Question 1

Function $f$ is $f ( x ) = \left\{ \begin{array} { c l } 
- 2 & \text { if } 0 \leq x < 14 \
- 3 x & \text { if } 14 \leq x < 28
\end{array} \right.$ .   
Find $f ( 27 )$ .

Accepted Answer

A) 2 
B)  -81 
C)  -83 
D)  -2 
E)  28 
A) 2 
B)  -81 
C)  -83 
D)  -2 
E)  28

Question 2

A piano manufacture has a daily fixed cost of $1,000 and a marginal cost of $1,500 per piano. Find the cost C of manufacturing x pianos in one day.

Accepted Answer

A)  $C ( x ) = 1,500 x - 1,000$ per day 
B)  $C ( x ) = 1,000 x - 1,500$ per day 
C)  $C ( x ) = 1,500 x$ per day 
D)  $C ( x ) = 1,000 x + 1,500$ per day 
E)  $C ( x ) = 1,500 x + 1,000$ per day 
A)  $C ( x ) = 1,500 x - 1,000$ per day 
B)  $C ( x ) = 1,000 x - 1,500$ per day 
C)  $C ( x ) = 1,500 x$ per day 
D)  $C ( x ) = 1,000 x + 1,500$ per day 
E)  $C ( x ) = 1,500 x + 1,000$ per day

Question 3

The demand for your college newspaper is 2,000 copies per week if the paper is given a way free of charge, and the demand drops to 1,000 if the charge is $0.25 per copy. However, the university is prepared to supply only 600 copies per week free of charge but will supply 3,600 per week at $0.50 per copy. At what price should the college newspapers be sold so that there is neither a surplus nor a shortage of papers  Round your answer to two decimal places.  
$ __________

Accepted Answer

The answer of The demand for your college newspaper is...

Question 4

Calculate the slope of the straight line through the points $( 2,1 )$ and $( 5,10 )$ . Try to do the calculations mentally.

Accepted Answer

A)  $m = 9$ 
B)   $m = - 3$ 
C)   $m = \frac { 1 } { 3 }$ 
D)   $m = - \frac { 1 } { 3 }$ 
E)   $m = 3$ 
A)  $m = 9$ 
B)   $m = - 3$ 
C)   $m = \frac { 1 } { 3 }$ 
D)   $m = - \frac { 1 } { 3 }$ 
E)   $m = 3$

Question 5

The value of U.S. trade with China from 1994 through 2002 can be approximated by $C ( t ) = 3 t ^ { 2 } - 7 t + 50$ billion dollars (t is time in years since 1994). 
Find an appropriate domain of C.

Accepted Answer

A)  $[ 0 , + \infty ]$ 
B)  $[ 1994,2002 ]$ 
C)  $[ 1994 , + \infty ]$ 
D)  $[ 0,8 ]$ 
E)  $[ 8 , + \infty ]$ 
A)  $[ 0 , + \infty ]$ 
B)  $[ 1994,2002 ]$ 
C)  $[ 1994 , + \infty ]$ 
D)  $[ 0,8 ]$ 
E)  $[ 8 , + \infty ]$

Question 6

Find the coefficient of correlation of the line that best fits the data set.   $\{ ( 0,8 ) , ( 2,8 ) , ( - 7,19 ) \}$

Accepted Answer

A)  $r = 1$ 
B)   $r = - 0.4887$ 
C)   $r = - 0.6841$ 
D)   $r = 0$ 
E)   $r = - 0.9774$ 
A)  $r = 1$ 
B)   $r = - 0.4887$ 
C)   $r = - 0.6841$ 
D)   $r = 0$ 
E)   $r = - 0.9774$

Question 7

In 2004 the Texas Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The table gives the approximate number of jobs for the citizens of Texas that would be created at various levels of recovery. Find the regression line. $$\begin{array} { | l | l | l | l | l | } 
\hline \text { Percent Recovery (\%) } - \boldsymbol { x } & 20 & 40 & 80 & 100 \
\hline \text { Jobs Created (Millions) } - \boldsymbol { y } & 3 & 6 & 9 & 15 \
\hline
\end{array}$$  Use the regression line to estimate the number of jobs that would be created at a recovery level of 85%.

