], ")"}], "2"]}], "+", "7"}], ",", "x"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.71963861412348*^9, 3.7196386227044983`*^9}, {
  3.719638683798464*^9, 
  3.7196387177539797`*^9}},ExpressionUUID->"0d744325-694d-47e3-b61a-\
3ec755936db3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"7.`", ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "6.`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.7196386996440787`*^9, 
  3.7196387186345434`*^9}},ExpressionUUID->"5b49ff8f-04c7-4b3c-9298-\
c3e5a1bf51ae"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Clear Function:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356217373616*^9},ExpressionUUID->"7d2047a5-69dd-4276-99f9-\
524b42b70bb7"],

Cell[BoxData[
 RowBox[{"Clear", "[", "f", "]"}]], "Input",
 CellChangeTimes->{{3.7196388673930187`*^9, 
  3.7196388862788987`*^9}},ExpressionUUID->"955fe60a-9f3a-4ec8-8490-\
e14a7fdab5ff"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nIndex Laws, Logarithms and Exponential Graphs",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.7373564071179943`*^9, 
  3.737356423610084*^9}},ExpressionUUID->"2295c1a0-bd01-4c5a-8996-\
9d55609d6dee"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Solve functions with indices:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356390870599*^9},ExpressionUUID->"b4392dd0-a04c-4556-8dec-\
5b25bc9a1155"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    FormBox[
     RowBox[{
      SuperscriptBox["3", 
       RowBox[{"3", "x"}]], "\[Times]", 
      SuperscriptBox["9", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "2"}], "x"}], "+", "1"}]]}],
     TraditionalForm], "\[Equal]", "27"}], ",", "x", ",", " ", "Reals"}], 
  "]"}]], "Input",
 CellChangeTimes->{
  3.7196379033104753`*^9, 3.719637971447973*^9, {3.7196390745395427`*^9, 
   3.719639101011696*^9}},ExpressionUUID->"44b52161-d495-4750-98d9-\
22f2bf93bd56"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", 
    RowBox[{"-", "1"}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{{3.7196390959105363`*^9, 
  3.71963910196758*^9}},ExpressionUUID->"a0dbedf0-b1b0-4760-abe8-\
ae61093ca558"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       StyleBox["3",
        FontFamily->"Times New Roman",
        FontWeight->"Regular"], 
       StyleBox["\[Times]",
        FontFamily->"Times New Roman",
        FontWeight->"Regular"], 
       FormBox[
        RowBox[{
         SuperscriptBox["4", "x"], "-", 
         RowBox[{"18", 
          RowBox[{"(", 
           SuperscriptBox["2", "x"], ")"}]}], "+", "24"}],
        TraditionalForm]}], "\[Equal]", "0"}], ",", "x", ",", "Reals"}], 
    "]"}], ",", "4"}], "]"}]], "Input",
 CellChangeTimes->{{3.7196391264356813`*^9, 
  3.7196391661928034`*^9}},ExpressionUUID->"4391df34-00e7-4996-ac25-\
6bdc63701509"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "0.5362176214664735009`4."}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "4.0487448792546826802`4."}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.7196391465315*^9, 
  3.71963916717321*^9}},ExpressionUUID->"b0699e27-7f43-47e4-ab0d-\
6b527c31f67b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{
     RowBox[{
      FormBox[
       SuperscriptBox["10", "x"],
       TraditionalForm], "\[Equal]", "18"}], ",", "x", ",", " ", "Reals"}], 
    "]"}], ",", "4"}], "]"}]], "Input",
 CellChangeTimes->{{3.719639219603593*^9, 
  3.719639257089035*^9}},ExpressionUUID->"718c6804-3c65-4f9a-b9a3-\
58980ce0892e"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", "1.2552725051033060699`4."}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.7196392363561745`*^9, 
  3.719639257952544*^9}},ExpressionUUID->"5ac7ed78-575b-4886-b285-\
3c18385bf5c2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{
     SuperscriptBox["4", 
      RowBox[{"3", "-", 
       RowBox[{"2", " ", "x"}]}]], "\[Equal]", "12"}], ",", "x", ",", 
    "Reals"}], "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.719646086113058*^9, 
  3.7196460883187485`*^9}},ExpressionUUID->"0ad1ecf4-0361-4340-9373-\
962fe13dde6b"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"x", "\[Rule]", "0.6037593748197109`"}], "}"}], "}"}]], "Output",
 CellChangeTimes->{
  3.719646091505458*^9},ExpressionUUID->"f4fbef89-20e9-4cca-bade-\
46ce8a007a9f"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Solving for the indices function:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.7373564757878313`*^9},ExpressionUUID->"e4b6611c-e113-40a9-b8b7-\
82165b0e1885"],

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{"equation", ",", 
   RowBox[{"indice", " ", "pronumeral"}], ",", "Reals"}], "]"}]], "Input",
 CellChangeTimes->{{3.7196482654279428`*^9, 3.7196482659756536`*^9}, 
   3.7196483108148336`*^9},ExpressionUUID->"32c1ca71-9f3d-460f-ae53-\
e4f8bf5201ec"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "/", "8"}], ")"}], "^", "f"}], "\[Equal]", "4"}], ",", "f",
    ",", "Reals"}], "]"}]], "Input",
 CellChangeTimes->{{3.7196483150405583`*^9, 
  3.7196483231592965`*^9}},ExpressionUUID->"54303b67-a94e-4018-a98e-\
cb3bbdc85758"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"f", "\[Rule]", 
    RowBox[{"-", 
     FractionBox["2", "3"]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{
  3.7196483242391176`*^9},ExpressionUUID->"2166a235-6893-4c22-9dbe-\
54bbf3139d15"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Solve (Reduce) Functions with inequalities:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356487674418*^9},ExpressionUUID->"802126c7-7aa1-495b-8fdc-\
4a13e5dce03d"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{"N", "[", 
   RowBox[{
    RowBox[{"Reduce", "[", 
     RowBox[{
      RowBox[{
       SuperscriptBox["3", "x"], "<", "5"}], ",", "x", ",", " ", "Reals"}], 
     "]"}], ",", "4"}], "]"}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.7196393204296417`*^9, 3.7196393213244123`*^9}, {
  3.7196393541844597`*^9, 
  3.7196394236116285`*^9}},ExpressionUUID->"5284f09b-ef09-4647-9931-\
dec486007c0a"],

Cell[BoxData[
 RowBox[{"x", "<", "1.4649735207179271672`4."}]], "Output",
 CellChangeTimes->{{3.7196394053819685`*^9, 
  3.719639424031832*^9}},ExpressionUUID->"acaedab6-41b3-4e35-9ca3-\
5a273d6708e4"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Basic Logarithm Functions (Place Log (Base, \
Logarithm)):",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356500097981*^9},ExpressionUUID->"5d391816-8604-4cf5-ba66-\
c4c2e4989125"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Log", "[", 
   RowBox[{"7", ",", "49"}], "]"}], "+", 
  RowBox[{"3", "*", 
   RowBox[{"Log", "[", 
    RowBox[{"2", ",", "8"}], "]"}]}], "-", "4"}]], "Input",
 CellChangeTimes->{{3.719646125260174*^9, 3.719646126101055*^9}, 
   3.7196461679997163`*^9},ExpressionUUID->"e9076a2b-c370-46c8-b9d0-\
4476aa0e0e4c"],

Cell[BoxData["7"], "Output",
 CellChangeTimes->{
  3.7196461694847636`*^9},ExpressionUUID->"9499865b-34b3-4455-b86f-\
2216eb861420"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Compound Interest formula function:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356510751405*^9},ExpressionUUID->"93619bad-95b7-470d-9b39-\
42823526f139"],

Cell[BoxData[
 RowBox[{
  RowBox[{"CI", " ", "=", " ", 
   RowBox[{"P", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", 
       FractionBox["r", "100"]}], ")"}], "t"], "               ", "R", " ", 
    "is", " ", "the", " ", "rate"}]}], ",", " ", 
  RowBox[{"T", " ", "is", " ", "the", " ", "time"}], ",", " ", 
  RowBox[{"P", " ", "is", " ", "the", " ", "principal"}], ",", " ", 
  RowBox[{"CI", " ", "is", " ", "Compound", " ", "Interest"}]}]], "Input",
 CellChangeTimes->{{3.7196464719656057`*^9, 3.7196465800101995`*^9}, {
  3.7196470301710787`*^9, 
  3.719647038029663*^9}},ExpressionUUID->"906a62cd-cbc9-410d-8a91-\
7b763883ab96"]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Simplifying equations with indices function \n(if can \
be simplified even more, do it mentally or on paper):",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737356522595675*^9, 
  3.737356560100062*^9}},ExpressionUUID->"1439a672-fb9a-4729-b771-\
58bb305f65de"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   SuperscriptBox["64", "x"], "*", 
   SuperscriptBox["4", 
    RowBox[{
     RowBox[{"2", " ", "x"}], "-", "1"}]]}], "]"}]], "Input",
 CellChangeTimes->{{3.719646615845101*^9, 
  3.7196466177092333`*^9}},ExpressionUUID->"9c0845ec-4699-4f3f-b555-\
9529faf3fed6"],

