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1. If a line that passes through the ordered pairs (4 – c, 2c) and (–c, –8) has a slope of , what is the value of c?
2. Two airplanes departed from different airports at 5:30 AM, both traveling nonstop to London Heathrow Airport (LHR). The distances the planes traveled are recorded in the table. The Washington, D.C. (DCA) flight flew through moderate cloud cover and as a result only averaged 338 mph. The flight from Miami (MIA) had good weather conditions for the first two-thirds of the trip and averaged 596 mph, but then encountered some turbulence and only averaged 447 mph for the last part of the trip. Which plane arrived first and how long was it at the London airport before the other plane arrived?
3. Which of the following quadratic equations has no solution?
A student looked at the graph above and determined based on the data that spending more money per student causes the gross domestic product (GDP) to increase. Which of the following statements is true?
5. In chemistry, the combined gas law formula gives the relationship between the volumes, temperatures, and pressures for two fixed amounts of gas. Which of the following gives p2 in terms of the other variables?
6. An object's weight is dependent upon the gravitational force being exerted upon the object. This is why objects in space are weightless. If 1 pound on Earth is equal to 0.377 pounds on Mars and 2.364 pounds on Jupiter, how many more pounds does an object weighing 1.5 tons on Earth weigh on Jupiter than on Mars?
When a drug company wants to introduce a new drug, it must subject the drug to rigorous testing. The final stage of this testing is human clinical trials, in which progressively larger groups of volunteers are given the drug and carefully monitored. One aspect of this monitoring is keeping track of the frequency and severity of side effects. The figure above shows the results for the side effect of headaches for a certain drug. According to the trial guidelines, all moderate and severe headaches are considered to be adverse reactions. Which of the following best describes the data?
8. In the legal field, "reciprocity" means that an attorney can take and pass a bar exam in one state, and be allowed to practice law in a different state that permits such reciprocity. Each state bar association decides with which other states it will allow reciprocity. For example, Pennsylvania allows reciprocity with the District of Columbia. It costs $25 less than 3 times as much to take the bar in Pennsylvania than in D.C. If both bar exams together cost $775, how much less expensive is it to take the bar exam in D.C. than in Pennsylvania?
9. A grain producer is filling a cylindrical silo 20 feet wide and 60 feet tall with wheat. Based on past experience, the producer has established a protocol for leaving the top 5% of the silo empty to allow for air circulation. Assuming the producer follows standard protocol, what is the maximum amount of wheat that should be put in the silo?
Mr. Juno took his driver's education class to the Department of Motor Vehicles to take their driver's license test. The number of questions missed by each student in the class is recorded in the bar graph above. Which of the following statements is true?
11. If the graph of the equation y = ax2 + bx + c passes through the points (0, 2), (–6, –7), and (8, –14), what is the value of a + b + c?
12. A bakery sells three sizes of muffins—mini, regular, and jumbo. The baker plans daily muffin counts based on the size of his pans and how they fit in the oven, which results in the following ratios: mini to regular equals 5 to 2, and regular to jumbo equals 5 to 4. When the bakery caters events, it usually offers only the regular size, but it recently decided to offer a mix of mini and jumbo instead of regular. If the baker wants to keep the sizes in the same ratio as his daily counts, what ratio of mini to jumbo should he use?
13. If the system of linear equations shown above has no solution, and k is a constant, what is the value of k?
14. What is the value of ?
15. If a right cone is three times as wide at its base as it is tall, and the volume of the cone is 384π cubic inches, what is the diameter in inches of the base of the cone?
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