Chapter 1

\((-4 h)(-7 h)\)

\(\sqrt{15}\)

The International Association for Wireless Communication predicted annual wireless data revenues in 2011 of \(\$ 55.4\) billion, compared to \(\$ 280.8\) million in 1996 . Find the increase in revenues, writing the answer in place value notation. (Source: www.ctia.org, Oct. 11, 2011)

\((7 a)(-3 b)\)

\(\sqrt{18}\)

The International Association for Wireless Communication predicted \(196.9\) billion text messages in 2011 , compared to \(33.5\) million text messages sent in 1996 . Fin the increase in the number of text messages, writing the answer in place value notation. (Source: www.ctia.org, Oct. 11, 2011)

\((8 c)(-2 d)\)

\(\sqrt{49 \mathrm{~km}^{2}}\)

The beginning balance on a bank account is \(\$ 285\). A bank statement shows two deposits: \(\$ 650\) and \(\$ 1324\). It shows many debit card transactions: \(-\$ 39,-\$ 58,-\$ 61\) \(-\$ 475,-\$ 173\), and \(-\$ 81\). Find the new balance in this account. Use negative numbers to represent debits.

\(-8(9 m)\)

\(\sqrt{64 \mathrm{~km}^{2}}\)

An employee has her monthly paycheck of \(\$ 2080\) depo: ited directly into her bank account. Her fixed monthly expenses include rent of \(\$ 425\), car payment of \(\$ 320\), cel phone payment of \(\$ 50\), utilities payment of \(\$ 75\), and cable bill payment of \(\$ 60\). After paying fixed expenses, find the amount of money that she has left per month. Use negative numbers to represent payments.

\(-6(5 v)\)

\(\sqrt{-49}\)

A patient with heart disease needs to lose 96 pounds. The physician's assistant recommends an average loss of 3 pounds per week. Find the number of weeks needec to lose the weight. Use negative numbers to represent weight loss.

In 2011 , about 593 grizzly bears lived in Wyoming, Montana, and Idaho, a reduction from the 602 bears who lived there in 2010 . Find the percent decrease. Round to the nearest tenth of a percent. (Source: www.lmtribune com, Oct. 14, 2011)

A runner is training for a marathon. She wants to reduce the time it takes her to run 6 miles by 3 minutes. She plans to reduce her time by 12 seconds every week. Find the number of weeks needed for her to meet her goal. Use negative numbers to represent loss of time.

Explain why \(\sqrt{-16}\) cannot be a real number.

On January 4 , the high temperature in Minneapolis was \(9^{\circ} \mathrm{F}\). The low temperature was \(-4^{\circ} \mathrm{F}\). Find the difference of these temperatures.

\(100 a+8 b+4+250 a+16 b-51\)

Explain why \(\sqrt{25}\) does not equal \(-5\) even though \((-5)(-5)=25 .\)

\(5 h+200 k+11+8 h+130 k-17\)

Given that \(\sqrt{9}=3\) and \(\sqrt{16}=4\), explain why \(\sqrt{10}\) must be between 3 and 4 .

The enrollment of a college in 2011 was 3000 students. In 2012 , the enrollment increased by 600 students. Find the percent increase.

The price of a popular toy is \(\$ 49.99\). A customer with \(\$ 765\) in a checking account bought three of these toys with her debit card. Find the ending balance in the account. Use a negative number to represent a debit.

In 2011 , there were 600 children playing in a soccer league. In 2012 , the number playing increased by 150 children. Find the percent increase.

The price of a place setting of dishes is \(\$ 20.99\). A customer with \(\$ 845\) in a checking account bought eight place settings with her debit card. Find the ending balance in the account. Use a negative number to represent a debit.

The annual take-home pay of a teacher is \(\$ 34,000\). His monthly house payment is \(\$ 976\). After making all of his house payments for the year, find the remaining amount of his annual take-home pay. Use a negative number to represent a house payment.

The annual take-home pay of a chemist is \(\$ 69,000\). Her monthly house payment is \(\$ 1255\). After making all of her house payments for the year, find the remaining amount of her annual take-home pay. Use a negative number to represent a house payment.

In the second quarter of 2007 , a biotechnology company that sells cancer drugs earned profits of \(\$ 747\) million. In the second quarter of 2006 , it earned profits of \(\$ 531\) million. Find the percent increase in reported profits. Round to the nearest percent. (Source: Www.nytimes .com, July 12,2007 )

Find the number of 2350 individual policyholders who will have their premiums raised. Anthem Blue Cross, which plans to raise premiums for about four-fifths of the ... individual policyholders ... has outraged members, many of whom have ... price increases of more than 30 percent. (Source: www.sfgate.com, Feb. 11, 2009)

\(6+15 \div 3\)

\( 3^{3}\)

In the second quarter of 2006 , the revenue of a biotechnology company that sells cancer drugs was \(\$ 2.2\) billion. In the second quarter of 2007 , its revenue was \(\$ 3\) billion. Find the percent increase in revenue. Round to the nearest percent. (Source: www.nytimes.com, July 12,2007 )

\(8+20 \div 2\)

\(\sqrt[3]{216}\)

The width of a standard seam in home sewing is \(\frac{5}{8}\) inch. A sewer decreases the width by \(\frac{1}{4}\) inch. Find the new width of the seam.

\(16 \div 8 \cdot 2\)

\(\sqrt[3]{27}\)

The ingredients of a recipe includes \(\frac{3}{8}\) cup grated cheese. If an additional \(\frac{1}{4}\) cup of cheese is used, find the total amount of cheese.

\(12 \div 6 \cdot 2\)

\(\sqrt[3]{-216}\)

In 2001, there were 37 robberies in Central Park in New York City. In 2011, there were 17 robberies. Find the percent decrease in robberies. Round to the nearest percent. (Source: www.nytimes.com, Dec. 28, 2011)

If two grandchildren each received \(\frac{1}{32}\) of an estate and their mother received \(\frac{1}{3}\) of the estate, find the total fraction of the estate received by the mother and her two children.

\(3(2 x+1)-7(4 x-9)\)

\(16 \div(8 \cdot 2)\)

. \(\sqrt[3]{-27}\)

In 2009, Jeff Gordon scored 6473 points and won \(\$ 6,476,460\) in the NASCAR Sprint Cup Series. In 2010 , he scored 6176 points and won \(\$ 5,703,710\). Find the percent decrease in the number of points. Round to the nearest tenth of a percent. (Source: www.nascar.com)

A building lot is \(\frac{1}{6}\) acre. If it is combined with an adjoining lot that is \(\frac{5}{32}\) acre, find the total area of the combined lots.

\(4(3 x+5)-8(6 x-1)\)