Chapter 7

Find the number of 1000 8-year-old children in the United States who have cerebral palsy. Round to the nearest tenth. Cerebral palsy is the most common motor disability in childhood, affecting approximately 1 in 303 8-year-old children in the U.S. (Source: www.cdc.gov, Aug. 29, 2011)

A convenience store owner is setting the regular price for 1 gal of \(2 \%\) milk. When the milk goes on sale at a discount of \(30 \%\) later this week, the sale price will be \(\$ 2.99\) per gallon. Find the regular price that the owner should charge for the milk. Round to the nearest hundredth.

For exercises 87-90, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Solve: \(\frac{2}{x-2}+\frac{8}{x}=\frac{x}{x-2}\) Incorrect Answer: \(\frac{2}{x-2}+\frac{8}{x}=\frac{x}{x-2}\) \(x(x-2)\left(\frac{2}{x-2}+\frac{8}{x}\right)=x(x-2)\left(\frac{x}{x-2}\right)\) \(x(x-2)\left(\frac{2}{x-2}\right)+x(x-2)\left(\frac{8}{x}\right)=x^{2}\) \(2 x+(x-2) 8=x^{2}\) \(2 x+8 x-16=x^{2}\) \(10 x-16=x^{2}\) \(0=x^{2}-10 x+16\) \(0=(x-8)(x-2)\) \(x-8=0 \quad\) or \(\quad x-2=0\) \(x=8 \quad\) or \(\quad x=2\)

If \(\$ 500\) is invested for 10 years and earns simple interest, find the annual simple interest rate needed to earn \(\$ 425\) in interest.

A group of military veterans that took a survey included 134 women and 577 men. Find the percent of the group who were women. Round to the nearest percent. (Source: www.pewsocialtrends.org, Dec. 22, 2011)

A homeowner is comparing the price of putting a fence around the pool area in his backyard and the price of putting a fence around the entire backyard. The pool area is a rectangle that is \(30 \mathrm{ft}\) wide and \(45 \mathrm{ft}\) long. The backyard is a rectangle that is \(80 \mathrm{ft}\) wide and \(100 \mathrm{ft}\) long. The average price of fencing and gates is \(\$ 10.50\) per foot. Find the difference in price to fence the two areas.

In November, 2011, North Dakota natural gas production was \(15,635,813\) million cubic feet. Because of a shortage of gas processing plants and other infrastructure, more than one-third of the gas is burned off or "flared" instead of being processed and sold. Find the minimum amount of natural gas that was burned off in November 2011. Round to the nearest million cubic feet. (Sources: www.businessweek.com, Jan. 13, 2012; www.dmr.nd.gov, 2011)

Target Corporation paid \(\$ 751,000\) for 15 acres of land in Westfield, Massachusetts. Target will pay about \(\$ 727,000\) each year in taxes for nine years and then will pay about \$1.8 million per year. Find the total amount of taxes that Target will pay in 15 years. (Source: St. Paul Pioneer Press, March 14, 2009)

An athlete and her advisor are planning her schedule for the next term. She must take at least 12 credits to keep her scholarship. Her coach does not want her to take more than 18 credits. She must take at least 6 credits in courses that meet the requirements of the general education core curriculum. Let \(x=\) credits in general education, and let \(y=\) credits outside of general education. a. Write four inequalities that describe the constraints on the credits the athlete can take. b. Graph the constraints.

The proposed Nabucco pipeline will transport oil from the eastern coast of Turkey to Austria. The pipeline travels \(3900 \mathrm{~km}\) through Bulgaria, Romania, and Hungary and will cost \(7.9\) billion euros. Find the cost of the pipeline per mile in U.S. dollars. ( \(1 \mathrm{mi}=1.6 \mathrm{~km} ; 1\) euro \(=\) \(1.3145\) U.S. dollars.) Round to the nearest hundredth of a million. (Sources: www.nabucco-pipeline.com; www.ecb .int, Jan. 27, 2012)

A fruit drink is \(15 \%\) white grape juice. Use a system of two linear equations to find the amount of pure white grape juice and the amount of this fruit drink needed to make 15 gal of a new drink that is \(21 \%\) white grape juice. Round to the nearest tenth.