Cell[BoxData[
 SuperscriptBox["4", 
  RowBox[{
   RowBox[{"-", "1"}], "+", 
   RowBox[{"5", " ", "x"}]}]]], "Output",
 CellChangeTimes->{
  3.7196466574882135`*^9},ExpressionUUID->"f2ccfae8-b08f-483b-992a-\
9f1e99e13ce0"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Plotting Exponential graphs:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356570314211*^9},ExpressionUUID->"6cab994a-8b2f-4d73-bb4f-\
ab9269b5554a"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"g", "[", "x_", "]"}], ":=", 
  RowBox[{
   SuperscriptBox["4", 
    RowBox[{"x", "-", "3"}]], "-", "7"}]}], "\[IndentingNewLine]", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"g", "[", "x", "]"}], ",", 
     RowBox[{"-", "7"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "10"}], ",", "20"}], "}"}]}], ",", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"Blue", ",", 
      RowBox[{"{", 
       RowBox[{"Red", ",", "Dashed"}], "}"}]}], "}"}]}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.719647044275886*^9, 
  3.719647062093154*^9}},ExpressionUUID->"725f3164-0640-4cb2-b7ec-\
fc77cdc9a374"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0, 0, 1], AbsoluteThickness[1.6], Opacity[1.], 
      LineBox[CompressedData["
1:eJwd2Hc8lV8cB3B7r+vea9xrq0SJEJXyHAlpKtKUklSKikgDDbQ07GgZJaNI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       "]]},
     Annotation[#, "Charting`Private`Tag$36052#1"]& ], 
    TagBox[
     {RGBColor[1, 0, 0], AbsoluteThickness[1.6], Opacity[1.], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQXfvc99P//8oHGMBA5sCUkgTvhtkI/mrG4iUM5gg+
a6q7kWSsEpwvfONozqKJinB+0OFZyZqnFOD86ve2ORMey8P5O8pnZa33l4Pz
/SaFKvybKQPnu8/d6+fxRgrOX3a88lpxtCScH9cyRfT8CnE4vy6BeR23sBic
z6Arv9+5VQTOv9U9s331VSE4X4YrY+UXJ0E4P9tUi/W2DD+cn2x+b8Xhw9xw
vlaF1f+8JRxw/sK7wUcqHVnh/OeNojbuEkxw/q6pGq4vwv7uh/ENXt78oj/3
G5zvsus259+wD3B+wcr1PwSFH8P5YWnKCy/VnITzj5+52WUcfMIexrfSPbgp
YPpjOJ+pTPROiuQHOJ+dJ6Ax6d03OL/5wTXnosV/4fwNs9sC6j4xOsD4+YtS
BJ6EscL5cVmzZNsbOeD8zsAyS+M53HA+i8jUZ/W/+OD866dbP7TwC8L5odVJ
ZrMOC8H5Odyvlc5FicD58quPTWN7JQrnV+9wDuafLQ7nFyzL2WamLwnn8zCZ
J+k9lYLzXXNDpmpNloHzJXbK5ruqyMH5k4o6Jhpcl4fzg9r8deduU4DztaJb
QpfUKsL5155xLpocqgTnn0t66igkrwznqy2VlOrsR/Ch+QXOBwD7B+ks
       "]]},
     Annotation[#, "Charting`Private`Tag$36052#2"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-9.999999591836735, 9.999999591836735}, {-10, 20}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.7196471374297667`*^9},ExpressionUUID->"60904b97-5581-4bc8-aa9e-\
a27a4cd3881d"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   FractionBox["1", 
    RowBox[{
     SuperscriptBox["x", "2"], "+", "x", "-", "6"}]], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "10"}], ",", "10"}], "}"}]}], ",", 
   RowBox[{"GridLines", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "3"}], ",", "2"}], "}"}], ",", "None"}], "}"}]}], ",", 
   RowBox[{"GridLinesStyle", "\[Rule]", 
    RowBox[{"Directive", "[", 
     RowBox[{"Gray", ",", " ", "Dashed"}], "]"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7188686878726997`*^9, 3.718868815608602*^9}, {
  3.7188688538606462`*^9, 3.718868859677561*^9}},
 Background->RGBColor[
  1., 1., 0.85],ExpressionUUID->"02f9681a-f596-4088-8933-33897ea1d355"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwdknc4FYz7h43SGeY59j5mVETiLS/PkTJKUhlvSSkzSVJG9ovqEGWVEZmZ
kZGRxCMRQiIiZCQlQkK27/v7fa7rvu6/7v8+tAtXTtixMDExLfzH/9nv29G5
zU1ptJSU1b51ngHjPvwL/WvSmPdUMVDFiQHG3EN/KpalcaGG6j/ixgDJfa7r
V35L4yO1Jy+OhTDgVVg0YXhcGg2S3NPsshlAUPoojm3SeMk8Vtt7mgGx162P
BD6UxqdDjCLrwFDIZ76WyaQhjd1hXSobpWGw1U5fVchKCisyU95VpkYAtbfB
OT2Khnnvc2W1nCIBd6QxQu7ScJfqhwLS1UhwDvDNtL9Dw/jj/0YPeEZCo9ye
AcWbNLzlVhsYcTMSvN1Tj5R60dBag24lkxYJoxQfxdfnaChnGcBQ6IuEkqO7
v3/dRcNXt+8qFBpFwYn6RBuFFkl8xXf+eeyBaJD5MPb5TaMkTsWcmzA4Eg2L
Y0qn7eslMd34diiraTQksNWbZFRLopdjhFq4XTQMG05qiT2VRDni7+lJRjRc
7tAU5ImVxF7mX4M/OqKBMTjQumQliYl9lLcC9jHgM6PlHPlFAjeTdsd/zIqF
pPMa3+mDEli6nS5aUBQL1V27bX/1SCBvbfZkaFUsbFRInznRIoFfgm3CTrXH
QlAg0Yi3WAIbvi4mHl+MhTCe7h3x/hLodWXtdb7+fUjc4zyZIiSBz8836NNn
70OlZ6LT02PiGKDr+/bd6TiQsr36uNdAHKmKzSnPHeIgwsRgmPmAOG5MPkwp
vB4HFxQWzUzVxJGd6mBRdTcOyP3HdZYFxZHwXkn6dH0cnNUmCuqOiuEHGUvj
N0rxwLrVq6Hnuhief1yR8pIzAVx+GTMxuYjhY9cG9+1iCdA7KKup4CCGr2yj
jVN3JMCT8q4in1NiqBmZY1hhkADmjspJktpiyDZppBYSnAA5b8fdnLaJYasR
e27OagIYR5tJbiSIYoTOX5bxi4ngrcplqB8jiqU0n/AbbA8hq7PpamS4KFKD
7K5d5H8IG5S/66UCRDG3iVLorv4QCmKk7PVtRbFLZX5Wx/MhsN+fyY9UEkWJ
j9snqlYfQktcqIZ0vQiCqVd0LXcyLGroWjtXi6DkoPWzR1LJINW7xigrE0H7
Vt+d99SSwVvQ9ZN+jggqiar4Zf6TDAoJ5n7OESKo+aRlf0ZaMjASpevLLETw
9kObEDaNR6Cf/NLYYEoY5Wfyrwm6psBsxMDalnFhJG+OnFsMSoFE/9W8uiFh
JIWx/DV+PwWmzu3bptkljDH/HCSvvUiBaKmy2l1VwqgT1O7675ZU+Jz9ZDeV
IYyPHMt9DE+mgkfJQ8pnaWF05fiZum8pFSQzqjBRTBgnzdtZh1nSoDmmz8VC
QBhvHT20JYojDUTdBd52kIQx2M9EiCqdBq80YoLrfwkhbdvxfQnGacD5Mmw+
p1YI95fs663KToOsNzd6rlkKYbdQW2/DhXRIUPXQzTUVwrnK85ljV9IhPNmt
6PNRIdR9UG1F8UsHt2uXwgzpQpiVbLmcGJcOWhJW2hKyQqgtZO5r05YOHzzo
WS3TgvjtPlPSN80MYJHb5kELEkRz8bEpD9lMWIhk/WLuI4gxfS2lj9Uy4fvq
5rHw64K4g/1G+7huJrS/X1L4Yy+IueEU39QLmZDg92Ow9Yggsql0qyykZsLu
7rZDXnyCWP90yys67TGcDYnle5cjgOY9bMrmKlnQDovbvNIFMFszV/6LThbA
qsWKZJIAVrqGbQSfyAJJN5Eht3sCeEWL1s58PQtGz6Xn8HsIYKl+Z/mviiyw
1yzSPKsrgBuiT7FONxtc5t6e/znIj+Lcyj47nXPgc8Eu0wcf+dFj7nSeb0AO
HLt4Tw/e82NToGnk1+gc2D18YkfUa358EeOhxlKVA3NtffNq+fxozu4zdImY
Cx653277evEjg0eJrliQC/7WrIVkKj9+DfX7UkHMh6J3+nc/sPPjD6PNBLJk
Poxqh7sks/GjjmX9CT/1fNAT41NWXuHDWRGN4hc2+cD5Sa7oxAgffrKtCc+r
zYdHJw+XJDzlw7Gs7YRbfk+gVi+qXN6ID+uES8lM1EKYK+t+MHuID4tCYtXv
7SoEGVlhz+fAh/cI620HDQqBwZqhcWQPH2akjgTK+BeCCT6rdBHmw0vrJwZq
Jgth+L/blH3nxXMxt4Jy258C0y6JWt2bvBheM6H481MR+PLrnL3pz4vdmRt7
j00VwZ/NC+uNnrz4YarhY/t6EUx3ZmkeduJF4x2OzNtpxdDvpVRpcowXf1hn
cx6+WAzlr7WKrYR4MW3p4rGozWJQLTxnkkLhxeCulppZSgkUxP07M0zmxcmf
4zVuciWQ6dSwy3aDinOMk91DR0sgmvtontMXKt7hWTrl+KgELp85k+FZQMXH
l+cGbumVwvdD/geeZ1FRfdAgU/NMKdgqp46spFDxm7iFpJBbKZxmGZPwj6ai
Ha/77LFHpWCQcykpxJOKVgQLq+dLpSAz730/SoeKM3sUtMfKnsGnOwm387sp
WHSYJH7ArBy6GiSfWL+j4JeRPX7yV8qhdTO7g6+Zgn8b5Z2F0HKouVYuFFhN
QZ775V8JNeWQbtmVb5pBwe21AtupihXgtIOjY92VgsFvxdgi2CvBxi52vsSJ
gjrvDU1HFSrhTIqIkKMtBSmdmtLX9SvBmKp4odOCgkwR6SImwZWguqo3n6VN
QcGOGqaN9UpYbQkUNGGnoPtly+Whzecwv4WgtZWNgp1r5Il/aFUwrX3vfNUm
DxIYF6VEdKtguCQ5T+Y3D5rsOSQWcLsKXidW/b3cx4MFOXE1Q9QXEO40b52e
zYMvmK5//6pZDaIkx9z5AzxYP0pu4XtfA2drWsOl/ubBhwONfx4y10Kam4qr
yV4etFf2evtYtRbk+lfUn8jzIBP/arLRg1pQfhLx2oadB/mXMz15VBEOGJcO
dXZzo7680MYaRx2EsAjWM73jRo1Wjp9jinXwptw3S6mJGx2dv/+kGdSBkYTe
5bAqbqzYe3s6NbgOzGd7V3RSuPF5Q8rhwY06uBi9wVfsyI0r7Q8U67bVwxM9
m+XP57lRK82ys0qxHqZX3gywW3KjoX4FQda4HtxsojIcj3Lj2nIz4+SDevBV
k1GRVOXG9+fpueY7X4N4QUy8+B8uvFGTWch3tQEy+KzOeU9wYf2gEceepAbY
7i8n19PPhcW/FdIm3jSAyrHnpRHIhYUbSwLKtEY4+Otz+1ooF143Mee90d8I
l/Yqbu0X5cJ8TxUdI7cmcNv6PNuDiwtN5U1YC7KbwLtb/zCFhQtlZZ1aBweb
IMzd7p7hN04kdCg7vzJqhryyVKHKYk6MZkpbk9nbAiU3latPZnLiEZ5eueir
LVBlVnN25gEn8huqnFgubIGWhf4MOV9ObDwlNtO28y1M7BVQuq/HiVv0By8e
2tsKs1uzOnbv40RylxlD3bsVlrrVrrXu4MSA1roSC2wFgseJSlYeTlxpXCgx
NGmD7eURB9z6OdCN4NvfG9AODupbLI65cqBH6AlT9pgOcGGLWf5xgQNNB4p7
Veo6wKOHlnTLjAPt5ZPZDsx2wC0PGHm5nwNp4gL3tY+/h6xy70s7t3Lg2ZXs
y/4SnVB4i8jZ9Icdp260XWsz64Ry8/gimx/seFT/UqF+RCc0LpYtJL5jxzi/
so9jm53wVf1XADGRHZsXtH2n5rtgii1Q6nE4O/pw9vG+3PsB5ns4G+gB7Hij
ec2e6vUBtnjuJHnZsmOYqtYSg7kbZCocYseV2PFFGVXskEIP7Ly9qB5E+69f
NxiY8uwBNYubfWK87Oihvt80uakHDv5JFzdbJmPm++paJ9ePYKPxOae+noyx
l7PbNQZ6wT5Hw1yvgozCP5KzltT7wEkoirU5j4y61PiP8rF94Lqqe7Y9ioyH
NRrtNMw/wTXnZPLxm2R0OP6PlfGLT+AxuFjZ5UXGkHsxfDrS/eBbm0vtO0dG
V+Oa1r/W+iFgN2ud5UkyWqY/Xvz38gAEpZ1x+axHxgOyO/2VRweAEczV/GUX
GVPblFMsegYhVt/df3qVhBVmp13bp4cgrrJ9x9UZEpauERlc9GFIVNje93uU
hHvjs22V7wxDKrl/z3IzCd8FdVufVhiBDF+1EZ+XJPw9PlhW4DsCWT8j7m4U
kbBSUcGV2DUCBe/oE6zxJJx+tNUqNHQUiuiJD27dIeEZw38SOX6MwrPi37rE
ABK++nxv5bTxF6iKyXrEaU9CRjK5Skt6DF5uYTKKOkXCFf1dT8xixwDdTy1T
j5Iw8HLYr79JX6HRgt1USI2EGpHxubh1HJqb7JiT5Em41fu+JjV8HFr31RaK
i5Cw+GUDf4bgN+gUcSPKsJAw+Fm1mZHed+gOf1uetUDEXIJk+KXv36F3XcZW
YYKIcK0uqyd6AoaGPtYodRDRMYJ0Rpt1EkZNVJyL64loKrJmUNcyCeN1YUJq
FUQktOtIpydPwYTqWGN5HhGLyyfdhn1/wlSG1vV9j4goYZ8XlXhxGmZ442jV
UUQ8Y6zuTrGbgbmbs+3aN4kYpzpRcuqvWVhyyFA46EzEDp9I8zvnfsFq71pP
4zkiDsm7J4+wzMGGoXmI4UkiTrpm1+mUzAHzi6cqrXpELKU6SHBc+Q1bdhKH
jPcT8XGDsdbg/nnYlnwh/P0uIhYV6V+6J7AAJM7qfaY0Ipp0s9ie3LYInAF8
33p4iWhVc3TsJfsf4Jl1iT1FIGLyeuTtYcUl4D3fpDOwSkAnudaXjnbLINhJ
mzk7Q8AovSG3JlwBEV2fpJFRAp4kGkg7H1gD8WcfDG17CMiSzNvL+msdaLJK
f8abCahhG7jv24dNkHlwO/PiSwKe+XwzyWSNiS6/beT4VBEBmb1fXe1XY6Er
eu3fdMkk4K4MB4exJFY6DhorfnlAQKmn0dBsv5VurmtjZhFKwH0uaq/Y7myj
T+V4Br71IeBap1jAIXkSPYgzPB9cCLj+rS+xzoGDLng9tafUmoCd1cc1sImb
Xtj3jHn7SQK6iE+eod+h0g9C886kQwS8ctAitcZagN6XOWjB/RcBvaou80Vy
i9FdSHNBIYoEVGEtHyHslqZLSD1pPaJAQKb/nwz9fzFGYjQ=
        "]], LineBox[CompressedData["
1:eJw1mHk41c/7/+2HeCNLoaSyVbRIRNRU1kpFolIhSYuSlJIIkShU9qXFlrKE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        "]], LineBox[CompressedData["
1:eJwdlGk0FI7bhmfGjH2bsWVNJlkalH62LM8jpEVZi6RESAglInvWrEVIqEgS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        "]]},
      Annotation[#, 
       "Charting`Private`Tag$36391#1"]& ], {}}, {{}, {}, {}}}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  GridLines->{{-3, 2}, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5], 
    Dashing[{Small, Small}]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-9.999999591836735, 9.999999591836735}, {-10, 10}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.719647301756936*^9},ExpressionUUID->"1c1852ac-9511-40b5-9120-\
4e350fa6215e"]
}, Open  ]],