Accepted Answer

A)  $y ( 85 ) = 10.525$ million jobs 
B)  $y ( 85 ) = 23.25$ million jobs 
C)  $y ( 85 ) = 12.625$ million jobs 
D)  $y ( 85 ) = 12.125$ million jobs 
E)  $y ( 85 ) = 11.625$ million jobs 
A)  $y ( 85 ) = 10.525$ million jobs 
B)  $y ( 85 ) = 23.25$ million jobs 
C)  $y ( 85 ) = 12.625$ million jobs 
D)  $y ( 85 ) = 12.125$ million jobs 
E)  $y ( 85 ) = 11.625$ million jobs

Question 8

Choose the graph of the function $f ( x ) = - \frac { x ^ { 3 } } { 3 }$ , domain $( - \infty , \infty )$ from the following:

Accepted Answer

A)    
B)     
C)     
D)     
A)    
B)     
C)     
D)

Question 9

Choose the graph of the function $f ( x ) = \frac { x ^ { 3 } } { 6 }$ , domain $[ 0 , \infty )$ from the following:

Accepted Answer

A)    
B)     
C)     
D)     
A)    
B)     
C)     
D)

Question 10

Calculate the slope of the straight line through the points (3, 3) and (8, 18). Try to do the calculations mentally.

Accepted Answer

The answer of Calculate the slope of the straight line...

Question 11

Function $f$ is $f ( x ) = \left\{ \begin{array} { c l } 
4 x & \text { if } 0 < x < 16 \
x + 3 & \text { if } 16 \leq x < 32 \
4 x & \text { if } 32 \leq x \leq 48
\end{array} \right.$ . 
Find $f ( 38 )$ .

Accepted Answer

A) 152 
B)  156 
C)  48 
D)  38 
E)  168 
A) 152 
B)  156 
C)  48 
D)  38 
E)  168

Question 12

Find the coefficient of correlation of the line that best fits the data set.   $\{ ( 2,9 ) , ( 5,15 ) , ( 9,23 ) \}$

Accepted Answer

A)  $r = 1$ 
B)   $r = - 1$ 
C)   $r = 0.6$ 
D)   $r = - 0.2$ 
E)   $r = 0.2$ 
A)  $r = 1$ 
B)   $r = - 1$ 
C)   $r = 0.6$ 
D)   $r = - 0.2$ 
E)   $r = 0.2$

Question 13

The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 1996 can be approximated by $A ( t ) = - 0.01 t ^ { 2 } + 0.24 t + 3.4$ billion dollars (t is time in years since 1983). 
Find an appropriate domain of A.

Accepted Answer

A)  $[ 0,13 ]$ 
B)  $[ 1983 , + \infty ]$ 
C)  $[ - \infty , 13 ]$ 
D)  $[ - \infty , 0 ]$ 
E)  $[ 1983,1996 ]$ 
A)  $[ 0,13 ]$ 
B)  $[ 1983 , + \infty ]$ 
C)  $[ - \infty , 13 ]$ 
D)  $[ - \infty , 0 ]$ 
E)  $[ 1983,1996 ]$

Question 14

If the income I is specified as a function of selling price s, which variable is independent and which one is dependent?

Choose the correct letter for each question.
-Dependent variable

Accepted Answer

A) Selling price 
B) Income 
A) Selling price 
B) Income

Question 15

Find the coefficient of correlation of the line that best fits the data set.
​ $\{ ( 1 , - 6 ) , ( - 3 , - 2 ) , ( 7 , - 12 ) \}$ ​
Please give the answer to four decimal places if necessary.

Accepted Answer

The answer of Find the coefficient of correlation of the...

Question 16

Find the linear equation that is the straight line through (5, 5) and parallel to the line $12 x - 6 y = 19$ .

Accepted Answer

A)  $y = x$ 
B)   $y = 2 x - 15$ 
C)   $y = x - 5$ 
D)   $y = 2 x + 5$ 
E)   $y = 2 x - 5$ 
A)  $y = x$ 
B)   $y = 2 x - 15$ 
C)   $y = x - 5$ 
D)   $y = 2 x + 5$ 
E)   $y = 2 x - 5$

Question 17

A piano manufacture has a daily fixed cost of $1,300 and a marginal cost of $1,400 per piano. Find the cost c of manufacturing ​x pianos in one day.

Accepted Answer

The answer of A piano manufacture has a daily fixed...

Question 18

Find the best-fit line associated with the set of points.
​ $( 1,3 )$ , $( 2,6 )$ , $( 3,10 )$ ​
Please enter your answer as an equation of line in the form $y = m x + b$ . Round m and b to the nearest hundredth if necessary.

Accepted Answer

The answer of Find the best-fit line associated with the...

