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1. According to the U.S. Department of Agriculture, the linear equation f = –3.7t + 872 estimates the number of acres of farmland f in the United States t years after 2010, where f is given in millions of acres. Based on this equation, at the start of what year will the amount of farmland be below 800 million acres?
2. If g(x) = x2 + 2x + 9, what is g(5) – g(–1)?
3. A North Carolina agricultural supply company is hoping to expand its services to three counties in rural Virginia. According to its research, there is a total of approximately 1,200 farms in these three counties. The company sends out surveys to a sample of 200 randomly selected farmers in the counties and finds that 120 are not satisfied with their current supply company. Based on other market research, the company is confident that it will be able to acquire 75% of the dissatisfied customers. Based on this information and the results of the sample survey, about how many customers should the company be able to acquire in these three counties?
Use the definition to write the expression above in simplest form.
5. Sometimes, companies will buy stock in businesses owned by one or more of their competitors in order to gain some control over the competing companies. Suppose Company X buys stock in two of its competitors. The first competitor is a small regional company. Five hundred shares of its stock cost $25,000 less than half as much as 500 shares of the other competitor, which is a large national company. Together, Company X pays $155,000 for all the stock. How many more thousands of dollars did Company X spend on acquiring the stock of the national competitor than the regional one? Enter your answer in thousands of dollars. (For example, enter $15,000 as 15.)
6. The Mackinac Bridge in Michigan is one of the longest suspension bridges in the Western Hemisphere, spanning approximately 1.63 miles from one end to the other. It has several pieces that are connected by anchorages (large blocks to which the suspension cables are attached). The longest piece is 3,800 feet long. In a scale drawing on a poster board, the length of the bridge is 28 inches. How many inches long should the longest piece be? Round your answer to the nearest tenth of an inch. (There are 5,280 feet in 1 mile.)
7. A restaurant sent out surveys to determine how long customers are willing to wait for a table on Friday night versus Saturday night. Participants randomly received either a Friday night or a Saturday night survey. Results are shown in the bar graph below.
If a customer is chosen at random from all of the survey respondents, what is the probability that the customer is willing to wait at least 30 minutes for a table?
8. A restaurant sent out surveys to determine how long customers are willing to wait for a table on Friday night versus Saturday night. Participants randomly received either a Friday night or a Saturday night survey. Results are shown in the bar graph below.
On average, how many minutes longer are customers willing to wait for a table on Saturday night than on Friday night? Round your answer to the nearest whole minute.
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