Exam 2: Linear Equations and Functions

Data from 2003 for various groups shows that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $60.85. When the median weekly income for whites was $665 and for blacks was $524. Let W represent the median weekly income for whites and B the median weekly income for blacks, and write the equation of the line that gives B as a linear function of W. ​

Given a cost function and a revenue function , where x represents the number of units produced and sold, find the profit function and then determine the marginal profit. ​

Solve the inequality. ​ ​

If a test that has reliability r is lengthened by a factor , the reliability R of the new test is given by ​ ​ ​If the reliability is r = 0.6, the equation becomes . When the test length is unchanged, the reliability r = R(1) = 0.6. If the length of the test is doubled, the reliability r = R(2). What percent improvement is there in the reliability when the test length is doubled? ​

A linear revenue function is , where x represents the number of units sold. If 15 units are currently produced, determine the marginal revenue. ​

A company distributes college logo sweatshirts and sells them for $50 each. The total cost function is linear, and the total cost for 100 sweatshirts is $4,620, whereas the total cost for 250 sweatshirts is $7,620. Find the equation for the total cost function where x is the number of sweatshirts produced and sold. ​

Mr. Jackson borrowed money from his bank and on his life insurance to start a business. His interest rate on the bank loan was 10%, and his rate on the insurance loan was 12%. If the total amount borrowed was $100,000 and his total yearly interest payment was $11,400, how much did he borrow from the bank? ​

Write the equation of the line through (2, -6) that is perpendicular to ​

Residential customers who heat their homes with natural gas have their monthly bills calculated by adding a base service charge of $5.48 per month and an energy charge of 48.59 cents per hundred cubic feet. Write an equation for the monthly charge y (in dollars) in terms of x, the number of hundreds of cubic feet used. ​

The equation gives the relation between temperature readings in Celsius and Fahrenheit. If a temperature has reading of 10 Fahrenheit, what is the corresponding reading in Celsius? ​

Solve the inequality and choose the graph of the solution. ​ ​

Solve the equation. ​ ​

Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function? ​ ​

A shoe store owner will buy 10 pairs of a certain shoe if the price is $75 per pair and 30 pairs if the price is $25. The supplier of the shoes is willing to provide 25 pairs if the price is $60 per pair but only 5 pairs if the price is $20. Assuming the supply and demand functions for the shoes are linear, find the market equilibrium point . ​

Choose the equation of the line with the given slope and y-intercept. ​ Slope: y-intercept : ​

Financial Paper, Inc. is a printer of checks and forms for financial institutions. For individual accounts, boxes of 200 checks cost $0.75 per box to print and package; they sell for $4.95 each. Financial Paper's monthly fixed costs for printing and packaging these checks for individuals are $1,245. Which of the following is the equation for the profit function where x denotes the number of boxes of checks produced and sold? ​

Suppose in the figure below. Find . ​ ​ ​

A social agency is charged with providing services to three types of clients, A, B, and C. A total of 450 clients are to be served, with $125,000 available for counseling and $85,000 available for emergency food and shelter. Type A clients require an average of $200 for counseling and $300 for emergencies, type B clients require an average of $500 for counseling and $200 for emergencies, and type C clients require an average of $300 for counseling and $100 for emergencies. How many of each type of client can be served? ​

A glass of skim milk supplies 0.1 mg of iron and 8.5 g of protein. A quarter pound of lean red meat provides 3.4 mg of iron and 22 g of protein. If a person on a special diet is to have 8.7 mg of iron and 73.75 g of protein, how many glasses of skim milk and how many quarter-pound servings of meat would provide this? Give the answer rounded to the nearest half serving. ​

Graph the equation with a graphing utility using the specified range and then using the standard viewing window. Does the graph below show the specified range or the standard window? ​ ​ ​