Cell["Gridlines are found by solving for x", "Text",
 CellChangeTimes->{{3.719647335897914*^9, 
  3.71964736693086*^9}},ExpressionUUID->"c8dda2d5-4c4e-4973-a8c1-\
fc4b2dab1246"]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["To substitute values command \n(slash and full stop \
and the variable with the arrow pointing to the value) :",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{{3.737356615241165*^9, 
  3.737356624731721*^9}},ExpressionUUID->"dc0c9aef-c667-45a1-a823-\
16edb0880bfa"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   SuperscriptBox["x", "2"], "+", 
   RowBox[{"b", "*", "x"}], "+", "b"}], "/.", 
  RowBox[{"b", "\[Rule]", " ", 
   RowBox[{"-", "3"}]}]}]], "Input",
 CellChangeTimes->{{3.719648108903596*^9, 3.7196481096633043`*^9}, {
  3.7196481472698545`*^9, 3.719648147930497*^9}, {3.7196481979701853`*^9, 
  3.7196482032307186`*^9}},ExpressionUUID->"546f74b5-46a1-4a01-844c-\
d68c4a680dfe"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "3"}], "-", 
  RowBox[{"3", " ", "x"}], "+", 
  SuperscriptBox["x", "2"]}]], "Output",
 CellChangeTimes->{
  3.719648210653231*^9},ExpressionUUID->"240867b0-ddf6-40ea-b202-\
9213945a8e0e"]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["\nStatistics ",
 FontSize->48]], "Subtitle",
 CellChangeTimes->{{3.737356658324205*^9, 3.737356665020273*^9}, {
  3.737950585419022*^9, 
  3.7379505984269657`*^9}},ExpressionUUID->"b82dadbc-76da-43d0-b822-\
735625e8b7fe"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Drawing Box Plots Function:",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.7373566381913967`*^9},ExpressionUUID->"78fd53a4-bfe2-4e41-9c48-\
20df89fce5ee"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Data1", "=", 
  RowBox[{"{", 
   RowBox[{
   "1", ",", "7", ",", "15", ",", "16", ",", "20", ",", "15", ",", "2", ",", 
    "3", ",", "7", ",", "13", ",", "15", ",", "2", ",", "77"}], 
   "}"}]}], "\[IndentingNewLine]", 
 RowBox[{"Data2", "=", 
  RowBox[{"{", 
   RowBox[{
   "7", ",", "6", ",", "7", ",", "15", ",", "23", ",", "1", ",", "11", ",", 
    "14", ",", "27", ",", "5", ",", "4"}], "}"}]}], "\[IndentingNewLine]", 
 RowBox[{"BoxWhiskerChart", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"Data1", ",", "Data2"}], "}"}], ",", "\"\<Outliers\>\"", ",", 
   RowBox[{"ChartLabels", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"\"\<Boys\>\"", ",", "\"\<Girls\>\""}], "}"}]}], ",", 
   RowBox[{"ChartLegends", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"\"\<Boys\>\"", ",", "\"\<Girls\>\""}], "}"}]}], ",", 
   RowBox[{"ChartStyle", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"Blue", ",", "Red"}], "}"}]}], ",", 
   RowBox[{"BarOrigin", "\[Rule]", " ", "Left"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.7196477611609764`*^9, 3.7196477623157473`*^9}, {
  3.719647814186408*^9, 
  3.719647830463247*^9}},ExpressionUUID->"cf891e3a-6403-4519-8c72-\
3f63f9c25700"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "1", ",", "7", ",", "15", ",", "16", ",", "20", ",", "15", ",", "2", ",", 
   "3", ",", "7", ",", "13", ",", "15", ",", "2", ",", "77"}], 
  "}"}]], "Output",
 CellChangeTimes->{
  3.719647831419549*^9},ExpressionUUID->"2fa51243-9fcc-47e3-9825-\
abbe68469343"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "7", ",", "6", ",", "7", ",", "15", ",", "23", ",", "1", ",", "11", ",", 
   "14", ",", "27", ",", "5", ",", "4"}], "}"}]], "Output",
 CellChangeTimes->{
  3.7196478314225483`*^9},ExpressionUUID->"d0a34bac-244d-4d1b-beee-\
d20ee9f51a41"],

Cell[BoxData[
 TemplateBox[{GraphicsBox[{{
      Opacity[0], 
      PointBox[{{-2.8000000000000003`, 0.3836399216673073}, {80.8, 
       2.6163600783326926`}}]}, {
      CapForm[None], 
      Directive[
       RGBColor[0.982864, 0.7431472, 0.3262672]], {{}, {
        Directive[
         RGBColor[0.982864, 0.7431472, 0.3262672]], {{
          Directive[
           RGBColor[0, 0, 1]], 
          TagBox[
           TooltipBox[
            DynamicBox[{
              FEPrivate`If[
               CurrentValue["MouseOver"], 
               EdgeForm[{
                 GrayLevel[0.5], 
                 AbsoluteThickness[1.5], 
                 Opacity[0.66]}], {}, {}], 
              GraphicsGroupBox[{Antialiasing -> False, 
                PolygonBox[
                 NCache[{{
                    Rational[61, 4], 0.7754133086869819}, {
                    Rational[61, 4], 1.2245866913130181`}, {
                    Rational[11, 4], 1.2245866913130181`}, {
                    Rational[11, 4], 0.7754133086869819}}, {{15.25, 
                  0.7754133086869819}, {15.25, 1.2245866913130181`}, {2.75, 
                  1.2245866913130181`}, {2.75, 
                  0.7754133086869819}}]], {}, {{}, {
                  InsetBox[
                   BoxData[
                    FormBox[
                    StyleBox["\"\[FilledSmallCircle]\"", 10, 
                    GrayLevel[0.5], StripOnInput -> False], 
                    TraditionalForm]], {77, 1.}]}}, {}, {
                 GrayLevel[0], 
                 GrayLevel[1], 
                 
                 LineBox[{{13, 1.2245866913130181`}, {
                   13, 0.7754133086869819}}]}, {}, {
                 GrayLevel[0], 
                 GrayLevel[0.5], 
                 LineBox[
                  NCache[{{{
                    Rational[11, 4], 1.}, {1, 1.}}, {{
                    Rational[61, 4], 1.}, {20, 1.}}}, {{{2.75, 1.}, {
                    1, 1.}}, {{15.25, 1.}, {20, 1.}}}]]}, {
                 GrayLevel[0], 
                 GrayLevel[0.5], 
                 
                 LineBox[{{{1, 1.112293345656509}, {
                    1, 0.8877066543434909}}, {{20, 1.112293345656509}, {
                    20, 0.8877066543434909}}}]}, {}}]}], 
            StyleBox[
             TagBox[
              GridBox[{{
                 StyleBox["\"max\"", Bold, StripOnInput -> False], "77"}, {
                 StyleBox["\"75%\"", Bold, StripOnInput -> False], 
                 FractionBox["61", "4"]}, {
                 StyleBox["\"median\"", Bold, StripOnInput -> False], "13"}, {
                 StyleBox["\"25%\"", Bold, StripOnInput -> False], 
                 FractionBox["11", "4"]}, {
                 StyleBox["\"min\"", Bold, StripOnInput -> False], "1"}}, 
               GridBoxAlignment -> {"Columns" -> {Center, ".", {Left}}}, 
               AutoDelete -> False, GridBoxDividers -> {"Columns" -> {
                   Directive[
                    GrayLevel[0.3]], {
                    Directive[
                    GrayLevel[0.3]]}, 
                   Directive[
                    GrayLevel[0.3]]}, "Rows" -> {
                   Directive[
                    GrayLevel[0.3]], {
                    Directive[
                    GrayLevel[0.3]]}, 
                   Directive[
                    GrayLevel[0.3]]}}, 
               GridBoxFrame -> {
                "ColumnsIndexed" -> {{{1, -1}, {1, -1}} -> GrayLevel[0]}}, 
               GridBoxItemSize -> {
                "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
               BaseStyle -> Directive[
                 AbsoluteThickness[1], 
                 Dashing[{}]]], "Grid"], {}, StripOnInput -> False]], 
           Annotation[#, 
            Style[
             Grid[{{
                Style["max", Bold], 77}, {
                Style["75%", Bold], 
                Rational[61, 4]}, {
                Style["median", Bold], 13}, {
                Style["25%", Bold], 
                Rational[11, 4]}, {
                Style["min", Bold], 1}}, Dividers -> {{
                 Directive[
                  GrayLevel[0.3]], {
                  Directive[
                   GrayLevel[0.3]]}, 
                 Directive[
                  GrayLevel[0.3]]}, {
                 Directive[
                  GrayLevel[0.3]], {
                  Directive[
                   GrayLevel[0.3]]}, 
                 Directive[
                  GrayLevel[0.3]]}}, Alignment -> {{Center, ".", {Left}}}, 
              Frame -> GrayLevel[0], BaseStyle -> Directive[
                AbsoluteThickness[1], 
                Dashing[{}]]], {}], "Tooltip"]& ]}, {
          Directive[
           RGBColor[1, 0, 0]], 
          TagBox[
           TooltipBox[
            DynamicBox[{
              FEPrivate`If[
               CurrentValue["MouseOver"], 
               EdgeForm[{
                 GrayLevel[0.5], 
                 AbsoluteThickness[1.5], 
                 Opacity[0.66]}], {}, {}], 
              GraphicsGroupBox[{Antialiasing -> False, 
                PolygonBox[
                 NCache[{{
                    Rational[59, 4], 1.7754133086869819`}, {
                    Rational[59, 4], 2.224586691313018}, {
                    Rational[21, 4], 2.224586691313018}, {
                    Rational[21, 4], 1.7754133086869819`}}, {{14.75, 
                  1.7754133086869819`}, {14.75, 2.224586691313018}, {5.25, 
                  2.224586691313018}, {5.25, 
                  1.7754133086869819`}}]], {}, {{}, {}}, {}, {
                 GrayLevel[0], 
                 GrayLevel[1], 
                 
                 LineBox[{{7, 2.224586691313018}, {
                   7, 1.775413308686982}}]}, {}, {
                 GrayLevel[0], 
                 GrayLevel[0.5], 
                 LineBox[
                  NCache[{{{
                    Rational[21, 4], 2.}, {1, 2.}}, {{
                    Rational[59, 4], 2.}, {27, 2.}}}, {{{5.25, 2.}, {
                    1, 2.}}, {{14.75, 2.}, {27, 2.}}}]]}, {
                 GrayLevel[0], 
                 GrayLevel[0.5], 
                 
