You purchase a remote-controlled drone for d dollars. Your friend purchases a drone that costs $35 more than your drone. Your brother purchases a drone that costs three times as much as your friend's drone. Write and simplify an expression that represents the cost (in dollars) of your brother's drone.

The height of a drone, in meters, above its launching platform that is 5 m above the ground, is modeled by

$$y = 0.1x^2 - 1.5x + 5,$$

where x is the time in seconds. The drone leaves the launch pad, flies down into a canyon, and then it flies back up again. a. What is the factored form of the equation for the height of the drone? b. After how many seconds will the drone be at ground level? c. After how many seconds will the drone come back to the height of its platform?

The market for grocery-store baggers is a competitive labor market, as shown in Figure 16P-7. Suppose a new federal law raises the minimum wage to $\$ 10$ per hour.

b. What are total labor earnings at the equilibrium wage?

The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon):

Make a scatterplot of mileage versus speed. Show that the correlation between speed and mileage is r=0. Explain why the correlation is 0 even though there is a strong relationship between speed and mileage.

If a pilot changes his permanent mailing address, how long can the pilot continue to exercise the privileges of their pilot certificate without notifying the FAA?

The market for grocery-store baggers is a competitive labor market, as shown in Figure 16P-7. Suppose a new federal law raises the minimum wage to $\$ 10$ per hour.

a. What is the equilibrium wage rate prior to the law being enacted?

Solve each equation. Check your answers. |2x - 1| = 5

Write a letter, as a British government official during the Industrial Revolution, to an official in a nonindustrial nation explaining how the railroad has changed Britain.

Consider a labor market that traditionally discriminates against hiring women. Suppose a new law effectively prohibits this practice. What would you expect to happen to the wages of men in this industry?

It takes 2 iron atoms and 6 chlorine atoms to make 2 iron (lll) chloride particles. How many chlorine atoms are required to make 18 iron (III) chloride particles?

Consider a corrupt provincial government in which each housing inspector examines two newly built structures each week. All the builders in the province are unethical and want to increase their profits by using substandard construction materials, but they can’t do that unless they can bribe a housing inspector into approving a substandard building. LO5.2 a. If bribes cost $1,000 each, how much will a housing inspector make each year in bribes? (Assume that each inspector works 52 weeks a year and gets bribed for every house he inspects.) b. There is a provincial construction supervisor who gets to hire all of the housing inspectors. He himself is corrupt and expects his housing inspectors to share their bribes with him. Suppose that 20 inspectors work for him and that each passes along half the bribes collected from builders. How much will the construction supervisor collect each year? c. Corrupt officials may have an incentive to reduce the provision of government services to help line their own pockets. Suppose that the provincial construction supervisor decides to cut the total number of housing inspectors from 20 to 10 in order to decrease the supply of new housing permits. This decrease in the supply of permits raises the equilibrium bribe from$1,000 to $2,500. How much per year will the construction supervisor now receive if he is still getting half of all the bribes collected by the 10 inspectors? How much more is the construction supervisor getting now than when he had 20 inspectors working in part b? Will he personally be happy with the reduction in government services? d. What if reducing the number of inspectors from 20 to 10 only increased the equilibrium bribe from$1,000 to $1,500? In this case, how much per year would the construction supervisor collect from his 10 inspectors? How much less is the construction supervisor getting than when he had 20 inspectors working in part b? In this case, will the construction supervisor be happy with the reduction in government services? Will he want to go back to using 20 inspectors?

Consider a specific example of the special-interest effect and the collective-action problem. In 2012, it was estimated that the total value of all corn-production subsidies in the United States was about $3 billion. The population of the United States was approximately 300 million people that year.

a. On average, how much did corn subsidies cost per person in the United States in 2012? (Hint: A billion is a 1 followed by nine zeros. A million is a 1 followed by six zeros.)

b. If each person in the United States is willing to spend only$0.50 to support efforts to overturn the corn subsidy, and if antisubsidy advocates can only raise funds from 10 percent of the population, how much money will they be able to raise for their lobbying efforts?

c. If the recipients of corn subsidies donate just 1 percent of the total amount that they receive in subsidies, how much could they raise to support lobbying efforts to continue the corn subsidy?

d. By how many dollars does the amount raised by the recipients of the corn subsidy exceed the amount raised by the opponents of the corn subsidy?

How do the concepts of pork-barrel politics and the special-interest effect relate to the items listed in the Last Word?

Verify each identity

$$\tan x + \frac { 1 } { \tan x } = \frac { 1 } { \sin x \cos x }$$