Question 1

Find a function that models the volume V of a box with height x , length 6 x and width x + 8.
A) V(x) = (6 x )( x + 8)
B) V(x) = ( x + 6 x ) ( x + 8)
C) V(x) = x (6 x + x + 8)
D) V(x) = x (6 x )( x + 8)
E) V(x) = x + (6 x ) + ( x + 8)

Accepted Answer

The volume of a box is found by multiplying its height, length, and width. Therefore, V(x) = x * (6x) * (x + 8), which matches choice D.

Question 2

Find a function that models the area A of a rectangle whose length is 9 ft more than twice its width x .
A) A(x) = x (9 + 2 x )
B) A(x) = x (9 x + 2)
C) A(x) = (9 + 2) x
D) A(x) = x (9 + x )
E) A(x) = 9 + 2 x

Accepted Answer

The area of a rectangle is given by the formula A = length * width. If the length is 9 ft more than twice its width, then the length can be expressed as 9 + 2x, where x is the width. Therefore, the area A as a function of x is A(x) = x(9 + 2x).

Question 3

For the function  , find the local maximum value of f . 
A) 1.6
B) -0.6
C) 0
D) 1
E) 0.25

Accepted Answer

The answer of For the function  , find the...

Question 4

For the function  , find the intervals on which  is increasing. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of For the function  , find the...

Question 5

Which of the following formulas express the average score for 4 exams?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following formulas express the...

Question 6

The table below shows the salary values for a job based on the number of years x worked. Find a linear model for the salary value S(x) as a function of the number of years x worked.

A) S(x) = 3000 x
B) S(x) = 36000 + 1000 x
C) S(x) = 1000 x
D) S(x) = 36000 + 3000 x
E) S(x) = 33000 + 1000 x

Accepted Answer

The answer of The table below shows the salary values...

Question 7

Does the equation 3 x - 5 y = 4 define the variable y as a function of the variable x ?

Accepted Answer

To solve for y as a function of x, we want to isolate y on one side of the equation. This can be done by adding 5y to both sides and then dividing by 5:

3x - 5y = 4 
3x = 5y + 4 
y = (3/5)x - (4/5)

So we have expressed y in terms of x, and hence y is a function of x.

Question 8

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the approximate number of rabbits on day 30? 
A) 40
B) 15
C) 10
D) 30
E) 83

Accepted Answer

The answer of A population of rabbits was tracked over...

Question 9

Solve the equation  for  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the equation  for  .
A)...

Question 10

The amount of an investment A after 36 months can be modeled by the formula  where P is the initial investment amount and r % is the interest rate. If Marcus invests $2000 in this account with an interest rate of 3.7500%, how much money will be in the account at the end of 36 months? (Rounded to the nearest hundredths)
A) $7,526.65
B) $2,006.25
C) $2000
D) $72,225.00
E) $2,237.75

Accepted Answer

The answer of The amount of an investment A after...

Question 11

The graphs of  and  are shown below. Find the value(s) of x for which  . 
A) -2.4 and 0.8
B) 0.8
C) -2.4 and -11.7
D) -2.4
E) -11.7 and 1.3

Accepted Answer

The answer of The graphs of  and  are...

Question 12

Does the equation x = ( y  6)  + 3 define the variable y as a function of the variable x ?

Accepted Answer

The answer of Does the equation x = ( y...

Question 13

Given the table below, is the variable y a function of the variable x ?

Accepted Answer

The answer of Given the table below, is the variable...

Question 14

A membership to a local fitness club costs $59 per month plus $1.15 for each hour spent in the club. Find a linear model for the monthly cost of membership C(x) as a function of the number of hours x spent in the club.
A) C(x) = 59 x + 1.15
B) C(x) = 1.15 x
C) C(x) = 59 x
D) C(x) = 59 + 1.15 x
E) C(x) = (59 + 1.15 )x

Accepted Answer

The monthly cost consists of a fixed cost of $59 and a variable cost of $1.15 per hour spent in the club. This can be represented by the equation C(x) = 59 + 1.15x, where x is the number of hours spent in the club. Therefore, the best choice is D.

Question 15

Given the table below, is the variable y a function of the variable x ?

Accepted Answer

The answer of Given the table below, is the variable...

Question 16

The graphs of  and  are shown below. Find the value(s) of x for which  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The graphs of  and  are...

Question 17

For the function  , find the local minimum value of f . 
A) -0.6
B) -0.185
C) -1
D) 1
E) 1.6

Accepted Answer

Without the actual function given, it is impossible to determine the value of the local minimum. Therefore, none of the answer choices can be definitively chosen.

Question 18

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the minimum number of rabbits during this time? 
A) 20
B) 37
C) 83
D) 5
E) 15

Accepted Answer

The minimum number of rabbits during the 55-day period is the lowest point on the graph, which is at the value of 5. Therefore, the correct answer is D) 5.

Question 19

The resistance R of a wire (in ohms) is related to its length L (in meters) and its diameter d (in meters) by the formula  . Find a formula for d .
A) 
B) 
C) 
D) 
E)

Accepted Answer

Rearranging the formula, we get d = 2*sqrt(R/(pi*L)). Therefore, the correct choice is B.

Question 20

Find a formula that models the speed s of a car that travels d miles in t minutes.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a formula that models the speed...

Quiz 1: Data, Functions, and Models

Find a function that models the volume V of a box with height x , length 6 x and width x + 8.

Find a function that models the area A of a rectangle whose length is 9 ft more than twice its width x .

For the function , find the local maximum value of f .

For the function , find the intervals on which is increasing.

Which of the following formulas express the average score for 4 exams?

The table below shows the salary values for a job based on the number of years x worked. Find a linear model for the salary value S(x) as a function of the number of years x worked.

Does the equation 3 x - 5 y = 4 define the variable y as a function of the variable x ?

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the approximate number of rabbits on day 30?

Solve the equation for .

The graphs of and are shown below. Find the value(s) of x for which .

Does the equation x = ( y 6) + 3 define the variable y as a function of the variable x ?

Given the table below, is the variable y a function of the variable x ?

A membership to a local fitness club costs $59 per month plus $1.15 for each hour spent in the club. Find a linear model for the monthly cost of membership C(x) as a function of the number of hours x spent in the club.

Given the table below, is the variable y a function of the variable x ?

The graphs of and are shown below. Find the value(s) of x for which .

For the function , find the local minimum value of f .

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the minimum number of rabbits during this time?

The resistance R of a wire (in ohms) is related to its length L (in meters) and its diameter d (in meters) by the formula . Find a formula for d .

Find a formula that models the speed s of a car that travels d miles in t minutes.