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The length of the tropical year is 365.24220 days, as compared to the length of 365.2425 days used by the Gregorian calender. a. What is the difference between the tropical year and the Gregorian calender year? (Express your answer in scientific notation.) b. How many years will it take for this small difference to amount to one day? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 3. A laser printer prints characters at a density of 300 dots per inch. a. How many dots can be printed across the width of 8.5 inches of a standard letter-sized piece of paper? b. How many dots can be printed down the length of 11.0 inches? c. If every dot was printed on the paper, how many dots would be printed? (Express your answer in scientific notation.) d. If each dot just touched the adjacent dot, what would be the diameter of a dot? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 5. A trip to the nearest star has been proposed. The nearest star is about 41/2 light years away. A light year is the distance that light can travel in a year. The speed of light is approximately 186,000 miles per second. a. Convert the speed of light to miles per year by multiplying the speed per second by the number of seconds in a year. This is how far light travels in a year. (Hint: Consider the number of days in a year, the number of hours in a day, etc.) (Express your answer in scientific notation.) b. How far away (in miles) is the nearest star? (Express your answer in scientific notation.) c. The spaceships that visited the moon traveled nearly 30,000 miles per hour. How many hours would it take at this speed to reach this nearest star? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 7. Diesel fuel can provide about 138,400 Btu per gallon. A tractor used 215 gallons of diesel fuel over a period of several days, a total of 56 hours running time. a. How many Btu of energy were provided by the fuel? (Express your answer in scientific notation, rounded to two decimal places.) b. If 2456 Btu in one hour is equivalent to 1 horsepower, how much horsepower was provided by the fuel during the 56 hours of running time? c. If the tractor is acually obtaining about 70 horsepower, what is the percentage of horsepower being obtained, compared to the horsepower being provided by the diesel fuel? (This is the thermal efficiency of the engine.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 9. A protected coastal wildlife area is surveyed and sampled for various forms of wildlife. The protected area is essentially rectangualr in shape, 92 miles long and 3.5 miles wide. Several 50-foot square sections were sampled throughout the area. The average population of a certain insect species in each section was 17. a. Determine the area of the protected area and convert it to square feet. (Express your answer in scientific notation.) b. Compute the area of each section that was sampled, and determine the average population of this insect per square foot. (Express your answer in scientific notation.) c. What is the estimated population of this insect within the boundaries of the protected wildlife area? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 11. You are making a bid to operate the concession stands at a play-off game. You expect a very large crowd, possibly as high as 85,000 fans. Past experience has shown that each fan in this region will purchase an average of about 1.75 cups of soft drink. a. How many cups of soft drink can you expect to sell? (Express your answer in scientific notation.) b. If each cup is filled with 6 oz of ice, how many ounces of ice can you expect to use? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 13. A report showed that nationwide consumer spending for professional services rose from $260,000,000,000 to $410,000,000,000 over a 10-year period. a. Express these amounts in scientific notation. b. What was the average growth in spending on services each year? (EXpress your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 15. In the past several years, the subcompact division of Luxury Motors produced a total of 17,400,000 cars from its 3 assembly plants. Reports of dissatisfaction over the steering wheel design of these models have been reported from 281 owners. What percent of the owners are dissatisfied? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 17. Suppose the national budget is $1.8 trillion ($1,800,000,000,000). a. Express this amount in scientific notation. b. If the population of the country is 250,000,000, what is each member of the populations portion of the budget? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 19. A computer sales brochure advertises that its system has a 16-megabyte memory and can store a total of nearly a half-gigabyte of data on its three hard disk drives. a. If a single character occupies a byte of memory or disk space, how many characters can be stored in the 16-megabyte memory? (Express your answer in scientific notation and standard notation.) b. About how many characters can be stored on each of the three identical disk drives? (Express your answer in scientific notation and standard notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 21. A synthetic thyroid preparation that is available in 25-microgram tablets is prescribed to a patient. The bottle of medication contains 30 tablets. a. Express the amount of medication in each tablet in grams, in scientific notation. b. How many grams of medication are in each bottle of medication? