Question 1

Which of the tables below show linear data? $\overline { \text { Table } 1 }$

Table 2

A) Table 1 only
B) Table 2 only
C) Both Table 1 and Table 2
D) Neither table is linear.

Accepted Answer

B

Question 2

The following table shows the number C , in millions, of cars sold in the U.S.  years after 2005. Use the regression line for the data to estimate the number of cars sold in 2012.

A) $3.27$ million
B) $4.53$ million
C) $3.25$ million
D) $4.25$ million

Accepted Answer

D

Question 3

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity $V$ , in feet per second, after  seconds is given by $V = 32 t + 8$ By how much does velocity increase over a 6-second period?
A) 32.17 feet per second
B) 192.15 feet per second
C) 32 feet per second
D) 192 feet per second

Accepted Answer

D

Question 4

The following table shows the running speed  , in feet per second, of animals of length L , in inches. Use the regression line for the data to estimate the running speed of animals that are 14 inches long. $$\begin{array} { | l | l | l | l | l | } 
\hline L & 3.5 & 6.3 & 9.4 & 9.8 \
\hline R & 8.28 & 15.73 & 24.04 & 24.92 \
\hline
\end{array}$$
A) 17.61 feet per second
B) 36.36 feet per second
C) 16.65 feet per second
D) 36.1 feet per second

Accepted Answer

The answer of The following table shows the running speed...

Question 5

Suppose $f$ is a linear function with $f ( 7 ) = 25.13$ . If the slope of $f$ is 2.59, what value of $x$ gives $f ( x ) = 12$ ?
A) $x =$38.95
B) $x =$1.93  
C) $x =$38.08 
D) $x =$2.42

Accepted Answer

Given $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We know $f(7) = 25.13$ and the slope $m = 2.59$. To find $b$, use $25.13 = 2.59(7) + b$. Solving for $b$, we get $b = 25.13 - 2.59(7)$. To find $x$ when $f(x) = 12$, set up $12 = 2.59x + b$ and solve for $x$, which gives $x = 1.93$.

Question 6

The following table shows the gross national product $G $ , in trillions of dollars,  years after 2005. Use linear regression to model G as a function of  .

A) $G = 13.01 t + 0.35$
B) $G = 0.35 t + 13.01$
C) $G = 0.35 t + 12.75$
D) $G = 0.84 t + 12.75$

Accepted Answer

The answer of The following table shows the gross national...

Question 7

Suppose $f$ is a linear function of $x$ . The slope is 2.42. An increase of 6 units in $x$ causes what change in $f$ ?
A) A decrease of 14.52 units
B) An increase of 14.52 units
C) An increase of 2.48 units
D) A decrease of 2.48 units

Accepted Answer

Since the slope of the linear function is 2.42, we know that for every increase of 1 unit in $x$, there is an increase of 2.42 units in $f$. Therefore, for an increase of 6 units in $x$, there will be an increase of 6×2.42=14.52 units in $f$.

Question 8

The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days.

A) $D = - 2 d + 795$
B) $D = 793.67 d + - 0.67$
C) $D = - 0.67 d + 793.67$
D) $D = 795 d + - 2$

Accepted Answer

Since we need to find a linear model for depth as a function of days, we need to look for a relationship between the two variables that can be expressed as a linear equation (y = mx + b) where y is the depth and x is the number of days. Looking at the table, we can see that as the number of days increases, the depth decreases. This suggests that there is a negative linear relationship between days and depth.

To find the equation of the line, we need to calculate the slope (m) and y-intercept (b) using two points from the table. Let's use the points (0, 794) and (6, 792) since they are easy to read from the table.

Slope: m = (y2 - y1)/(x2 - x1) = (792 - 794) / (6 - 0) = -0.67

Y-intercept: b = y1 - mx1 = 794 - (-0.67)(0) = 794

Putting it all together, we get the equation:

D = -0.67d + 793.67

Question 9

For a certain line, a run of 3 feet corresponds to a rise of 8 feet. What is the slope of this line?
A) 2.67 feet
B) 0.38 feet
C) 0.65 feet
D) 2.78 feet

Accepted Answer

The slope of a line is calculated by dividing the change in y (rise) by the change in x (run). In this case, the rise is 8 feet and the run is 3 feet, so the slope is 8/3 = 2.67 feet.

Question 10

The following table shows the money M left in your cookie jar after $\mathrm { W }$ withdrawals from the jar. Find a linear model for M in terms of W. 
A) $M = 133 w - 16$
B) $M = 181 w - 16$
C) $M = - 16 w + 133$
D) $M M = - 16 w + 181$

Accepted Answer

The answer of The following table shows the money M...

Question 11

At a distance 5 miles west of town, oil-bearing deposits are found 3044 feet deep. Also, 8 miles west of town, the oil is found 3164 feet down. Assuming the oil-bearing stratum lies on a straight line,
How deep would you expect to drill 10 miles west of town in order to find oil?
A) 3124 feet
B) 3124.35 feet
C) 3244.77 feet
D) 3244 feet

Accepted Answer

We can assume that there is a linear relationship between the distance west of town and the depth of the oil-bearing deposits. To find the equation of the line, we can use the two given points: (5, 3044) and (8, 3164).

