Question 1

Find the slope of the line.

Accepted Answer

The answer of Find the slope of the line. 
...

Question 2

The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Use the equation of the least squares line to predict the Growth of a plant if the temperature is 53.

Accepted Answer

The answer of The paired data below consist of the...

Question 3

Find the correlation coefficient.
-Consider the data points with the following coordinates:

Accepted Answer

The answer of Find the correlation coefficient.
-Consider the data points...

Question 4

Find the correlation coefficient

-Consider the data points with the following coordinates:

Accepted Answer

The answer of 
Find the correlation coefficient

-Consider the data points...

Question 5

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (-7,4) $ and $ (0,-5) $

Accepted Answer

The answer of Find an equation in slope-intercept form (where...

Question 6

Through (5, -4)and (-3, 3)127)

Accepted Answer

The slope (m) of the line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points (5, -4) and (-3, 3), the slope is $m = \frac{3 - (-4)}{-3 - 5} = \frac{7}{-8} = -\frac{7}{8}$. To find the y-intercept (b), use the point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say (5, -4): $-4 = -\frac{7}{8}(5) + b$, solving for b gives $b = \frac{3}{8}$. Thus, the equation is $y = -\frac{7}{8}x + \frac{3}{8}$.

Question 7

Find the slope of the line passing through the given pair of points. (6, 2)and (9, 4)

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 (6, 2) and (9, 4) into this formula gives $m = \frac{4 - 2}{9 - 6} = \frac{2}{3}$.

Question 8

Find the slope of the line passing through the given pair of points. (-5, -8)and (8, -8)143)

Accepted Answer

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. Here, $y_2 = y_1 = -8$, so $m = \frac{-8 - (-8)}{8 - (-5)} = \frac{0}{13} = 0$. The slope is 0, indicating a horizontal line.

Question 9

Find the equation of the least squares line.
-A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below.

Accepted Answer

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

Question 10

Find an equation in slope-intercept form (where possible) for the line.
-After two years on the job, an engineer's salary was $50,000. After seven years on the job, her salary was $66,000. Let y represent her salary after x years on the job. Assuming that the change in her Salary over time can be approximated by a straight line, give an equation for this line in the form y = mx + b.

Accepted Answer

To find the equation of the line in slope-intercept form (y = mx + b), first calculate the slope (m) using the given points (2, 50000) and (7, 66000). The slope m = (66000 - 50000) / (7 - 2) = 16000 / 5 = 3200. Then, use one of the points to solve for b, the y-intercept. Using the point (2, 50000), 50000 = 3200(2) + b, which simplifies to b = 43600. Therefore, the equation is y = 3200x + 43600.

Question 11

Find an equation for the least squares line representing weight, in pounds, as a function of height, in inches, of men. Then, predict the height of a man who is 145 pounds to the nearest tenth of an Inch. The following data are the (height, weight)pairs for 8 men: (66, 150), (68, 160), (69, 166), (70,175), (71, 181), (72, 191), (73, 198), (74, 206).

Accepted Answer

The least squares line is calculated using the given data points. After finding the slope and intercept, the equation is used to predict the height for a weight of 145 pounds, resulting in approximately 65.7 inches.

Question 12

Regrind, Inc. regrinds used typewriter platens. The cost per platen is $2.20. The fixed cost to run the grinding machine is $78 per day. If the company sells the reground platens for $4.20, how many Must be reground daily to break even?

Accepted Answer

To break even, the total cost must equal the total revenue. The total cost is the fixed cost plus the variable cost per platen times the number of platens, and the total revenue is the selling price per platen times the number of platens. Setting these equal gives: $78 + $2.20x = $4.20x$. Solving for x gives x = 39 platens.

Question 13

Find an equation in slope-intercept form (where possible) for the line.
-Through (6, 8), perpendicular to x = 7

Accepted Answer

The line x = 7 is a vertical line. A line perpendicular to a vertical line is a horizontal line. Horizontal lines have the equation y = k, where k is the y-coordinate of any point the line passes through. Since the line passes through (6, 8), the equation is y = 8.

Question 14

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (-1,-1.5) $ and $ (3,3.5) $

Accepted Answer

The slope (m) is calculated as $\frac{3.5 - (-1.5)}{3 - (-1)} = \frac{5}{4} = 1.25$. Using point-slope form with point (-1, -1.5), $y + 1.5 = 1.25(x + 1)$, simplifying gives $y = 1.25x - 0.25$.

Question 15

Find the slope of the line. $
4 x-5 y=-5
$

Accepted Answer

The answer of Find the slope of the line. \(
4...

Question 16

Find the slope of the line.
-A line perpendicular to 6x = 4y + 8

Accepted Answer

The slope of the given line is -2/3. A line perpendicular to this line will have a slope that is the negative reciprocal of -2/3, which is 3/2.

Question 17

The temperature of water in a certain lake on a day in October can be determined by using the model y = 15.2 - 0.537x where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the Water 10 degrees? (Round to the nearest foot.)

Accepted Answer

The answer of The temperature of water in a certain...

