Question: Jason earned $\$ 256$ interest last year on his investments. If $\$ 1600$ was invested at a certain rate of return and $\$ 2400$ was invested in a fund with a rate that was double the rate of the first fund, find the two rates of interest.

Answer: $\$ 1600 @ 4 \%$; $\$ 2400$ @ 8\%

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Question: Combine Like Terms: $9 n-1+n+4$

Answer: $10 n+3$

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Question: Evaluate the expression: $3-(-5)$

Answer: 8

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Question: Solve: $56 p-48=6 p+2$

Answer: 1

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Question: Simplify: $\sqrt{512 m^{4} n^{3}}$

Answer: $16 m^{2} n \sqrt{2 n}$

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Question: Solve the proportion: $\frac{n}{8}=\frac{n-4}{3}$

Answer: $n=\frac{32}{5}$

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Question: Simplify: $-2 \sqrt{6}-\sqrt{3}-3 \sqrt{6}$

Answer: $-5 \sqrt{6}-\sqrt{3}$

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Question: Convert $3.5 \mathrm{mph}$ (miles per hour) to feet per second.

Answer: $5.13 \mathrm{ft} / \mathrm{sec}$

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Question: Simplify: $\frac{4^{5}}{4^{3}}$

Answer: $4^{2}$

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Question: Solve the proportion: $\frac{x-5}{4}=\frac{-3}{x+3}$

Answer: $x=-1,3$

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Question: Multiply and simplify: $\sqrt{15}(\sqrt{5}-3 \sqrt{3 v})$

Answer: $5 \sqrt{3}-9 \sqrt{5 v}$

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Question: Combine the following radicals: $\sqrt[3]{5} \sqrt{6}$

Answer: $\sqrt[6]{5400}$

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Question: Jack can wash and wax the family car in one hour less than Bob can. The two working together can complete the job in $1 \frac{1}{5}$ hours. How much time would each require if they worked alone?

Answer: 2 and 3

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Question: Solve the equation $h=\mathrm{vt}-16 t^{2}$ for $\mathrm{v}$.

Answer: $v=\frac{16 t^{2}+h}{t}$

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Question: Solve the compound inequality and give interval notation: $9+n<2$ or $5 n>40$

Answer: $n<-7$ or $n>8:(-\infty-7), \bigcup(8, \infty)$

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Question: An average human heart beats 60 times per minute. If an average person lives to the age of 75 , how many times does the average heart beat in a lifetime?

Answer: $2,365,200,000$ beats/lifetime

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Question: A family drove to a resort at an average speed of $30 \mathrm{mph}$ and later returned over the same road at an average speed of $50 \mathrm{mph}$. Find the distance to the resort if the total driving time was 8 hours.

Answer: 150

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Question: Simplify and write the answer in scientific notation: $\left(9 \times 10^{-2}\right)^{-3}$

Answer: $1.372 \times 10^{3}$

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Question: Solve the equation: $\log _{11}(x-4)=-1$

Answer: $\frac{45}{11}$

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Question: Convert $234 \mathrm{oz}$ to tons.

Answer: $0.0073125 \mathrm{~T}$

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Question: Evaluate $\left(8 x^{3}+1\right)-\left(5 x^{4}-6 x^{3}+2\right)$.

Answer: $-5 x^{4}+14 x^{3}-1$

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Question: Add or subtract the rational expressions and simplify: $\frac{8}{9 t^{3}}+\frac{5}{6 t^{2}}$

Answer: $\frac{15 t+16}{18 t^{3}}$

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Question: Solve the following equation: $m^{4}-7 m^{2}-8=0$

Answer: $\pm i, \pm 2 \sqrt{2}$

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Question: Simplify. Your answer should contain only positive expontents: $\frac{3 y^{3}}{3 y x^{3} \cdot 2 x^{4} y^{-3}}$

Answer: $\frac{y^{5}}{2 x^{7}}$

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Question: Solve the compound inequality and give interval notation: $8-10 r \leqslant 8+4 r$ or $-6+8 r<2+8 r$

Answer: $\{$ All real numbers. $\}: \mathbb{R}$

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Question: Simplify: $(x y)^{3}$

Answer: $x^{3} y^{3}$

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Question: The number of kilograms of water in a human body varies directly as the mass of the body. A 96-kg person contains $64 \mathrm{~kg}$ of water. How many kilo grams of water are in a $60-\mathrm{kg}$ person?

Answer: $40 \mathrm{~kg}$

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Question: Find the product: $2(6 x+3)$

Answer: $12 x+6$

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Question: Build up each fraction by finding the Least Common Denominator: $\frac{x}{x^{2}-16}, \frac{3 x}{x^{2}-8 x+16}$

Answer: $\frac{x^{2}-4 x}{(x-4)^{2}(x+4)}, \frac{3 x^{2}+12 x}{(x-4)^{2}(x+4)}$

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Question: Evaluate $\left(7 x^{2}+2 x^{4}+7 x^{3}\right)+\left(6 x^{3}-8 x^{4}-7 x^{2}\right)$.

Answer: $-6 x^{4}+13 x^{3}$

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Question: Solve the equation: $-2 x+4=22$

Answer: -9

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Question: Simplify: $\frac{\left(2 y^{3} x^{2}\right)^{2}}{2 x^{2} y^{4} \cdot x^{2}}$

Answer: $2 y^{2}$

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Question: Find a quadratic equation with the solutions 0 and 0.

Answer: $x^{2}=0$

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Question: Add or subtract the rational expressions and simplify: $\frac{x-1}{4 x}-\frac{2 x+3}{x}$

Answer: $\frac{-7 x-13}{4 x}$

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Question: Simplify: $-3 \sqrt{3}+2 \sqrt{3}-2 \sqrt{3}$

Answer: $-3 \sqrt{3}$

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Question: Solve the equation: $\frac{1}{12}=\frac{4}{3} x+\frac{5}{3}\left(x-\frac{7}{4}\right)$

Answer: 1

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Question: Simplify: $\frac{12 x^{2}-42 x}{30 x^{2}-42 x}$

Answer: $\frac{2 x-7}{5 x-7}$

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Question: Evaluate the expression: $\frac{-9+5 i}{i}$

Answer: $9 i+5$

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Question: Simplify and express with positive exponents: $\frac{\left(u v^{2}\right)^{\frac{1}{2}}}{v^{-\frac{1}{4}} v^{2}}$

Answer: $\frac{u^{\frac{1}{2}}}{v^{\frac{3}{4}}}$

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Question: The cost of a private pilot course is $\$1,275$. The flight portion costs $\$625$ more than the ground school portion. What is the cost of each?

