Algebra/Unit 6 Quiz 1/Objective 1 Rewrite 1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Rewrite«/mi»«mo»§#160;«/mo»«mo»#«/mo»«msup»«mi»a«/mi»«mfrac bevelled=¨true¨»«mrow»«mo mathvariant=¨italic¨»#«/mo»«mi mathvariant=¨italic¨»m«/mi»«/mrow»«mrow»«mo mathvariant=¨italic¨»#«/mo»«mi mathvariant=¨italic¨»n«/mi»«/mrow»«/mfrac»«/msup»«mo mathvariant=¨italic¨»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»radical«/mi»«mo»§#160;«/mo»«mi»notation«/mi»«mo».«/mo»«mo»§#160;«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #a#m#n]]> #a#n#m]]> #b#n]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>^</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mo>#</mo><msup><mi>a</mi><mrow><mo>#</mo><mi>m</mi></mrow></msup></mrow><mrow><mo>#</mo><mi>n</mi></mrow></mroot></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mroot><mrow><mo>#</mo><mi>a</mi></mrow><mrow><mo>#</mo><mi>n</mi></mrow></mroot></mfenced><mrow><mo>#</mo><mi>m</mi></mrow></msup></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mo>#</mo><mi>b</mi></mrow><mrow><mo>#</mo><mi>n</mi></mrow></mroot></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_literal" correctAnswer="1"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="equivalent_literal" correctAnswer="2"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rewrite 2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Rewrite«/mi»«mo»§#160;«/mo»«mroot»«mrow»«mo»#«/mo»«msup»«mi»a«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mroot»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»rational«/mi»«mo»§#160;«/mo»«mi»exponent«/mi»«mo»§#160;«/mo»«mi»notation«/mi»«mo».«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #a#m#n]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><msup><mi>a</mi><mfrac><mrow><mo>#</mo><mi>m</mi></mrow><mrow><mo>#</mo><mi>n</mi></mrow></mfrac></msup></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rewrite 3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Rewrite«/mi»«mo»§#160;«/mo»«msup»«mfenced»«mroot»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mroot»«/mfenced»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»rational«/mi»«mo»§#160;«/mo»«mi»exponent«/mi»«mo»§#160;«/mo»«mi»notation«/mi»«mo».«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #a#m#n]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><msup><mi>a</mi><mfrac><mrow><mo>#</mo><mi>m</mi></mrow><mrow><mo>#</mo><mi>n</mi></mrow></mfrac></msup></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Algebra/Unit 6 Quiz 1/Objective 2 Evaluate 1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Evaluate«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»Round«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»nearest«/mi»«mo»§#160;«/mo»«mi»hundredth«/mi»«mo»§#160;«/mo»«mi»when«/mi»«mo»§#160;«/mo»«mi»necessary«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»#«/mo»«msup»«mi mathvariant=¨normal¨»a«/mi»«mfrac bevelled=¨true¨»«mrow»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/mrow»«/mfrac»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msup><mi>a</mi><mfrac><mi>m</mi><mi>n</mi></mfrac></msup><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>round</mi><mo>(</mo><mi>s</mi><mo>*</mo><mn>100</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_literal"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Algebra/Unit 6 Quiz 1/Objective 3 Solve 1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Solve«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»Round«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»nearest«/mi»«mo»§#160;«/mo»«mi»hundredth«/mi»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»necessary«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Put«/mi»«mo»§#160;«/mo»«mi»all«/mi»«mo»§#160;«/mo»«mi»solutions«/mi»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»double«/mi»«mo»§#160;«/mo»«mi»brackets«/mi»«mo».«/mo»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow/»«/mfenced»«/mfenced»«mspace linebreak=¨newline¨/»«mi»For«/mi»«mo»§#160;«/mo»«mi»example«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mo»§#160;«/mo»«mi»would«/mi»«mo»§#160;«/mo»«mi»look«/mi»«mo»§#160;«/mo»«mi»like«/mi»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mfenced»«mo».«/mo»«mo»§#160;«/mo»«mi»If«/mi»«mo»§#160;«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»have«/mi»«mo»§#160;«/mo»«mi»two«/mi»«mo»§#160;«/mo»«mi»answers«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»like«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»and«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»then«/mi»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«/mrow»«/mfenced»«mo»,«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo».«/mo»«mo»§#160;«/mo»«mi»Put«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»smaller«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mo»§#160;«/mo»«mi»first«/mi»«mo»!