Question 1

Solve the problem.
-Suppose the function y = 4t - 4.5 determines the actual time that has elapsed, in minutes, for t minutes of a person's estimate of the elapsed time. Find the actual time that has elapsed for an Estimate of t = 30 minutes.

Accepted Answer

The answer of Solve the problem.
-Suppose the function y =...

Question 2

Solve the problem.
-Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained Regarding their GPAs on entering the program versus their current GPAs. Use the equation of the
Least squares line to predict the current GPA of a student whose entering GPA is 3.9.

Accepted Answer

The answer of Solve the problem.
-Ten students in a graduate...

Question 3

Find an equation in slope-intercept form (where possible) for the line.
-Through (-4, -1), m = -1.5

Accepted Answer

The slope-intercept form is y = mx + b. Given m = -1.5 and point (-4, -1), substitute into y = mx + b to find b: -1 = -1.5(-4) + b, solving gives b = -7. Thus, the equation is y = -1.5x - 7.

Question 4

Graph the equation.
-For the following table of data, a. Draw a scatterplot.
B. Calculate the correlation coefficient.
C. Calculate the least squares line and graph it on the scatterplot.
D. Predict the y-value when x is 20.

Accepted Answer

The answer of Graph the equation.
-For the following table of...

Question 5

Find the slope of the line.

Accepted Answer

The answer of Find the slope of the line.

...

Question 6

Find an equation in slope-intercept form (where possible) for the line.
-The line with y-intercept -10 and perpendicular to x + 2y = 4

Accepted Answer

The given line x + 2y = 4 has a slope of -1/2. A line perpendicular to it will have a slope that is the negative reciprocal, which is 2. The line with this slope and y-intercept -10 is y = 2x - 10.

Question 7

Find the slope of the line passing through the given pair of points.(-8, 8)and (-4, -7)

Accepted Answer

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points (-8, 8) and (-4, -7) into this formula gives $m = \frac{-7 - 8}{-4 + 8} = \frac{-15}{4}$, which is option C.

Question 8

Solve the problem.
-A meteorologist in the Upper Peninsula of Michigan predicts an overnight low of -9° Fahrenheit. What would a Canadian meteorologist predict for the same location in Celsius?

Accepted Answer

To convert Fahrenheit to Celsius, use the formula: $C = \frac{5}{9}(F - 32)$. Plugging in -9°F gives: $C = \frac{5}{9}(-9 - 32) = \frac{5}{9}(-41) = -22.8°C$.

Question 9

Find the equation of the least squares line.
-Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

Accepted Answer

The answer of Find the equation of the least squares...

Question 10

Write a cost function for the problem. Assume that the relationship is linear.
-A cable TV company charges $21 for the basic service plus $7 for each movie channel. Let C(x)be the total cost in dollars of subscribing to cable TV, using x movie channels.

Accepted Answer

The cost function C(x) = 7x + 21 correctly represents the total cost as a function of x movie channels, where $21 is the fixed cost for basic service and $7 is the variable cost per movie channel.

Question 11

Solve the problem.
-The mathematical model C = 400x + 30,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, how much does it cost to produce 400 items?

Accepted Answer

To find the cost of producing 400 items, substitute x = 400 into the equation: C = 400(400) + 30,000 = 160,000 + 30,000 = 190,000.

Question 12

Let the demand and supply functions be represented by D(p)and S(p), where p is the price in dollars. Find the equilibrium price and equilibrium quantity for the given functions. 
$
\begin{array}{l}
\mathrm{D}(\mathrm{p})=5760-50 \mathrm{p} \
\mathrm{S}(\mathrm{p})=250 \mathrm{p}-1440
\end{array}
$

Accepted Answer

The answer of Let the demand and supply functions be...

Question 13

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (7,-9) $, with undefined slope

Accepted Answer

A line with an undefined slope is a vertical line, which means all points on the line have the same x-coordinate. The equation for a vertical line through (7, -9) is $x = 7$.

Question 14

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (-9,-3) $, perpendicular to $ 7 x+8 y=-87 $

Accepted Answer

The slope of the line perpendicular to $7x + 8y = -87$ is $-\frac{7}{8}$ (negative reciprocal of the original slope $ \frac{7}{8} $). Using the point $(-9, -3)$ to solve for $b$ in $y = mx + b$, we get $b = \frac{51}{7}$. Therefore, the correct equation is $y = -\frac{8}{7}x + \frac{51}{7}$.

Question 15

Solve the problem.
-On a summer day, the bottom water of a lake is at a temperature of 6° Celsius. What is this temperature in Fahrenheit?

Accepted Answer

To convert Celsius to Fahrenheit, use the formula F = (C × 9/5) + 32. Plugging in 6 for C gives F = (6 × 9/5) + 32 = 42.8°.

Question 16

.
-Find the slope of the linex = 10

Accepted Answer

The slope of a vertical line like x = 10 is undefined because it does not have a rate of change in y over a change in x.

Question 17

Find the equation of the least squares line.
-The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters).

Accepted Answer

The answer of Find the equation of the least squares...

Question 18

Solve the problem.
-The relationship between the list price, x, in thousands of dollars, and the dealer invoice price, y, also in thousands of dollars, for pickup trucks can be approximated by the linear equation Y = 0.715x + 2.82. Use this equation to predict the dealer invoice price for a pickup truck with a list
Price of 18.0 thousand dollars.