                 LineBox[{{{1, 2.112293345656509}, {1, 1.887706654343491}}, {{
                    27, 2.112293345656509}, {
                    27, 1.887706654343491}}}]}, {}}]}], 
            StyleBox[
             TagBox[
              GridBox[{{
                 StyleBox["\"max\"", Bold, StripOnInput -> False], "27"}, {
                 StyleBox["\"75%\"", Bold, StripOnInput -> False], 
                 FractionBox["59", "4"]}, {
                 StyleBox["\"median\"", Bold, StripOnInput -> False], "7"}, {
                 StyleBox["\"25%\"", Bold, StripOnInput -> False], 
                 FractionBox["21", "4"]}, {
                 StyleBox["\"min\"", Bold, StripOnInput -> False], "1"}}, 
               GridBoxAlignment -> {"Columns" -> {Center, ".", {Left}}}, 
               AutoDelete -> False, GridBoxDividers -> {"Columns" -> {
                   Directive[
                    GrayLevel[0.3]], {
                    Directive[
                    GrayLevel[0.3]]}, 
                   Directive[
                    GrayLevel[0.3]]}, "Rows" -> {
                   Directive[
                    GrayLevel[0.3]], {
                    Directive[
                    GrayLevel[0.3]]}, 
                   Directive[
                    GrayLevel[0.3]]}}, 
               GridBoxFrame -> {
                "ColumnsIndexed" -> {{{1, -1}, {1, -1}} -> GrayLevel[0]}}, 
               GridBoxItemSize -> {
                "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
               BaseStyle -> Directive[
                 AbsoluteThickness[1], 
                 Dashing[{}]]], "Grid"], {}, StripOnInput -> False]], 
           Annotation[#, 
            Style[
             Grid[{{
                Style["max", Bold], 27}, {
                Style["75%", Bold], 
                Rational[59, 4]}, {
                Style["median", Bold], 7}, {
                Style["25%", Bold], 
                Rational[21, 4]}, {
                Style["min", Bold], 1}}, Dividers -> {{
                 Directive[
                  GrayLevel[0.3]], {
                  Directive[
                   GrayLevel[0.3]]}, 
                 Directive[
                  GrayLevel[0.3]]}, {
                 Directive[
                  GrayLevel[0.3]], {
                  Directive[
                   GrayLevel[0.3]]}, 
                 Directive[
                  GrayLevel[0.3]]}}, Alignment -> {{Center, ".", {Left}}}, 
              Frame -> GrayLevel[0], BaseStyle -> Directive[
                AbsoluteThickness[1], 
                Dashing[{}]]], {}], 
            "Tooltip"]& ]}}}, {}, {}}}, {{{{{{{}, {}}, {}}, {{{}, {}}, {}}}, \
{}}, {}}, {}}, {}}, {
    AspectRatio -> NCache[GoldenRatio^(-1), 0.6180339887498948], 
     Axes -> {False, False}, AxesLabel -> {None, None}, 
     AxesOrigin -> {-2.8000000000000003`, 0.70295463955568}, 
     BaseStyle -> {FontFamily -> "Arial"}, Frame -> True, 
     FrameLabel -> {{None, None}, {None, None}}, FrameTicks -> {{{{1., 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0.008, 0}}, {1., 
          FormBox["\"Boys\"", TraditionalForm], 0}, {2., 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0.008, 0}}, {2., 
          FormBox["\"Girls\"", TraditionalForm], 0}, {0.7754133086869819, 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0, 0}}, {
         2.224586691313018, 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0, 0}}}, {{1., 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0.008, 0}}, {2., 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0.008, 0}}, {
         0.7754133086869819, 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0, 0}}, {
         2.224586691313018, 
          FormBox[
           TemplateBox[{0}, "Spacer1"], TraditionalForm], {0, 0}}}}, {
       Automatic, Automatic}}, GridLinesStyle -> Directive[
       GrayLevel[0.5, 0.4]], PlotRangePadding -> {{
        Scaled[0.05], 
        Scaled[0.05]}, {
        Scaled[0.05], 
        Scaled[0.05]}}, Ticks -> {Automatic, {{1., 
         FormBox[
          TemplateBox[{0}, "Spacer1"], TraditionalForm], {0.008, 0}}, {1., 
         FormBox["\"Boys\"", TraditionalForm], 0}, {2., 
         FormBox[
          TemplateBox[{0}, "Spacer1"], TraditionalForm], {0.008, 0}}, {2., 
         FormBox["\"Girls\"", TraditionalForm], 0}, {0.7754133086869819, 
         FormBox[
          TemplateBox[{0}, "Spacer1"], TraditionalForm], {0, 0}}, {
        2.224586691313018, 
         FormBox[
          TemplateBox[{0}, "Spacer1"], TraditionalForm], {0, 0}}}}}],FormBox[
    FormBox[
     TemplateBox[{"\"Boys\"", "\"Girls\""}, "SwatchLegend", 
      DisplayFunction -> (FormBox[
        StyleBox[
         StyleBox[
          PaneBox[
           TagBox[
            GridBox[{{
               TagBox[
                GridBox[{{
                   GraphicsBox[{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[1, 0, 0]], 
                    RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, 
                    AspectRatio -> Full, ImageSize -> {10, 10}, 
                    PlotRangePadding -> None, ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
                   GraphicsBox[{
                    Directive[
                    EdgeForm[
                    Directive[
                    Opacity[0.3], 
                    GrayLevel[0]]], 
                    PointSize[0.5], 
                    AbsoluteThickness[1.6], 
                    RGBColor[0, 0, 1]], 
                    RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, 
                    AspectRatio -> Full, ImageSize -> {10, 10}, 
                    PlotRangePadding -> None, ImagePadding -> Automatic, 
                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}}, 
                 GridBoxAlignment -> {
                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
                 AutoDelete -> False, 
                 GridBoxDividers -> {
                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
                  GridBoxSpacings -> {
                  "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, 
             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
             AutoDelete -> False, 
             GridBoxItemSize -> {
              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
            "Grid"], Alignment -> Left, AppearanceElements -> None, 
           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
         False], TraditionalForm]& ), 
      InterpretationFunction :> (RowBox[{"SwatchLegend", "[", 
         RowBox[{
           RowBox[{"{", 
             RowBox[{
               RowBox[{"Directive", "[", 
                 InterpretationBox[
                  ButtonBox[
                   TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[0, 0, 1], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0., 0., 0.6666666666666666], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 
                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
                    Magnification])}]], "RGBColor[0, 0, 1]"], Appearance -> 
                   None, BaseStyle -> {}, BaselinePosition -> Baseline, 
                   DefaultBaseStyle -> {}, ButtonFunction :> 
                   With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[0, 0, 1]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                   Automatic, Method -> "Preemptive"], 
                  RGBColor[0, 0, 1], Editable -> False, Selectable -> False], 
                 "]"}], ",", 
               RowBox[{"Directive", "[", 
                 InterpretationBox[
                  ButtonBox[
                   TooltipBox[
                    GraphicsBox[{{
                    GrayLevel[0], 
                    RectangleBox[{0, 0}]}, {
                    GrayLevel[0], 
                    RectangleBox[{1, -1}]}, {
                    RGBColor[1, 0, 0], 
                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
                    FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], 
                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
                    Dynamic[{
                    Automatic, 
                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
                    Magnification])}]], "RGBColor[1, 0, 0]"], Appearance -> 
                   None, BaseStyle -> {}, BaselinePosition -> Baseline, 
                   DefaultBaseStyle -> {}, ButtonFunction :> 
                   With[{Typeset`box$ = EvaluationBox[]}, 
                    If[
                    Not[
                    AbsoluteCurrentValue["Deployed"]], 
                    SelectionMove[Typeset`box$, All, Expression]; 
                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
                    FrontEnd`Private`$ColorSelectorInitialColor = 
                    RGBColor[1, 0, 0]; 
                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
                    MathLink`CallFrontEnd[
                    FrontEnd`AttachCell[Typeset`box$, 
                    FrontEndResource["RGBColorValueSelector"], {
                    0, {Left, Bottom}}, {Left, Top}, 
                    "ClosingActions" -> {
                    "SelectionDeparture", "ParentChanged", 
                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
                   Automatic, Method -> "Preemptive"], 
                  RGBColor[1, 0, 0], Editable -> False, Selectable -> False], 
                 "]"}]}], "}"}], ",", 
           RowBox[{"{", 
             RowBox[{#, ",", #2}], "}"}], ",", 
           RowBox[{"LegendMarkers", "\[Rule]", 
             RowBox[{"{", 
               RowBox[{"{", 
                 RowBox[{"Automatic", ",", "Automatic"}], "}"}], "}"}]}], ",", 
           RowBox[{"LabelStyle", "\[Rule]", 
             RowBox[{"{", "}"}]}], ",", 
           RowBox[{"LegendLayout", "\[Rule]", "\"ReversedColumn\""}]}], 
         "]"}]& ), Editable -> True], TraditionalForm], TraditionalForm]},
  "Legended",
  DisplayFunction->(GridBox[{{
      TagBox[
       ItemBox[
        PaneBox[
         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
       "SkipImageSizeLevel"], 
      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
    AutoDelete -> False, GridBoxItemSize -> Automatic, 
    BaselinePosition -> {1, 1}]& ),
  Editable->True,
  InterpretationFunction->(RowBox[{"Legended", "[", 
     RowBox[{#, ",", 
       RowBox[{"Placed", "[", 
         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
 CellChangeTimes->{
  3.719647831960441*^9},ExpressionUUID->"df8c3aa6-9f4e-41ee-b1c3-\
e2817ff9ec9e"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["To find Mean of the data (Function):",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356684249074*^9},ExpressionUUID->"c9eeb498-6029-4bb3-9d41-\
3ec002e63c95"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Mean", "[", "Data1", "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.7196478978192067`*^9, 3.719647898115265*^9}, 
   3.7196479285892982`*^9},ExpressionUUID->"6964acf8-168c-4efa-b1dc-\
e80a1107bf6b"],

Cell[BoxData["14.846153846153847`"], "Output",
 CellChangeTimes->{
  3.7196479294066105`*^9},ExpressionUUID->"577a69cf-1770-4bad-aba6-\
cdd7c754783a"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["To find the Mean Deviation for the data (Function):",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356700734188*^9},ExpressionUUID->"771e7b1f-59c8-40f9-a188-\
d0e1c54b26fb"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"MeanDeviation", "[", "Data1", "]"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.7196479349872327`*^9, 3.7196479355585346`*^9}, 
   3.719647985350995*^9},ExpressionUUID->"26eb83ba-b10a-48a4-818f-\
45aa95d952d8"],

Cell[BoxData["10.603550295857989`"], "Output",
 CellChangeTimes->{
  3.7196479862342987`*^9},ExpressionUUID->"a169061d-abc9-4ae7-86f4-\
f25422d131b7"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["To find the median for the data (Function):",
 FontColor->RGBColor[1, 0, 1]]], "Section",
 CellChangeTimes->{
  3.737356714069604*^9},ExpressionUUID->"ca38f398-4412-4794-8c98-\
be4edd76e0e5"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Median", "[", "Data1", "]"}]], "Input",
 CellChangeTimes->{{3.719648471415694*^9, 
  3.7196484810410476`*^9}},ExpressionUUID->"59709651-6f5c-460f-84c0-\
53e6a1633a2e"],