First, we can find the slope of the line: 
slope = (3164 - 3044) / (8 - 5) = 40

Then, we can use the point-slope form of a line to find the equation:
y - 3044 = 40(x - 5)
y = 40x - 156

Finally, we can use the equation to find the expected depth at 10 miles west of town:
y = 40(10) - 156 = 344
So, we would expect to drill 10 miles west of town to a depth of 3244 feet. The closest answer choice is D.

Question 12

Find a linear model for the following data table. Round the slope to three decimal places.

A) $y = 2.193 x + 0.42$
B) $y = 0.421 x + 2.19$
C) $y = 2.193 x + 7$
D) $y = 7 x + 2.19$

Accepted Answer

To find the linear model, we need to determine the slope and y-intercept. Using the slope formula, we get:

slope = (change in y) / (change in x)
slope = (5.6 - 3.3) / (2.4 - 0.6)
slope = 2.3 / 1.8
slope = 1.278

Round the slope to three decimal places gives 1.278.

Next, we can use the point-slope formula to find the y-intercept:

y - y1 = m(x - x1)

Using the first point (0.6, 3.3) and the slope we just calculated, we get:

y - 3.3 = 1.278(x - 0.6)

Simplifying and solving for y, we get:

y = 2.193x + 0.42

Therefore, the linear model for the data is y = 2.193 x + 0.42. Choice A is the only option that matches this equation.

Question 13

Find a linear model for the following data table.

A) $y = 2 x + 3$
B) $y = 3 x + 2$
C) $y = 4 x + 1$
D) $y = 1 x + 4$

Accepted Answer

The answer of Find a linear model for the following...

Question 14

The following table shows the running speed  , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Use linear regression to model running speed as a function of
Temperature.

A) $R = 0.02 T + 2.97$
B) $T = 0.02 R + 2.97$
C) $R = 0.23 T - 3.21$
D) $T = 0.23 R - 3.21$

Accepted Answer

The answer of The following table shows the running speed...

Question 15

Suppose $f$ is a linear function with $f ( 6 ) = 20.98$ and $f ( 10 ) = 30.3$ . Find an equation for $f$ .
A) $f ( x ) = 0.43 x + 20.98$
B) $f ( x ) = 20.98 x + 0.43$
C) $f ( x ) = 2.33 x + 7$
D) $f ( x ) = 7 x + 2.33$

Accepted Answer

To find the equation of a linear function $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we first calculate the slope $m = \frac{f(10) - f(6)}{10 - 6} = \frac{30.3 - 20.98}{4} = \frac{9.32}{4} = 2.33$. Then, to find $b$, we can use one of the given points, for example, $f(6) = 20.98$, so $20.98 = 2.33 \cdot 6 + b$, solving for $b$ gives $b = 20.98 - 13.98 = 7$. Therefore, the equation is $f(x) = 2.33x + 7$.

Question 16

At the outside wall the roof is 10 feet high. Also, 4 horizontal feet from the outside wall to- ward the interior of the room, the roof is 13 feet tall. If the roof is extended beyond the outside wall, what is
The height of the roof 5 horizontal feet from the outside wall toward the exterior of the room?
A) 6.9 feet
B) 8.46 feet
C) 6.25 feet
D) 9.22 feet

Accepted Answer

The answer of At the outside wall the roof is...

Question 17

The sales tax $T$ , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by $T = 0.09 D$ .
If I decide to buy $38 more in merchandise, how much additional sales tax will I have to pay?
A) $3.42
B) $3.91
C) $0.81
D) $0.09

Accepted Answer

The additional sales tax for buying $38 more in merchandise is calculated by multiplying the sales tax rate (0.09) by the additional amount ($38), which equals $3.42 (0.09 * 38 = 3.42).

Question 18

The following table shows the running speed  , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Based on the regression equation, how fast would an ant run
When the temperature is 30.9 degrees Celsius? $$\begin{array} { | l | l | l | l | l | } 
\hline T & 25.6 & 30.3 & 32.3 & 34.8 \
\hline R & 2.28 & 3.21 & 4.85 & 5.08 \
\hline
\end{array}$$
A) 5.9 centimeters per second
B) 4.95 centimeters per second
C) 4.97 centimeters per second
D) 3.99 centimeters per second

Accepted Answer

The answer of The following table shows the running speed...

Question 19

The figure below shows a simplified pattern for a wrap skirt that is 20 inches long and has a top hem of 57 inches. The bottom hem has a length of 63 inches. Suppose you decide to alter the pattern to
Make a wrap skirt with the same top hem length but a length of 24 inches. How long should be the bottom
Hem? 
A) 64.65 inches
B) 63.6 inches
C) 63.19 inches
D) 64.2 inches

Accepted Answer

The answer of The figure below shows a simplified pattern...

Question 20

A line through (5, 8) has slope 0.69. What is the vertical intercept?
A) -6.4
B) 4.55
C) 5.38
D) -6.59

Accepted Answer

The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Given the slope (m = 0.69) and a point (5, 8), we can substitute these values into the equation to solve for b: 8 = 0.69(5) + b. Solving for b gives b = 8 - 0.69*5 = 4.55.