Answer: 325,950

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Question: Solve the equation: $\frac{216}{6^{-2 a}}=6^{3 a}$

Answer: 3

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Question: Simplify and leave your answer as an improper fraction: $\frac{25}{20}$

Answer: $\frac{5}{4}$

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Question: Evaluate $\left(5 n^{4}+6 n^{3}\right)+\left(8-3 n^{3}-5 n^{4}\right)$.

Answer: $3 n^{3}+8$

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Question: Find the product: $\left(5 k^{2}+3 k+3\right)\left(3 k^{2}+3 k+6\right)$

Answer: $15 k^{4}+24 k^{3}+48 k^{2}+27 k+18$

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Question: Solve: $-8(6+6 x)+4(-3+6 x)=-12$

Answer: -2

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Question: Find quotient: $\frac{-1}{9} \div \frac{-1}{2}$

Answer: $\frac{2}{9}$

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Question: Solve the equation lwh $=\mathrm{V}$ for $\mathrm{w}$.

Answer: $w=\frac{V}{\ell h}$

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Question: Find product: $\left(\frac{1}{2}\right)\left(\frac{5}{7}\right)$

Answer: $\frac{5}{14}$

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Question: Find product: $\left(-\frac{3}{7}\right)\left(-\frac{11}{8}\right)$

Answer: $\frac{33}{56}$

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Question: Evaluate the expression: $\log _{36} 6$

Answer: $\frac{1}{2}$

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Question: Simplify and leave your answer as an improper fraction: $\frac{27}{18}$

Answer: $\frac{3}{2}$

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Question: Solve the absolute value equation: $|8+6 m|=50$

Answer: $7,-\frac{29}{3}$

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Question: Solve: $-4-\left[2+4(-6)-4-\left|2^{2}-5 \cdot 2\right|\right]$

Answer: 28

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Question: A farmer has some cream which is $21 \%$ butterfat and some which is $15 \%$ butter fat. How many gallons of each must be mixed to produce 60 gallons of cream which is $19 \%$ butterfat?

Answer: 40,20

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Question: Solve: $n^{2}-n=-41$

Answer: $\frac{1+i \sqrt{163}}{2}, \frac{1-i \sqrt{163}}{2}$

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Question: Simplify: $\frac{\sqrt{5}}{4 \sqrt{125}}$

Answer: $\frac{1}{20}$

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Question: Convert $5,500 \mathrm{~cm}^{3}$ to cubic yards.

Answer: $0.0072 \mathrm{yd}^{3}$

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Question: Find the product: $\left(8 n^{2}+4 n+6\right)\left(6 n^{2}-5 n+6\right)$

Answer: $48 n^{4}-16 n^{3}+64 n^{2}-6 n+36$

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Question: Find quotient: $\frac{-12}{7} \div \frac{-9}{5}$

Answer: $\frac{20}{21}$

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Question: Solve the compound inequality and give interval notation: $1+5 k \leqslant 7 k-3$ or $k-10>2 k+10$

Answer: $k \geqslant 2$ or $k<-20:(-\infty,-20) \cup[2, \infty)$

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Question: Find the Least Common Denominator: $x, x-7, x+1$

Answer: $x(x-7)(x+1)$

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Question: Simplify: $6 \sqrt{80 x y^{2}}$

Answer: $24 y \sqrt{5 x}$

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Question: Convert $435,000 \mathrm{~m}^{2}$ to sqaure kilometers.

Answer: $0.435 \mathrm{~km}^{2}$

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Question: Solve: $\frac{\frac{x}{3 x-2}}{\frac{x}{9 x^{2}-4}}$

Answer: $3 x+2$

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Question: Find the product: $(b-7)(b+7)$

Answer: $b^{2}-49$

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Question: Find the inverse of the function: $g(x)=\frac{-x+2}{3}$

Answer: $g^{-1}(x)=-3 x+2$

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Question: Find product: $(6 i)(-8 i)$

Answer: 48

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Question: Simplify: $-2(n+1)$

Answer: $-2 n-2$

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Question: Harry and his sister collected $240$ stamps in total. Harry collected $3$ times as many stamps as his sister. How many stamps did each of them collect?

Answer: 60,180

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Question: Simplify and write the answer in scientific notation: $\left(7 \times 10^{-1}\right)\left(2 \times 10^{-3}\right)$

Answer: $1.4 \times 10^{-3}$

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Question:
Solve the following system of equations by elimination:
$-6 x+9 y=3$
$6 x-9 y=-9$

Answer: No solution

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Question: Solve the equation $Q_{1}=P\left(Q_{2}-Q_{1}\right)$ for $Q_{2}$.

Answer: $Q_{2}=\frac{Q_{1}+\mathrm{PQ}_{1}}{P}$

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Question: Divide: $\frac{3 m^{4}+18 m^{3}+27 m^{2}}{9 m^{2}}$

Answer: $\frac{m^{2}}{3}+2 m+3$

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Question: Find a quadratic equation with the solutions 2 and $\frac{2}{9}$.

Answer: $9 x^{2}-20 x+4=0$

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Question: Find the angle measure to the nearest degree given $\sin Z=0.4848$

Answer: $29^{\circ}$

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Question: Solve the equation for $x$: $\frac{x}{x-1}-\frac{2}{x+1}=\frac{4 x^{2}}{x^{2}-1}$

Answer: $\frac{2}{3}$

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Question: Simplify and write the answer in scientific notation: $\left(1.8 \times 10^{-5}\right)^{-3}$

Answer: $1.715 \times 10^{14}$

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Question: Multiply and simplify: $3 \sqrt{5} \cdot-4 \sqrt{16}$

Answer: $-48 \sqrt{5}$

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Question: Given the points $(6,2)$ and $(x, 6)$ and a slope of $-\frac{4}{5}$, find the value of $x$.

Answer: 1

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Question: Solve: $(3-2 x)^{\frac{4}{3}}=-81$

Answer: No Solution

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Question: Simplify the expression: $\frac{x^{2}+3 x-10}{x^{2}+6 x+5} \cdot \frac{2 x^{2}-x-3}{2 x^{2}+x-6} \div \frac{8 x+20}{6 x+15}$

Answer: $\frac{3(x-2)}{4(x+2)}$

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Question: Brandon is 9 years older than Ronda. In four years the sum of their ages will be 91 . How old are they now?

Answer: 37,46

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Question: A tea that is $20 \%$ jasmine is blended with a tea that is $15 \%$ jasmine. How many pounds of each tea are used to make $5 \mathrm{lb}$ of tea that is $18 \%$ jasmine?