Cell[BoxData["13"], "Output",
 CellChangeTimes->{
  3.719648482354776*^9},ExpressionUUID->"634f4bb7-8e17-4162-8b87-\
11aab43bddbd"]
}, Open  ]]
}, Closed]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{Full, Full},
WindowMargins->{{-8, Automatic}, {Automatic, -8}},
Magnification:>1.25 Inherited,
FrontEndVersion->"11.2 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \
10, 2017)",
StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", 
  CharacterEncoding -> "UTF-8"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 465, 6, 198, "Title",ExpressionUUID->"b0ef0f06-84a0-46fa-a12c-6d805de792a5"],
Cell[1048, 30, 217, 4, 80, "Subtitle",ExpressionUUID->"16450fb1-7f6a-40ca-bfb3-4637e33b6a6f"],
Cell[CellGroupData[{
Cell[1290, 38, 237, 4, 87, "Section",ExpressionUUID->"fde2863a-706e-43aa-84e4-bdca58946f69"],
Cell[CellGroupData[{
Cell[1552, 46, 209, 4, 81, "Subsection",ExpressionUUID->"0c3499a5-6151-4698-aa2b-41835b94fbd0"],
Cell[1764, 52, 159, 3, 82, "Text",ExpressionUUID->"fd26895d-66f3-478c-84f8-a6f9c6bab878"]
}, Open  ]],
Cell[CellGroupData[{
Cell[1960, 60, 161, 3, 81, "Subsection",ExpressionUUID->"5bfe5877-f6cc-4be1-bbcc-dc431bf0c1ca"],
Cell[2124, 65, 161, 3, 82, "Text",ExpressionUUID->"4da526b5-bcae-4eeb-8748-e2f1c4499c6e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2322, 73, 163, 3, 81, "Subsection",ExpressionUUID->"2db884f4-d02f-4e03-af07-9b477da89d8a"],
Cell[2488, 78, 161, 3, 82, "Text",ExpressionUUID->"46627abb-ce3a-4570-bedd-6e1858a66aaa"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[2698, 87, 249, 4, 68, "Section",ExpressionUUID->"06afeb0b-3922-47bc-9d98-e6ef21fbdfb7"],
Cell[CellGroupData[{
Cell[2972, 95, 217, 4, 81, "Subsection",ExpressionUUID->"9f666182-37a0-48d9-8d3b-7fa326dcdd33"],
Cell[3192, 101, 157, 3, 82, "Text",ExpressionUUID->"640a3026-c480-4beb-9084-5839a1d42079"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3386, 109, 211, 4, 81, "Subsection",ExpressionUUID->"1301e941-0574-40c8-9472-214749288cd3"],
Cell[3600, 115, 245, 5, 82, "Text",ExpressionUUID->"4847bccc-6eab-48b9-903a-61a4aaddbe8e",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3882, 125, 224, 4, 81, "Subsection",ExpressionUUID->"916df522-938e-46af-ba79-a6767050fc2d"],
Cell[4109, 131, 246, 5, 82, "Text",ExpressionUUID->"76d6449d-53a2-4679-b83b-cdf059aad0a2",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4392, 141, 229, 4, 81, "Subsection",ExpressionUUID->"5a9b799b-66f3-49a3-8a81-6e8cd83c58d6"],
Cell[4624, 147, 247, 5, 82, "Text",ExpressionUUID->"fcd996d8-7792-4940-a82a-f6cdb06f1ca7",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4908, 157, 216, 4, 81, "Subsection",ExpressionUUID->"6a6c4df8-fcc1-4bc2-96ad-6811e542206f"],
Cell[5127, 163, 248, 5, 82, "Text",ExpressionUUID->"4c5c6773-8ebd-4b32-997d-542d48ef0685",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5412, 173, 222, 4, 81, "Subsection",ExpressionUUID->"ac4c80b8-1f9e-4fd9-b9ed-984b7be19683"],
Cell[5637, 179, 246, 5, 82, "Text",ExpressionUUID->"ddf7d5ef-daae-46ab-b999-290eaf34f793",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5920, 189, 216, 4, 81, "Subsection",ExpressionUUID->"5effcf03-c572-4b8b-8e22-bcd5a7d08019"],
Cell[6139, 195, 247, 5, 82, "Text",ExpressionUUID->"36ff7dc9-6241-4a9d-9b60-7d943971be24",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6423, 205, 180, 3, 81, "Subsection",ExpressionUUID->"f5b4aba1-db65-46a6-ac1f-c5949c89a40d"],
Cell[6606, 210, 245, 5, 128, "Text",ExpressionUUID->"7b9ee778-f66c-47f7-88a6-fa3165ac5779",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6888, 220, 172, 3, 126, "Subsection",ExpressionUUID->"d55ff143-92dd-4ad4-b343-174bf07ff468"],
Cell[7063, 225, 246, 5, 128, "Text",ExpressionUUID->"afc9e6dc-7510-4b37-b4ab-d6456d82b5ec",
 CellGroupingRules->"NormalGrouping"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7346, 235, 200, 3, 126, "Subsection",ExpressionUUID->"ab97e1ec-5bca-47d6-b191-e3f7b5bef78c"],
Cell[7549, 240, 862, 22, 306, "Text",ExpressionUUID->"4187de2b-ffd5-4352-87bc-07ae6125faa7"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[8460, 268, 371, 6, 159, "Subtitle",ExpressionUUID->"636e6fd5-e9e0-433a-bd2e-460ac08c94b8"],
Cell[CellGroupData[{
Cell[8856, 278, 309, 5, 87, "Section",ExpressionUUID->"a8c89097-6ba4-475b-9152-992dd7d9d99b"],
Cell[CellGroupData[{
Cell[9190, 287, 304, 8, 276, "Subsection",ExpressionUUID->"41bfbcda-1250-406b-9411-9badbce2f065"],
Cell[CellGroupData[{
Cell[9519, 299, 435, 10, 141, "Subsubsection",ExpressionUUID->"c8a98c55-81b5-4605-81f4-6e6fd8dbddbb"],
Cell[CellGroupData[{
Cell[9979, 313, 576, 13, 202, "Input",ExpressionUUID->"4ae42663-5978-4477-9861-64f41d7c45a7"],
Cell[10558, 328, 172, 2, 97, "Output",ExpressionUUID->"d89fc5fe-3b3c-4745-9710-d67d17e01fbe"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[10779, 336, 215, 4, 77, "Subsubsection",ExpressionUUID->"778c1618-3356-4f76-98ed-47fa56455355"],
Cell[CellGroupData[{
Cell[11019, 344, 598, 15, 202, "Input",ExpressionUUID->"e56277e9-83eb-4f7e-b174-2df1392490c8"],
Cell[11620, 361, 246, 5, 97, "Output",ExpressionUUID->"86801a85-9e21-4822-a9ab-53c8b00e9b08"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[11939, 374, 213, 4, 68, "Section",ExpressionUUID->"fb7a770a-cf17-4fa4-be42-4bfc3a91ea21"],
Cell[CellGroupData[{
Cell[12177, 382, 195, 3, 81, "Subsection",ExpressionUUID->"ff1c0071-5aea-45af-a5e6-c347a92b5112"],
Cell[CellGroupData[{
Cell[12397, 389, 326, 10, 78, "Subsubsection",ExpressionUUID->"5b8b6dec-38ab-4622-9028-e1924e79ee1d"],
Cell[CellGroupData[{
Cell[12748, 403, 593, 17, 188, "Input",ExpressionUUID->"132dbb1d-31d4-4188-918c-30e38418a8ba"],
Cell[13344, 422, 152, 2, 97, "Output",ExpressionUUID->"1ee06608-2935-4df9-bdcb-80498aff673f"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[13545, 430, 294, 9, 78, "Subsubsection",ExpressionUUID->"314877f4-109a-4672-abdf-d5e7dd743ef7"],
Cell[CellGroupData[{
Cell[13864, 443, 262, 5, 97, "Input",ExpressionUUID->"a5783735-e583-4f70-8844-a2ca8385bbe2"],
Cell[14129, 450, 153, 2, 97, "Output",ExpressionUUID->"e162976c-9281-4422-a412-58c75f91b275"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[14331, 458, 295, 9, 78, "Subsubsection",ExpressionUUID->"2672cdc1-df09-412f-931c-7116aeeb2c2a"],
Cell[CellGroupData[{
Cell[14651, 471, 260, 5, 97, "Input",ExpressionUUID->"06c0b8cf-a49a-44da-adf2-580b143bf459"],
Cell[14914, 478, 152, 2, 97, "Output",ExpressionUUID->"a829cfec-9bd2-4a24-bf51-15280c5f56ce"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[15139, 488, 215, 4, 68, "Section",ExpressionUUID->"1a40cdcb-f067-4e6a-bd0e-39ed7e510a8a"],
Cell[CellGroupData[{
Cell[15379, 496, 330, 8, 147, "Subsection",ExpressionUUID->"6c5d65ca-4b3f-4e8a-8adf-39d7fec7292b"],
Cell[CellGroupData[{
Cell[15734, 508, 426, 10, 188, "Input",ExpressionUUID->"32bd7c35-99b9-452d-8b4e-17e7910777b1"],
Cell[16163, 520, 170, 3, 132, "Output",ExpressionUUID->"29c237e3-8d7a-4962-b2fe-7fd675568421"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[16406, 531, 205, 4, 159, "Subtitle",ExpressionUUID->"0e6fe98c-5287-4dca-a206-e807bc9d1b41"],
Cell[CellGroupData[{
Cell[16636, 539, 229, 4, 87, "Section",ExpressionUUID->"e76e7b26-e519-4de6-85c1-aa5c6ca0b10f"],
Cell[CellGroupData[{
Cell[16890, 547, 290, 7, 118, "Subsection",ExpressionUUID->"fa17f597-5dd1-4ccc-a33a-a27579043e60"],
Cell[CellGroupData[{
Cell[17205, 558, 807, 20, 121, "Input",ExpressionUUID->"f5076070-ab5e-4ae2-a254-3ad65114f2af"],
Cell[18015, 580, 209, 5, 78, "Output",ExpressionUUID->"b7f3519d-5bd8-461f-9c3b-19078e5ca198"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[18297, 593, 229, 7, 121, "Subtitle",ExpressionUUID->"1f479103-3305-4378-a488-13dd7f574b1a"],
Cell[CellGroupData[{
Cell[18551, 604, 214, 4, 87, "Section",ExpressionUUID->"a298839f-c4ab-488a-82e0-e2ac9e865fc1"],
Cell[CellGroupData[{
Cell[18790, 612, 227, 5, 65, "Subsection",ExpressionUUID->"bfcead0b-efbd-4717-ad25-479e9fec5b25"],
Cell[CellGroupData[{
Cell[19042, 621, 474, 13, 156, "Input",ExpressionUUID->"f93960a7-9e48-41a7-a230-a81917b0bc46"],
Cell[19519, 636, 153, 4, 107, "Output",ExpressionUUID->"5ed712aa-b86f-4d32-9472-ccc3647ccbbd"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[19733, 647, 214, 4, 68, "Section",ExpressionUUID->"bd6776b3-e9bc-49ad-b6a8-60bc7a197c78"],
Cell[CellGroupData[{
Cell[19972, 655, 266, 6, 65, "Subsection",ExpressionUUID->"905f2d34-8012-4504-a12f-6baef1467562"],
Cell[CellGroupData[{
Cell[20263, 665, 475, 14, 163, "Input",ExpressionUUID->"bff0e671-8282-4083-8157-dd77c72771b8"],
Cell[20741, 681, 159, 3, 78, "Output",ExpressionUUID->"3ea4acde-7332-41dd-943e-2b1860051a6d"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[20961, 691, 210, 4, 68, "Section",ExpressionUUID->"3a215b5a-572a-4df8-9650-84e238ce54d3"],
Cell[CellGroupData[{
Cell[21196, 699, 326, 7, 118, "Subsection",ExpressionUUID->"d856b67c-1864-4082-aae2-8d4885463ebf"],
Cell[CellGroupData[{
Cell[21547, 710, 402, 11, 138, "Input",ExpressionUUID->"57f4c99c-8ace-4e32-afa0-344f6916daa0"],
Cell[21952, 723, 166, 5, 82, "Output",ExpressionUUID->"3de0cd78-0672-4f09-a193-15a7010509b4"]
}, Open  ]]
}, Open  ]],
Cell[22145, 732, 77, 0, 65, "Subsection",ExpressionUUID->"8fbe765c-7608-4deb-a7e2-bf57c4e1a78c"]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[22271, 738, 278, 7, 121, "Subtitle",ExpressionUUID->"c1d6440a-a585-45f5-ba4f-7d9cf40fd79d"],
Cell[CellGroupData[{
Cell[22574, 749, 237, 4, 87, "Section",ExpressionUUID->"a2b4b697-ea49-4a34-a521-04cc40b18c26"],
Cell[CellGroupData[{
Cell[22836, 757, 364, 7, 118, "Subsection",ExpressionUUID->"f10a8f2e-3de0-4729-953d-0fa7e6c011fd"],
Cell[CellGroupData[{
Cell[23225, 768, 545, 14, 178, "Input",ExpressionUUID->"73388cf3-3ecd-4075-9fd4-0ba869ed8e2a"],
Cell[23773, 784, 154, 3, 78, "Output",ExpressionUUID->"a28d020d-6005-4356-9e45-bcd708f1a090"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[23976, 793, 228, 5, 65, "Subsection",ExpressionUUID->"51fcff16-d501-487a-ae9f-f34c8cfcf6bc"],
Cell[CellGroupData[{
Cell[24229, 802, 457, 13, 181, "Input",ExpressionUUID->"a23c4c14-1f1f-479b-a7df-99fd61d3a5d5"],
Cell[24689, 817, 178, 4, 107, "Output",ExpressionUUID->"2fcd3aa7-cdac-477f-8e15-8610caae74e6"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[24940, 829, 345, 6, 237, "Subtitle",ExpressionUUID->"2a27004c-4bda-449b-b510-36505e4fd01b"],
Cell[CellGroupData[{
Cell[25310, 839, 320, 5, 87, "Section",ExpressionUUID->"aecc5405-4ef2-44a8-abcf-13ef02d2281c"],
Cell[CellGroupData[{
Cell[25655, 848, 624, 13, 175, "Subsection",ExpressionUUID->"7f858c78-3f24-48d5-a645-6abcb45594d1"],
Cell[CellGroupData[{
Cell[26304, 865, 287, 7, 41, "Subsubsection",ExpressionUUID->"4cf4dd62-456d-4810-88c8-4f4ecc134cf7"],
Cell[CellGroupData[{
Cell[26616, 876, 394, 9, 51, "Input",ExpressionUUID->"b1241c13-a32e-403c-8ff5-efb1565cf157"],
