List of all conversion factors

HW1.5

1. Convert 8 miles to kilometers. Use the table of Unit Equivalencies in Lesson 1.5 to create conversion factors. Show all conversion factors needed. Some spaces don't require numbers - in which case enter 1. Some units will be blank - in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed.

Correct Correct

Correct Correct

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Incorrect Correct

Incorrect Correct

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2. Convert the height of a person who is 7 feet tall to centimeters. Include the inches-centimeter conversion factor. Use the table of Unit Equivalencies in Lesson 1.5 to create conversion factors. Show all conversion factors needed. Some spaces don't require numbers - in which case enter 1. Some units will be blank - in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional analysis that you learned. If it doesn't, resize the window on your computer, if possible.

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3. Convert the area of 228 square meters to square feet. Include the acres-hectare conversion factor. Use the conversion factors from the table in Lesson 1.5. Show all needed conversion factors. Some spaces don't require numbers - in which case enter 1. Some units will be blank - in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional analysis that you learned. If it doesn't, resize the window on your computer, if possible.

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4. Convert a person's weight of 114 pounds to kilograms. Use the table of Unit Equivalencies in Lesson 1.5 to create conversion factors. Show all conversion factors needed. Some spaces don't require numbers - in which case enter 1. Some units will be blank - in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional analysis that you learned. If it doesn't, resize the window on your computer, if possible.

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5. Convert the flow rate of 44 cubic meters per minute to gallons per second. Include the quart to liter conversion factor. Convert the numerator first, then convert the denominator. Use the table of Unit Equivalencies in Lesson 1.5 to create conversion factors. Show all needed conversion factors. Some spaces may not require numbers - in which case enter 1. Some units may be blank - in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional analysis that you learned. If it doesn't, resize the window on your computer, if possible.

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HM1.6

#1 Points possible: 15. Total attempts: 5

Which of the following was one of the main mathematical ideas of the lesson?

· There are many hidden costs in driving such as insurance, registration and maintenance

· It is possible to convert miles per hour to feet per second

· Units can be used to set up conversion problems by using the fact that common factors in the numerator and denominator of a fraction can be subtracted to equal 0

· Units can be used to set up conversion problems by using the fact that common factors in the numerator and denominator of a fraction divide out to 1

#2 Points possible: 5. Total attempts: 5

As of September, 2011, Florence Griffith-Joyner held the women’s world record for the 100 meter dash. She set the record with a time of 10.49 seconds in 19881. Which of the following calculations are correctly set up to convert this speed into miles per hour?

· 100meters10.49seconds ⋅ 3.28feet1meter ⋅ 1mile5,280ft ⋅ 60seconds1minute ⋅ 60minutes1hour100meters10.49seconds ⋅ 3.28feet1meter ⋅ 1mile5,280ft ⋅ 60seconds1minute ⋅ 60minutes1hour

· 10.49seconds100meters ⋅ 1meter3.28feet ⋅ 5,280ft1mile ⋅ 60seconds1minute ⋅ 60minutes1hour10.49seconds100meters ⋅ 1meter3.28feet ⋅ 5,280ft1mile ⋅ 60seconds1minute ⋅ 60minutes1hour

· 10.49seconds100meters ⋅ 1meter3.28feet ⋅ 5,280ft1mile ⋅ 1minute60seconds ⋅ 1hour60minutes10.49seconds100meters ⋅ 1meter3.28feet ⋅ 5,280ft1mile ⋅ 1minute60seconds ⋅ 1hour60minutes

#3 Points possible: 5. Total attempts: 5

Find the answer to the conversion from the previous question, converting 10.49 seconds for the 100 meter dash to miles per hour. Round to the nearest tenth of a mile per hour.

mi/hr

#4 Points possible: 5. Total attempts: 5

A 2010 Toyota Prius hybrid vehicle gets 48 mpg for highway driving. The tank holds 11.9 gallons of fuel. Typically the low fuel warning light comes on when approximately two gallons of fuel remain in the tank. Which of the following calculations can be used to find the distance that can be traveled after the fuel light comes on and before the car runs out of gasoline?

