Exam 2: Linear Equations and Functions

Two of the processes (functions) used by a manufacturer of factory-built homes are sanding (denote this as function p) and painting (denote this as function s). Choose the correct explanation for the functional expression . ​

A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbohydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two slices of whole grain bread supply 2.2 mg of iron, 10 g of protein, and 12 g of carbohydrates. If a person on a special diet must have 9.1 mg of iron, 62.5 g of protein, and 53 g of carbohydrates, how many glasses of skim milk, how many quarter-pound servings of meat, and how many two-slice servings of whole grain bread will supply this? ​

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

Solve the equation.

Solve the inequality. ​ ​

The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the wind speed is 25 mph, the wind chill WC depends on the temperature t (in degrees Fahrenheit) according to . For what temperatures does it feel at least 25°F colder than the air temperature? That is, find t such that . Round your answer to two decimal places. ​

Use a graphing utility with the standard viewing window and to graph the function. Choose the correct graph below. ​ ​

A small business recaps and sells tires. The business has a revenue function and a cost function , where x represents the number of sets of four tires recapped and sold. Find the number of sets of recaps that must be sold to break even. ​

Let and . Does ? ​

Choose the graph that represents the equation below. ​ ​

Suppose the percent of U.S. high school seniors from 1975 to 2001 who used marijuana can be modeled by , where x is the number of years past 1975. What is the slope of the graph of this function? ​

A $680,000 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 $377,000? Round your answer to the nearest whole number of months. ​

If , find . ​

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

For and , find . ​

A linear cost function is , where x represents the number of units produced. If 50 units are currently produced, determine the marginal cost. ​

If the demand and supply functions for Z-brand phones are and respectively, compare the quantity demanded and the quantity supplied when . Note that q is the quantity produced or sold. Are there surplus phones or not enough to meet demand? ​

Assume that the price for a pair of shoes has been set at $40. The demand for a pair of shoes is given by and the supply for the same pair of shoes is . In both cases p is price per pair and q is the quantity produced or sold. Compare the quantity demanded and the quantity supplied. Will there be a surplus or shortfall at this price? ​

In wildlife management, the capture-mark-recapture technique is used to estimate the populations of fish or birds in an area or to measure the infestation of insects such as Japanese beetles. Suppose 100 individuals of the species being studied are caught, marked, and released, and one week later 100 more are caught. To estimate the total number of individuals, the following relationship is used: ​ ​ Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 59 are marked. What is the population estimate? ​

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