Answer: 3,2

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Question: Given $k(x)=-2 \cdot 4^{2 x-2}$, find $k(2)$

Answer: -32

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Question: Find the square: $(7 k-7)^{2}$

Answer: $49 k^{2}-98 k+49$

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Question: Solve the equation: $625^{-n-2}=\frac{1}{125}$

Answer: $-\frac{5}{4}$

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Question: Simplify and leave your answer as an improper fraction: $\frac{36}{27}$

Answer: $\frac{4}{3}$

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Question: Find the slope of the line through the points $(-5,-10)$ and $(-5,20)$.

Answer: Undefined

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Question: Evaluate $\left(8 x^{4}+2 x^{3}+2 x\right)+\left(2 x+2-2 x^{3}-x^{4}\right)-\left(x^{3}+5 x^{4}+8 x\right)$.

Answer: $2 x^{4}-x^{3}-4 x+2$

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Question: Solve: $5 x^{2}+5 x=-31-5 x$

Answer: $\frac{5+i \sqrt{130}}{5}, \frac{5-i \sqrt{130}}{5}$

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Question: Simplify: $\left(x^{3} y^{4} \cdot 2 x^{2} y^{3}\right)^{2}$

Answer: $4 x^{10} y^{14}$

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Question: Add or subtract the rational expressions and simplify: $\frac{x+2}{x^{2}-4 x+3}+\frac{4 x+5}{x^{2}+4 x-5}$

Answer: $\frac{5 x+5}{x^{2}+2 x-15}$

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Question: Solve the equation: $\log _{11}(10 v+1)=-1$

Answer: $-\frac{1}{11}$

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Question: State the excluded values for $\frac{56 x-48}{24 x^{2}+56 x+32}$

Answer: $\frac{9 r}{5(r+1)}$

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Question: Build up each fraction by finding the Least Common Denominator: $\frac{3 x}{x-4}, \frac{2}{x+2}$

Answer: $\frac{3 x^{2}+6 x}{(x-4)(x+2)}, \frac{2 x-8}{(x-4)(x+2)}$

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Question: Find a quadratic equation with the solutions 2 and 5.

Answer: $x^{2}-7 x+10=0$

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Question: Solve: $x^{2}=-10 x-29$

Answer: $-5+2 i,-5-2 i$

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Question: Find a quadratic equation with the solutions $-2 \pm 4 i$.

Answer: $x^{2}+4 x+20=0$

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Question: Find a quadratic equation with the solutions 3 and $-1$.

Answer: $x^{2}-2 x-3=0$

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Question: Simplify the following expression: $\frac{\sqrt{a b^{3} c}}{\sqrt[5]{a^{2} b^{3} c^{-1}}}$

Answer: $\sqrt[10]{a b^{9} c^{7}}$

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Question: Find the inverse of the function: $f(x)=\frac{-2 x-2}{x+2}$

Answer: $f^{-1}(x)=\frac{-2 x-2}{x+2}$

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Question: Find a quadratic equation with the solutions $6 \pm i \sqrt{3}$.

Answer: $x^{2}-12 x+39=0$

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Question: Solve: $\frac{\frac{y}{y+2}-\frac{y}{y-2}}{\frac{y}{y+2}+\frac{y}{y-2}}$

Answer: $-\frac{2}{y}$

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Question: Solve the equation: $6x - 18 = -42$

Answer: -4

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Question: Convert $153 \mathrm{ft} / \mathrm{s}$ (feet per second) to miles per hour.

Answer: $104.32 \mathrm{mi} / \mathrm{hr}$

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Question: Find product: $(4)(-6)$

Answer: -24

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Question: Find the product: $3 n^{2}(6 n+7)$

Answer: $18 n^{3}+21 n^{2}$

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Question: Solve the following equation: $b^{4}-10 b^{2}+9=0$

Answer: $\pm 3, \pm 1$

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Question: The number of aluminum cans used each year varies directly as the number of people using the cans. If 250 people use 60,000 cans in one year, how many cans are used each year in Dallas, which has a population of $1,008,000$ ?

Answer: $241,920,000$ cans

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Question: Find the square: $(a+5)^{2}$

Answer: $a^{2}+10 a+25$

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Question: Evaluate the square root of $-45$

Answer: $3 i \sqrt{5}$

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Question: Simplify: $(-4-i)+(1-5 i)$

Answer: $-3-6 i$

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Question: The stopping distance of a car after the brakes have been applied varies directly as the square of the speed $\mathrm{r}$. If a car, traveling $60 \mathrm{mph}$ can stop in 200 $\mathrm{ft}$, how fast can a car go and still stop in $72 \mathrm{ft}$ ?

Answer: $\mathrm{r}=36$

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Question: Solve: $-6 v-29=-4 v-5(v+1)$

Answer: 8

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Question: Build up each fraction by finding the Least Common Denominator: $\frac{x+2}{x-3}, \frac{x-3}{x+2}$

Answer: $\frac{x^{2}+4 x+4}{(x-3)(x+2)}, \frac{x^{2}-6 x+9}{(x-3)(x+2)}$

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Question: Solve: $(2 x+3)^{\frac{4}{3}}=16$

Answer: $-\frac{11}{2}, \frac{5}{2}$

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Question: Simplify and leave your answer as an improper fraction: $\frac{30}{24}$

Answer: $\frac{5}{4}$

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Question: Evaluate the expression: $\frac{-10-9 i}{6 i}$

Answer: $\frac{10 i-9}{6}$

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Question: Solve the equation: $8x - 14 = 4x + 3$

Answer: $\frac{17}{4}$

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Question: Simplify: $\frac{2+\sqrt{6}}{2+\sqrt{3}}$

Answer: $4-2 \sqrt{3}+2 \sqrt{6}-3 \sqrt{2}$

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Question: Evaluate the expression: $\frac{6}{5}-\frac{8}{5}$

Answer: $-\frac{2}{5}$

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Question: Find quotient: $\frac{80}{-8}$

Answer: -10

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Question: Simplify and express with positive exponents: $\frac{2 x^{\frac{1}{2}} y^{\frac{1}{3}}}{2 x^{\frac{4}{3}} y^{-\frac{7}{4}}}$

Answer: $\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

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Question: Write the number in scientific notation: 15000

Answer: $1.5 \times 10^{4}$

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Question: Simplify: $\frac{a+\sqrt{\mathrm{ab}}}{\sqrt{a}+\sqrt{b}}$

Answer: $\frac{1}{3}$

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Question: Solve the equation: $-6=15+3 p$

Answer: -7

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Question: Evaluate $\frac{b+2}{b^{2}+4 b+4}$ when $b=0$

Answer: $\frac{1}{2}$

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Question: Solve the equation: $-14=x-18$

Answer: 4

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Question: Solve: $-2-5(2-4 m)=33+5 m$

Answer: 3

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Question: Evaluate the expression: $(-1)-8$

Answer: -9

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Question: Find the square of $-7 i$

Answer: -49

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Question: A sink has two faucets, one for hot water and one for cold water. The sink can be filled by a cold-water faucet in 3.5 minutes. If both faucets are open, the sink is filled in 2.1 minutes. How long does it take to fill the sink with just the hot-water faucet open?