Cell[27013, 887, 150, 3, 51, "Output",ExpressionUUID->"366ef63f-8e0f-49d2-85cd-245c03186381"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[27212, 896, 376, 8, 74, "Subsubsection",ExpressionUUID->"161afa52-f35f-438f-91fb-6bd28172b5e6"],
Cell[CellGroupData[{
Cell[27613, 908, 270, 6, 35, "Subsubsubsection",ExpressionUUID->"bdecef72-3317-4066-a9fe-76c0c3d6455d"],
Cell[CellGroupData[{
Cell[27908, 918, 359, 9, 51, "Input",ExpressionUUID->"c2882756-0bc0-46f1-a672-4cb6bd17a9ad"],
Cell[28270, 929, 149, 3, 51, "Output",ExpressionUUID->"2b1d7a35-ad70-47cd-9e0c-3c5560e754f7"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[28468, 938, 328, 6, 35, "Subsubsubsection",ExpressionUUID->"1849d6f3-ecde-4bb8-8c59-16733c8f4c1c"],
Cell[CellGroupData[{
Cell[28821, 948, 368, 9, 51, "Input",ExpressionUUID->"523f479b-0546-4f3c-8545-b58ac6d3691e"],
Cell[29192, 959, 149, 3, 51, "Output",ExpressionUUID->"b7bc236e-3bb4-43ab-bb88-9ff412dd71cd"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[29402, 969, 490, 10, 138, "Subsubsection",ExpressionUUID->"0b4d06c9-e0b5-4893-ac69-25dd3128d516"],
Cell[29895, 981, 505, 13, 51, "Input",ExpressionUUID->"8e5e5819-4042-4080-8285-83e8164b169d"],
Cell[CellGroupData[{
Cell[30425, 998, 348, 9, 51, "Input",ExpressionUUID->"065c002b-d3cd-4d6a-a5f5-74fa2e7b299c"],
Cell[30776, 1009, 350, 9, 29, "Message",ExpressionUUID->"868a32cc-6846-45ee-9998-5dac8c6c1e23"],
Cell[31129, 1020, 2227, 62, 80, "Output",ExpressionUUID->"ec811c7b-520e-4ce3-bd0e-f0d5aa99355d"]
}, Open  ]],
Cell[33371, 1085, 417, 10, 51, "Input",ExpressionUUID->"8a86ef30-c06d-4db1-b332-67b19f23482d"],
Cell[CellGroupData[{
Cell[33813, 1099, 473, 14, 51, "Input",ExpressionUUID->"a9ca5e43-f88b-4539-8a5f-6d95e7cddda8"],
Cell[34289, 1115, 1011, 28, 268, "Output",ExpressionUUID->"d21b826e-d659-41c4-9ba7-5ea7395ab088"]
}, Open  ]],
Cell[35315, 1146, 158, 3, 43, "Text",ExpressionUUID->"2339955c-ad04-4c78-bcf8-9eb4f3d56cb5"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[35534, 1156, 240, 4, 87, "Section",ExpressionUUID->"1b89bcc7-b79e-4164-b357-0777053a83ee"],
Cell[CellGroupData[{
Cell[35799, 1164, 764, 20, 151, "Input",ExpressionUUID->"f1997178-d379-4a47-bc35-83f2a0b45d0a"],
Cell[36566, 1186, 9522, 202, 603, "Output",ExpressionUUID->"ec5ee9a2-a17b-4874-8d87-7eed4b12367c"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[46137, 1394, 227, 4, 68, "Section",ExpressionUUID->"4a6a48c0-a20a-4100-a754-acc2d1fbdb51"],
Cell[46367, 1400, 636, 12, 340, "Subsection",ExpressionUUID->"25d6b4cc-71e9-4e06-9afc-b907d3a131c5"],
Cell[CellGroupData[{
Cell[47028, 1416, 374, 6, 78, "Subsection",ExpressionUUID->"a36dfe7b-8d67-46d5-bb6b-867d6be4e6af"],
Cell[CellGroupData[{
Cell[47427, 1426, 265, 5, 66, "Subsubsubsection",ExpressionUUID->"828888a5-69ed-4b78-bdc3-4efbadd8e46f"],
Cell[CellGroupData[{
Cell[47717, 1435, 445, 9, 97, "Input",ExpressionUUID->"f8352939-bc20-4ef4-9992-b279429c0086"],
Cell[48165, 1446, 173, 3, 133, "Output",ExpressionUUID->"fc5cc479-2c01-4e70-b714-4ad6b5b4ab4d"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[48387, 1455, 217, 4, 66, "Subsubsubsection",ExpressionUUID->"88c8f347-80fc-440e-8357-a419f6d94356"],
Cell[CellGroupData[{
Cell[48629, 1463, 387, 8, 97, "Input",ExpressionUUID->"4632b873-cdeb-49b7-9cba-d7e07e80a9f0"],
Cell[49019, 1473, 172, 3, 133, "Output",ExpressionUUID->"5c16cdd9-247f-4ea7-9bb8-3bd6b1f880fd"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[49276, 1485, 345, 6, 159, "Subtitle",ExpressionUUID->"9a06586b-9805-4db0-8d4b-f55b319382f7"],
Cell[CellGroupData[{
Cell[49646, 1495, 260, 5, 87, "Section",ExpressionUUID->"75c21fc3-7c32-4fa9-8029-282be88f4ee3"],
Cell[CellGroupData[{
Cell[49931, 1504, 600, 11, 431, "Subsection",ExpressionUUID->"86cbef4a-e462-4f82-aa63-87e60e705179"],
Cell[CellGroupData[{
Cell[50556, 1519, 207, 5, 125, "Subsubsection",ExpressionUUID->"0c937a80-ffe0-4a61-ae2d-2ac71be050cd"],
Cell[CellGroupData[{
Cell[50788, 1528, 396, 9, 152, "Input",ExpressionUUID->"fe9e2464-8af0-4765-90cc-834d05d4628e"],
Cell[51187, 1539, 167, 2, 152, "Output",ExpressionUUID->"61cdd3da-8891-4e06-9fea-3ad3a1c47ad2"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[51403, 1547, 234, 6, 125, "Subsubsection",ExpressionUUID->"a19d447f-05d2-4fe1-a6d4-d80e92650900"],
Cell[CellGroupData[{
Cell[51662, 1557, 417, 9, 152, "Input",ExpressionUUID->"db7823df-f9b9-42ab-8f45-49b65030336c"],
Cell[52082, 1568, 167, 2, 157, "Output",ExpressionUUID->"acaf1d9e-8eab-490b-b9cb-81a8f49723c7"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[52298, 1576, 222, 6, 125, "Subsubsection",ExpressionUUID->"eb505847-2ae2-4f53-a67e-8a47ed456bf4"],
Cell[CellGroupData[{
Cell[52545, 1586, 302, 6, 152, "Input",ExpressionUUID->"1dc5fff6-ed96-4c66-97f3-cb52476afbd6"],
Cell[52850, 1594, 166, 2, 152, "Output",ExpressionUUID->"3325c4f4-66e2-49da-87a4-d3e5013162ca"]
}, Open  ]],
Cell[53031, 1599, 551, 10, 218, "Text",ExpressionUUID->"40291466-e0c0-4f74-9bc1-9529f8fb5936"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[53643, 1616, 374, 6, 68, "Section",ExpressionUUID->"70fe83a7-e0bd-45f9-85a7-23161200852a"],
Cell[54020, 1624, 263, 6, 147, "Subsection",ExpressionUUID->"6df0be3e-5e0f-4e4b-87d9-85f051f2575a"],
Cell[CellGroupData[{
Cell[54308, 1634, 438, 8, 145, "Subsection",ExpressionUUID->"20588c9b-707a-4c65-a25f-9c9b8f86b75e"],
Cell[CellGroupData[{
Cell[54771, 1646, 256, 6, 78, "Subsubsection",ExpressionUUID->"6b49a7db-2ee7-4e6e-bab7-9c7aec7b319f"],
Cell[CellGroupData[{
Cell[55052, 1656, 458, 10, 97, "Input",ExpressionUUID->"4022dc82-58e7-43eb-81c2-f273adea00df"],
Cell[55513, 1668, 170, 2, 97, "Output",ExpressionUUID->"b2640796-9321-40aa-a178-b229e0705de4"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[55732, 1676, 279, 6, 78, "Subsubsection",ExpressionUUID->"ab12e1e5-ce60-4b0a-8091-20c89c56aab6"],
Cell[CellGroupData[{
Cell[56036, 1686, 433, 10, 97, "Input",ExpressionUUID->"a6e36c50-aba2-4843-872e-1cbac4f68851"],
Cell[56472, 1698, 167, 2, 97, "Output",ExpressionUUID->"848f6fbf-2cde-4fd3-91fd-2f8580bc80be"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[56688, 1706, 288, 6, 78, "Subsubsection",ExpressionUUID->"752caf8f-db60-43ad-bbec-9e9682d9c1ea"],
Cell[CellGroupData[{
Cell[57001, 1716, 424, 9, 97, "Input",ExpressionUUID->"e2fee661-80c7-4d3c-b8e5-50742bf8c882"],
Cell[57428, 1727, 169, 2, 97, "Output",ExpressionUUID->"d718b02e-5c64-4d41-8aaa-cdf02ebc75d5"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[57646, 1735, 365, 7, 143, "Subsubsection",ExpressionUUID->"d89f0a17-f2f8-4e33-9f60-c2dcf7f2f790"],
Cell[CellGroupData[{
Cell[58036, 1746, 343, 8, 97, "Input",ExpressionUUID->"a1201dd2-de65-44d4-8462-a40399e95a7f"],
Cell[58382, 1756, 166, 2, 152, "Output",ExpressionUUID->"95471f8a-3a5b-486d-a354-1dd11bdb5225"]
}, Open  ]],
Cell[58563, 1761, 212, 5, 128, "Text",ExpressionUUID->"f151956a-bb99-45ac-9dd6-93a7f1f9d877"]
}, Open  ]]
}, Open  ]],
Cell[58802, 1770, 77, 0, 81, "Subsection",ExpressionUUID->"156ffc83-4934-40d5-941d-fecdfd61ce10"]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[58928, 1776, 216, 4, 80, "Subtitle",ExpressionUUID->"2f13d95b-948b-4e15-9ae9-b47f11fa88f9"],
Cell[CellGroupData[{
Cell[59169, 1784, 236, 4, 87, "Section",ExpressionUUID->"0c87da2e-4069-4556-9112-0f9019837b1a"],
Cell[CellGroupData[{
Cell[59430, 1792, 184, 3, 81, "Subsection",ExpressionUUID->"462adcbf-bc58-4353-a343-af0d8de3fea7"],
Cell[CellGroupData[{
Cell[59639, 1799, 219, 4, 97, "Input",ExpressionUUID->"be8a354e-2f4b-4795-9282-de7c6be7cad6"],
Cell[59861, 1805, 148, 2, 97, "Output",ExpressionUUID->"767c1d5a-9778-4702-8e28-83257670eef4"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60046, 1812, 220, 4, 97, "Input",ExpressionUUID->"01ae0173-d38d-470e-bd15-463b3f76acb7"],
Cell[60269, 1818, 151, 2, 97, "Output",ExpressionUUID->"e9e662fd-24e7-404c-9377-d95b7808213d"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[60481, 1827, 294, 5, 68, "Section",ExpressionUUID->"8e035bc5-e846-4de8-a7ac-94e4e7e5a699"],
Cell[CellGroupData[{
Cell[60800, 1836, 167, 3, 81, "Subsection",ExpressionUUID->"c2d166c2-70f8-464c-bfca-9b07aed8078a"],
Cell[CellGroupData[{
Cell[60992, 1843, 490, 12, 141, "Input",ExpressionUUID->"1e315af4-1417-4e07-b3ec-466bd4b4642c"],
Cell[61485, 1857, 7811, 146, 612, "Output",ExpressionUUID->"d1d7ce08-c1e9-443e-830d-899479b0698e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[69333, 2008, 437, 12, 141, "Input",ExpressionUUID->"6a382e3e-4e9a-4111-b26c-e49ca9646fec"],
Cell[69773, 2022, 7796, 145, 613, "Output",ExpressionUUID->"7bd6f152-90a5-43ef-bf24-8ba8837e958a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[77606, 2172, 437, 12, 141, "Input",ExpressionUUID->"abab4e91-f189-41f9-9dc9-dfb235128311"],
Cell[78046, 2186, 7859, 147, 601, "Output",ExpressionUUID->"302a2b6e-b386-42ff-9f36-2c7fe2ebd049"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[85954, 2339, 171, 3, 81, "Subsection",ExpressionUUID->"e3eea411-63e6-4b9c-90d7-b36ca922f7ea"],
Cell[86128, 2344, 354, 8, 101, "Input",ExpressionUUID->"ef608d02-6c60-4ba9-82d3-81add1c77019"],
Cell[CellGroupData[{
Cell[86507, 2356, 415, 10, 97, "Input",ExpressionUUID->"20c62965-b8ba-41ab-aa87-843785c26c8f"],
Cell[86925, 2368, 9164, 169, 608, "Output",ExpressionUUID->"52df9e78-7ae8-4d12-b793-a7c37eee9259"]
}, Open  ]],
Cell[CellGroupData[{
Cell[96126, 2542, 419, 10, 97, "Input",ExpressionUUID->"1d51226d-7226-4c97-a8ce-2de5d63f075a"],
Cell[96548, 2554, 4265, 87, 601, "Output",ExpressionUUID->"a71e60ad-3d7d-41bb-8c05-484c4868c0af"]
}, Open  ]],
Cell[CellGroupData[{
Cell[100850, 2646, 401, 10, 97, "Input",ExpressionUUID->"3f232a2b-c697-4d4b-9e9f-4da11fef75b0"],
Cell[101254, 2658, 6078, 118, 608, "Output",ExpressionUUID->"dc7f1c8a-91d8-4256-9b3b-b6b995eb06bd"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[107381, 2782, 156, 3, 81, "Subsection",ExpressionUUID->"9741036b-707b-462d-8b2c-d9975aa44fb9"],
Cell[CellGroupData[{
Cell[107562, 2789, 383, 10, 97, "Input",ExpressionUUID->"f9e33a13-3002-478f-9759-3ccb6f36e036"],
Cell[107948, 2801, 3849, 81, 608, "Output",ExpressionUUID->"47ab987c-3cb6-4e5a-8617-644733ba141f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[111834, 2887, 405, 11, 97, "Input",ExpressionUUID->"698412c6-d8fb-4bad-a21a-bcfad8596f22"],
Cell[112242, 2900, 3912, 82, 608, "Output",ExpressionUUID->"df598669-dcfe-4b00-bce1-56f63e96b5b5"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[116227, 2990, 298, 5, 159, "Subtitle",ExpressionUUID->"a60a4d30-7e71-443b-ad2e-fae84455a656"],
Cell[CellGroupData[{
Cell[116550, 2999, 229, 4, 108, "Section",ExpressionUUID->"6d5991f4-5cec-47fa-9666-cda6ee5d2d54"],
Cell[CellGroupData[{
Cell[116804, 3007, 429, 13, 151, "Subsection",ExpressionUUID->"a699304a-b994-4a23-82d5-6e43d4560a44"],
