Question 1

The research and development department of an automobile manufacturer has determined that when a driver is required to stop quickly to avoid an accident, the distance (in feet) the car travels during the driver's reaction time is given by  , where x is the speed of the car in miles per hour.The distance (in feet) traveled while the driver is braking is given by  .Find the function that represents the total stopping distance T. ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The research and development department of an...

Question 2

​Find  and the domain of the composite function. ​  ​
A)  Domain of  : all real numbers x except 
B)  Domain of  : all real numbers x except 
C)  Domain of  : all real numbers x except 
D)  Domain of  : all real numbers x except 
E)  Domain of  : all real numbers x except

Accepted Answer

The answer of ​Find  and the domain of the...

Question 3

Find  and the domain of the composite function. ​  ​
A)  Domain of  : all real numbers x
B)  Domain of  : all real numbers x
C)  Domain of  : all real numbers x
D)  Domain of  : all real numbers x
E)  Domain of  : all real numbers x

Accepted Answer

The answer of Find  and the domain of the...

Question 4

From 2003 through 2008, the sales  (in thousands of dollars) for one of two restaurants owned by the same parent company can be modeled by ​  ​
Where t = 3 represents 2003.During the same six-year period, the sales  (in thousands of dollars) for the second restaurant can be modeled by
​  ​
Write a function  that represents the total sales of the two restaurants owned by the same parent company.
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of From 2003 through 2008, the sales ...

Question 5

Find  and the domain of the composite function. ​  ​
A)  Domain of  : all real numbers x
B)  Domain of  : all real numbers x
C)  Domain of  : all real numbers x
D)  Domain of  : all real numbers x
E)  Domain of  : all real numbers x

Accepted Answer

These are two different composite functions. The first one has "_c915_" in the middle while the second one has "_c914_". This means that they have different values at the specific point where the underscore is. Therefore, we can only determine the domain of the second function, which is all real numbers x.

Question 6

Find  and the domain of the composite function. ​  ​
A)  Domain of  : all real numbers x
B)  Domain of  : all real numbers x
C)  Domain of  : all real numbers x
D)  Domain of  : all real numbers x
E)  Domain of  : all real numbers x

Accepted Answer

The answer of Find  and the domain of the...

Question 7

The weekly cost C of producing units x in a manufacturing process is given by  .The number of units x produced in t hours is given by  . ​
Find the cost of the units produced in 6 hours.
​
A)11,855
B)11,850
C)11,846
D)13,350
E)11,854

Accepted Answer

The answer of The weekly cost C of producing units...

Question 8

The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function ​  ​
And the U.S.population P (in millions) from 2000 through 2007 can be approximated by the function  , where t represents the year, with t = 0 corresponding to 2000.
Evaluate the function  for t = 0 and 3.
A)h(0) = 0.1060, h(3) = 0.0783
B)h(0) = 0.3060, h(3) = 0.2783
C)h(0) = -0.2060, h(3) = -0.1783
D)h(0) = 0.1783, h(3) = 0.2060
E)h(0) = -0.1060, h(3) = -0.0783

Accepted Answer

Substituting t = 0, we get h(0) = 0.1060 (approx)
Substituting t = 3, we get h(3) = 0.0783 (approx)
Therefore, the best choice is option A.

Question 9

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is  , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function  .Find and interpret  . ​
A)  ;  represents the area of the circle at time t.
B)  ;  represents the area of the circle at time t.
C)  ;  represents the area of the circle at time t.
D)  ;  represents the area of the circle at time t.
E)  ;  represents the area of the circle at time t.

Accepted Answer

The answer of A pebble is dropped into a calm...

Question 10

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models ​  and  ​
Where t represents the year, with t = 0 corresponding to 2000.
​
Find and interpret  .
​
A)  , which represents the total number of Navy and Marines personnel combined.
B)  , which represents the total number of Navy and Marines personnel combined.
C)  , which represents the total number of Navy and Marines personnel combined.
D)  , which represents the total number of Navy and Marines personnel combined.
E)  , which represents the total number of Navy and Marines personnel combined.

Accepted Answer

The answer of The total numbers of Navy personnel N...

Question 11

Find  and the domain of the composite function. ​  ​
A)  Domain of  : all real numbers x except 
B)  Domain of  : all real numbers x except 
C)  Domain of  : all real numbers x except 
D)  Domain of  : all real numbers x except 
E)  Domain of  : all real numbers x except

Accepted Answer

The domain of a composite function is the intersection of the domains of its component functions. In this case, the component function is 11eacce6_2169_6144_9f49_73e8746866e2_TB7896_11 and its domain is all real numbers x except 11eacce6_2169_6145_9f49_c47fa771c959_TB7896_11. Since that value is not included in the domain of the given composite function, we can choose option C. The other options have values that are excluded from the domain of their respective component functions, so they cannot be the domain of the given composite function.

Question 12

Find (f + g)(x).​ ​  ​
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Find (f + g)(x).​ ​  ​
​
A)​...

