AnswersPrecalculusModeling with Rational Functions

Modeling with Rational Functions — Quiz Answers

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The function y is equal to 60 over x relates y , the time in hours that it takes Michael to travel to his grandparents’ house, to x , his average speed in miles per hour. What does the number 60 in the function represent?

A
the distance, in miles, that must be traveled to get to Michael’s grandparents’ house
B
the fuel, in gallons, that is used to get to Michael’s grandparents’ house
C
the rate, in miles per hour, that Michael travels to get to his grandparents’ house
D
the time, in hours, that it takes to get to Michael’s grandparents’ house
2
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Sarah plans to sell homemade birdhouses at the local craft fair. She spent 90 dollars on new tools and estimates that she spends 6 dollars in materials for each birdhouse. Which rational function models the average cost per birdhouse, y , in dollars of building x birdhouses?

A
y is equal to 90 over x
B
y is equal to the fraction with numerator 90 plus 6 x and denominator x
C
y is equal to 90 over 6 x
D
y is equal to the fraction with numerator 90 times open paren x plus 6 close paren and denominator x
3

The function f of x is equal to the fraction with numerator 600 plus 2 x and denominator x yields the average cost in dollars for a company to produce x calendars. Which statement best fits the situation modeled by the function?

A
The company spends 600 dollars on a new computer and printer before beginning the project.
B
The company will sell the calendars for 2 point 0 0 dollars each.
C
The company takes 600 photos before selecting which ones to use for its calendars.
D
The company expects to sell 600 calendars each month.
4

Frank joined a fitness club. He paid a 50 dollars registration fee, and dues are 12 dollars per month. Which expression can be used to find the average monthly cost of an x -month membership at the club?

A
y is equal to the fraction with numerator 50 x plus 12 and denominator x
B
y is equal to the fraction with numerator 50 plus 12 x and denominator x
C
y is equal to the fraction with numerator open paren 50 plus 12 close paren times x and denominator x
D
y is equal to the fraction with numerator 50 plus 12 and denominator x
6

The function f of x is equal to the fraction with numerator 80 comma 000 plus 0 point 2 x and denominator x yields the average cost in dollars for a company to produce x copies of a comic book. Which statement best fits the situation modeled by the function?

A
The company spends 20 cents on materials to produce each copy.
B
The company earns 20 cents as profit from each copy sold.
C
The company earns 20 percent of the issue price as profit from each copy sold.
D
The company spends 20 percent of the issue price on materials to produce each copy.
7

A pharmacist has 80 milliliters of a 25 percent saline solution. Which expression can be used to find the percentage concentration of the final solution if she adds x milliliters of a 10 percent saline solution?

A
y is equal to the fraction with numerator 0 point 2 5 repeating 80 plus 0 point 1 x and denominator x times 100
B
y is equal to the fraction with numerator 0 point 2 5 repeating 80 plus 0 point 1 x and denominator 80 plus x times 100
C
y is equal to the fraction with numerator 0 point 2 5 repeating 80 plus 0 point 1 x and denominator 80 times 100
D
y is equal to the fraction with numerator 0 point 2 5 repeating 80 plus 0 point 1 x and denominator 80 plus 0 point 1 x times 100
8

Craig bought a treadmill for 400 dollars He estimates that the annual costs to maintain the machine will be 36 dollars Which rational function yields the average annual cost in dollars of owning the treadmill for x years?

A
f of x is equal to the fraction with numerator 400 x plus 36 and denominator x
B
f of x is equal to the fraction with numerator 400 plus 36 x and denominator x
C
f of x is equal to the fraction with numerator 400 x plus 36 x and denominator x
D
f of x is equal to the fraction with numerator 400 plus 36 and denominator x

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