Accepted Answer

To predict the dealer invoice price for a pickup truck with a list price of 18.0 thousand dollars, substitute x = 18.0 into the equation Y = 0.715x + 2.82. This gives Y = 0.715(18) + 2.82 = 12.87 + 2.82 = 15.69 thousand dollars.

Question 19

Evaluate the function as indicated.
-Find f(9)when f(x)= -3x + 1

Accepted Answer

f(9) = -3(9) + 1 = -27 + 1 = -26

Question 20

Graph the equation.4x - 16y = 0

Accepted Answer

The answer of Graph the equation.4x - 16y = 0...

Quiz 1: Linear Functions

Solve the problem. -Suppose the function y = 4t - 4.5 determines the actual time that has elapsed, in minutes, for t minutes of a person's estimate of the elapsed time. Find the actual time that has elapsed for an Estimate of t = 30 minutes.

Find an equation in slope-intercept form (where possible) for the line. -Through (-4, -1) , m = -1.5

Graph the equation. -For the following table of data, a. Draw a scatterplot. B. Calculate the correlation coefficient. C. Calculate the least squares line and graph it on the scatterplot. D. Predict the y-value when x is 20.

Find the slope of the line. $Find the slope of the line. A) \frac{3}{2} B) 3 C) undefined D) 0$

Find an equation in slope-intercept form (where possible) for the line. -The line with y-intercept -10 and perpendicular to x + 2y = 4

Find the slope of the line passing through the given pair of points.(-8, 8) and (-4, -7)

Solve the problem. -A meteorologist in the Upper Peninsula of Michigan predicts an overnight low of -9° Fahrenheit. What would a Canadian meteorologist predict for the same location in Celsius?

Find the equation of the least squares line. -Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

Write a cost function for the problem. Assume that the relationship is linear. -A cable TV company charges $21 for the basic service plus $7 for each movie channel. Let C(x) be the total cost in dollars of subscribing to cable TV, using x movie channels.

Solve the problem. -The mathematical model C = 400x + 30,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, how much does it cost to produce 400 items?

Let the demand and supply functions be represented by D(p) and S(p) , where p is the price in dollars. Find the equilibrium price and equilibrium quantity for the given functions. $\begin{array}{l}\mathrm{D}(\mathrm{p}) =5760-50 \mathrm{p} \\\mathrm{S}(\mathrm{p}) =250 \mathrm{p}-1440\end{array}$

Find an equation in slope-intercept form (where possible) for the line. -Through $(7,-9)$ , with undefined slope

Find an equation in slope-intercept form (where possible) for the line. -Through $(-9,-3)$ , perpendicular to $7 x+8 y=-87$

Solve the problem. -On a summer day, the bottom water of a lake is at a temperature of 6° Celsius. What is this temperature in Fahrenheit?

. -Find the slope of the linex = 10

Find the equation of the least squares line. -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters) .

Evaluate the function as indicated. -Find f(9) when f(x) = -3x + 1

Graph the equation.4x - 16y = 0

Quiz 1: Linear Functions

Solve the problem. -Suppose the function y = 4t - 4.5 determines the actual time that has elapsed, in minutes, for t minutes of a person's estimate of the elapsed time. Find the actual time that has elapsed for an Estimate of t = 30 minutes.

Find an equation in slope-intercept form (where possible) for the line. -Through (-4, -1) , m = -1.5

Graph the equation. -For the following table of data, a. Draw a scatterplot. B. Calculate the correlation coefficient. C. Calculate the least squares line and graph it on the scatterplot. D. Predict the y-value when x is 20.

Find the slope of the line.

Find an equation in slope-intercept form (where possible) for the line. -The line with y-intercept -10 and perpendicular to x + 2y = 4

Find the slope of the line passing through the given pair of points.(-8, 8) and (-4, -7)

Solve the problem. -A meteorologist in the Upper Peninsula of Michigan predicts an overnight low of -9° Fahrenheit. What would a Canadian meteorologist predict for the same location in Celsius?

Find the equation of the least squares line. -Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

Write a cost function for the problem. Assume that the relationship is linear. -A cable TV company charges $21 for the basic service plus $7 for each movie channel. Let C(x) be the total cost in dollars of subscribing to cable TV, using x movie channels.

Solve the problem. -The mathematical model C = 400x + 30,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, how much does it cost to produce 400 items?

Find an equation in slope-intercept form (where possible) for the line. -Through (7,−9) (7,-9) (7,−9) , with undefined slope

Find an equation in slope-intercept form (where possible) for the line. -Through (−9,−3) (-9,-3) (−9,−3) , perpendicular to 7x+8y=−87 7 x+8 y=-87 7x+8y=−87

Solve the problem. -On a summer day, the bottom water of a lake is at a temperature of 6° Celsius. What is this temperature in Fahrenheit?

. -Find the slope of the linex = 10

Find the equation of the least squares line. -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters) .

Evaluate the function as indicated. -Find f(9) when f(x) = -3x + 1

Graph the equation.4x - 16y = 0

Find the slope of the line. $Find the slope of the line. A) \frac{3}{2} B) 3 C) undefined D) 0$

Find an equation in slope-intercept form (where possible) for the line. -Through $(7,-9)$ , with undefined slope

Find an equation in slope-intercept form (where possible) for the line. -Through $(-9,-3)$ , perpendicular to $7 x+8 y=-87$