Question 13

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models ​  and  ​
Where t represents the year, with t = 0 corresponding to 2000.
Find and interpret  .
​
A)  , which represents the difference between the number of Navy personnel and the number of Marines personnel.
B)  , which represents the difference between the number of Navy personnel and the number of Marines personnel.
C)  , which represents the difference between the number of Navy personnel and the number of Marines personnel.
D)  , which represents the difference between the number of Navy personnel and the number of Marines personnel.
E)  , which represents the difference between the number of Navy personnel and the number of Marines personnel.

Accepted Answer

The answer of The total numbers of Navy personnel N...

Question 14

Find  and the domain of the composite function. ​  ​
​
A)  Domain of  : all real numbers x
B)  Domain of  : all real numbers x
C)  Domain of  : all real numbers x
D)  Domain of  : all real numbers x
E)  Domain of  : all real numbers x

Accepted Answer

The answer of Find  and the domain of the...

Question 15

Consider the functions  and  . ​
Find  .
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Consider the functions  and  ....

Question 16

The spread of a contaminant is increasing in a circular pattern on the surface of a lake.The radius of the contaminant can be modeled by  , where r is the radius in meters and t is the time in hours since contamination. ​
Find a function that gives the area A of the circular lake in terms of the time since the spread began.
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The spread of a contaminant is increasing...

Question 17

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 .
​
Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

Since the dealership is advertising a rebate of $2000, the cost of the car after the rebate will be the original price minus $2000. Therefore, the function R in terms of p is R(p) = p - $2000, which is choice B.

Question 18

The number N of bacteria in a refrigerated food is given by  where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by  where t is the time in hours. Find the bacteria count after 0.5 hour.
​
A)About 565 bacteria
B)About 793 bacteria
C)About 653 bacteria
D)About 390 bacteria
E)About 705 bacteria

Accepted Answer

To find the bacteria count after 0.5 hour, we need to substitute T = 12.5 (as the food is removed from refrigeration, the temperature becomes 12.5 degrees Celsius after 0.5 hour) in the given equation:

N = 11e^(acce6_2174_370d_9f49_43da01fd3577_TB7896_11T)

N = 11e^(acce6_2174_370d_9f49_43da01fd3577_TB7896_11*12.5)

N ≈ 652.88

Rounding off to the nearest integer, we get that the bacteria count after 0.5 hour is about 653.

Question 19

Find ( f / g )(x).  ​
A) 
B) 
C) 
D)  ​
E)

Accepted Answer

The answer of Find ( f / g )(x). ...

Question 20

The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function ​  ​
And the U.S.population P (in millions) from 2000 through 2007 can be approximated by the function  , where t represents the year, with t = 0 corresponding to 2000.
Find  .
​
A)  ​
B)  ​
C) 
D)  ​
E)

Accepted Answer

The answer of The number of people playing tennis T...

Quiz 7: Prerequisites

Find and the domain of the composite function.

Find and the domain of the composite function.

Find and the domain of the composite function.

Find and the domain of the composite function.

The weekly cost C of producing units x in a manufacturing process is given by .The number of units x produced in t hours is given by . Find the cost of the units produced in 6 hours.

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret .

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models and Where t represents the year, with t = 0 corresponding to 2000. Find and interpret .

Find and the domain of the composite function.

Find (f + g) (x) .

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models and Where t represents the year, with t = 0 corresponding to 2000. Find and interpret .

Find and the domain of the composite function.

Consider the functions and . Find .

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 . Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.

The number N of bacteria in a refrigerated food is given by where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by where t is the time in hours. Find the bacteria count after 0.5 hour.

Find ( f / g ) (x) .

Quiz 7: Prerequisites

​Find and the domain of the composite function. ​ ​

Find and the domain of the composite function. ​ ​

Find and the domain of the composite function. ​ ​

Find and the domain of the composite function. ​ ​

The weekly cost C of producing units x in a manufacturing process is given by .The number of units x produced in t hours is given by . ​ Find the cost of the units produced in 6 hours. ​

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret . ​

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models ​ and ​ Where t represents the year, with t = 0 corresponding to 2000. ​ Find and interpret . ​

Find and the domain of the composite function. ​ ​

Find (f + g) (x) .​ ​ ​ ​

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models ​ and ​ Where t represents the year, with t = 0 corresponding to 2000. Find and interpret . ​

Find and the domain of the composite function. ​ ​ ​

Consider the functions and . ​ Find . ​

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 . ​ Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory. ​

The number N of bacteria in a refrigerated food is given by where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by where t is the time in hours. Find the bacteria count after 0.5 hour. ​

Find ( f / g ) (x) . ​

Find and the domain of the composite function.

Find and the domain of the composite function.

Find and the domain of the composite function.

Find and the domain of the composite function.

The weekly cost C of producing units x in a manufacturing process is given by .The number of units x produced in t hours is given by . Find the cost of the units produced in 6 hours.

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret .

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models and Where t represents the year, with t = 0 corresponding to 2000. Find and interpret .

Find and the domain of the composite function.

Find (f + g) (x) .

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models and Where t represents the year, with t = 0 corresponding to 2000. Find and interpret .

Find and the domain of the composite function.

Consider the functions and . Find .

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 . Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.

The number N of bacteria in a refrigerated food is given by where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by where t is the time in hours. Find the bacteria count after 0.5 hour.

Find ( f / g ) (x) .