Identify the slope of the line represented by $$ y=\left(\frac{40 \mathrm{mi}}{1 \mathrm{hr}}\right) x $$

For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Evaluate: \(\frac{11}{15}+\frac{2}{15}\) Incorrect Answer: \(\frac{11}{15}+\frac{2}{15}\) $$ =\frac{13}{30} $$

For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Simplify: \(\frac{c}{c-1}+\frac{4}{c+2}\) Incorrect Answer: The least common denominator is \((c-1)(c+2)\). $$ \begin{aligned} &\frac{c}{c-1}+\frac{4}{c+2} \\ &=\frac{c}{c-1} \cdot \frac{(c+2)}{(c+2)}+\frac{4}{c+2} \cdot \frac{(c-1)}{(c-1)} \\ &=\frac{c^{2}+2 c}{(c-1)(c+2)}+\frac{4 c-4}{(c-1)(c+2)} \\ &=\frac{c^{2}+6 c-4}{(c-1)(c+2)} \\ &=\frac{c^{2}+6 c-4}{c^{2}+c-2} \\ &=\frac{6 c-4}{c-2} \end{aligned} $$

$$ \text { Solve: } 800=5 k $$

For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Simplify: \(\frac{x^{2}}{x^{2}-5 x-24}-\frac{5 x+40}{x^{2}-5 x-24}\) Incorrect Answer: \(\frac{x^{2}}{x^{2}-5 x-24}-\frac{3 x+40}{x^{2}-5 x-24}\) $$ =\frac{x^{2}-3 x+40}{x^{2}-5 x-24} $$

$$ \text { Solve: } 0.75=\frac{k}{60} $$

For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Simplify: \(\frac{y+4}{2 y+10}-\frac{5}{y^{2}-25}\) Incorrect Answer: The least common denominator is \(2(y-5)(y+5)\). $$ \begin{aligned} &\frac{y+4}{2 y+10}-\frac{5}{y^{2}-25} \\ &=\frac{y+4}{2(y+5)} \cdot \frac{(y-5)}{(y-5)}-\frac{5}{(y-5)(y+5)} \cdot \frac{2}{2} \\ &=\frac{y^{2}+4 y-5 y-20}{2(y-5)(y+5)}-\frac{10}{2(y-5)(y+5)} \\ &=\frac{y^{2}-y-30}{2(y-5)(y+5)} \\ &=\frac{(y+6)(y-5)}{2(y-5)(y+5)} \\ &=\frac{y+6}{2(y+5)} \end{aligned} $$

For exercises \(95-98\), evaluate. $$ \frac{\frac{10}{3}}{\frac{2}{3}} $$

For exercises \(95-98\), evaluate. \(\frac{3}{4}+\frac{5}{6}\)

For exercises 95-97, evaluate. $$ \frac{5}{21}+\frac{2}{21} $$

\text { Describe how to divide two fractions. }

For exercises \(95-98\), evaluate. $$ \frac{5}{7}-\frac{2}{9} $$

For exercises 95-97, evaluate. $$ \frac{8}{15}+\frac{7}{15} $$

Evaluate: \(\frac{3}{4} \div \frac{5}{6}\)

For exercises \(95-98\), evaluate. $$ \frac{\frac{6}{1}}{\frac{1}{2}} $$

For exercises \(95-98\), evaluate. $$ \frac{11}{12}-\frac{3}{4} $$

For exercises 95-97, evaluate. $$ \frac{16}{21}-\frac{2}{21} $$

Evaluate: \(8 \div \frac{1}{2}\)

For exercises \(95-98\), evaluate. $$ \frac{\frac{3}{4}}{\frac{1}{4}} $$

For exercises \(95-98\), evaluate. $$ \frac{1}{3}+\frac{1}{2}+\frac{1}{4} $$

Evaluate: \(\frac{3}{8} \div 6\)

Some math students "negative self-talk" about math. They may speak using negative language such as "I can't do math," instead of using positive language as in "I can do some math already, and with hard work, I'll be able to do more." They may say, "I should be able to work faster" instead of "I can work fast enough to pass the course." Write a different example of negative self-talk about math. Then rewrite it as a positive statement.

Many students have some anxiety about their classes. They worry about giving speeches, taking tests, writing papers, or simply getting all of their class work done. Worrying can be motivating, or worrying can be paralyzing. Describe how worrying affects you.

Write a paragraph or two describing your "math history." Include any positive or negative experiences that have strongly influenced your attitudes about math.

Using a scale of 1 to 10 , with 10 describing overwhelming anxiety that makes it difficult for you to do math, rate your own math anxiety.