· 2 gallons1 ⋅ 48 miles1 gallon=96 miles2 gallons1 ⋅ 48 miles1 gallon=96 miles

· 12 gallons ⋅ 48 miles1 gallon=24 miles12 gallons ⋅ 48 miles1 gallon=24 miles

· 2 gallons1 ⋅ 1 gallon48 miles=96 miles2 gallons1 ⋅ 1 gallon48 miles=96 miles

· 11.9 gallons1 ⋅ 48 miles1 gallon=571.2 miles11.9 gallons1 ⋅ 48 miles1 gallon=571.2 miles

#5 Points possible: 10. Total attempts: 5

In Lesson 1.4, you learned about a water footprint. Part of a person’s water footprint is the water used for cleaning. In this question, you will calculate the cost of water for laundry and bathing. You will use the City of New York 2011 rate of $7.64/100 cubic feet of water. Calculate the cost of each of the following based on this rate. Use the conversion factor of 7.48 gallons per cubic foot.3

a. A standard washing machine uses approximately 50 gallons of water per load4. A household washes one load of laundry per week for 52 weeks. Find the total cost per year. $ /yr

b. According to one study, the average American shower lasts for 8.2 minutes and uses 17.2 gallons. A person showers once a day for a year. Find the total cost per year.5 $ /yr

#6 Points possible: 5. Total attempts: 5

A shower has a flow rate of 2.3 gallons per minute. If a person takes an average of 6 showers per week and the average length of a shower is 15 minutes, then how much water is used in a year? gallons/yr

If the same person replaces the shower head with a low-flow shower head that has a flow rate of 1.5 gallons per minute, how much water will be saved in a year? Assume the length and frequency of showers does not change. gallons/yr

#7 Points possible: 5. Total attempts: 5

A new LED light bulb uses 10 watts of power. Since energy=power×timeenergy=power×time , then the energy used for this light bulb can be found my multiplying the power times the time the bulb is lit. If the bulb is lit for one hour, the energy used will be 10 watt*hours or 10 Wh. If three 10 watt bulbs in one room are kept on for 5 hours, how many watt*hours of energy are used? Wh

Parents sometimes yell at their children for leaving the light on in their bedroom when they aren't in the room. If the child's room is lit with two 10 watt bulbs for one extra hour a day for everyday of the year (365), and the cost of energy is $0.068 per kilowatt*hour (kWh), how much money is wasted on lighting that isn't being used, to the nearest cent. $ /yr

#8 Points possible: 5. Total attempts: 5

In the US, the fuel economy is measured in miles per gallon. In Canada, the fuel economy is measured in liters per 100 km. If a car gets 30 miles per gallon, how many liters are needed per 100 km? L/100 km

HW 1.7

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas of the lesson?

· When using a formula, you do not really need to know what the variables mean.

· Formulas are useful because they allow us to generalize a rule to many different situations.

· Formulas use variables.

· Geometry can be useful in home improvement projects.

#2 Points possible: 5. Total attempts: 5

http://s3.amazonaws.com/wamapdata/ufiles/2/QW321DSU41.jpgRefer to the figure of the box shown here. Which of the following would be appropriate units of measurement for the different parts of the figure?

· Bottom edge (L), the area of the top, and the volume are all measured in inches.

· Bottom edge (L) is measured in square inches, the area of the top is measured in inches and the volume is measured in cubic inches.

· Bottom edge (L), the area of the top and the volume are all measured in square inches.

· Bottom edge (L) is measured in inches, the area of the top is measured in square inches and the volume is measured in cubic inches.

#3 Points possible: 10. Total attempts: 5

Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.89 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 8 inches by 11 feet 8 inches. Find the area of the dining room floor, rounded up to the next square foot, and the cost of the work.