«/mo»«mspace linebreak=¨newline¨/»«mi»If«/mi»«mo»§#160;«/mo»«mi»there«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi»no«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»use«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»editor«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»type«/mi»«mo»§#160;«/mo»«mo»§#8709;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»can«/mi»«mo»§#160;«/mo»«mi»find«/mi»«mo»§#160;«/mo»«mi»this«/mi»«mspace linebreak=¨newline¨/»«mi»in«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»§#160;«/mo»«mi»menu«/mi»«mo»)«/mo»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 3.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>solve</mi><mo>(</mo><msup><mi>x</mi><mi>n</mi></msup><mo>+</mo><mi>c</mi><mo>=</mo><mi>s</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Solve 2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Solve«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»Round«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»nearest«/mi»«mo»§#160;«/mo»«mi»hundredth«/mi»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»necessary«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»a«/mi»«msup»«mtext»x«/mtext»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mtext»-«/mtext»«mo»#«/mo»«mi»c«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Put«/mi»«mo»§#160;«/mo»«mi»all«/mi»«mo»§#160;«/mo»«mi»solutions«/mi»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»double«/mi»«mo»§#160;«/mo»«mi»brackets«/mi»«mo».«/mo»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow/»«/mfenced»«/mfenced»«mspace linebreak=¨newline¨/»«mi»For«/mi»«mo»§#160;«/mo»«mi»example«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mo»§#160;«/mo»«mi»would«/mi»«mo»§#160;«/mo»«mi»look«/mi»«mo»§#160;«/mo»«mi»like«/mi»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mfenced»«mo».«/mo»«mo»§#160;«/mo»«mi»If«/mi»«mo»§#160;«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»have«/mi»«mo»§#160;«/mo»«mi»two«/mi»«mo»§#160;«/mo»«mi»answers«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»like«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»and«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»then«/mi»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»,«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»If«/mi»«mo»§#160;«/mo»«mi»there«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi»no«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»use«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»editor«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»type«/mi»«mo»§#160;«/mo»«mo»§#8709;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»can«/mi»«mo»§#160;«/mo»«mi»find«/mi»«mo»§#160;«/mo»«mi»this«/mi»«mspace linebreak=¨newline¨/»«mi»in«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»§#160;«/mo»«mi»menu«/mi»«mo»)«/mo»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 3.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>n</mi></msup><mo>-</mo><mi>c</mi><mo>=</mo><mi>s</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Solve 3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Solve«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»Round«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»nearest«/mi»«mo»§#160;«/mo»«mi»hundredth«/mi»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»necessary«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Put«/mi»«mo»§#160;«/mo»«mi»all«/mi»«mo»§#160;«/mo»«mi»solutions«/mi»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»double«/mi»«mo»§#160;«/mo»«mi»brackets«/mi»«mo».«/mo»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow/»«/mfenced»«/mfenced»«mspace linebreak=¨newline¨/»«mi»For«/mi»«mo»§#160;«/mo»«mi»example«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mo»§#160;«/mo»«mi»would«/mi»«mo»§#160;«/mo»«mi»look«/mi»«mo»§#160;«/mo»«mi»like«/mi»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mfenced»«mo».«/mo»«mo»§#160;«/mo»«mi»If«/mi»«mo»§#160;«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»have«/mi»«mo»§#160;«/mo»«mi»two«/mi»«mo»§#160;«/mo»«mi»answers«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»like«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»and«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»then«/mi»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»,«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»If«/mi»«mo»§#160;«/mo»«mi»there«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi»no«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»use«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»editor«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»type«/mi»«mo»§#160;«/mo»«mo»§#8709;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»can«/mi»«mo»§#160;«/mo»«mi»find«/mi»«mo»§#160;«/mo»«mi»this«/mi»«mspace linebreak=¨newline¨/»«mi»in«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»§#160;«/mo»«mi»menu«/mi»«mo»)«/mo»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 3.