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 23. Suppose a particular bacterium can divide into two bacteria, once each hour. Thus, in one hour, one bacteria becomes two. After two hours, two bacteria can become four (2x2). In three hours, they become eight (2 x 2 x 2), and so on. If this process continues for a total of 48 hours, how many bacteria will there be? (Write this number both in scientific notation, and in standard notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 25. A 10-gram soil sample is analyzed to determine how many bacteria it contains. The sample is mixed with distilled water to form 100 ml of solution. A sample of this solution is diluted to 1/10 strength, and 0.1 ml is cultured. From this dilution, a sample is again diluted to 1/10 strength (now 1/10 x 1/10 of full strength) and cultured. This process is continued until a culture is obtained that produces individual colonies (that is, starting with individual bacterium). The culture from the ninth dilution produces 23 colonies. a. What is the strength of the ninth dilution, as a decimal fraction (expressed in scientific notation) of the strength of the initial soil solution? b. If 23 bacteria were present in 0.1 ml of the ninth dilution, how many bacteria were present in the 100 ml of the ninth dilution? c. Divide the number of bacteria in the ninth dilution (determined in Part b) by the strength of the ninth dilution (determined in Part a) to arrive at an estimate of the number of bacteria present in the initial soil sample. (Express this number in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 27. The spark plugs in most automotive engines must provide a spark for every two revolutions of the engine. While driving at normal speeds, the engine may be running at about 2500 revolutions per minute (rpm). a. If an average speed of 1 mile per minute is assumed for an annual mileage of 10,000 miles, approximately how many minutes is the car driven during the year? b. At 2400 revolutions per minute, or 1200 sparks per minute, during the years driving, about how many times does the spark fire during the year? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 29. A certain isotope of radioactive uranium has a half-life of 4.5 x 109 years. This means that after one half-life, the sample will have one-half of the beginning level of radioactivity. a. What is the half-life of this isotope in standard notation? b. If a generation is considered to be 40 years, how many generations will it take for this isotopes radioactivity to be reduced by half? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 31. A quartz crystal is commonly used in a digital watch to provide a stable time base. A certain crystal oscillates with a frequency of 5.0 MHz (megahertz). One hertz (Hz) is equivalent to one vibration or cycle per second. a. Express the quartz frequency of vibration in scientific notation, with units of hertz. b. With such a frequency, very small time divisions are possible. The period of one cycle can be computed by calculating 1/frequency. How many seconds is the smallest time division using this quartz crystal? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 33. A computer is advertised as having a processing speed of 11 mips, or 11 million instructions per second. a. Express this speed in scientific notation. b. On the average, how long does it take to process each instruction at such a speed? c. How many nanoseconds is this? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 35. A furnace used to process aluminum consumes approximately 25,000,000 watt- hours of energy per ton (2000 lb) of aluminum processed. a. Express the energy figure above in scientific notation. b. If a furnace processes 3200 tons of aluminum during a given period, about how much energy is used? (Express your answer in scientific notation.) c. Energy is usually reported in kilowatt-hours (kWh) rather than watt-hours. Express the answer to Part b in terms of kWh. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 37. Electricity travels at very near the speed of light, 3.0 x 108 meters per second. A surge suppressor - used to protect computer equipment for example - advertises a 1-ns clamping time. That is, it can suppress a voltage spike in 1 nanosecond. a. Express the advertised clamping time in scientific notation, with units of seconds. b. Multiply the speed of the electricity in a wire by the clamping time to estimate how far along the wire (in meters) a voltage spike will travel before being brought under control by the surge suppressor. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 39. Security coding, for example of automatic garage door openers, is done by setting a bank of switches. Since the number of possible switch settings is so great, it is assumed that the likelihood of an intruder accidentally guessing the setting is very small. For example, with three such switches that can be set to ON or OFF, the number of possible settings is 2 x 2 x 2, or 8 settings. Some switches have three possible settings, indicated as +1, 0, or -1, yielding a total of 3 x 3 x 3, or 27 possible settings for three switches. a. How many possible settings are in a switch bank of 8 switches with three settings for each? (Express your answer in scientific notation.) b. How many possible settings are in a bank of 12 switches with three settings for each? (Express your answer in scientific notation.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): DSET|(H->"9 *6*>"9DSET(H-9>96*=9DSETR ----   -Unit 12 Odd Questions