Area = square feet Cost = $

#4 Points possible: 10. Total attempts: 5

http://s3.amazonaws.com/wamapdata/ufiles/2/QW321DSU7.jpgAfter doing some work in the house, Bob and Carol want to put a concrete patio on the side of the house to keep people from tracking mud inside. The dimensions of the rectangular patio are 23 feet 9 inches by 10 feet 1 inch. The patio will need to be at least 4 inches deep.

a. Calculate the volume of concrete needed, in cubic feet, rounding up to the nearest cubic foot. cubic feet

b. The delivered cost of the concrete is "$6 per cubic foot plus a $50 surcharge for orders less than 100 cubic feet." Find the total cost having the concrete delivered. $

#5 Points possible: 10. Total attempts: 5

Find the perimeter and area of the figure pictured below. 7.3 m2.3 m4.5 m9.2 m Perimeter = mm Area = m2m2

#6 Points possible: 5. Total attempts: 5

Here is a figure made of a circle inscribed in a square.

https://wamaps3.s3.amazonaws.com/qimages/CircleinSquarewdia_0.JPG

26

What is the area of the shaded region? m2m2 (You may round answer to a whole number.)

#7 Points possible: 5. Total attempts: 5

If the radius of a circle is doubled, will the area also double? Hint: Compare the areas of two circles: one with a radius of 10 inches and the other with a radius of 20 inches.

· Yes, the area will also double

· No, the area will remain the same

· No, the area will quadruple

· No, the area will triple

HW 1.8

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas of the lesson?

· Percentages are a ratio of a number out of 100. For example, 16% means 16 out of 100.

· You should always calculate percentages exactly.

· Percentages are used to calculate sale prices.

· To calculate 35% of a number, multiply the number by 0.35.

#2 Points possible: 5. Total attempts: 5

Refer back to Lessons 1.1 and 1.2. Which statement below is a good description of how the important mathematical ideas of Lessons 1.1 and 1.2 connect to this lesson (1.8)?

· Large numbers are hard to understand.

· Estimation is used in quantitative reasoning for many things, including estimating measurements, understanding large numbers, and making quick mental calculations.

· Many people worry that the world population is growing too rapidly. The rate of growth has been increasing throughout history.

· Calculating percentages is an important skill in quantitative reasoning because percentages are used in many situations.

Reference Information on Percentages, Fractions, and Estimation

There are many ways to do calculations with percents. The following videos and websites show some examples of methods.

· Calculate the percentage rate [+]

· Finding the percent of a number [+]

· Both problems types, in text form

Language of Percentages and Fractions

There are several important vocabulary words you should know and use.

· A ratio is a comparison of two numbers by division. You will see many different types of ratios in this course. In this lesson, you worked with a special type of ratio called a percentage. A percentage is a ratio because it is a number compared to 100.

· Percentages are a relationship between two values: the comparison value and the reference value. The relationship is described as a percentage rate, which is shown with a percentage symbol (%). This indicates that the rate is out of 100.

Example: 10 is 20% of 50. 10 is the comparison value. 50 is the reference value. 20% is the percentage rate; it can be written as a decimal by using the relationship to 100: 20100=0.2.20100=0.2.

· Fractions have two parts: numeratordenominatornumeratordenominator

· Every fraction can be written in equivalent forms (e.g., 23=46=6923=46=69 ). It is often useful to write the fraction in the form with the smallest numbers. This is called simplified or reduced. In the example, 2323 is in simplest form.

The Language of Estimation

Certain words or phrases are often used to indicate that a number is an estimate rather than an exact figure. Read the following statement: “Almost 30% of the patients had less pain.” The word almost indicates that the percentage was a little less than 30. Some words and phrases that are commonly used to signal estimates are shown below.

almost

about

approximately

more than

less than

close to

just over

just under

nearly

#3 Points possible: 10. Total attempts: 5

3. At Gillway Community College, 43 out of 381 students earned honors. At Montessa Valley Community College, 17 out of 108 students earned honors.

a. Estimate the rate at which Gillway CC students earned honors. %

b. Estimate the rate at which Montessa Valley CC students earned honors. %

c. Which school had a higher rate of students earning honors?