Answer: $5 \frac{1}{4} \mathrm{~min}$

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Question: Simplify: $8 \sqrt{112 p^{2}}$

Answer: $32 p \sqrt{7}$

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Question: Evaluate the expression: $\frac{1}{3}+\left(-\frac{4}{3}\right)$

Answer: -1

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Question: Combine Like Terms: $r-9+10$

Answer: $r+1$

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Question: Simplify: $\sqrt[3]{64 u^{5} v^{3}}$

Answer: $4 u v \sqrt[3]{u^{2}}$

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Question: You lend $\$ 100$ at $10 \%$ continuous interest. If you are repaid 2 months later, what is owed?

Answer: 101.68

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Question: Find the product: $(2 r+3)(2 r-3)$

Answer: $4 r^{2}-9$

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Question: Simplify and express with positive exponents: $\frac{\left(m^{2} n^{\frac{1}{2}}\right)^{0}}{n^{\frac{3}{4}}}$

Answer: $\frac{1}{n^{\frac{3}{4}}}$

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Question: Solve: $\frac{\frac{x+1}{x-1}-\frac{1-x}{1+x}}{\frac{1}{(x+1)^{2}}+\frac{1}{(x-1)^{2}}}$

Answer: $x^{2}-1$

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Question: Simplify: $(7 i)-(3-2 i)$

Answer: $-3+9 i$

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Question: Carolyn's age is triple her daughter's age. In eight years the sum of their ages will be 72 . How old are they now?

Answer: 14,42

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Question: Simplify: $\frac{5 x^{2}}{4 \sqrt{3 x^{3} y^{3}}}$

Answer: $\frac{5 \sqrt{3 x y}}{12 y^{2}}$

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Question: Simplify: $\frac{4 x^{3} y^{4}}{3 x y^{3}}$

Answer: $\frac{4 x^{2} y}{3}$

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Question: Simplify: $\left(7 a^{2}+7 a\right)-\left(6 a^{2}+4 a\right)$

Answer: $a^{2}+3 a$

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Question: Simplify the expression: $\frac{12 x+24}{10 x^{2}+34 x+28} \cdot \frac{15 x+21}{5}$

Answer: $\frac{18}{5}$

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Question: A kerosene lamp is 95 years old, and an electric lamp is 55 years old. How many years ago was the kerosene lamp twice the age of the electric lamp?

Answer: 15

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Question: Simplify: $\frac{4}{\sqrt{2}-2}$

Answer: $-2 \sqrt{2}-4$

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Question: Solve the proportion: $\frac{9}{n+2}=\frac{3}{9}$

Answer: $n=25$

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Question: Simplify: $\frac{28 m+12}{36}$

Answer: $\frac{7 m+3}{9}$

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Question: Find the product: $(8 n+7)(8 n-7)$

Answer: $64 n^{2}-49$

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Question: Pat is 20 years older than his son James. In two years Pat will be twice as old as James. How old are they now?

Answer: 18,38

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Question: Evaluate the expression: $\frac{1}{5}+\frac{3}{4}$

Answer: $\frac{19}{20}$

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Question: Solve the equation: $22=16+m$

Answer: 6

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Question: Solve the equation: $\frac{m}{4}-1=-2$

Answer: -4

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Question: Find quotient: $\frac{27}{3}$

Answer: 9

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Question: Evaluate the expression: $1+(-1)$

Answer: 0

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Question: Solve each equation by completing the square: $8 a^{2}+16 a-1=0$

Answer: $\frac{-4+3 \sqrt{2}}{4}, \frac{-4-3 \sqrt{2}}{4}$

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Question: A purse contains $\$ 3.90$ made up of dimes and quarters. If there are 21 coins in all, how many dimes and how many quarters were there?

Answer: $9 \mathrm{~d}, 12 \mathrm{q}$

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Question: Divide: $\frac{4 n^{2}-23 n-38}{4 n+5}$

Answer: $n-7-\frac{3}{4 n+5}$

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Question: Distribute: $3(8 v+9)$

Answer: $24 v+27$

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Question: Simplify: $-2 \sqrt[3]{-48 v^{7}}$

Answer: $4 v^{2} \sqrt[3]{6 v}$

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Question: Find a quadratic equation with the solutions $\frac{-2 \pm i \sqrt{15}}{2}$.

Answer: $4 x^{2}+8 x+19=0$

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Question: A candy mix sells for $\$ 2.20$ per kilogram. It contains chocolates worth $\$ 1.80$ per kilogram and other candy worth $\$ 3.00$ per kilogram. How much of each are in 15 kilograms of the mixture?

Answer: 10,5

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Question: Evaluate the expression: $\frac{1}{2}-\frac{11}{6}$

Answer: $-\frac{4}{3}$

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Question: Two people working together can complete a job in 6 hours. If one of them works twice as fast as the other, how long would it take the faster person, working alone, to do the job?

Answer: 9 hours

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Question: A man walks at the rate of 4 miles per hour. How far can he walk into the country and ride back on a trolley that travels at the rate of 20 miles per hour, if he must be back home 3 hours from the time he started?

Answer: 10

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Question: Simplify: $2 x\left(x^{4} y^{4}\right)^{4}$

Answer: $2 x^{17} y^{16}$

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Question: Simplify and leave your answer as an improper fraction: $\frac{35}{25}$

Answer: $\frac{7}{5}$

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Question:
Solve the following systems of equation:
$4 x-7 y+3 z=1$
$3 x+y-2 z=4$
$4 x-7 y+3 z=6$

Answer: no solution

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Question: It takes 10 hours to fill a pool with the inlet pipe. It can be emptied in $15 \mathrm{hrs}$ with the outlet pipe. If the pool is half full to begin with, how long will it take to fill it from there if both pipes are open?