Question 19

Use the graph of the function $f$ to find $f ( 6 )$ .

Accepted Answer

A) 11 
B)  9 
C)  16 
D)  12 
E)  10 
A) 11 
B)  9 
C)  16 
D)  12 
E)  10

Question 20

A table of values for a linear function is given. Find $f ( 1 )$ . $$\begin{array} { | l | l | l | } 
\hline \boldsymbol { x } & - 1 & 0 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 7 & 11 \
\hline
\end{array}$$

Accepted Answer

A)  $f ( 1 ) = - 7$ 
B)   $f ( 1 ) = - 3$ 
C)   $f ( 1 ) = 8$ 
D)   $f ( 1 ) = 4$ 
E)   $f ( 1 ) = 15$ 
A)  $f ( 1 ) = - 7$ 
B)   $f ( 1 ) = - 3$ 
C)   $f ( 1 ) = 8$ 
D)   $f ( 1 ) = 4$ 
E)   $f ( 1 ) = 15$

Function $f$ is $f ( x ) = \left\{ \begin{array} { c l } - 2 & \text { if } 0 \leq x < 14 \\- 3 x & \text { if } 14 \leq x < 28\end{array} \right.$ . Find $f ( 27 )$ .

A piano manufacture has a daily fixed cost of $1,000 and a marginal cost of $1,500 per piano. Find the cost C of manufacturing x pianos in one day.

Calculate the slope of the straight line through the points $( 2,1 )$ and $( 5,10 )$ . Try to do the calculations mentally.

The value of U.S. trade with China from 1994 through 2002 can be approximated by $C ( t ) = 3 t ^ { 2 } - 7 t + 50$ billion dollars (t is time in years since 1994). Find an appropriate domain of C.

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 0,8 ) , ( 2,8 ) , ( - 7,19 ) \}$

Choose the graph of the function $f ( x ) = - \frac { x ^ { 3 } } { 3 }$ , domain $( - \infty , \infty )$ from the following:

Choose the graph of the function $f ( x ) = \frac { x ^ { 3 } } { 6 }$ , domain $[ 0 , \infty )$ from the following:

Calculate the slope of the straight line through the points (3, 3) and (8, 18). Try to do the calculations mentally.

Function $f$ is $f ( x ) = \left\{ \begin{array} { c l } 4 x & \text { if } 0 < x < 16 \\x + 3 & \text { if } 16 \leq x < 32 \\4 x & \text { if } 32 \leq x \leq 48\end{array} \right.$ . Find $f ( 38 )$ .

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 2,9 ) , ( 5,15 ) , ( 9,23 ) \}$

The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 1996 can be approximated by $A ( t ) = - 0.01 t ^ { 2 } + 0.24 t + 3.4$ billion dollars (t is time in years since 1983). Find an appropriate domain of A.

If the income I is specified as a function of selling price s, which variable is independent and which one is dependent? Choose the correct letter for each question. -Dependent variable

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 1 , - 6 ) , ( - 3 , - 2 ) , ( 7 , - 12 ) \}$ Please give the answer to four decimal places if necessary.

Find the linear equation that is the straight line through (5, 5) and parallel to the line $12 x - 6 y = 19$ .

A piano manufacture has a daily fixed cost of $1,300 and a marginal cost of $1,400 per piano. Find the cost c of manufacturing x pianos in one day.

Find the best-fit line associated with the set of points. $( 1,3 )$ , $( 2,6 )$ , $( 3,10 )$ Please enter your answer as an equation of line in the form $y = m x + b$ . Round m and b to the nearest hundredth if necessary.

Use the graph of the function $f$ to find $f ( 6 )$ .

A table of values for a linear function is given. Find $f ( 1 )$ . -1 0 ( ) 7 11

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 1: Functions and Applications

Function fff is f(x)={−2 if 0≤x<14−3x if 14≤x<28f ( x ) = \left\{ \begin{array} { c l } - 2 & \text { if } 0 \leq x < 14 \\- 3 x & \text { if } 14 \leq x < 28\end{array} \right.f(x)={−2−3x​ if 0≤x<14 if 14≤x<28​ . Find f(27)f ( 27 )f(27) .

A piano manufacture has a daily fixed cost of $1,000 and a marginal cost of $1,500 per piano. Find the cost C of manufacturing x pianos in one day.

Calculate the slope of the straight line through the points (2,1)( 2,1 )(2,1) and (5,10)( 5,10 )(5,10) . Try to do the calculations mentally.