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>c</mi><msup><mo>)</mo><mi>n</mi></msup><mo>=</mo><mi>s</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Solve 4 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Solve«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»Round«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»nearest«/mi»«mo»§#160;«/mo»«mi»hundredth«/mi»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»necessary«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Put«/mi»«mo»§#160;«/mo»«mi»all«/mi»«mo»§#160;«/mo»«mi»solutions«/mi»«mo»§#160;«/mo»«mi»in«/mi»«mo»§#160;«/mo»«mi»double«/mi»«mo»§#160;«/mo»«mi»brackets«/mi»«mo».«/mo»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow/»«/mfenced»«/mfenced»«mspace linebreak=¨newline¨/»«mi»For«/mi»«mo»§#160;«/mo»«mi»example«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»if«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mo»§#160;«/mo»«mi»would«/mi»«mo»§#160;«/mo»«mi»look«/mi»«mo»§#160;«/mo»«mi»like«/mi»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mfenced»«mo».«/mo»«mo»§#160;«/mo»«mi»If«/mi»«mo»§#160;«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»have«/mi»«mo»§#160;«/mo»«mi»two«/mi»«mo»§#160;«/mo»«mi»answers«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»like«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»and«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»then«/mi»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»,«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»If«/mi»«mo»§#160;«/mo»«mi»there«/mi»«mo»§#160;«/mo»«mi»is«/mi»«mo»§#160;«/mo»«mi»no«/mi»«mo»§#160;«/mo»«mi»solution«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»use«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»editor«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»type«/mi»«mo»§#160;«/mo»«mo»§#8709;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»you«/mi»«mo»§#160;«/mo»«mi»can«/mi»«mo»§#160;«/mo»«mi»find«/mi»«mo»§#160;«/mo»«mi»this«/mi»«mspace linebreak=¨newline¨/»«mi»in«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»§#160;«/mo»«mi»menu«/mi»«mo»)«/mo»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>*</mo><mroot><mi>a</mi><mi>n</mi></mroot></mrow></mfenced><mi>m</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Simplify 2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Simplify«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mroot»«mrow»«mo mathvariant=¨italic¨»#«/mo»«mi mathvariant=¨italic¨»a«/mi»«/mrow»«mn mathvariant=¨italic¨»3«/mn»«/mroot»«mo»§#183;«/mo»«mroot»«mrow»«mo»#«/mo»«mi mathvariant=¨normal¨»b«/mi»«/mrow»«mn»3«/mn»«/mroot»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mroot><mi>a</mi><mn>3</mn></mroot><mo>*</mo><mroot><mi>b</mi><mn>3</mn></mroot></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Simplify 3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Simplify«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»a«/mi»«mroot»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mroot»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mroot»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mroot»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mroot><mi>b</mi><mi>n</mi></mroot><mo>+</mo><mi>c</mi><mo>*</mo><mroot><mi>b</mi><mi>n</mi></mroot></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Simplify 4 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Simplify«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mroot»«mrow»«mo»#«/mo»«mi»c«/mi»«mo»#«/mo»«mi»x«/mi»«mo»#«/mo»«mi»y«/mi»«mo»#«/mo»«mi»z«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mroot»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>b</mi><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>n</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><msup><mi>z</mi><mrow><mn>3</mn><mo>*</mo><mi>n</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>simplify</mi><mo>(</mo><mroot><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>*</mo><mi>z</mi></mrow><mi>n</mi></mroot><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Simplify 5 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Simplify«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»a«/mi»«msqrt»«mo»#«/mo»«mi»b«/mi»«/msqrt»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«msqrt»«mo»#«/mo»«mi»d«/mi»«/msqrt»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>o</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mfrac><mi>m</mi><mi>n</mi></mfrac><mo>-</mo><mfrac><mi>o</mi><mi>p</mi></mfrac></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>a</mi><mi>b</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Simplify 7 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Simplify«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»#«/mo»«msup»«mi»a«/mi»«mfrac bevelled=¨true¨»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mfrac»«/msup»«mo»§#183;«/mo»«mo»#«/mo»«msup»«mi»a«/mi»«mfrac bevelled=¨true¨»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/msup»«/math»

]]> 2.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>o</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mfrac><mi>m</mi><mi>n</mi></mfrac><mo>+</mo><mfrac><mi>o</mi><mi>p</mi></mfrac></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>a</mi><mi>b</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>