Cell[CellGroupData[{
Cell[117258, 3024, 390, 9, 222, "Input",ExpressionUUID->"d7c47b23-47ad-4101-9435-1b05e4d73e72"],
Cell[117651, 3035, 278, 8, 250, "Output",ExpressionUUID->"7e1b4ece-69fb-4f11-8bba-434148e3d652"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[118002, 3051, 336, 6, 198, "Subtitle",ExpressionUUID->"245d058a-40cc-40ed-8f5a-2c56801512b4"],
Cell[CellGroupData[{
Cell[118363, 3061, 283, 5, 108, "Section",ExpressionUUID->"42684e1d-8400-422b-98ec-82879fb98a03"],
Cell[118649, 3068, 211, 3, 128, "Text",ExpressionUUID->"86c728c4-0403-4519-ada0-9a7bda2d6a5b"],
Cell[CellGroupData[{
Cell[118885, 3075, 404, 10, 152, "Input",ExpressionUUID->"5086749f-66ab-4b07-a35b-e87a196c85aa"],
Cell[119292, 3087, 723, 21, 260, "Output",ExpressionUUID->"7d13e075-f5f7-49b2-bd88-608d9db29973"]
}, Open  ]],
Cell[CellGroupData[{
Cell[120052, 3113, 185, 4, 152, "Input",ExpressionUUID->"4aad1002-124b-4a4a-9eb5-1c93600eb66c"],
Cell[120240, 3119, 767, 23, 253, "Output",ExpressionUUID->"30c6710d-c936-4e7a-9487-1f9eb5558bb4"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[121056, 3148, 227, 4, 85, "Section",ExpressionUUID->"6f72b227-baa5-4b18-9bf8-3d94bba78be4"],
Cell[CellGroupData[{
Cell[121308, 3156, 156, 3, 126, "Subsection",ExpressionUUID->"7a280568-9133-4feb-af2a-2ac524b8977f"],
Cell[CellGroupData[{
Cell[121489, 3163, 608, 18, 152, "Input",ExpressionUUID->"a69e315e-99f4-42a9-bad0-2e8387509654"],
Cell[122100, 3183, 734, 21, 253, "Output",ExpressionUUID->"5284fad4-cdd9-416c-8e88-fe81bcb0379f"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[122883, 3210, 158, 3, 126, "Subsection",ExpressionUUID->"59b965f0-3264-4149-bd7f-be57bf15124d"],
Cell[CellGroupData[{
Cell[123066, 3217, 579, 17, 152, "Input",ExpressionUUID->"d0f5ecac-3a35-44a8-9d4b-23b022dc162e"],
Cell[123648, 3236, 777, 23, 253, "Output",ExpressionUUID->"e523d36c-4736-41b8-8e92-829e5fe9c396"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[124486, 3266, 281, 5, 85, "Section",ExpressionUUID->"de0ade0b-890a-4bbb-b84e-e7afb39c97d3"],
Cell[CellGroupData[{
Cell[124792, 3275, 162, 3, 126, "Subsection",ExpressionUUID->"03b9db56-1ff7-40a4-9a3b-9f2135b397f4"],
Cell[CellGroupData[{
Cell[124979, 3282, 632, 18, 152, "Input",ExpressionUUID->"10bed3f8-0233-48b0-bf76-a63cdc1b3313"],
Cell[125614, 3302, 735, 21, 253, "Output",ExpressionUUID->"ba312895-1e97-465d-b185-0ac65636f4c0"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[126398, 3329, 156, 3, 126, "Subsection",ExpressionUUID->"caa52839-2df8-4b8b-9a97-95e6febad77c"],
Cell[CellGroupData[{
Cell[126579, 3336, 582, 17, 152, "Input",ExpressionUUID->"12b27982-5105-48b3-ba69-21adc815b1b8"],
Cell[127164, 3355, 909, 27, 308, "Output",ExpressionUUID->"9c11f731-d1a7-4e61-81ef-9b085d464939"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[128134, 3389, 233, 4, 85, "Section",ExpressionUUID->"920edcda-f646-40ae-83a9-1ec216a3a9f2"],
Cell[CellGroupData[{
Cell[128392, 3397, 437, 15, 63, "Input",ExpressionUUID->"d2aea1f6-35a5-489f-b641-43d8680f8d5b"],
Cell[128832, 3414, 778, 23, 105, "Output",ExpressionUUID->"7f613190-18fb-4f5b-a8bf-cc7bc1738a5e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[129647, 3442, 165, 3, 52, "Subsection",ExpressionUUID->"dd1cfebc-04f3-4109-9057-2aa087c887a1"],
Cell[CellGroupData[{
Cell[129837, 3449, 472, 16, 63, "Input",ExpressionUUID->"46351e68-d3e5-497b-a648-70de18bcea84"],
Cell[130312, 3467, 273, 9, 63, "Output",ExpressionUUID->"88014ed0-cf60-443c-bf43-cfee54f0ff68"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[130658, 3484, 329, 5, 198, "Subtitle",ExpressionUUID->"6c4100c8-1ffa-4f6b-8b25-934c6b73c27b"],
Cell[CellGroupData[{
Cell[131012, 3493, 267, 5, 108, "Section",ExpressionUUID->"b3a45641-7a81-43f7-aef0-5da0739aa497"],
Cell[CellGroupData[{
Cell[131304, 3502, 176, 3, 103, "Subsubsubsection",ExpressionUUID->"ee175631-fc87-483e-89a5-134058e3ab21"],
Cell[CellGroupData[{
Cell[131505, 3509, 664, 18, 165, "Input",ExpressionUUID->"c33fcf45-f3b1-4942-946d-a11272762ea2"],
Cell[132172, 3529, 10799, 196, 977, "Output",ExpressionUUID->"e7ff2925-133a-4b6f-917e-58e4d8c132df"]
}, Open  ]],
Cell[CellGroupData[{
Cell[143008, 3730, 661, 19, 165, "Input",ExpressionUUID->"84b1ce21-da31-4b93-9a83-b015b527ee3d"],
Cell[143672, 3751, 5149, 102, 1000, "Output",ExpressionUUID->"6616951d-1dd6-4e9c-9337-a1bb37044e69"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[148882, 3860, 258, 5, 85, "Section",ExpressionUUID->"629e28e5-f6f1-4317-b95c-f7d865526d81"],
Cell[149143, 3867, 381, 7, 187, "Subsubsubsection",ExpressionUUID->"2c9cbce1-5e87-4114-a6b1-431bc1cc95f8"],
Cell[CellGroupData[{
Cell[149549, 3878, 229, 5, 120, "Subsubsection",ExpressionUUID->"14d19d5c-7d73-479f-a2f3-24b2779b4f39"],
Cell[149781, 3885, 433, 12, 157, "Input",ExpressionUUID->"18f4ae55-e8ea-4dec-9134-273683fe3108"],
Cell[CellGroupData[{
Cell[150239, 3901, 339, 8, 152, "Input",ExpressionUUID->"5b32e9b0-93da-44ae-bf80-c4f09fc9fe37"],
Cell[150581, 3911, 285, 6, 152, "Output",ExpressionUUID->"f8040880-a658-4e6b-80dc-3e9f26d90ae2"]
}, Open  ]]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[150939, 3925, 512, 8, 296, "Subtitle",ExpressionUUID->"e811121f-46c6-4705-a3b8-51ccee61f12a"],
Cell[CellGroupData[{
Cell[151476, 3937, 225, 4, 108, "Section",ExpressionUUID->"ed7b49c9-fcc8-4f92-94c5-43078f659908"],
Cell[CellGroupData[{
Cell[151726, 3945, 202, 3, 52, "Subsection",ExpressionUUID->"19ad7b44-af7b-415c-874b-8b08331ac2d4"],
Cell[CellGroupData[{
Cell[151953, 3952, 410, 12, 63, "Input",ExpressionUUID->"9a71d743-4918-423c-9c44-11a745fe7fea"],
Cell[152366, 3966, 164, 5, 66, "Output",ExpressionUUID->"9fa14039-98c0-4dff-bad1-f1fc6c95fc66"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[152591, 3978, 192, 4, 108, "Section",ExpressionUUID->"c7b52a9d-0ded-49e9-8bc2-8f97362e67e8"],
Cell[152786, 3984, 622, 17, 233, "Input",ExpressionUUID->"871414a5-8c4a-4ebf-b0b6-874de043ae40"],
Cell[CellGroupData[{
Cell[153433, 4005, 265, 7, 152, "Input",ExpressionUUID->"06370c14-53fa-447c-a4a9-3c393e40a197"],
Cell[153701, 4014, 359, 11, 207, "Output",ExpressionUUID->"969b4c3b-34db-4ae5-b57c-76dd30aa705d"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[154109, 4031, 266, 5, 85, "Section",ExpressionUUID->"be0542c2-414e-47e4-9fd3-1c39b45a95d6"],
Cell[154378, 4038, 870, 22, 53, "Subsubsubsection",ExpressionUUID->"d73030fe-474d-4150-bb22-9ea91c08a110"],
Cell[CellGroupData[{
Cell[155273, 4064, 236, 4, 50, "Subsubsection",ExpressionUUID->"2a7df301-f921-4bd3-b3ba-c6fb7010015c"],
Cell[155512, 4070, 503, 16, 53, "Text",ExpressionUUID->"3f3536c8-bd1d-4498-91a1-df23f1ee90e1"],
Cell[CellGroupData[{
Cell[156040, 4090, 343, 8, 88, "Input",ExpressionUUID->"311d2c8a-dbe1-4a47-b46e-00b25b6dd246"],
Cell[156386, 4100, 172, 4, 63, "Output",ExpressionUUID->"cbbe2895-9fcc-4339-822b-e98e5b53b1cc"]
}, Open  ]],
Cell[156573, 4107, 184, 3, 53, "Text",ExpressionUUID->"6e36ff0b-0379-434c-87d4-bf1a22d76a04"],
Cell[CellGroupData[{
Cell[156782, 4114, 333, 7, 63, "Input",ExpressionUUID->"4e30d7e4-3a3c-4d36-ba9e-952e4c082c8c"],
Cell[157118, 4123, 308, 6, 63, "Output",ExpressionUUID->"5c4f6e9d-143d-4197-ad61-3bcef4255159"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[157487, 4136, 347, 6, 108, "Section",ExpressionUUID->"998460aa-17ee-41a7-9cb6-48f39571b576",
 CellGroupingRules->{"SectionGrouping", Inherited}],
Cell[CellGroupData[{
Cell[157859, 4146, 1049, 29, 98, "Input",ExpressionUUID->"833fe1e1-c290-4220-b275-53e2b96da2e9"],
Cell[158911, 4177, 1845, 38, 536, "Output",ExpressionUUID->"d56ed259-86db-49be-bc39-903ccc4e02a8"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[160805, 4221, 195, 4, 108, "Section",ExpressionUUID->"a24fb3da-9a23-4958-b3b4-1a66f605c8ee"],
Cell[CellGroupData[{
Cell[161025, 4229, 1273, 48, 253, "Input",ExpressionUUID->"818d8b80-0c00-4e5f-b352-e689f74a492c"],
Cell[162301, 4279, 149, 4, 152, "Output",ExpressionUUID->"e1d81b3d-61c2-4352-a9cf-6772cfa427d6"],
Cell[162453, 4285, 312, 10, 206, "Output",ExpressionUUID->"59930920-9abf-4005-878f-9442347145db"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[162814, 4301, 187, 4, 85, "Section",ExpressionUUID->"a201d07e-9f69-4e71-8201-68325ab09ce3"],
Cell[CellGroupData[{
Cell[163026, 4309, 647, 20, 165, "Input",ExpressionUUID->"a819a227-5060-492f-adaa-bc86c73bca2c"],
Cell[163676, 4331, 5284, 106, 1000, "Output",ExpressionUUID->"db859691-70f4-4c66-a969-a6d681f5109c"]
}, Open  ]],
Cell[168975, 4440, 1045, 34, 212, "Input",ExpressionUUID->"1247a84c-00d5-4ef6-9c3e-3544dc46f09a"]
}, Closed]],
Cell[CellGroupData[{
Cell[170057, 4479, 246, 4, 85, "Section",ExpressionUUID->"fb7e8340-adab-4d23-93bf-702c87664545"],
Cell[CellGroupData[{
Cell[170328, 4487, 159, 3, 126, "Subsection",ExpressionUUID->"5d463261-d258-4939-b61b-08ae2992e051"],
Cell[CellGroupData[{
Cell[170512, 4494, 674, 18, 165, "Input",ExpressionUUID->"150bd53c-8e84-4543-afd8-f15c3e78d3fe"],
Cell[171189, 4514, 17699, 306, 1441, "Output",ExpressionUUID->"25e1b52f-f41a-48ae-90e6-d796fe8e423d"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[188937, 4826, 158, 3, 126, "Subsection",ExpressionUUID->"e0572fde-5395-4a06-9413-4d1da78fb83f"],
Cell[CellGroupData[{
Cell[189120, 4833, 668, 18, 152, "Input",ExpressionUUID->"e7506b55-738c-4328-a7e7-2eeb0b4131b5"],
Cell[189791, 4853, 16968, 295, 1441, "Output",ExpressionUUID->"3983e872-dc23-4b67-ab60-3f89070adacf"]
}, Open  ]]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[206820, 5155, 222, 4, 85, "Section",ExpressionUUID->"8350f85e-3f3d-4ad4-a33c-5c88f6020cd9"],
Cell[CellGroupData[{
Cell[207067, 5163, 667, 19, 165, "Input",ExpressionUUID->"2b2226d8-c002-4974-ba7f-f9983536d2ae"],
Cell[207737, 5184, 4553, 91, 1463, "Output",ExpressionUUID->"caa3fdab-24b9-41ff-9185-569d5958357c"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[212339, 5281, 234, 4, 85, "Section",ExpressionUUID->"b363190d-012e-4cd7-b559-050193774c20"],
Cell[CellGroupData[{
Cell[212598, 5289, 597, 15, 165, "Input",ExpressionUUID->"1206d525-c786-4a80-b92b-351dd5387358"],
Cell[213198, 5306, 13535, 240, 1441, "Output",ExpressionUUID->"0e12ea93-a942-48af-ae1d-8cb9fa8cadae"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[226782, 5552, 201, 4, 85, "Section",ExpressionUUID->"967fbcb0-fe7f-40bc-8afa-110dfd3fc970"],
Cell[CellGroupData[{
Cell[227008, 5560, 543, 14, 165, "Input",ExpressionUUID->"8713ce27-99e5-46bd-8e05-82a112e16533"],
Cell[227554, 5576, 801, 23, 165, "Output",ExpressionUUID->"8de2ca51-f6b3-4d37-95de-e8dba8cca6ae"]
}, Open  ]],
Cell[228370, 5602, 174, 3, 128, "Text",ExpressionUUID->"54c93a6a-90b6-4882-b6fc-49b938d503b5"],
Cell[CellGroupData[{
Cell[228569, 5609, 372, 11, 238, "Input",ExpressionUUID->"552a3ead-cd08-4280-8b2a-102e7f289bee"],
Cell[228944, 5622, 130, 3, 152, "Output",ExpressionUUID->"beda450e-7fad-49f7-a984-1808f916c560"],