The value of U.S. trade with China from 1994 through 2002 can be approximated by C(t)=3t2−7t+50C ( t ) = 3 t ^ { 2 } - 7 t + 50C(t)=3t2−7t+50 billion dollars (t is time in years since 1994). Find an appropriate domain of C.

Find the coefficient of correlation of the line that best fits the data set. {(0,8),(2,8),(−7,19)}\{ ( 0,8 ) , ( 2,8 ) , ( - 7,19 ) \}{(0,8),(2,8),(−7,19)}

Choose the graph of the function f(x)=−x33f ( x ) = - \frac { x ^ { 3 } } { 3 }f(x)=−3x3​ , domain (−∞,∞)( - \infty , \infty )(−∞,∞) from the following:

Choose the graph of the function f(x)=x36f ( x ) = \frac { x ^ { 3 } } { 6 }f(x)=6x3​ , domain [0,∞)[ 0 , \infty )[0,∞) from the following:

Calculate the slope of the straight line through the points (3, 3) and (8, 18). Try to do the calculations mentally.

Find the coefficient of correlation of the line that best fits the data set. {(2,9),(5,15),(9,23)}\{ ( 2,9 ) , ( 5,15 ) , ( 9,23 ) \}{(2,9),(5,15),(9,23)}

If the income I is specified as a function of selling price s, which variable is independent and which one is dependent? Choose the correct letter for each question. -Dependent variable

Find the coefficient of correlation of the line that best fits the data set. ​ {(1,−6),(−3,−2),(7,−12)}\{ ( 1 , - 6 ) , ( - 3 , - 2 ) , ( 7 , - 12 ) \}{(1,−6),(−3,−2),(7,−12)} ​ Please give the answer to four decimal places if necessary.

Find the linear equation that is the straight line through (5, 5) and parallel to the line 12x−6y=1912 x - 6 y = 1912x−6y=19 .

A piano manufacture has a daily fixed cost of $1,300 and a marginal cost of $1,400 per piano. Find the cost c of manufacturing ​x pianos in one day.

Find the best-fit line associated with the set of points. ​ (1,3)( 1,3 )(1,3) , (2,6)( 2,6 )(2,6) , (3,10)( 3,10 )(3,10) ​ Please enter your answer as an equation of line in the form y=mx+by = m x + by=mx+b . Round m and b to the nearest hundredth if necessary.

Use the graph of the function fff to find f(6)f ( 6 )f(6) .

A table of values for a linear function is given. Find f(1)f ( 1 )f(1) . -1 0 ( ) 7 11

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Function $f$ is $f ( x ) = \left\{ \begin{array} { c l } - 2 & \text { if } 0 \leq x < 14 \\- 3 x & \text { if } 14 \leq x < 28\end{array} \right.$ . Find $f ( 27 )$ .

Calculate the slope of the straight line through the points $( 2,1 )$ and $( 5,10 )$ . Try to do the calculations mentally.

The value of U.S. trade with China from 1994 through 2002 can be approximated by $C ( t ) = 3 t ^ { 2 } - 7 t + 50$ billion dollars (t is time in years since 1994). Find an appropriate domain of C.

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 0,8 ) , ( 2,8 ) , ( - 7,19 ) \}$

Choose the graph of the function $f ( x ) = - \frac { x ^ { 3 } } { 3 }$ , domain $( - \infty , \infty )$ from the following:

Choose the graph of the function $f ( x ) = \frac { x ^ { 3 } } { 6 }$ , domain $[ 0 , \infty )$ from the following:

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 2,9 ) , ( 5,15 ) , ( 9,23 ) \}$

Find the coefficient of correlation of the line that best fits the data set. $\{ ( 1 , - 6 ) , ( - 3 , - 2 ) , ( 7 , - 12 ) \}$ Please give the answer to four decimal places if necessary.

Find the linear equation that is the straight line through (5, 5) and parallel to the line $12 x - 6 y = 19$ .

A piano manufacture has a daily fixed cost of $1,300 and a marginal cost of $1,400 per piano. Find the cost c of manufacturing x pianos in one day.

Find the best-fit line associated with the set of points. $( 1,3 )$ , $( 2,6 )$ , $( 3,10 )$ Please enter your answer as an equation of line in the form $y = m x + b$ . Round m and b to the nearest hundredth if necessary.

Use the graph of the function $f$ to find $f ( 6 )$ .

A table of values for a linear function is given. Find $f ( 1 )$ . -1 0 ( ) 7 11