Answer: 15 hours

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Question: Evaluate $\left(8-b+7 b^{3}\right)-\left(3 b^{4}+7 b-8+7 b^{2}\right)+\left(3-3 b+6 b^{3}\right)$.

Answer: $-3 b^{4}+13 b^{3}-7 b^{2}-$

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Question: Solve: $-57=-(-p+1)+2(6+8 p)$

Answer: -4

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Question: Solve the following equation: $x^{4}-2 x^{2}-3=0$

Answer: $\pm i, \pm \sqrt{3}$

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Question: Find the square: $(5+2 r)^{2}$

Answer: $25+20 r+4 r^{2}$

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Question: Simplify: $6 \sqrt{128}$

Answer: $48 \sqrt{2}$

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Question: Solve the equation: $14=b+3$

Answer: 11

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Question: Simplify: $\frac{2+\sqrt{10}}{\sqrt{2}+\sqrt{5}}$

Answer: $\sqrt{2}$

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Question: How many ounces of water evaporated from 50 oz of a $12 \%$ salt solution to produce a $15 \%$ salt solution?

Answer: 10

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Question: Simplify: $3 \sqrt[4]{2}-2 \sqrt[4]{2}-\sqrt[4]{243}$

Answer: $\sqrt[4]{2}-3 \sqrt[4]{3}$

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Question: Find the value: $\sin 50^{\circ}$

Answer: 0.7660

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Question: Solve each equation by completing the square: $5 k^{2}-10 k+48=0$

Answer: $\frac{5+i \sqrt{215}}{5}, \frac{5-i \sqrt{215}}{5}$

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Question: Find product: $(-7)(-2)$

Answer: 14

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Question: A, who travels 4 miles an hour starts from a certain place 2 hours in advance of B, who travels 5 miles an hour in the same direction. How many hours must B travel to overtake A?

Answer: 8

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Question: Solve the equation: $\frac{1}{3}\left(-\frac{7}{4} k+1\right)-\frac{10}{3} k=-\frac{13}{8}$

Answer: $\frac{1}{2}$

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Question: Given $f(t)=3^{t}-2$, find $f(-2)$

Answer: $-\frac{17}{9}$

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Question: Solve: $2 p^{2}-p+56=-8$

Answer: $\frac{1+i \sqrt{511}}{4}, \frac{1-i \sqrt{511}}{4}$

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Question: Find quotient: $\frac{5}{3} \div \frac{7}{5}$

Answer: $\frac{25}{21}$

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Question: Add or subtract the rational expressions and simplify: $\frac{5 x+3 y}{2 x^{2} y}-\frac{3 x+4 y}{x y^{2}}$

Answer: $\frac{3 y^{2}-3 x y-6 x^{2}}{2 x^{2} y^{2}}$

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Question: Solve the equation: $-\frac{8}{3}-\frac{1}{2} x=-\frac{4}{3} x-\frac{2}{3}\left(-\frac{13}{4} x+1\right)$

Answer: $-\frac{3}{2}$

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Question: Solve the proportion: $\frac{7}{6}=\frac{2}{k}$

Answer: $k=\frac{12}{7}$

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Question: Solve the equation: $\log _{11} k=2$

Answer: 121

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Question: A cargo container is $50 \mathrm{ft}$ long, $10 \mathrm{ft}$ wide, and $8 \mathrm{ft}$ tall. Find its volume in cubic yards and cubic meters.

Answer: $148.15 \mathrm{yd}^{3} ; 113 \mathrm{~m}^{3}$

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Question: $\$ 3.75$ is made up of quarters and half dollars. If the number of quarters exceeds the number of half dollars by 3, how many coins of each denomination are there?

Answer: $7 \mathrm{q}, 4 \mathrm{~h}$

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Question: Solve the equation $\mathrm{E}=\mathrm{mc}^{2}$ for $\mathrm{m}$.

Answer: $m=\frac{E}{c^{2}}$

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Question: Simplify the expression: $\frac{8 x^{2}}{9} \cdot \frac{9}{2}$

Answer: $4 x^{2}$

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Question: Solve the equation: $4^{2 n}=4^{2-3 n}$

Answer: $\frac{2}{5}$

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Question: Find the principal that will amount to $\$ 3000$ if invested at $3 \%$ interest compounded semiannually for 10 years.

Answer: 2227.41

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Question: Solve the following equation: $x^{\frac{2}{3}}-35=2 x^{\frac{1}{3}}$

Answer: $-125,343$

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Question: Divide: $\frac{n^{2}-4}{n-2}$

Answer: $n+2$

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Question: Solve the equation $\mathrm{L}=\pi\left(r_{1}+r_{2}\right)+2 d$ for $r_{1}$.

Answer: $r_{1}=\frac{L-2 d-\pi r^{2}}{\pi}$

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Question: Simplify: $\frac{-1+\sqrt{5}}{2 \sqrt{5}+5 \sqrt{2}}$

Answer: $\frac{2 \sqrt{5}-5 \sqrt{2}-10+5 \sqrt{10}}{30}$

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Question: Solve: $(3 x-2)^{\frac{4}{5}}=16$

Answer: $-\frac{34}{3},-10$

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Question: Let the first angle of a triangle be $x$ degrees. Find the measures of the second and third angles.

Answer: $30,90,60$

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Question: Simplify: $3 m \cdot 4 m n$

Answer: $12 m^{2} n$

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Question:
Solve the following system of equations by elimination:
$9 x+6 y=-21$
$-10 x-9 y=28$

Answer: $(-1,-2)$

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Question: Find a quadratic equation with the solutions 20 and 2.

Answer: $x^{2}-22 x+40=0$

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Question: Combine the following radicals: $\sqrt[5]{a^{2} b^{3}} \sqrt[4]{a^{2} b}$

Answer: $\sqrt[20]{a^{18} b^{17}}$

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Question: Simplify. Your answer should contain only positive expontents: $\frac{2 y x^{2} \cdot x^{-2}}{\left(2 x^{0} y^{4}\right)^{-1}}$

Answer: $4 y^{5}$

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Question: Find product: $(9)(-4)$

Answer: -36

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Question: Find quotient: $\frac{-49}{-7}$

Answer: 7

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Question: Simplify: $\sqrt{72 a^{3} b^{4}}$

Answer: $6 b^{2} a \sqrt{2 a}$

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Question: Simplify: $(-8 i)-(7 i)-(5-3 i)$

Answer: $5-12 i$

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Question: Reduce the following radical: $\sqrt[8]{x^{6} y^{4} z^{2}}$

Answer: $\sqrt[4]{x^{3} y^{2} z}$

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Question: Find the inverse of the function: $g(x)=\frac{8-5 x}{4}$

Answer: $g^{-1}(x)=\frac{-4 x+8}{5}$

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Question: A postal clerk sold some $15 \mathbb{C}$ stamps and some $25 \mathbb{C}$ stamps. Altogether, 15 stamps were sold for a total cost of $\$ 3.15$. How many of each type of stamps were sold?