Quiz 3: Straight Lines and Linear Functions

The following table shows the number C , in millions, of cars sold in the U.S. years after 2005. Use the regression line for the data to estimate the number of cars sold in 2012.

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity $V$ , in feet per second, after seconds is given by $V = 32 t + 8$ By how much does velocity increase over a 6-second period?

Suppose $f$ is a linear function with $f ( 7 ) = 25.13$ . If the slope of $f$ is 2.59, what value of $x$ gives $f ( x ) = 12$ ?

The following table shows the gross national product $G$ , in trillions of dollars, years after 2005. Use linear regression to model G as a function of .

Suppose $f$ is a linear function of $x$ . The slope is 2.42. An increase of 6 units in $x$ causes what change in $f$ ?

The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days.

For a certain line, a run of 3 feet corresponds to a rise of 8 feet. What is the slope of this line?

At a distance 5 miles west of town, oil-bearing deposits are found 3044 feet deep. Also, 8 miles west of town, the oil is found 3164 feet down. Assuming the oil-bearing stratum lies on a straight line, How deep would you expect to drill 10 miles west of town in order to find oil?

Find a linear model for the following data table. Round the slope to three decimal places.

Find a linear model for the following data table.

The following table shows the running speed , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Use linear regression to model running speed as a function of Temperature.

Suppose $f$ is a linear function with $f ( 6 ) = 20.98$ and $f ( 10 ) = 30.3$ . Find an equation for $f$ .

The sales tax $T$ , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by $T = 0.09 D$ . If I decide to buy $38 more in merchandise, how much additional sales tax will I have to pay?

A line through (5, 8) has slope 0.69. What is the vertical intercept?

Quiz 3: Straight Lines and Linear Functions

Which of the tables below show linear data? Table 1‾\overline { \text { Table } 1 } Table 1 Table 2

The following table shows the number C , in millions, of cars sold in the U.S. years after 2005. Use the regression line for the data to estimate the number of cars sold in 2012.

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity VVV , in feet per second, after seconds is given by V=32t+8V = 32 t + 8V=32t+8 By how much does velocity increase over a 6-second period?

Suppose fff is a linear function with f(7) =25.13f ( 7 ) = 25.13f(7) =25.13 . If the slope of fff is 2.59, what value of xxx gives f(x) =12f ( x ) = 12f(x) =12 ?

The following table shows the gross national product GG G , in trillions of dollars, years after 2005. Use linear regression to model G as a function of .

Suppose fff is a linear function of xxx . The slope is 2.42. An increase of 6 units in xxx causes what change in fff ?

The following table shows the depth D , in inches, of water in a pond after ddd days of eva- poration. Find a linear model for depth as a function of days.

For a certain line, a run of 3 feet corresponds to a rise of 8 feet. What is the slope of this line?

The following table shows the money M left in your cookie jar after W\mathrm { W }W withdrawals from the jar. Find a linear model for M in terms of W.

At a distance 5 miles west of town, oil-bearing deposits are found 3044 feet deep. Also, 8 miles west of town, the oil is found 3164 feet down. Assuming the oil-bearing stratum lies on a straight line, How deep would you expect to drill 10 miles west of town in order to find oil?

Find a linear model for the following data table. Round the slope to three decimal places.

Find a linear model for the following data table.

The following table shows the running speed , in centimeters per second, of ants as a func- tion of the temperature TTT in degrees Celsius. Use linear regression to model running speed as a function of Temperature.

Suppose fff is a linear function with f(6) =20.98f ( 6 ) = 20.98f(6) =20.98 and f(10) =30.3f ( 10 ) = 30.3f(10) =30.3 . Find an equation for fff .

The sales tax TTT , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by T=0.09DT = 0.09 DT=0.09D . If I decide to buy $38 more in merchandise, how much additional sales tax will I have to pay?

A line through (5, 8) has slope 0.69. What is the vertical intercept?

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity $V$ , in feet per second, after seconds is given by $V = 32 t + 8$ By how much does velocity increase over a 6-second period?

Suppose $f$ is a linear function with $f ( 7 ) = 25.13$ . If the slope of $f$ is 2.59, what value of $x$ gives $f ( x ) = 12$ ?

The following table shows the gross national product $G$ , in trillions of dollars, years after 2005. Use linear regression to model G as a function of .

Suppose $f$ is a linear function of $x$ . The slope is 2.42. An increase of 6 units in $x$ causes what change in $f$ ?

The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days.

The following table shows the running speed , in centimeters per second, of ants as a func- tion of the temperature $T$ in degrees Celsius. Use linear regression to model running speed as a function of Temperature.

Suppose $f$ is a linear function with $f ( 6 ) = 20.98$ and $f ( 10 ) = 30.3$ . Find an equation for $f$ .

The sales tax $T$ , in dollars, I have to pay when I buy D dollars worth of merchandise is giv- en by $T = 0.09 D$ . If I decide to buy $38 more in merchandise, how much additional sales tax will I have to pay?