1.7.2: Exercise 1.7

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MAKING CONNECTIONS TO THE COLLABORATION

(1) Which of the following was one of the main mathematical ideas of the collaboration?

(i) Ratios are a way to compare measurements in different situations.

(ii) A water footprint measures the amount of water used by a person or group. This includes water used for cooking, drinking, cleaning, and to produce all the goods and services used by the person.

(iii) The number 333,000,000 can be written in scientific notation as 3.33 × 10⁸.

(iv) A nation’s water footprint can be calculated by dividing the nation’s population by the amount of water used in that nation.

DEVELOPING SKILLS AND UNDERSTANDING

(2) The website for the nonprofit organization Charity: Water discusses the need for clean water around the world.

(a) The website states that worldwide “Access to clean water and basic sanitation can save around 16,000 lives per week… 43% of those deaths are children under the age of five years old.”¹⁹ The following statements are all correct interpretations of this statistic. Which gives the most complete information?

(i) 6,880 children die every week from unsafe water and unhygienic living conditions.

(ii) 6,880 out of the 16,000 deaths that occur every week from unsafe water and unhygienic living conditions are of children under five years old.

(iii) 43% of deaths from unsafe water and unhygienic living conditions are of children under five years old.

(iv) 43 out of 100 deaths that occur every week from unhealthy living conditions are of children under five years old.

(b) On their website, the organization Action Against Hunger claims: “Nearly two billion people worldwide drink unsafe water.”²⁰ If there are 7.9 × 10⁹ people in the world, then approximately what percent of them live without clean drinking water? Round to the nearest tenth of a percent.

(3) According to data on the website for the Centers for Disease Control and Prevention (CDC), 41.9% of American adults were obese in 2020.²¹ In this report, adults were considered to be 20 years of age or older.

(a) According to the U.S. Census Bureau, about 75% of Americans are adults (20 and over). Use the U.S. population estimate of 332 million people to calculate the number of American adults age 20 and older. Write your answer as a number in standard form.

(b) According to the CDC, about how many of the American adults (20 and over) were obese? Round to the nearest hundred thousand adults. Write your answer as a number in standard form.

(i) 0.104331 × 10⁸ adults

(ii) 0.104331 × 10⁹ adults

(iii) 1.04331 × 10⁷ adults

(iv) 1.04331 × 10⁸ adults

(v) 10.4331 × 10⁷ adults

(4) From 2007 to 2020, there was a substantial increase in obesity rates in the United States. The following information comes from an earlier CDC report on obesity:²²

“Results from the 2007–2008 National Health and Nutrition Examination Survey (NHANES), using measured heights and weights, indicate that an estimated 34.2% of U.S. adults aged 20 years and over are overweight, 33.8% are obese, and 5.7% are extremely obese.”

Use the information in the paragraph above to answer the following questions:

(a) In 2007-2008, approximately ________ out of 100 adults aged 20 years and older in the United States were obese. Round to the nearest adult.

(b) Use your answer from part (a) to calculate how many of the 220 million American adults aged 20 years and older in 2007-2008 were obese. Round to the nearest million adults. Write your answer as a number in standard form.

(c) About how many more American adults (20 and over) were obese in 2020 than in 2007-2008? (Hint: Use your answers from 3(b) and 4(b).)

(i) 2.93 × 10⁶ adults

(ii) 2.93 × 10⁷ adults

(iii) 4.4 × 10⁶ adults

(iv) 4.4 × 10⁸ adults

(v) 7.5 × 10⁷ adults

MAKING CONNECTIONS ACROSS THE COURSE

(5) Tannika has a health insurance plan that will reimburse her for 60% of her family’s health care expenses after she pays a $2,000 deductible. A deductible is the amount a person pays (to a hospital, for example) before an insurance company will begin to pay for a percentage of the remaining expenses. Tannika has to pay the deductible and the percentage not covered by the insurance company. These are called “out-of-pocket expenses” because they are paid for by the person who owns the policy.

Tannika records the total of her health care expenses in the spreadsheet below.

Screen capture showing Tanika's spreadsheet, indicating the following: A1 = Service B1 = Cost D1 = Amount Paid by Insurance A2 = Doctors visits B2 = $1,235 D2 = Out-of-pocket expenses A3 = Prescriptions B3 = $1,044 A4 = Hospital bills B4 = $8,270 A5 = Lab tests B5 = $600

(a) Which of the following formulas could Tannika use in Cell E1 to calculate the amount paid by her insurance?

(i) = 0.6(B2 + B3 + B4 + B5) – 2000

(ii) = 0.6 * B2 + B3 + B4 + B5 – 2000

(iii) = 2000 − 0.6(B2 + B3 + B4 + B5)

(iv) = 0.6(B2 + B3 + B4 + B5 – 2000)

(b) Which of the following formulas could Tannika use in Cell E2 to calculate her out-of-pocket expenses? There may be more than one correct answer.

(i) = 0.4(B2 + B3 + B4 + B5 – 2000) + 2000

(ii) = 0.4 * B2 + B3 + B4 + B5 + 2000

(iii) = 2000 + 0.4(B2 + B3 + B4 + B5)

(iv) = (B2 + B3 + B4 + B5) – E1

___________________________________________

¹⁹ http://www.charitywater.org/whywater/

²⁰ http://www.actionagainsthunger.org/impact/water-sanitation-hygiene

²¹ https://www.cdc.gov/obesity/data/adult.html

²² http://www.cdc.gov/nchs/data/hestat/obesity_adult_07_08/obesity_adult_07_08.htm

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