Answer: $615 \mathbb{C}, 925 \mathbb{C}$

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Question: Solve the equation: $216^{2 n}=36$

Answer: $\frac{1}{3}$

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Question: Solve the absolute value equation: $|x|=8$

Answer: $8,-8$

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Question: Given $h(n)=5^{n-1}+1$, find $h\left(\frac{n}{2}\right)$

Answer: $5^{\frac{-2+n}{2}}+1$

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Question: Solve: $(x-1)^{-\frac{5}{2}}=32$

Answer: $\frac{5}{4}$

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Question: Find a quadratic equation with the solutions $\frac{3}{7}$ and 4.

Answer: $7 x^{2}-31 x+12=0$

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Question: Simplify: $-8 x+9(-9 x+9)$

Answer: $-89 x+81$

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Question: Add or subtract the rational expressions and simplify: $\frac{x+5}{8}+\frac{x-3}{12}$

Answer: $\frac{5 x+9}{24}$

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Question: Simplify the expression: $\frac{a^{3}+b^{3}}{a^{2}+3 \mathrm{ab}+2 b^{2}} \cdot \frac{3 a-6 b}{3 a^{2}-3 \mathrm{ab}+3 b^{2}} \div \frac{a^{2}-4 b^{2}}{a+2 b}$

Answer: $\frac{1}{a+2 b}$

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Question: The total cost for tuition plus room and board at State University is $\$2,584$. Tuition costs $\$704$ more than room and board. What is the tuition fee?

Answer: 1644

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Question: Reduce the following radical: $\sqrt[12]{x^{6} y^{9}}$

Answer: $\sqrt[4]{x^{2} y^{3}}$

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Question: Add or subtract the rational expressions and simplify: $\frac{2 r}{r^{2}-s^{2}}+\frac{1}{r+s}-\frac{1}{r-s}$

Answer: $\frac{2}{r+s}$

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Question: Solve the absolute value equation: $|3-x|=6$

Answer: $-3,9$

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Question: Simplify: $\left(3-7 n^{2}\right)+\left(6 n^{2}+3\right)$

Answer: $-n^{2}+6$

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Question: Add or subtract the rational expressions and simplify: $\frac{5}{6 r}-\frac{5}{8 r}$

Answer: $\frac{5}{24 r}$

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Question: A dealer bought a number of sheep for $\$ 440$. After 5 had died he sold the remainder at a profit of $\mathbb{\$} 2$ each making a profit of $\mathbb{\$} 60$ for the sheep. How many sheep did he originally purchase?

Answer: 55

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Question: Combine the following radicals: $\sqrt[3]{3 x y^{2} z} \sqrt[4]{9 x^{3} y z^{2}}$

Answer: $x \sqrt[12]{59049 x y^{11} z^{10}}$

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Question: Solve the following equation: $(x-3)^{2}-2(x-3)=35$

Answer: $-2,10$

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Question: Solve the proportion: $\frac{v-5}{v+6}=\frac{4}{9}$

Answer: $v=\frac{69}{5}$

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Question: Find the product: $(3 a-8)(3 a+8)$

Answer: $9 a^{2}-64$

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Question: Simplify: $4 \sqrt[3]{250 a^{6}}$

Answer: $20 a^{2} \sqrt[3]{2}$

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Question: Find the slope of a line parallel to the given line: $x-y=4$

Answer: 1

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Question: You lend out $\$ 5500$ at $10 \%$ compounded monthly. If the debt is repaid in 18 months, what is the total owed at the time of repayment?

Answer: 6386.12

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Question: Simplify: $\frac{9 v+54}{v^{2}-4 v-60}$

Answer: $\frac{9}{v-10}$

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Question: Find the square: $(v+4)^{2}$

Answer: $v^{2}+8 v+16$

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Question: Divide: $\frac{n^{2}+13 n+32}{n+5}$

Answer: $n+8-\frac{8}{n+5}$

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Question: Evaluate the expression: $\left(-\frac{1}{2}\right)+\frac{3}{2}$

Answer: 1

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Question: Simplify the expression: $\frac{1}{a-6} \cdot \frac{8 a+80}{8}$

Answer: $\frac{a+10}{a-6}$

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Question: Solve: $(5 x+1)^{4}=16$

Answer: $\frac{1}{5},-\frac{3}{5}$

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Question: Find the value that completes the square and then rewrite as a perfect square: $m^{2}-36 m+$

Answer: $324 ;(m-18)^{2}$

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Question: Solve the equation: $\frac{16}{9}=-\frac{4}{3}\left(-\frac{4}{3} n-\frac{4}{3}\right)$

Answer: 0

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Question: Find the slope of a line parallel to the given line: $y=2 x+4$

Answer: 2

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Question:
Solve the following system of equations by elimination:
$4 x+2 y=0$
$-4 x-9 y=-28$

Answer: $(-2,4)$

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Question: Solve the compound inequality and give interval notation: $-5 b+10 \leqslant 30$ and $7 b+2 \leqslant-40$

Answer: No solution : $\oslash$

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Question: Simplify: $3 \sqrt{24}-3 \sqrt{27}+2 \sqrt{6}+2 \sqrt{8}$

Answer: $8 \sqrt{6}-9 \sqrt{3}+4 \sqrt{2}$

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Question: Simplify: $\frac{\sqrt{12}}{\sqrt{3}}$

Answer: 2

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Question: Simplify: $2 \sqrt[4]{2}+2 \sqrt[4]{3}+3 \sqrt[4]{64}-\sqrt[4]{3}$

Answer: $2 \sqrt[4]{2}+\sqrt[4]{3}+6 \sqrt[4]{4}$

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Question: Simplify: $\frac{3 n m^{2}}{3 n}$

Answer: $m^{2}$

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Question: Simplify the expression: $\frac{7 r}{7 r(r+10)} \div \frac{r-6}{(r-6)^{2}}$

Answer: $\frac{r-6}{r+10}$

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Question: Solve each equation by completing the square: $n^{2}-8 n-12=0$

Answer: $4+2 \sqrt{7}, 4-2 \sqrt{7}$

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Question: Simplify: $9(6 b+5)-4 b(b+3)$