Question 18

A book publisher found that the cost to produce 1000 calculus textbooks is $25,600, while the cost to produce 2000 calculus textbooks is $50,300. Assume that the cost C(x)is a linear function of x, the Number of textbooks produced. What is the marginal cost of a calculus textbook?

Accepted Answer

The marginal cost is the change in cost divided by the change in quantity. Here, the change in cost is $50,300 - $25,600 = $24,700, and the change in quantity is 2000 - 1000 = 1000 textbooks. So, the marginal cost per textbook is $24,700 / 1000 = $24.70.

Question 19

Find the correlation coefficient.
-Let the supply and demand functions for raspberry-flavored licorice be given by 
$
p=S(q)=\frac{5}{4} q \quad \text { and } p=D(q)=90-\frac{5}{4} q \text {, }
$

where $ \mathrm{p} $ is the price in dollars and $ \mathrm{q} $ is the number of batches. Graph these functions on the same axes (graph the supply function as a dashed line and the demand function as a solid line). Also, find the equilibrium quantity and the equilibrium price.

Accepted Answer

The answer of  Find the correlation coefficient.
-Let the supply...

Question 20

Find the correlation coefficient.
-The following are costs of advertising (in thousands of dollars)and the number of products sold thousands):

Accepted Answer

The answer of  Find the correlation coefficient.
-The following are...

Quiz 1: Linear Functions

Find the slope of the line. $Find the slope of the line. A) -2 B) -\frac{1}{2} C) 2 D) \frac{1}{2}$

Find the correlation coefficient. -Consider the data points with the following coordinates:

Find the correlation coefficient -Consider the data points with the following coordinates:

Find an equation in slope-intercept form (where possible) for the line. -Through $(-7,4)$ and $(0,-5)$

Through (5, -4) and (-3, 3) 127)

Find the slope of the line passing through the given pair of points. (6, 2) and (9, 4)

Find the slope of the line passing through the given pair of points. (-5, -8) and (8, -8) 143)

Find the equation of the least squares line. -A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below.

Regrind, Inc. regrinds used typewriter platens. The cost per platen is $2.20. The fixed cost to run the grinding machine is $78 per day. If the company sells the reground platens for $4.20, how many Must be reground daily to break even?

Find an equation in slope-intercept form (where possible) for the line. -Through (6, 8) , perpendicular to x = 7

Find an equation in slope-intercept form (where possible) for the line. -Through $(-1,-1.5)$ and $(3,3.5)$

Find the slope of the line. $4 x-5 y=-5$

Find the slope of the line. -A line perpendicular to 6x = 4y + 8

A book publisher found that the cost to produce 1000 calculus textbooks is $25,600, while the cost to produce 2000 calculus textbooks is $50,300. Assume that the cost C(x) is a linear function of x, the Number of textbooks produced. What is the marginal cost of a calculus textbook?

Find the correlation coefficient. -The following are costs of advertising (in thousands of dollars) and the number of products sold thousands) :

Quiz 1: Linear Functions

Find the slope of the line.

The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters) . Use the equation of the least squares line to predict the Growth of a plant if the temperature is 53.

Find the correlation coefficient. -Consider the data points with the following coordinates:

Find the correlation coefficient -Consider the data points with the following coordinates:

Find an equation in slope-intercept form (where possible) for the line. -Through (−7,4) (-7,4) (−7,4) and (0,−5) (0,-5) (0,−5)

Through (5, -4) and (-3, 3) 127)

Find the slope of the line passing through the given pair of points. (6, 2) and (9, 4)

Find the slope of the line passing through the given pair of points. (-5, -8) and (8, -8) 143)

Find the equation of the least squares line. -A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below.

Regrind, Inc. regrinds used typewriter platens. The cost per platen is $2.20. The fixed cost to run the grinding machine is $78 per day. If the company sells the reground platens for $4.20, how many Must be reground daily to break even?

Find an equation in slope-intercept form (where possible) for the line. -Through (6, 8) , perpendicular to x = 7

Find an equation in slope-intercept form (where possible) for the line. -Through (−1,−1.5) (-1,-1.5) (−1,−1.5) and (3,3.5) (3,3.5) (3,3.5)

Find the slope of the line. 4x−5y=−54 x-5 y=-54x−5y=−5

Find the slope of the line. -A line perpendicular to 6x = 4y + 8

A book publisher found that the cost to produce 1000 calculus textbooks is $25,600, while the cost to produce 2000 calculus textbooks is $50,300. Assume that the cost C(x) is a linear function of x, the Number of textbooks produced. What is the marginal cost of a calculus textbook?

Find the correlation coefficient. -The following are costs of advertising (in thousands of dollars) and the number of products sold thousands) :

Find the slope of the line. $Find the slope of the line. A) -2 B) -\frac{1}{2} C) 2 D) \frac{1}{2}$

Find an equation in slope-intercept form (where possible) for the line. -Through $(-7,4)$ and $(0,-5)$

Find an equation in slope-intercept form (where possible) for the line. -Through $(-1,-1.5)$ and $(3,3.5)$

Find the slope of the line. $4 x-5 y=-5$