Exam 1: Linear Equations and Functions

The number (in millions) of women in the work force, given as a function f, of the year for selected years from 1920 to 2000, is shown in the figure below. Estimate and explain its meaning. ​​ ​

When a $837,000 building is depreciated for tax purposes (by the straight-line method), its value y after x months of use is given by . How many months will it be before the building is fully depreciated (that is, its value is $0)? ​

If a line is vertical, then its slope is undefined.

The relation defined by the table is a function. Choose the correct domain and range. ​

Approximate the zeros of the function below by approximating the x-intercepts with a graphing utility. Round your answer to four decimal places ​ ​

Find the domain and range of the function below. ​ ​

Find the slope m and y-intercept b of the line whose equation is given below. ​ X = - ​

Suppose in the figure below. How many values of x satisfy ? ​ ​

As the price of a commodity increases, what happens to supply? ​

A $670,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building y, after x months of use is given by dollars. After how many months will the value of the building be $339,000? Round your answer to the nearest whole number of months. ​

Suppose that a certain product has the following demand and supply functions, where p is the price per unit in dollars and q is the quantity produced. ​ Demand: Supply: ​ If a $44 tax is placed on each unit of the product of the following. What is the new equilibrium point? ​

One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $156,600 to invest would like to have an income of $25,000 per year from her investments. How much should she invest at each rate? ​

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 $140,000 available for counseling and $100,000 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? ​

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 = 0.5, the equation becomes . When the test length is unchanged, the reliability r = R(1) = 0.5. 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? ​

Solve for t. ​

Use the x-intercept method to find the solution of the equation below where . Round your answer to five decimal places. ​ ​

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 5.6 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. ​

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. ​ ​ ​

If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense? ​

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. ​ ​