Answer: $-42 b-45-4 b^{2}$

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Question: Solve: $(2 x-3)^{\frac{2}{3}}=4$

Answer: $\frac{11}{2},-\frac{5}{2}$

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Question: Solve: $3+(8) \div|4|$

Answer: 5

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Question: Simplify and leave your answer as an improper fraction: $\frac{126}{108}$

Answer: $\frac{7}{6}$

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Question: Solve the absolute value equation: $|5+8 a|=53$

Answer: $6,-\frac{29}{4}$

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Question: Simplify the following expression: $\frac{\sqrt[3]{(2 x+1)^{2}}}{\sqrt[5]{(2 x+1)^{2}}}$

Answer: $\sqrt[15]{(2 x+1)^{4}}$

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Question: Simplify and express with positive exponents: $\left(\frac{m^{\frac{3}{2}} n^{-2}}{\left(m n^{\frac{4}{3}}\right)^{-1}}\right)^{\frac{7}{4}}$

Answer: $\frac{m^{\frac{35}{8}}}{n^{\frac{7}{6}}}$

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Question: Simplify: $\frac{2 b a^{7} \cdot 2 b^{4}}{b a^{2} \cdot 3 a^{3} b^{4}}$

Answer: $\frac{4 a^{2}}{3}$

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Question: Convert $11.2 \mathrm{mg}$ to grams.

Answer: $0.0112 \mathrm{~g}$

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Question: Solve the compound inequality and give interval notation: $-9 m+2<-10-6 m$ or $-m+5 \geqslant 10+4 m$

Answer: $m>4$ or $m \leqslant-1:(-\infty,-1] \cup(4, \infty)$

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Question: Solve the compound inequality and give interval notation: $\frac{n}{3} \leqslant-3$ or $-5 n \leqslant-10$

Answer: $n \leqslant-9$ or $n \geqslant 2:(-\infty,-9] \cup[2, \infty)$

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Question: Find a quadratic equation with the solutions 3 and 6.

Answer: $x^{2}-9 x+18=0$

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Question: Solve the equation: $m-4=-13$

Answer: -9

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Question: Evaluate using the given values: $c^{2}-(a-1)$; $a=3$ and $c=5$

Answer: 23

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Question: Solve: $5 x^{2}=-26+10 x$

Answer: $\frac{5+i \sqrt{105}}{5}, \frac{5-i \sqrt{105}}{5}$

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Question: Hooke's law states that the distance that a spring is stretched by hanging object varies directly as the mass of the object. If the distance is $20 \mathrm{~cm}$ when the mass is $3 \mathrm{~kg}$, what is the distance when the mass is $5 \mathrm{~kg}$ ?

Answer: $33.3 \mathrm{~cm}$

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Question: How many kilograms of soil supplement that costs $\$ 7.00$ per kilogram must be mixed with $20 \mathrm{~kg}$ of aluminum nitrate that costs $\$ 3.50$ per kilogram to make a fertilizer that costs $\$ 4.50$ per kilogram?

Answer: 8

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Question: Solve: $-a-5(8 a-1)=39-7 a$

Answer: -1

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Question: Let the first angle of a triangle be $x$ degrees. Find the measures of the second and third angles.

Answer: $28,84,68$

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Question: Given the points $(-2,y)$ and $(2,4)$ and a slope of $\frac{1}{4}$, find the value of $y$.

Answer: 3

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Question: Evaluate the expression: $(-1)-\left(-\frac{1}{3}\right)$

Answer: $-\frac{2}{3}$

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Question: Simplify: $-2 \sqrt[3]{16}+2 \sqrt[3]{16}+2 \sqrt[3]{2}$

Answer: $2 \sqrt[3]{2}$

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Question: Simplify the expression: $\frac{2 n^{2}-12 n-54}{n+7} \div(2 n+6)$

Answer: $\frac{n-9}{n+7}$

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Question: Find the product: $5(2 x-1)(4 x+1)$

Answer: $40 x^{2}-10 x-5$

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Question: $\$ 1750$ is invested in an account earning $13.5 \%$ interest compounded monthly for a 2 year period. What is the balance at the end of 9 years?

Answer: 2288.98

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Question: Solve the equation: $-8+\frac{n}{12}=-7$

Answer: 12

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Question: Evaluate the expression: $i^{251}$

Answer: $-i$

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Question: Solve each equation by completing the square: $m^{2}-8 m-3=6$

Answer: $9,-1$

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Question: Evaluate the expression: $\frac{3}{2}-\frac{15}{8}$

Answer: $-\frac{3}{8}$

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Question: Solve the equation: $\log _{2}-8 r=1$

Answer: $-\frac{1}{4}$

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Question: Solve: $-8 n-19=-2(8 n-3)+3 n$

Answer: 5

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Question: A pitcher is 30 years old, and a vase is 22 years old. How many years ago was the pitcher twice as old as the vase?

Answer: 14

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Question: Find product: $(-4)(-2)$

Answer: 8

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Question: Simplify: $5+(-6-6 i)$

Answer: $-1-6 i$

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Question: Given the points $(2,-5)$ and $(3, y)$ and a slope of 6, find the value of $y$.

Answer: 1

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Question: Simplify: $\frac{y x^{2} \cdot\left(y^{4}\right)^{2}}{2 y^{4}}$

Answer: $\frac{y^{5} x^{2}}{2}$

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Question: Solve: $\frac{\frac{3}{2 a-3}+2}{\frac{-6}{2 a-3}-4}$

Answer: $-\frac{1}{2}$

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Question: Find a quadratic equation with the solutions $\frac{5}{3}$ and $-\frac{1}{2}$.

Answer: $6 x^{2}-7 x-5=0$

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Question: Simplify: $-2 \sqrt{128 n}$

Answer: $-16 \sqrt{2 n}$

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Question: Find quotient: $-2 \div \frac{-3}{2}$

Answer: $\frac{4}{3}$

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Question: Reduce the following radical: $\sqrt[15]{x^{9} y^{12} z^{6}}$

Answer: $\sqrt[5]{x^{3} y^{4} z^{2}}$

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Question: Build up each fraction by finding the Least Common Denominator: $\frac{3 a}{5 b^{2}}, \frac{2}{10 a^{3} b}$

Answer: $\frac{6 a^{4}}{10 a^{3} b^{2}}, \frac{2 b}{10 a^{3} b^{2}}$

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Question: Solve: $\frac{1+\frac{1}{x}}{1-\frac{1}{x^{2}}}$

Answer: $\frac{x}{x-1}$

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Question: Simplify: $-7 \sqrt{64 x^{4}}$

Answer: $-56 x^{2}$

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Question: Simplify the expression $x^{2}+9 x+23$ when $x=-3$.