Cell[229077, 5627, 132, 3, 152, "Output",ExpressionUUID->"d33c131d-a81b-4fb1-9d13-8cbf22178128"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[229258, 5636, 186, 3, 85, "Section",ExpressionUUID->"b3a9a228-2da8-450b-8400-8040326b8d8f"],
Cell[CellGroupData[{
Cell[229469, 5643, 401, 12, 152, "Input",ExpressionUUID->"e58ca135-9660-416b-b717-c62370415099"],
Cell[229873, 5657, 153, 4, 152, "Output",ExpressionUUID->"771e6afb-5d7d-4a83-b939-96bd89075628"]
}, Open  ]],
Cell[CellGroupData[{
Cell[230063, 5666, 460, 15, 165, "Input",ExpressionUUID->"3ca6b87f-30c0-4296-be74-9e32cefa53ca"],
Cell[230526, 5683, 268, 8, 152, "Output",ExpressionUUID->"31beb3b9-ab02-434b-b706-bdeb4abc0d23"]
}, Open  ]],
Cell[CellGroupData[{
Cell[230831, 5696, 424, 13, 152, "Input",ExpressionUUID->"4624b164-981b-412f-9300-29e6bc07c418"],
Cell[231258, 5711, 293, 8, 152, "Output",ExpressionUUID->"79bdb1fa-fa8a-4551-9b8f-a095b405cc79"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[231600, 5725, 189, 4, 85, "Section",ExpressionUUID->"2c0e32e4-05c2-4d8b-bf4f-a38422a1604f"],
Cell[CellGroupData[{
Cell[231814, 5733, 305, 8, 165, "Input",ExpressionUUID->"8550c007-e6f1-4d49-8414-56c7577d8a9a"],
Cell[232122, 5743, 279, 9, 141, "Output",ExpressionUUID->"d3c727b9-bfa7-4b84-a67b-8b3dba0d602f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[232438, 5757, 481, 16, 165, "Input",ExpressionUUID->"3b5c2308-366a-4656-9c52-27d843465a1b"],
Cell[232922, 5775, 355, 12, 141, "Output",ExpressionUUID->"0c241957-a501-4fbc-badb-a9f6248403cf"]
}, Open  ]],
Cell[CellGroupData[{
Cell[233314, 5792, 328, 10, 165, "Input",ExpressionUUID->"41c03852-6302-42f9-97b5-98bbc4c9714b"],
Cell[233645, 5804, 307, 10, 141, "Output",ExpressionUUID->"16322ea2-ade0-44a9-a2e2-4bf3a80e67e6"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[234001, 5820, 188, 4, 85, "Section",ExpressionUUID->"93729601-a315-4a98-9aad-85223eb938d9"],
Cell[CellGroupData[{
Cell[234214, 5828, 315, 9, 165, "Input",ExpressionUUID->"4d10019d-8e82-48e3-ba58-da3ed2245848"],
Cell[234532, 5839, 308, 10, 152, "Output",ExpressionUUID->"a5e1c0ec-fbb9-451c-b616-fd52fe96a4e2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[234877, 5854, 369, 12, 152, "Input",ExpressionUUID->"e880e88b-5625-40f0-9133-fc3734689d38"],
Cell[235249, 5868, 281, 8, 152, "Output",ExpressionUUID->"eff2628b-8367-42e5-af95-2a37cb76ad8a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[235567, 5881, 298, 9, 165, "Input",ExpressionUUID->"5e09c9d4-95e2-41e4-8367-8687bcef245f"],
Cell[235868, 5892, 385, 12, 152, "Output",ExpressionUUID->"ac1fe86a-9df6-4287-8e96-21cbbecfd9cf"]
}, Open  ]],
Cell[CellGroupData[{
Cell[236290, 5909, 348, 11, 165, "Input",ExpressionUUID->"b534451b-4999-45ba-9cb5-b0f036f79b9a"],
Cell[236641, 5922, 559, 19, 207, "Output",ExpressionUUID->"90a496ff-cd34-46e5-9aab-cc8950725f6f"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[237249, 5947, 221, 3, 85, "Section",ExpressionUUID->"3befe438-a994-4c0d-b797-6e759b2edf24"],
Cell[CellGroupData[{
Cell[237495, 5954, 361, 10, 68, "Input",ExpressionUUID->"cb228cb0-a33d-48e6-b90f-45811ab8c897"],
Cell[237859, 5966, 311, 9, 65, "Output",ExpressionUUID->"a042d608-c758-4835-82ad-7d184812b87a"]
}, Open  ]],
Cell[238185, 5978, 188, 4, 63, "Input",ExpressionUUID->"cf67ee17-4276-4042-bcc8-c84908a2f113"],
Cell[238376, 5984, 184, 4, 63, "Input",ExpressionUUID->"834274ab-3a86-4535-8e42-b7d07af56e6e"],
Cell[CellGroupData[{
Cell[238585, 5992, 571, 17, 68, "Input",ExpressionUUID->"ec146eed-3f3b-4dc7-a583-479019068661"],
Cell[239159, 6011, 394, 13, 86, "Output",ExpressionUUID->"4a1d5a48-1046-438c-a685-2802fe0738b9"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[239602, 6030, 194, 4, 108, "Section",ExpressionUUID->"a4ffdef9-3ebb-4b96-a152-bf053f63cd70"],
Cell[CellGroupData[{
Cell[239821, 6038, 320, 9, 68, "Input",ExpressionUUID->"09e80b31-be4c-4447-a2bc-af4220a57604"],
Cell[240144, 6049, 132, 3, 63, "Output",ExpressionUUID->"9b5ab5e4-aab2-4dc1-95dc-08c0d1938aaa"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[240325, 6058, 212, 4, 108, "Section",ExpressionUUID->"d34f7950-fcf5-4d60-a9de-cba01d2c66ad"],
Cell[CellGroupData[{
Cell[240562, 6066, 441, 12, 68, "Input",ExpressionUUID->"23522bea-ed07-41a0-9d37-450d5764c4f8"],
Cell[241006, 6080, 307, 8, 63, "Output",ExpressionUUID->"a565a5dc-7221-4c66-9895-eb99db7a0e9d"]
}, Open  ]],
Cell[CellGroupData[{
Cell[241350, 6093, 415, 13, 68, "Input",ExpressionUUID->"0d744325-694d-47e3-b61a-3ec755936db3"],
Cell[241768, 6108, 262, 7, 63, "Output",ExpressionUUID->"5b49ff8f-04c7-4b3c-9298-c3e5a1bf51ae"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[242079, 6121, 187, 4, 108, "Section",ExpressionUUID->"7d2047a5-69dd-4276-99f9-524b42b70bb7"],
Cell[242269, 6127, 188, 4, 152, "Input",ExpressionUUID->"955fe60a-9f3a-4ec8-8490-e14a7fdab5ff"]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[242506, 6137, 230, 4, 198, "Subtitle",ExpressionUUID->"2295c1a0-bd01-4c5a-8996-9d55609d6dee"],
Cell[CellGroupData[{
Cell[242761, 6145, 201, 4, 108, "Section",ExpressionUUID->"b4392dd0-a04c-4556-8dec-5b25bc9a1155"],
Cell[CellGroupData[{
Cell[242987, 6153, 538, 17, 165, "Input",ExpressionUUID->"44b52161-d495-4750-98d9-22f2bf93bd56"],
Cell[243528, 6172, 250, 7, 152, "Output",ExpressionUUID->"a0dbedf0-b1b0-4760-abe8-ae61093ca558"]
}, Open  ]],
Cell[CellGroupData[{
Cell[243815, 6184, 730, 23, 163, "Input",ExpressionUUID->"4391df34-00e7-4996-ac25-6bdc63701509"],
Cell[244548, 6209, 355, 10, 152, "Output",ExpressionUUID->"b0699e27-7f43-47e4-ab0d-6b527c31f67b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[244940, 6224, 389, 12, 163, "Input",ExpressionUUID->"718c6804-3c65-4f9a-b9a3-58980ce0892e"],
Cell[245332, 6238, 257, 7, 152, "Output",ExpressionUUID->"5ac7ed78-575b-4886-b285-3c18385bf5c2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[245626, 6250, 368, 11, 165, "Input",ExpressionUUID->"0ad1ecf4-0361-4340-9373-962fe13dde6b"],
Cell[245997, 6263, 223, 6, 152, "Output",ExpressionUUID->"f4fbef89-20e9-4cca-bade-46ce8a007a9f"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[246269, 6275, 207, 4, 85, "Section",ExpressionUUID->"e4b6611c-e113-40a9-b8b7-82165b0e1885"],
Cell[246479, 6281, 295, 6, 152, "Input",ExpressionUUID->"32c1ca71-9f3d-460f-ae53-e4f8bf5201ec"],
Cell[CellGroupData[{
Cell[246799, 6291, 338, 10, 152, "Input",ExpressionUUID->"54303b67-a94e-4018-a98e-cb3bbdc85758"],
Cell[247140, 6303, 251, 8, 207, "Output",ExpressionUUID->"2166a235-6893-4c22-9dbe-54bbf3139d15"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[247440, 6317, 215, 4, 85, "Section",ExpressionUUID->"802126c7-7aa1-495b-8fdc-4a13e5dce03d"],
Cell[CellGroupData[{
Cell[247680, 6325, 432, 12, 61, "Input",ExpressionUUID->"5284f09b-ef09-4647-9931-dec486007c0a"],
Cell[248115, 6339, 201, 4, 63, "Output",ExpressionUUID->"acaedab6-41b3-4e35-9ca3-5a273d6708e4"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[248365, 6349, 230, 5, 108, "Section",ExpressionUUID->"5d391816-8604-4cf5-ba66-c4c2e4989125"],
Cell[CellGroupData[{
Cell[248620, 6358, 344, 9, 152, "Input",ExpressionUUID->"e9076a2b-c370-46c8-b9d0-4476aa0e0e4c"],
Cell[248967, 6369, 132, 3, 152, "Output",ExpressionUUID->"9499865b-34b3-4455-b86f-2216eb861420"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[249148, 6378, 207, 4, 85, "Section",ExpressionUUID->"93619bad-95b7-470d-9b39-42823526f139"],
Cell[249358, 6384, 652, 15, 212, "Input",ExpressionUUID->"906a62cd-cbc9-410d-8a91-7b763883ab96"]
}, Closed]],
Cell[CellGroupData[{
Cell[250047, 6404, 305, 5, 145, "Section",ExpressionUUID->"1439a672-fb9a-4729-b771-58bb305f65de"],
Cell[CellGroupData[{
Cell[250377, 6413, 314, 9, 165, "Input",ExpressionUUID->"9c0845ec-4699-4f3f-b555-9529faf3fed6"],
Cell[250694, 6424, 221, 7, 157, "Output",ExpressionUUID->"f2ccfae8-b08f-483b-992a-9f1e99e13ce0"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[250964, 6437, 200, 4, 85, "Section",ExpressionUUID->"6cab994a-8b2f-4d73-bb4f-ab9269b5554a"],
Cell[CellGroupData[{
Cell[251189, 6445, 831, 26, 238, "Input",ExpressionUUID->"725f3164-0640-4cb2-b7ec-fc77cdc9a374"],
Cell[252023, 6473, 12709, 228, 981, "Output",ExpressionUUID->"60904b97-5581-4bc8-aa9e-a27a4cd3881d"]
}, Open  ]],
Cell[CellGroupData[{
Cell[264769, 6706, 894, 25, 222, "Input",ExpressionUUID->"02f9681a-f596-4088-8933-33897ea1d355"],
Cell[265666, 6733, 19727, 343, 981, "Output",ExpressionUUID->"1c1852ac-9511-40b5-9120-4e350fa6215e"]
}, Open  ]],
Cell[285408, 7079, 177, 3, 128, "Text",ExpressionUUID->"c8dda2d5-4c4e-4973-a8c1-fc4b2dab1246"]
}, Closed]],
Cell[CellGroupData[{
Cell[285622, 7087, 306, 5, 145, "Section",ExpressionUUID->"dc0c9aef-c667-45a1-a823-16edb0880bfa"],
Cell[CellGroupData[{
Cell[285953, 7096, 414, 10, 157, "Input",ExpressionUUID->"546f74b5-46a1-4a01-844c-d68c4a680dfe"],
Cell[286370, 7108, 227, 7, 157, "Output",ExpressionUUID->"240867b0-ddf6-40ea-b202-9213945a8e0e"]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[286658, 7122, 245, 5, 198, "Subtitle",ExpressionUUID->"b82dadbc-76da-43d0-b822-735625e8b7fe"],
Cell[CellGroupData[{
Cell[286928, 7131, 201, 4, 108, "Section",ExpressionUUID->"78fd53a4-bfe2-4e41-9c48-20df89fce5ee"],
Cell[CellGroupData[{
Cell[287154, 7139, 1190, 29, 395, "Input",ExpressionUUID->"cf891e3a-6403-4519-8c72-3f63f9c25700"],
Cell[288347, 7170, 302, 8, 152, "Output",ExpressionUUID->"2fa51243-9fcc-47e3-9825-abbe68469343"],
Cell[288652, 7180, 279, 7, 152, "Output",ExpressionUUID->"d0a34bac-244d-4d1b-beee-d20ee9f51a41"],
Cell[288934, 7189, 18910, 416, 933, "Output",ExpressionUUID->"df8c3aa6-9f4e-41ee-b1c3-e2817ff9ec9e"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[307893, 7611, 208, 4, 85, "Section",ExpressionUUID->"c9eeb498-6029-4bb3-9d41-3ec002e63c95"],
Cell[CellGroupData[{
Cell[308126, 7619, 238, 5, 152, "Input",ExpressionUUID->"6964acf8-168c-4efa-b1dc-e80a1107bf6b"],
Cell[308367, 7626, 150, 3, 152, "Output",ExpressionUUID->"577a69cf-1770-4bad-aba6-cdd7c754783a"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[308566, 7635, 223, 4, 85, "Section",ExpressionUUID->"771e7b1f-59c8-40f9-a188-d0e1c54b26fb"],
Cell[CellGroupData[{
Cell[308814, 7643, 247, 5, 152, "Input",ExpressionUUID->"26eb83ba-b10a-48a4-818f-45aa95d952d8"],
Cell[309064, 7650, 150, 3, 152, "Output",ExpressionUUID->"a169061d-abc9-4ae7-86f4-f25422d131b7"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[309263, 7659, 215, 4, 85, "Section",ExpressionUUID->"ca38f398-4412-4794-8c98-be4edd76e0e5"],
Cell[CellGroupData[{
Cell[309503, 7667, 191, 4, 152, "Input",ExpressionUUID->"59709651-6f5c-460f-84c0-53e6a1633a2e"],
Cell[309697, 7673, 131, 3, 152, "Output",ExpressionUUID->"634f4bb7-8e17-4162-8b87-11aab43bddbd"]
}, Open  ]]
}, Closed]]
}, Open  ]]
}, Open  ]]
}
]
*)