Quiz 2

Quiz 2

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1. Convert the following.

a. 2682 inches to yards

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. Convert the following.

b. 2 miles to inches.

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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1. Convert the following.

c. 40640 ounces to tons.

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1. Convert the following.

d. 3 gallons to cups.

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2. Convert the following. (Write in expanded form. Ex: Three million is written as 3,000,000)

a. 5 kilometers to nanometers.

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. Convert the following.

b. 7000 deciliters to milliliters

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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2. Convert the following.

c. 900,000 milligrams to kilograms

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2. Convert the following.

d. 100 seconds to milliseconds

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3. Convert the following.

a. 124 inches to meters.

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. Convert the following.

b. 38 liters to gallons.

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3. Convert the following.

c. 5 pounds to grams

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3. Convert the following.

d. 43°C to °F

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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3. Convert the following.

e. 83° F to K

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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.)

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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5. One cubic foot holds 7.48 gallons of water, and one gallon of water weighs 8.33 pounds. How much does 3.8 cubic feet of water weigh in pounds? in ounces (avoirdupois)?

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5. One cubic foot holds 7.48 gallons of water, and one gallon of water weighs 8.33 pounds. How much does 3.8 cubic feet of water weigh in pounds? in ounces (avoirdupois)?

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6. Use the currency exchange rates from Table 2.4 to answer the following questions.

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

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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6. Use the currency exchange rates from Table 2.4 to answer the following questions.

b. You are traveling back from Japan with 3,000 yen. How many dollars will this be when you exchange it for US currency?

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6. Use the currency exchange rates from Table 2.4 to answer the following questions.

c. You are traveling to Mexico with $350.00. How many pesos can you buy?

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7. Your utility company charges $0.13 per kilowatt-hour of electricity.

a. What is the daily cost of keeping lit a 70-watt bulb for 16 hours each day?

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7. Your utility company charges $0.13 per kilowatt-hour of electricity.

b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 10 watts of power?

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

a. What is the density of the cube of wood?

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

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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?

First, find the absolute differences. Start with Jane.

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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?

Now find absolute difference for Mark.

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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?

Next, we need to find relative differences. Start with Jane. (Percent two decimal places)

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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?

Find Mark's relative difference.

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

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10. Complete the following statements:

a. Robert is 68% taller than Ahmad.

Robert’s height is

% of Ahmad’s height.

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10. Complete the following statements:

b. Jennifer’s salary is 75% of Susan’s salary.

Jennifer salary is

% less than Susan’s salary.

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11. In 2014, the percentage of online adults using two or more social media sites was 42%. In 2015, the percentage of online adults using two or more social media sites grew to 52%.

a. Describe the change in terms of percentage points.

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11. In 2014, the percentage of online adults using two or more social media sites was 42%. In 2015, the percentage of online adults using two or more social media sites grew to 52%.

b. Describe the change as a relative change in terms of a percentage. (Two decimal places.)

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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14. Convert the following from scientific to standard notation.

a.  $5.48\times10^5$  

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14. Convert the following from scientific to standard notation.

b.  $3.143\times10^{-3}$  

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14. Convert the following from scientific to standard notation.

c.  $2.569\times10^6$  

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15. Convert the following from standard notation to scientific notation. (Ex: For Quizziz 789,000 or  $7.89\times10^5$ can be written as 7.89x10^5 with no spaces, use x for multiplies and ^ for exponents)

a. 368,000,000

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15. Convert the following from standard notation to scientific notation.

b. 0. 000 000 463

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15. Convert the following from standard notation to scientific notation.

c. 689

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16. Use the data from Table 3.1 to determine how many average candy bars an adult would have to eat to supply the energy needed for five hours of running.

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17. There are approximately 4.2 million births per year in the country of Ghidorah. Express this number in births per second.

(Two decimal places.)

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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?

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

b. How much would you need to maintain the same standard of living in 2008?

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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.

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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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.

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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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.

b. Suppose that a patient has a positive mammogram. What is the chance that they really have cancer?

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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.

c. What is the chance of a negative mammogram, given that the patient doesn’t have cancer?