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1. A railway company normally charges $35 round trip from the suburbs of a city into downtown. The company also offers a deal for commuters who use the train frequently to commute from their homes in the suburbs to their jobs in the city. Commuters can purchase a discount card for $900, after which they only have to pay $12.50 per round trip. How many round trips, t, must a commuter make in order for the discount card to be a better deal?
2. Most people save money before going on vacation. Suppose Etienne saved $800 to spend during vacation, 20 percent of which he uses to pay for gas. If he budgets 25 percent of the remaining money for food, allots $300 for the hotel, and spends the rest of the money on entertainment, what percentage of the original $800 did he spend on entertainment?
3. A microbiologist placed a bacteria sample containing approximately 2,000 microbes in a petri dish. For the first 7 days, the number of microbes in the dish tripled every 24 hours. If n represents the number of microbes after h hours, then which of the following equations is the best model for the data during the 7-day period?
4. A survey is conducted regarding a proposed change in the attendance policy at a law school. The table above categorizes the results of the survey by year of the student (1L, 2L, or 3L) and whether they are for, against, or undecided about the new policy. What fraction of all 1Ls and 2Ls are against the new policy?
5. Which of the following expressions is equivalent to (6 + 5i)3? (Note: )
If an exponential function is used to model the data shown in the figure, and it is written in the form f(x) = f(0)(1 + r)x, what would be the value of r?
7. The Great Pyramid of Giza, built in the 26th century BC just outside of Cairo, Egypt, had an original height of 480 feet, 8 inches, before some of the stones in which it was encased fell away. Inside the pyramid is a 53.75-foot passage, called the Dead End Shaft, which archeologists have yet to discover the purpose of. Suppose a museum is building a scale model of the pyramid for patrons to explore. Because of the museum's ceiling height, they can only make the pyramid 71 feet, 6 inches tall. About how long should the museum's Dead End Shaft be?
Which of the following is equivalent to the expression above, given that x ≠ 2?
9. Ethanol is an alcohol commonly added to gasoline to reduce the use of fossil fuels. A commonly used ratio of ethanol to gasoline is 1:4. Another less common and more experimental additive is methanol, with a typical ratio of methanol to gasoline being 1:9. A fuel producer wants to see what happens to cost and fuel efficiency when a combination of ethanol and methanol are used. In order to keep the ratio of gasoline to total additive the same, what ratio of ethanol to methanol should the company use?
Julia and Ravi are meeting at a museum. The figure above represents the drives from their homes to the museum. Based on the figure, which of the following statements is true?
11. If the graph of the function g(x) passes through the point (8, –3), then through which point does the graph of –g(x – 4) – 6 pass?
12. If f(x) = x – 1, g(x) = x3, and x ≤ 0, which of the following could not be in the range of f(g(x))?
13. Given the equation y = -3(x – 5)2 + 8, which of the following statements is not true?
14. Every weekend for 48 hours, a law firm backs up all client files by scanning and uploading them to a secure remote server. On average, the size of each client file is 2.5 gigabytes. The law firm's computer can upload the scans at a rate of 5.25 megabytes per second. What is the maximum number of client files the law firm can back up each weekend? (1 gigabyte = 1,000 megabytes)
15. Main Street and 2nd Street run parallel to each other. Both are one-way streets. Main Street runs north, and 2nd Street runs south. The city is planning to build a new road, also one-way, that runs toward the southeast and cuts through both streets at an angle. Traffic turning off of Main Street would have to make a 125° turn onto the new road. What angle would traffic turning off of 2nd Street have to make turning onto the new road?
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