Pre-Calc/Chapter 1: Functions and Graphs/1.7 Modeling with Functions Alcohol Mixture How many liters of a 10% alcohol solution must be mixed with #a liters of a 80% solution to get a 30% solution? Round to the nearest tenth of a liter.

]]> 1.0000000 0.3333333 0 0 #answer]]> Nice work!

]]> 1.0000000 0.3333333 0 0 #answer]]> Great job!

]]> 1.0000000 0.3333333 0 0 #answer]]> Nice work!

]]> 1.0000000 0.3333333 0 true Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> A rectangular building lot is #a times as long as it is wide. Find a function to represent its area A in terms of the width w.

]]> A=#a w^2 A poster is #b inches longer than it is wide. Find a function to represent its area A in terms of the width w.

]]> A=#b w + w^2 A height of a cylinder is #c times its radius. Find a function to represent its Volume V in terms of the radius r.

]]> V=3.14*#c*r^2 A=(#a+ w)^2 A=#b w + #b w^2 <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>4</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>8</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>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><options><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="casSession"/></localData></question> Max Volume of Box (needs work) A square of side x inches is cut out of each corner of a #a in. by #b in. piece of cardboard, and the sides are folded up to form an open-topped box. Use your graphing calculator to determine the dimensions of the cut-out squares that will produce the box of maximum volume. Round to the nearest tenth.
(Hint: you will first need to write the volume of the box V as a function of x.)

]]> 1.0000000 0.3333333 0 0 #answer]]> Great job!

]]> 1.0000000 0.3333333 0 0 #answer]]> Nice work.

]]> 1.0000000 0.3333333 0 0 #answer]]> Nice work!

]]> 1.0000000 0.3333333 0 0 0 abc 0 .02*{a}/.04 0.1 1 1 1 Great job!

]]> 0 0.1000000 3 0 private a calculatedsimple uniform 1.0 10.0 1 20 1 5.7 2 2.3 3 9.7 4 2.6 5 4.8 6 1.9 7 3.5 8 4.8 9 5.7 10 3.9 11 8.3 12 4.8 13 8.5 14 2.7 15 4.9 16 4.5 17 6.8 18 7.5 19 2.6 20 4.5 20 Solve the problem. Anne and Nancy use a metal alloy that is 24.34% copper ... Solve the problem.

Anne and Nancy use a metal alloy that is 24.34% copper to make jewelry. How many ounces of a 22% alloy must be mixed with a 28% alloy to form 100 ounces of the desired alloy?]]> 1.0000000 0.3333333 0 true true abc 61 ounces Correct 39 ounces Incorrect 44 ounces Incorrect 63 ounces Incorrect Solve the problem. How many liters of a 10% alcohol solution must be mixed... Solve the problem.

How many liters of a 10% alcohol solution must be mixed with 50 liters of a 80% solution to get a 30% solution?]]> 1.0000000 0.3333333 0 true true abc 12.5 L Incorrect 17.5 L Incorrect 175 L Incorrect 125 L Correct Solve the problem. In a chemistry class, 9 liters of a 4% silver iodide ... Solve the problem.

In a chemistry class, 9 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?]]> 1.0000000 0.3333333 0 true true abc 9.0 L Incorrect 3.5 L Incorrect 4.5 L Correct 5.5 L Incorrect Solve the problem. Sue invested $10,000, part at 5.1% annual interest and ... Solve the problem.

Sue invested $10,000, part at 5.1% annual interest and the balance at 7.9% annual interest. How much is invested at each rate if a 1-year interest payment is

]]> 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 1.0000000 0.3333333 0 true true abc $4040 at 5.1% and $5960 at 7.9% Correct $4140 at 5.1% and $5860 at 7.9% Incorrect $3940 at 5.1% and $5140 at 7.9% Incorrect $5960 at 5.1% and $4040 at 7.9% Incorrect Swimming Pool Dimensions A construction company builds a swimming pool with a perimeter of #a m. The length is 5 m more than the width. Find the dimensions of the swimming pool to the nearest meter.

]]> 1.0000000 0.3333333 0 0 Width= #widLength= #len]]> Correct!

]]> <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><mo>{</mo><mn>46</mn><mo>,</mo><mo> </mo><mn>50</mn><mo>,</mo><mo> </mo><mn>54</mn><mo>,</mo><mo> </mo><mn>58</mn><mo>,</mo><mo> </mo><mn>62</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wid</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mn>10</mn></mrow><mn>4</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>len</mi><mo>=</mo><mi>wid</mi><mo>+</mo><mn>5</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>t</mi><mi>h</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>w</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mspace linebreak="newline"/><mi>L</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>g</mi><mi>t</mi><mi>h</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>l</mi><mi mathvariant="normal">e</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Use an equation to solve the problem.A tire of a moving bicycle has radius ... Use an equation to solve the problem.

A tire of a moving bicycle has radius 15 inches. If the tire is making 1.8 rotations per second, find the bicycle's speed in miles per hour.]]> 1.0000000 0.3333333 0 true true abc 9.6 mph Correct 11.1 mph Incorrect 10.4 mph Incorrect 5.4 mph Incorrect Use an equation to solve the problem.A construction company builds a swimming... Use an equation to solve the problem.

A construction company builds a swimming pool with a perimeter of 54 m. The length is 5 m more than the width. Find the dimensions of the swimming pool?]]> 1.0000000 0.3333333 0 true true abc 16 m × 5 m Incorrect 21 m × 11 m Incorrect 16 m × 11 m Correct 11 m × 11 m Incorrect Use an equation to solve the problem.A square of side x inches is cut out of ... Use an equation to solve the problem.

A square of side x inches is cut out of each corner of an 8 in. by 12 in. piece of cardboard, and the sides are folded up to form an open-topped box. Use your graphing calculator to determine the dimensions of the cut-out squares that will produce the box of maximum volume.
(Hint: you will first need to write the volume of the box V as a function of x.)]]> 1.0000000 0.3333333 0 true true abc 1.4 inches by 1.4 inches Incorrect 1.8 inches by 1.8 inches Incorrect 1.7 inches by 1.7 inches Incorrect 1.6 inches by 1.6 inches Correct Write a mathematical expression for the quantity described verbally.A salary ... Write a mathematical expression for the quantity described verbally.

A salary after a 4.7% increase, if the original salary is x dollars]]> 1.0000000 0.3333333 0 true true abc 1.047x Correct 4.7x Incorrect 5.7x Incorrect 0.047x Incorrect Write a mathematical expression for the quantity described verbally.The ... Write a mathematical expression for the quantity described verbally.

The revenue when each item sells for $25,000.]]> 1.0000000 0.3333333 0 true true abc 25,000x Correct 25,000 - x Incorrect 25,000 + x Incorrect x - 25,000 Incorrect Write a mathematical expression for the quantity described verbally.The total... Write a mathematical expression for the quantity described verbally.

The total cost if $20,000 plus $3.25 for each item produced.]]> 1.0000000 0.3333333 0 true true abc $(20,000 - 3.25x) Incorrect $(20,000 + 3.25)x Incorrect $(20,000x + 3.25) Incorrect $(20,000 + 3.25x) Correct