Question 1

Solve the problem.
-Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run the molding machine is $5616 per week. If the company sells the handles for $4.00 each, how many Handles must be molded weekly to break even?

Accepted Answer

The answer of Solve the problem.
-Northwest Molded molds plastic handles...

Question 2

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 -19.

Accepted Answer

The answer of For the following table of data, 
A....

Question 3

Suppose that the demand and price for a certain model of graphing calculator are related by $ p=D(q)=96-1.5 q $, where $ p $ is the price (in dollars) and $ q $ is the demand (in hundreds). Find the price if the demand is 600 calculators.

Accepted Answer

Given the demand function $ p = 96 - 1.5q $ and the demand $ q = 600 $ calculators, we first convert the demand into hundreds, as the function requires, giving us $ q = 6 $. Substituting $ q = 6 $ into the demand function gives $ p = 96 - 1.5(6) = 96 - 9 = 87 $. Therefore, the price is $ \$87.00 $.

Question 4

Evaluate the function as indicated.
-Find $ g\left(c^{2}\right) $ when $ g(x)=-8+3 x $.

Accepted Answer

To find $ g(c^2) $, substitute $ x $ with $ c^2 $ in the function $ g(x) = -8 + 3x $. This gives $ g(c^2) = -8 + 3(c^2) $, which matches option D.

Question 5

Suppose that the population of a certain town, in thousands, was 105 in 1990 and 141 in 2002. Assume that the population growth can be approximated by a straight line. Find the equation of a Line which will estimate the population of the town, in thousands, in any given year since 1990.

Accepted Answer

The slope of the line is calculated by the change in population over the change in years, which is (141 - 105) / (2002 - 1990) = 36 / 12 = 3. The equation of the line is y = 3x + 105, where x is the number of years since 1990, making option B correct.

Question 6

Find an equation in slope-intercept form (where possible) for the line.
-Through $ (8,-10) $, parallel to $ -5 x+3 y=-46 $

Accepted Answer

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

Question 7

Find the slope of the line passing through the given pair of points.
-$ (19,-4) $ and $ (-3,14) $

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, we get $m = \frac{14 - (-4)}{-3 - 19} = \frac{18}{-22} = -\frac{9}{11}$.

Question 8

A biologist recorded 9 snakes on 14 acres in one area and 18 snakes on 21 acres in another area. Let y be the number of snakes in x acres. Write a linear equation for the number of snakes.

Accepted Answer

The answer of A biologist recorded 9 snakes on 14...

Question 9

Let the supply and demand functions for a certain model of electric pencil sharpener be given by $ p=S(q)=\frac{2}{3} q \quad $ and $ p=D(q)=12-\frac{2}{3} q $ where p is the price in dollars and q is the quantity of pencil sharpeners (in hundreds). 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 Let the supply and demand functions for...

Question 10

Solve the problem.
-The bank's temperature display shows that it is 22° Celsius. What is the temperature in Fahrenheit?

Accepted Answer

To convert Celsius to Fahrenheit, use the formula $F = \frac{9}{5}C + 32$. For 22°C, it's $F = \frac{9}{5} \times 22 + 32 = 71.6°F$.

Question 11

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Use the equation of the least squares line to predict the score on the Test of a student who studies 13 hours.

Accepted Answer

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

Question 12

Write a cost function for the problem. Assume that the relationship is linear.
-A cab company charges a base rate of $1.00 plus 10 cents per minute. Let C(x)be the cost in dollars of u

Accepted Answer

The cost function $ C(x)=0.10x+1.00 $ correctly represents the cost of using the cab for x minutes, with a base rate of $1.00 plus 10 cents per minute.

Question 13

Assume that the sales of a certain appliance dealer can be approximated by a straight line. Suppose that sales were $13,500 in 1982 and $65,000 in 1987. Let x = 0 represent 1982. Find the equation
Giving yearly sales S.

Accepted Answer

To find the equation of the line, we first calculate the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $y_2 = 65,000$, $y_1 = 13,500$, $x_2 = 1987 - 1982 = 5$, and $x_1 = 0$. So, $m = \frac{65,000 - 13,500}{5} = 10,300$. The equation of the line is $S = mx + b$, where $b$ is the y-intercept, which is the sales in 1982 or $13,500. Therefore, the equation is $S = 10,300x + 13,500$.

Question 14

Graph the equation.
-x = -5

Accepted Answer

The answer of Graph the equation.
-x = -5  
...

Question 15

The information in the chart below gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24,100)and (3, 26,300). Then use this function to predict The salary for the year 2005.

Accepted Answer

The answer of The information in the chart below gives...

Question 16

The outdoor temperature rises to 22° Fahrenheit. What is this temperature in Celsius?

Accepted Answer

To convert Fahrenheit to Celsius, use the formula: $C = \frac{5}{9}(F - 32)$. Plugging in 22 for F gives $C = \frac{5}{9}(22 - 32) = \frac{5}{9}(-10) = -5.6°$.

Question 17

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 18

Solve the problem.
-Find an equation for the least squares line representing weight, in pounds, as a function of height, in inches, of men. Then, predict the weight of a man who is 68 inches tall to the nearest tenth of a Pound. 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

161.2 poundsTo find the least squares line, we first calculate the slope (m) and y-intercept (b) of the line using the formula for a linear regression line, which involves summing the products of the differences from the mean for each variable and dividing by the sum of the squares of the differences from the mean of the independent variable. After calculating m and b, we use the equation of the line (y = mx + b) to predict the weight for a height of 68 inches. The calculation involves detailed steps not shown here due to the format constraint, but the result for a man who is 68 inches tall is approximately 161.2 pounds, making option A correct.

