Chapter 1

Solve each formula for the specified variable. See Example 5. $$ P=2(w+h+l) \quad \text { for } h $$

Evaluate each expression. See Example \(6 .\) $$ \left(-\frac{4}{3}\right)^{3} $$

The set of composite numbers less than 10

Use the given equation to complete each table. $$ y=2 x+15 $$ (table cant copy)

Multiply. See Example 4 $$5\left(9 r^{2}-12 t-3\right)$$

Find each square root. See Example 7 . $$ \sqrt{64} $$

The set of positive odd integers less than 12

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. \(s\) subtracted from \(S\) b. \(S\) subtracted from \(s\)

The active ingredient used in most insect repellents is known as DEET (N-Diethyl-meta-toluamide). How many ounces of a \(1.25 \%\) DEET solution and how many ounces of a \(5 \%\) DEET solution should be mixed to produce 10 ounces of a \(2.5 \%\) DEET solution? (Hint: Express the results as mixed numbers.)

Multiply. See Example 4 $$25\left(2 a^{2}-3 a+1\right)$$

Solve each equation. Check each result. See Example 6. $$ \frac{2}{3}(b+3)=\frac{5}{4} b+\frac{17}{12} $$

Solve each formula for the specified variable. See Example 5. $$ S=C(1-r) \text { for } C $$

Find each square root. See Example 7 . $$ \sqrt{121} $$

The set of negative even integers greater than \(-7\)

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. the product of 4 and \(d,\) decreased by 15 b. the product of 4 and \(d\) decreased by 15

Suppose, as registered dietitian for a school district, you must make sure that only extra lean ground beef ( \(16 \%\) fat) is served in the cafeteria. Further suppose that the kitchen has 8 pounds of Further suppose that the kitchen has 8 pounds of regular ground beef ( \(30 \%\) fat) on hand. How many pounds of extra lean ground beef (12\% fat) must be purchased and added to the regular ground beef to obtain a mixture that has the correct fat content?

Multiply. See Example 4 $$3\left(\frac{4}{3} x-\frac{5}{3} y+\frac{1}{3}\right)$$

Solve each equation. Check each result. See Example 6. $$ \frac{1}{2}(3 y+2)-\frac{5}{8}=\frac{3}{4} y $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. the absolute value of the difference of \(a\) and 2 b. the difference of the absolute value of \(a\) and 2

How many liters of a \(1 \%\) glucose solution should a pharmacist mix with 0.5 liter of a \(5 \%\) glucose solution to obtain a \(2 \%\) glucose solution?

Multiply. See Example 4 $$6\left(-\frac{4}{3}+\frac{7}{6} s+\frac{16}{3} t\right)$$

Solve each formula for the specified variable. See Example 5. $$ S=\frac{n}{2}(f+l) \quad \text { for } n $$

The set of odd natural numbers less than or equal to 5

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. the quotient of a number and 6 increased by the number b. the quotient of a number and \(6,\) increased by the number

Cream is approximately \(22 \%\) butterfat. How many gallons of cream must be mixed with milk testing at \(2 \%\) butterfat to get 20 gallons of milk containing \(4 \%\) butterfat?

Multiply. See Example 4 $$(16 t+24) \frac{1}{8}$$

Solve each equation. Check each result. See Example 7. $$ \frac{a+1}{3}-\frac{a-1}{5}=\frac{8}{15} $$

Find each square root. See Example 7 . $$ -\sqrt{\frac{9}{16}} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -9 \quad-8 $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. 6 miles more than \(15.5 \%\) of the altitude b. \(15.5 \%\) of 6 miles more than the altitude

One website recommends a \(6 \%\) chlorine bleach-water solution to remove mildew. A chemical lab has \(3 \%\) and \(15 \%\) chlorine bleach-water solutions in stock. How many gallons of each should be mixed to obtain 100 gallons of the mildew spray?

Multiply. See Example 4 $$(18 q+9) \frac{1}{9}$$

Find each square root. See Example 7 . $$ -\sqrt{\frac{81}{49}} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -11 \quad-12 $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. twice the sum of the tax and 200 b. the sum of twice the tax and 200

How much water should be added to 20 ounces of a \(15 \%\) solution of alcohol to dilute it to a \(10 \%\) alcohol solution? (EQUATION NOT COPY)

Solve each formula for the specified variable. See Example 5. $$ v=\frac{1}{t}\left(d_{1}-d_{2}\right) \quad \text { for } t $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -(-5) \quad-10 $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. the square of 14 less than a number b. 14 less than the square of a number

Multiply. See Example 4 $$(2 t+5)(-2)$$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ |-3|-(-6) $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. a. double the cube of a number b. the cube of double a number

If a car travels at 60 mph for 30 minutes, explain why the distance traveled is not \(60 \cdot 30=1,800\) miles.

Simplify by combining like terms. See Example 5 . $$3 x+15 x$$

If a mixture is to be made from solutions with concentrations of \(12 \%\) and \(30 \%,\) can the mixture have a concentration less than \(12 \% ?\) Can the mixture have a concentration greater than \(30 \% ?\) Explain.

Solve each equation. Check each result. See Example 8. $$ 0.02 x+0.0175(15,000-x)=277.5 $$

Simplify by combining like terms. See Example 5 . $$12 y-17 y$$

Evaluate each expression. See Example \(8 .\) $$ 12-2 \cdot 3 $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -6.07 \quad-\frac{17}{6} $$

Solve each equation. Check each result. See Example 8. $$ 0.04(12)+0.01 t-0.02(12+t)=0 $$