Quiz 2

Quiz 2

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1.) a. 2682 inches to yards

• Start with 2682 inches

•  $\frac{2682\ inches}{1}\cdot\frac{1\ feet}{12\ inches}\cdot\frac{1\ yard}{3\ feet}$  

•  $2682\div36=74.5\ yards$  

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1.) b. 2 miles to inches.

•  $\frac{2\ miles}{1}\cdot\frac{5280\ feet}{1\ mile}\cdot\frac{12\ inches}{1\ foot}$  

• 126,720 inches

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2. a. Convert 5 kilometers to nanometers.

•  $\frac{5\ kilometers}{1}\cdot\frac{10^3\ meters}{1\ kilometer}\cdot\frac{1\ nanometer}{10^{-9}meters}$  

•  $\frac{5}{1}\cdot\frac{10^3}{10^{-9}}$ nanometers 

•  $5\times10^{3-\left(-9\right)}$  

•  $5\times10^{12}\ \ \ or\ \ 5,000,000,000,000\ nanometers$  

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2.) b. 7000 deciliters to milliliters

•  $\frac{7000\ deciliters}{1}\cdot\frac{10^{-1}\ liters}{1\ deciliter}\cdot\frac{1\ millilter}{10^{-3}\ liters}$  

•  $7,000\times\frac{10^{-1}}{10^{-3}}$  

•  $7,000\times10^2$  

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a. 124 inches to meters.

•  $\frac{124\ inches}{1}\cdot\ \frac{2.54\ centimeters}{1\ inch}\cdot\frac{1\ meter}{100\ centimeters}$  

• Another way,  $\frac{124\ inches}{1}\cdot\frac{1\ centimeter}{0.3938\ inches}\cdot\frac{10^{-2}\ meters}{1\ centimeter}$  

• = 3.1496 or 3.15 meters

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3.) d. 43°C to °F

•  $F=1.8\left(C\right)+32$  

•  $1.8\left(43\right)+32$  

• =109.4°F

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4. A rectangular garden measures 13 feet wide, 32 feet long, and is to be filled to with 3 inches (0.25 feet) of soil. The store sales soil in bulk by the cubic yard. How many cubic yards of soil would you need to purchase to fill the garden with soil? (Round to the nearest cubic yard.)

•  $13\ feet\ \cdot\ 32\ feet\cdot0.25\ feet\ =104\ cubic\ feet$  

• If you divide by 3 (3ft=1yd), you're part ways there. Don't forget DIMENSIONAL analysis. Do it two more times.

•  $\frac{104\ feet\ \cdot feet\cdot feet}{1}\cdot\frac{1\ yard}{3\ feet}\cdot\frac{1\ yard}{3\ feet}\cdot\frac{1\ yard}{3\ feet}$  

• Divided by 27, we obtain 3.85185 or 4 yards.

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a. You are traveling to Canada with $128.00 in U.S. dollars. How many Canadian dollars can you buy?

•  $\frac{128\ dollars}{1}\cdot\frac{1.318\ Canadian}{1\ dollar}$  

•  $\frac{128\ dollars}{1}\cdot\frac{1\ Canadian}{0.7586\ dollars}$  

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Multiple Choice

8. A cube of wood measures 5 centimeters on a side and weighs 100 grams.

b. Will it float in water? (Density of water is 1 gr/cm³ )

• Sink

• Float

Multiple Choice

9. Jane’s salary increased from $32,000 to $41,500 over a four year period. Mark’s salary increased from $25,000 to $33,750 during the same time span. Whose salary increased more in absolute terms? In relative terms?

Whose salary increased more in ABSOLUTE terms?

• Jane

• Mark

Multiple Choice

9. Jane’s salary increased from $32,000 to $41,500 over a four year period. Mark’s salary increased from $25,000 to $33,750 during the same time span. Whose salary increased more in absolute terms? In relative terms?

Whose salary increased more in RELATIVE terms?

• Jane

• Mark

Open Ended

12. Anthony thinks that if his tax rate decreases by 12% for the next 3 years, then his tax rate will decrease by a total of 36% over the three year period. Is Anthony correct in his assumption? Explain.

12. Anthony thinks that if his tax rate decreases by 12% for the next 3 years, then his tax rate will decrease by a total of 36% over the three year period. Is Anthony correct in his assumption? Explain.

• Try something out and see if it works. Assume he owes $100 in taxes. (A 36% decrease would mean he is taxed $64 by the end of 3 years.)

• First year he will decrease by 12% of $100 which is $12, so 100 - 12 = 88 dollars is his new tax amount.

• Second year, he will decrease by 12% of $88 which is $10.56, so 88 - 10.56 = 77.44 is his new tax amount.

• Third year, he will decrease by 12% of $77.44 which is $9.29, so 77.44 - 9.29 = 68.15 is the final tax amount and it not the 64 as suggested.

• Nope. Changing reference values.

Open Ended

13. You teach two separate classes. Your first class, which consists of 27 students, has a mean score of 83% on the midterm exam. Your second class, with 14 students, had a mean score of 85% on the same exam. Does it follow that the mean score for both classes combine is 84%? Explain.

13. You teach two separate classes. Your first class, which consists of 27 students, has a mean score of 83% on the midterm exam. Your second class, with 14 students, had a mean score of 85% on the same exam. Does it follow that the mean score for both classes combine is 84%? Explain.

• To keep things simpler, this can happen if everyone in the first class scores an 83 and everyone in the second class scores an 85. Does this average to 84?

• For the first class, the average would look something like: $\frac{83+83+...+83+83}{27}=\frac{2,241}{27}=83$  where I'm adding the number 83 a total of 27 times for the 27 different students.

• For the second,  $\frac{85+85+...+85+85}{14}=\frac{1190}{14}=85$  

• Combining the two classes,  $\frac{\left(83+...+83\right)+\left(85+..+85\right)}{27+14}=\frac{2,241+1,190}{41}=\frac{3,431}{41}\approx83.6829$  

• The mean score is slightly lower than the 84% guessed. In general, we don't average percentage.

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18. Use Table 3.4 to answer the following. Suppose you need $15,000 to maintain a particular standard of living in 1977.

a. How much would you need to maintain the same standard of living in 1999?

•  $Amount\ in\ 1999\ =\ Amount\ in\ 1977\ \cdot\frac{CPI_{1999}}{CPI_{1977}}$  

•  $Amount\ in\ 1999\ =\ 15,000\ \cdot\frac{166.6}{60.6}$  

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19. Use Table 3.4 to answer the following. The average price of tuition and fees at public 4–year colleges and universities increased from $1,770 in 1991 to $6,700 in 2009. Calculate the relative change in price from 1991 to 2009 and compare it to the overall rate of inflation as measured by the Consumer Price Index.

•  $\frac{new-old}{old}=\frac{6700-1770}{1770}\approx2.7853$  

• 278.53%

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Multiple Choice

20. The table below shows the efficacy of two different treatments for kidney stones.

a. Which treatment did better with small stones?

• Treatment A

• Treatment B

Multiple Choice

20. The table below shows the efficacy of two different treatments for kidney stones.

b. Which treatment did better with large stones?

• Treatment A

• Treatment B

Multiple Choice

20. The table below shows the efficacy of two different treatments for kidney stones.

c. Which treatment did better overall?

• Treatment A

• Treatment B

Open Ended

20. The table below shows the efficacy of two different treatments for kidney stones.

d. Explain. Is this possible?

Open Ended

21. The following table shows a summary of the results from 1,240 mammograms. The table is based on the assumption that 5% of breast tumors are malignant and that mammogram screening is 90% accurate.

a. Verify that the numbers in the table are correct.

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