Question 19

Find the slope of the line.
-A line parallel to $ -2 y+5 x=7 $

Accepted Answer

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

Question 20

In the table below, x represents the number of years since 2000 and y represents annual sales (in thousands of dollars)for a clothing company. Use the least squares regression equation to Estimate sales in the year 2006. Round to the nearest thousand dollars.

Accepted Answer

The answer of In the table below, x represents the...

Quiz 1: Linear Functions

Solve the problem. -Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run the molding machine is $5616 per week. If the company sells the handles for $4.00 each, how many Handles must be molded weekly to break even?

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 -19.

Suppose that the demand and price for a certain model of graphing calculator are related by $p=D(q) =96-1.5 q$ , where $p$ is the price (in dollars) and $q$ is the demand (in hundreds) . Find the price if the demand is 600 calculators.

Evaluate the function as indicated. -Find $g\left(c^{2}\right)$ when $g(x) =-8+3 x$ .

Suppose that the population of a certain town, in thousands, was 105 in 1990 and 141 in 2002. Assume that the population growth can be approximated by a straight line. Find the equation of a Line which will estimate the population of the town, in thousands, in any given year since 1990.

Find an equation in slope-intercept form (where possible) for the line. -Through $(8,-10)$ , parallel to $-5 x+3 y=-46$

Find the slope of the line passing through the given pair of points. - $(19,-4)$ and $(-3,14)$

A biologist recorded 9 snakes on 14 acres in one area and 18 snakes on 21 acres in another area. Let y be the number of snakes in x acres. Write a linear equation for the number of snakes.

Solve the problem. -The bank's temperature display shows that it is 22° Celsius. What is the temperature in Fahrenheit?

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Use the equation of the least squares line to predict the score on the Test of a student who studies 13 hours.

Write a cost function for the problem. Assume that the relationship is linear. -A cab company charges a base rate of $1.00 plus 10 cents per minute. Let C(x) be the cost in dollars of u

Assume that the sales of a certain appliance dealer can be approximated by a straight line. Suppose that sales were $13,500 in 1982 and $65,000 in 1987. Let x = 0 represent 1982. Find the equation Giving yearly sales S.

Graph the equation. -x = -5

The outdoor temperature rises to 22° Fahrenheit. What is this temperature in Celsius?

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

Find the slope of the line. -A line parallel to $-2 y+5 x=7$

Quiz 1: Linear Functions

Solve the problem. -Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run the molding machine is $5616 per week. If the company sells the handles for $4.00 each, how many Handles must be molded weekly to break even?

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 -19.

Suppose that the demand and price for a certain model of graphing calculator are related by p=D(q) =96−1.5q p=D(q) =96-1.5 q p=D(q) =96−1.5q , where p p p is the price (in dollars) and q q q is the demand (in hundreds) . Find the price if the demand is 600 calculators.

Evaluate the function as indicated. -Find g(c2) g\left(c^{2}\right) g(c2) when g(x) =−8+3x g(x) =-8+3 x g(x) =−8+3x .

Suppose that the population of a certain town, in thousands, was 105 in 1990 and 141 in 2002. Assume that the population growth can be approximated by a straight line. Find the equation of a Line which will estimate the population of the town, in thousands, in any given year since 1990.

Find an equation in slope-intercept form (where possible) for the line. -Through (8,−10) (8,-10) (8,−10) , parallel to −5x+3y=−46 -5 x+3 y=-46 −5x+3y=−46

Find the slope of the line passing through the given pair of points. - (19,−4) (19,-4) (19,−4) and (−3,14) (-3,14) (−3,14)

A biologist recorded 9 snakes on 14 acres in one area and 18 snakes on 21 acres in another area. Let y be the number of snakes in x acres. Write a linear equation for the number of snakes.

Solve the problem. -The bank's temperature display shows that it is 22° Celsius. What is the temperature in Fahrenheit?

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Use the equation of the least squares line to predict the score on the Test of a student who studies 13 hours.

Write a cost function for the problem. Assume that the relationship is linear. -A cab company charges a base rate of $1.00 plus 10 cents per minute. Let C(x) be the cost in dollars of u

Assume that the sales of a certain appliance dealer can be approximated by a straight line. Suppose that sales were $13,500 in 1982 and $65,000 in 1987. Let x = 0 represent 1982. Find the equation Giving yearly sales S.

Graph the equation. -x = -5

The information in the chart below gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24,100) and (3, 26,300) . Then use this function to predict The salary for the year 2005.

The outdoor temperature rises to 22° Fahrenheit. What is this temperature in Celsius?

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

Find the slope of the line. -A line parallel to −2y+5x=7 -2 y+5 x=7 −2y+5x=7

In the table below, x represents the number of years since 2000 and y represents annual sales (in thousands of dollars) for a clothing company. Use the least squares regression equation to Estimate sales in the year 2006. Round to the nearest thousand dollars.

Suppose that the demand and price for a certain model of graphing calculator are related by $p=D(q) =96-1.5 q$ , where $p$ is the price (in dollars) and $q$ is the demand (in hundreds) . Find the price if the demand is 600 calculators.

Evaluate the function as indicated. -Find $g\left(c^{2}\right)$ when $g(x) =-8+3 x$ .

Find an equation in slope-intercept form (where possible) for the line. -Through $(8,-10)$ , parallel to $-5 x+3 y=-46$

Find the slope of the line passing through the given pair of points. - $(19,-4)$ and $(-3,14)$

Find the slope of the line. -A line parallel to $-2 y+5 x=7$