· Gillway Community College

· Montessa Valley Community College

d. Write a statement about the estimated percentage of students who earned honors at Gillway CC. (Use a word or phrase from the list above.) You may want to refer to the Writing Principle from Lesson 1.2 and the handout on writing about quantitative information.

#4 Points possible: 6. Total attempts: 5

Select all of the options that are either exactly equal to the given ratio or a good estimate of the ratio. There may be more than one correct answer.

a. 60%

· 6 out of 100

· 1 out of 6

· 6 out of 10

· 1 out of 60

· close to 2323

b. 8 out of 1,000

· about 1818

· more than 8%

· about 8%

· less than 1%

· 0.8%

c. 81008100

· almost 10%

· 8 out of 10

· 2 out of 25

· 80%

· less than 1%

For the situations in the next few questions, decide if it would be more appropriate to make an estimate or to do an exact calculation. Give your answer, and specify if the number represents an estimate or acalculation.

#5 Points possible: 7. Total attempts: 5

You are completing a tax form. The tax is 15.3% of $47,000.

a. How much do you have to pay? $

b. Is the answer an estimate or calculation?

· Estimate

· Calculation

#6 Points possible: 7. Total attempts: 5

During an election for city council, you hear a candidate say that 68% of children in the city live in poverty. A typical school in this city has about 1,200 students.

a. Based on the candidate's statement, about how many children in a typical school live in poverty?

b. Is the answer an estimate or calculation?

· Estimate

· Calculation

#7 Points possible: 7. Total attempts: 5

You are a teacher and are grading a test. A student got 42 out 58 points.

a. What is the student's grade as a percentage? Round to the nearest whole percent. %

b. Is the answer an estimate or calculation?

· Estimate

· Calculation

#8 Points possible: 7. Total attempts: 5

Your bill at a restaurant is $23.17. You want to leave about 20% for a tip.

a. How much should you leave? $

b. Is the answer an estimate or calculation?

· Estimate

· Calculation

#9 Points possible: 2. Total attempts: 5

Some checking accounts pay a small amount of interest on the money in the account. In this case, interest is money that is paid to the account holder by the financial institution issuing the checking account. The interest is a percentage of the amount of money in the account. The percentage is called the annual interest rate. Compare the following two offers.

· Bank of Avalon pays 0.8% with no annual fee.

· Cypress Savings pays 1.5%, but charges a $10 annual fee.

Which would be the better offer if you have $1,000 in an account for 1 year?

· Cypress Savings

· Bank of Avalon

#10 Points possible: 5. Total attempts: 5

There are about 300 million people in the United States. A 2007 report 1 claimed that the richest 1% of Americans controlled 42% of the nation’s wealth. About how many people is this?

· 30,000,000

· 126,000,000

· 3,000,000

· 10,000,000

· 1,000,000

#11 Points possible: 5. Total attempts: 5

The same report claims that the poorest 80% of Americans controlled only 7% of the nation's wealth. About how many people is this?

· 21,000,000

· 7,000,000

· 240,000,000

· 60,000,000

· 6,000,000

· 24,000,000

#12 Points possible: 5. Total attempts: 5

The nation's wealth in 2007 was about $72 trillion dollars. About how much money did the richest 1% of Americans control? (Recall that they controlled 42% of the nation's wealth.)

· $56,000,000,000

· $30,000,000,000,000

· $5,000,000,000

· $720,000,000,000,000

· $720,000,000

#13 Points possible: 8. Total attempts: 5

Order the numbers below from smallest (1) to largest (8)

· 112112

· 1313

· 50%

· 0.1

· 0.7

· 0.3

· 25%

· 34

1

1.6

kilometers

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miles

13

8