1. A solution consisting of 135 mg of dopamine in 15 mL of solution is administered at a rate of 44 mL/hr. What is the flow rate in mg of dopamine per hour?
2. A doctor administers a drug to a 36kg patient, using a dosage formula of 50 mg/kg/day. Assume that the drug is available in a 300 mg per 5 mL suspension or in 400 mg tablets. How many tablets should a 36-kg patient take every four hours? The suspension with a drop factor of 10 gtt/mL delivers the drug intravenously to the patient over a twelve-hour period. What flow rate should be used in units of gtt/hr?
3. Solar (photovoltaic) cells convert sunlight directly into electricity. If solar cells were 100% efficient, they would generate about 1000 watts of power per square meter of surface area when exposed to direct sunlight. With lower efficiency, they generate proportionally less power. For example, 10% efficient cells generate 100 watts of power in direct sunlight. Suppose you want to supply 2 kilowattss of power to a house by putting solar panels on its roof. For solar cells with the average power of 27 watts per square meter of solar panels, how many square meters of solar panels would you need? Assume you can make use of the average power from the solar cells (by, for example, storing energy in batteries until it is needed).
4. A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming wind farms typically generate 35% of their capacity, how much energy, in kilowatt-hours, can the region’s wind farms generate in one year? Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms? Simplify your answer.
5. Suppose that 8 turns of a wire are wrapped around a pipe with a length of 60 inches and a circumference of 4 inches, so that the wire reaches from the bottom of the pipe to the top. What is the length of the wire? (Hint: Picture cutting the pipe along its length and pressing it flat.)
6. A stereo system is being installed in a room with a rectangular floor measuring 20 feet by 19 feet and a 17-foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. You must run a wire from the amplifier to the speaker, and the wire must run along the floor or walls (not through the air). What is the shortest length (ft) of wire you can use for the connection? (Hint: Turn the problem into an equivalent simpler problem by imagining cutting the room along its vertical corners and unfolding it so that it is flat. You will be able to apply the Pythagorean theorem.)
7. Express the first number as a percentage of the second number. 26 pounds of recyclable trash in a barrel of 53 pounds of trash. Round to the nearest 10th as needed.
8. In the following statement, express the first number as a percentage of the second number. The full-time year-round median salary for U.S. men in 2010 was $41500 and the full-time year-round salary for U.S. women in 2010 was $34200. Round to the nearest 10th as needed.
9. The percentage of people accessing the Internet increased from 68% in 2000 to 89% in 2012. Describe the change as an absolute change in terms of percentage points.
10. Between 2000 and 2010, the percentage of households with cordless phones increased by 15.9% to 92%.What percentage of households had cordless phones in 2000?
11. The unemployment rate has risen more than a percentage point to 8.9% in February from 6.7% last November. What is the relative change in the unemployment rate expressed as a percentage?
12. Convert 5 years to hours (neglecting leap years).
13. A solution consisting of 117 mg of dopamine in 13 mL of solution is administered at a rate of 5 mL/hr. What is the flow rate in mg of dopamine per hour? If a patient is prescribed to receive 360 mg of dopamine, how long should the infusion last?
14. Express the given percentage as a reduced fraction and a decimal. 325%.
15. Express the first number as a percentage of the second number. 27 pounds of recyclable trash in a barrel of 58 pounds of trash.
16. The sales tax rate in a city is 8.3%. Find the tax charged on a purchase of $253 and the total cost.
17. Rewrite the following statement using a number in scientific notation. The diameter of a certain bacterium is about 0.00000005 meters.
18. What is the order of magnitude estimate for the number of steps you take in an average day?
a. The order of magnitude estimate is 3000 to 4000 steps; assuming an average person walks 2 miles per day.
b. The order of magnitude estimate is 375 to 575 steps; assuming an average person walks 16 miles per day.
c. The order of magnitude estimate is 100 to 200 steps; assuming an average person walks 8 miles per day.
d. The order of magnitude estimate is 375 to 500 steps; assuming an average person walks 1/4
of a mile per day.
19. Dropping less than two inches per mile after emerging from the mountains, a river drains into the ocean. One day’s discharge at its mouth, 8.4 trillion gallons, could supply all of country A’s households for seven months. Based on this statement, determine how much water an average household uses each month. Assume that there are 200 million households in country A.
20. Use the four basic rules of algebra to solve the following equation. 6x-16 =56 + 4x. simplify your answer.
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