Chapter 1

Chemistry. The pH scale is used to measure the strength of acids and bases (alkalines). It can be thought of as a number line. On the scale, graph and label each pH measurement given below. $$ \begin{array}{|l|r|} \hline \text { Solution } & \mathrm{pH} \\ \hline \text { Seawater } & 8.5 \\ \hline \text { Cola } & 2.9 \\ \hline \text { Battery acid } & 1.0 \\ \hline \text { Milk } & 6.6 \\ \hline \text { Blood } & 7.4 \\ \hline \text { Ammonia } & 11.9 \\ \hline \text { Saliva } & 6.1 \\ \hline \text { Oven cleaner } & 13.2 \\ \hline \text { Black coffee } & 5.0 \\ \hline \text { Toothpaste } & 9.9 \\ \hline \text { Tomato juice } & 4.1 \\ \hline \end{array} $$

Simplify. See Example \(6 .\) $$24\left(\frac{5}{6} y-\frac{9}{8}\right)-24\left(\frac{3}{24} y\right)$$

Solve each equation. $$ -(2 t-0.71)=0.9(1.4-t) $$

Solve for the specified variable. $$ d=\frac{4}{3} \pi h \quad \text { for } h $$

Evaluate each expression. See Example \(9 .\) $$ \frac{-2-5}{-7+(-7)} $$

Simplify. See Example \(6 .\) $$18\left(\frac{11}{18} w-\frac{7}{2}\right)-18\left(\frac{1}{9} w\right)$$

Solve each equation. $$ -(9 m-11.13)=7.7(6+m) $$

Solve for the specified variable. $$ I_{Q}=\frac{100 M}{C} \text { for } C $$

Evaluate each expression. See Example \(9 .\) $$ \frac{-3-(-1)}{-2+(-2)} $$

Solve each equation. $$ 2(2 x+1)=x+15+2 x $$

Evaluate each expression. See Example \(9 .\) $$ \frac{|-25|-2(-5)}{2^{4}-9} $$

Explain why the whole numbers are a subset of the integers.

Simplify. See Example \(6 .\) $$-5[3(x-4)-2(x+2)]-7(x-3)$$

Solve each equation. $$ -2(x+5)=x+30-2 x $$

Aluminum Foil. Find the number of square feet of aluminum foil on a roll if the dimensions printed on the box are \(8 \frac{1}{3}\) yards \(\times 12\) inches.

Evaluate each expression. See Example \(9 .\) $$ \frac{2[-4-2(3-1)]}{3(3)(2)} $$

What is a real number? Give examples.

Simplify. See Example \(6 .\) $$2\left[6\left(\frac{1}{3} a+2 b\right)-8\left(\frac{1}{4} a-2 b\right)+3\right]$$

Solve each equation. $$ \frac{5}{2} a-12=\frac{1}{3} a+1 $$

Evaluate each expression. See Example \(9 .\) $$ \frac{3[-9+2(7-3)]}{(8-5)(9-7)} $$

Explain why there are no even prime numbers greater than 2 .

Simplify. See Example \(6 .\) $$10\left[\frac{3}{5}(2 s+2 t)-\frac{4}{5}(s-t)+1\right]$$

Solve each equation. $$ 3(x-2)+4=3 x-2 $$

Hockey. A goal is scored in hockey when the puck, a vulcanized rubber disk \(2.5 \mathrm{cm}(1 \text { in. ) thick and } 7.6 \mathrm{cm}(3 \mathrm{in.})\) in diameter, is driven into the opponent's goal. Find the volume of a puck in cubic centimeters and cubic inches. Round to the nearest tenth.

Evaluate each expression. See Example \(9 .\) $$ \frac{(6-5)^{4}+21}{27-(\sqrt{16})^{2}} $$

Explain why every integer is a rational number, but not every rational number is an integer.

Simplify each expression. $$-(a+2 A+1)-(a-A+2)$$

Solve each equation. $$ \frac{4}{5} a=-12 $$

Is \(\frac{3 x-4}{2}\) an equation or an expression?

Simplify each expression. $$3 T-2(t-T)+t$$

Solve each equation. $$ 4 j+12.54=18.12 $$

Translate into mathematical symbols: The weight of an object in ounces is the product of 16 and its weight in pounds.

Simplify each expression. $$8(2 c d+7 c)-2(c d-3 c)$$

Solve each equation. $$ 0.06(a+200)+0.1 a=172 $$

Fill in the blank: A ____ is a letter that stands for a number.

Simplify each expression. $$2 t z+5(t z-4)-10(8-t z)$$

Solve each equation. $$ 0.03 x+0.05(6,000-x)=280 $$

Electronics. The illustration below is a diagram of a resistor connected to a voltage source of 60 volts. As a result, the resistor loses power in the form of heat. The power \(P\) lost when a voltage \(E\) is placed across a resistance \(R\) (in ohms) is given by the formula $$ P=\frac{E^{2}}{R} $$ Solve for \(R\). If \(P\) is 4.8 watts and \(E\) is 60 volts, find \(R\). (IMAGE CANT COPY)

Complete the table. $$ T=x-1.5 $$ $$ \begin{array}{|c|c|} \hline x & T \\ \hline 3.7 & \\ \hline 10 & \\ \hline \end{array} $$

Simplify each expression. $$6.4 a^{2}+11.8 a-9.2 a+5.7$$

Solve each equation. $$ -4[p-(3-p)]=3(6 p-2) $$

How many integers have an absolute value that is less than \(1,000 ?\)

Simplify each expression. $$9.1 m^{2}-6.1 m+12.3 m-4.9$$

Solve each equation. $$ 2[5(4-a)+2(a-1)]=3-a $$

Investments. An amount \(P\), invested at a simple interest rate \(r\) will grow to an amount \(A\) in \(t\) years according to the formula \(A=P(1+r t) .\) Solve for \(P .\) Suppose a man invested some money at \(5.5 \%\). If after 5 years, he had \(\$ 6,693.75\) on deposit, what amount did he originally invest?

Find a fraction whose decimal equivalent is \(0 . \overline{61}\)

Simplify each expression. $$-\frac{7}{16} x-\frac{3}{4} x$$

Solve each equation. $$ 2(x-2)=\frac{2}{3}(3 x+8)-2 $$

Cost of Electricity. The cost of electricity in a city is given by the formula \(C=0.07 n+6.50,\) where \(C\) is the cost in dollars and \(n\) is the number of kilowatt hours used. Solve for \(n .\) Then find the number of kilowatt hours used each month by a homeowner whose checks to pay the monthly clectric bills are: \(\$ 49.97, \$ 76.50,\) and \(\$ 125\)

The trichotomy property of real numbers states that if \(a\) and \(b\) are real numbers, then \(ab .\) Explain why this is true.