Chapter 1

Complete each statement so that the indicated property is illustrated. See Example 1. $3+7= ______ Commutative property of addition

Describe the set of rational numbers using set-builder notation.

Perform the operations. See Example 2 . $$ -3-4 $$

In \(2010,78\) million, or \(68.7 \%,\) of U.S. households had personal computers with an Internet connection. How many U.S. households were there in \(2010 ?\) Round to the nearest million. (Source: U.S. Census)

Solve each equation. Check each result. See Example 2. $$ \frac{m}{3}+10=8 $$

Use an area formula to find the unknown measurement. See Example 2. First Aid. \(\quad\) A rectangular band-aid covers \(2 \frac{1}{2}\) in. \(^{2}\) of skin. If the width of the band-aid is \(\frac{5}{8}\) in., find its length.

Complete each statement so that the indicated property is illustrated. See Example 1. \(2(5 \cdot 97)=\) ______ Associative property of multiplication

Perform the operations. See Example 2 . $$ -11-(-17) $$

Pension Funds. \(\quad\) A pension fund owns \(2,000\) fewer shares in mutual stock funds than mutual bond funds. Currently, the stock funds sell for \(\$ 12\) per share, and the bond funds sell for \(\$ 15\) per share. How many shares of each does the pension fund own if their total value is \(\$ 165,000 ?\)

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. 100 less than triple the attendance \(a\)

According to the Insurance Information Institute, \(6.5 \%\) of the \(4,730\) recreational boating accidents in 2009 involved alcohol use. How many boating accidents were alcohol-related? Round up to the nearest one accident. (Source: U.S. Coast Guard)

Solve each equation. Check each result. See Example 2. $$ 1.6 a+(-4)=0.032 $$

Use an area formula to find the unknown measurement. See Example 2. Windsurfing. The area of a triangular sail on a windsurfing board is \(42 \mathrm{ft}^{2}\). If the length of the base of the sail is 7 feet, what is its height'?

Complete each statement so that the indicated property is illustrated. See Example 1. $3(2+d)= _____ Distributive property

What set of numbers does each symbol represent? a. \(\mathbb{Q}\) b. \(\mathbb{H}\) c. \(\mathbb{R}\)

Perform the operations. See Example 2 . $$ -3.3-(-3.3) $$

Pension Funds. A pension fund owns \(2,000\) fewer shares in mutual stock funds than mutual bond funds. Currently, the stock funds sell for \(\$ 12\) per share, and the bond funds sell for \(\$ 15\) per share. How many shares of each does the pension fund own if their total value is \(\$ 165,000 ?\)

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. \(w\) reduced by 500

Basketball. The following data is for the 2009 NCAA men's college basketball season. What was the average number of three-point shots made per game? Round to the nearest hundredth. THREE-POINT SHOTS Average number of attempts per game: 18.33 Percent made: \(34.40 \%\) (Souce: \(\mathrm{NCAA}\) )

Windsurfing. The area of a triangular sail on a windsurfing board is \(42 \mathrm{ft}^{2}\). If the length of the base of the sail is 7 feet, what is its height'? Camping. The area of a trapezoid-shaped canvas flap on a tent is 110 in. \(^{2}\) If the upper base of the flap is 8 in. long, and the height is 11 in., find the length of its lower base.

List two other ways that the fraction \(-\frac{2}{3}\) can be written.

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. \(8,000\) split \(n\) equal ways

Solve each equation. Check each result. See Example 2. $$ 0.7-4 y=1.74 $$

Complete each statement so that the indicated property is illustrated. See Example 1. $c+0= ______ Additive identity property

Perform the operations. See Example 2 . $$ \text { Subtract }-\frac{3}{5} \text { from } \frac{1}{2} $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. 150 feet per \(m\) minutes

\(\quad\) A bedroom set regularly sells for \(\$ 983 .\) If it is on sale for \(\$ 737.25,\) what is the percent of markdown?

Find the circumference of each circle to the nearest hundredth. See Example 3. (Answers may vary slightly depending on which approximation of is used.) A circle with diameter \(6 \frac{1}{4} \mathrm{m}\)

Complete each statement so that the indicated property is illustrated. See Example 1. $-4(x-2)= ______ Distributive property and simplifying

Determine whether each statement is true or false. $$ 9 \in \mathbb{N} $$

Perform the operations. See Example 2 . $$ \text { Subtract } \frac{11}{13} \text { from } \frac{1}{26} $$

Flea Markets. \(\quad\) A vendor sells tool chests at a flea market for \(\$ 65 .\) If she makes a profit of \(30 \%\) on each unit sold, what does she pay the manufacturer for each tool chest? (Hint: The retail price \(=\) the wholesale price \(+\) the markup.)

Solve each equation. Check each result. See Example 2. $$ -6-y=-13 $$

Complete each statement so that the indicated property is illustrated. See Example 1. \(25 \cdot \frac{1}{25}=\) ______ Multiplicative inverse property

Determine whether each statement is true or false. $$ -5 \notin \mathbb{Z} $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. 7 times the total of \(77, h,\) and 88

Bookstores. \(\quad\) A bookstore sells a textbook for \(\$ 39.20 .\) If the bookstore makes a profit of \(40 \%\) on each sale, what does the bookstore pay the publisher for each book? (Hint: The retail price \(=\) the wholesale price \(+\) the markup.)

Find the circumference of each circle to the nearest hundredth. See Example 3. (Answers may vary slightly depending on which approximation of is used.) A circle with radius 12.3 yd

Perform the operations. See Example 2 . $$ 5-(-3)-2 $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. decrease a number by \(-1\)

Solve each equation. Check each result. See Example 3. $$ \frac{2}{3} c=10 $$

Complete each statement so that the indicated property is illustrated. See Example 1. \(8+(7+a)= _______\) Associative property of addition

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. triple the number of waiters

Greenhouse Gases. The U.S. energy-related carbon dioxide emissions in 2008 were \(5,802\) million metric tons. In 2007 , that figure was \(5,967\) million metric tons. Find the percent of decrease and round to the nearest tenth of one percent. (Source: Energy Information Administration)

Solve each equation. Check each result. See Example 3. $$ \frac{9}{7} d=81 $$

Complete each statement so that the indicated property is illustrated. See Example 1. _____ \(\cdot 3=3\) Multiplicative identity property

Find the area of each circle to the nearest tenth. See Example 3. (Answers may vary slightly depending on which approximation of is used.) A circle with radius \(5 \frac{3}{4} \mathrm{cm}\)

Isosceles Triangles. Find the measure of one base angle of an isosceles triangle if the measure of the vertex angle is \(101^{\circ} .\)Isosceles Triangles. Find the measure of one base angle of an isosceles triangle if the measure of the vertex angle is \(101^{\circ} .\)

Solve each equation. Check each result. See Example 3. $$ -\frac{4}{5} s=2 $$

Geometry. In the illustration, lines \(r\) and \(s\) are cut by a third line \(l\) to form \(\angle 1\) (angle 1 ) and \(\angle 2\). When lines \(r\) and \(s\) are parallel, \(\angle 1\) and \(\angle 2\) are parallel, \(\angle 1\) and \(\angle 2\) are supplementary. If \(\angle 1=x+50^{\circ}\) \(\angle 2=2 x-20^{\circ},\) and lines \(r\) and \(s\) are parallel, find \(x\)