Answer: 5

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Question: Simplify. Your answer should contain only positive expontents: $\left(\frac{\left(2 x^{-3} y^{0} z^{-1}\right)^{3} \cdot x^{-3} y^{2}}{2 x^{3}}\right)^{-2}$

Answer: $\frac{x^{30} z^{6}}{16 y^{4}}$

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Question: Evaluate the expression: $\log _{2} 64$

Answer: 6

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Question: Find the value: $\sin 75^{\circ}$

Answer: 0.9659

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Question: Solve: $\sqrt{7 x+2}-\sqrt{3 x+6}=6$

Answer: 46

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Question: Simplify and express with positive exponents: $\left(\frac{y^{\frac{1}{3}} y^{-2}}{\left(x^{\frac{5}{3}} y^{3}\right)^{-\frac{3}{2}}}\right)^{\frac{3}{2}}$

Answer: $x^{\frac{15}{4}} y^{\frac{17}{4}}$

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Question: Solve the equation for $x$: $\frac{x}{x+1}-\frac{3}{x+3}=\frac{-2 x^{2}}{x^{2}+4 x+3}$

Answer: 1

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Question: Distribute: $-8(x-4)$

Answer: $-8 x+32$

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Question: Evaluate the expression: $i^{73}$

Answer: $i$

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Question: Distribute: $2 x(8 x-10)$

Answer: $16 x^{2}-20 x$

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Question: Simplify the expression: $\frac{9 m}{5 m^{2}} \cdot \frac{7}{2}$

Answer: $\frac{63}{10 m}$

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Question: Evaluate the expression: $\frac{-4+2 i}{3 i}$

Answer: $\frac{4 i+2}{3}$

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Question: Specify the domain of the function: $f(x)=\frac{-2}{x^{2}-3 x-4}$

Answer: $x \neq-1,4$

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Question: Find the product: $(3 v-4)(5 v-2)$

Answer: $15 v^{2}-26 v+8$

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Question: Solve the equation for $m$: $\frac{3 m}{2 m-5}-\frac{7}{3 m+1}=\frac{3}{2}$

Answer: -5

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Question: Find the slope of the line through the points $(11,-2)$ and $(1,17)$.

Answer: $-\frac{19}{10}$

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Question: A motorboat leaves a harbor and travels at an average speed of $18 \mathrm{mph}$ to an island. The average speed on the return trip was $12 \mathrm{mph}$. How far was the island from the harbor if the total trip took $5 \mathrm{~h}$?

Answer: 36

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Question: Find the square: $(x-8)^{2}$

Answer: $x^{2}-16 x+64$

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Question: Simplify the expression: $\frac{x^{2}-12 x+32}{x^{2}-6 x-16} \cdot \frac{7 x^{2}+14 x}{7 x^{2}+21 x}$

Answer: $\frac{x-4}{x+3}$

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Question: A thousand dollars is left in a bank savings account drawing $7 \%$ interest, compounded quarterly for 10 years. What is the balance at the end of that time?

Answer: 2001.60

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Question: Specify the domain of the function: $f(x)=\sqrt{x-16}$

Answer: $x \geqslant 16$

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Question: Solve the equation for $x$: $\frac{x}{x+3}-\frac{4}{x-2}=\frac{-5 x^{2}}{x^{2}+x-6}$

Answer: -1

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Question: Find the principal that will amount to $\$ 1750$ if invested at $3 \%$ interest compounded quarterly for 5 years.

Answer: 1507.08

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Question: Add or subtract the rational expressions and simplify: $\frac{3 a}{4 a-20}+\frac{9 a}{6 a-30}$

Answer: $\frac{9 a}{4(a-5)}$

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Question: Solve: $(x-1)^{-\frac{5}{3}}=32$

Answer: $\frac{9}{8}$

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Question:
Solve the following system of equations by elimination:
$3 x+7 y=-8$
$4 x+6 y=-4$

Answer: $(2,-2)$

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Question: How many liters of a solvent that costs $\$ 80$ per liter must be mixed with $6 \mathrm{~L}$ of a solvent that costs $\$ 25$ per liter to make a solvent that costs $\$ 36$ per liter?

Answer: 1.5

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Question: Evaluate the expression: $(-7)-(-5)$

Answer: -2

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Question: A man having ten hours at his disposal made an excursion, riding out at the rate of 10 miles an hour and returning on foot, at the rate of 3 miles an hour. Find the distance he rode.

Answer: $\frac{300}{13}$

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Question: Find the product: $(6 x-7)(4 x+1)$

Answer: $24 x^{2}-22 x-7$

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Question:
State if the given functions are inverses:
$f(x)=\sqrt[5]{\frac{x+1}{2}}$
$g(x)=2 x^{5}-1$

Answer: Yes

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Question: Simplify. Your answer should contain only positive expontents: $\frac{u^{-3} v^{-4}}{2 v\left(2 u^{-3} v^{4}\right)^{0}}$

Answer: $\frac{1}{2 u^{3} v^{5}}$

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Question: Evaluate the expression: $5-(-6)$

Answer: 11

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Question:
Solve the following systems of equation:
$p+q+r=1$
$p+2 q+3 r=4$
$4 p+5 q+6 r=7$

Answer: $\propto$ solutions

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Question: Build up each fraction by finding the Least Common Denominator: $\frac{5}{x^{2}-6 x}, \frac{2}{x}, \frac{-3}{x-6}$

Answer: $\frac{5}{x(x-6)}, \frac{2 x-12}{x(x-6)}, \frac{-3 x}{x(x-6)}$

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Question: Find a quadratic equation with the solutions $\pm 11 i$.

Answer: $x^{2}+121=0$

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Question: A is now 34 years old, and $\mathrm{B}$ is 4 years old. In how many years will A be twice as old as B?

Answer: 26

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Question: A chemist wants to make $50 \mathrm{ml}$ of a $16 \%$ acid solution by mixing a $13 \%$ acid solution and an $18 \%$ acid solution. How many milliliters of each solution should the chemist use?

Answer: 20,30

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Question: Solve the proportion: $\frac{10}{a}=\frac{6}{8}$

Answer: $\frac{40}{3}=a$

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Question: Divide: $\frac{48 k^{2}-70 k+16}{6 k-2}$

Answer: $8 k-9-\frac{1}{3 k-1}$

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Question: Find the square: $(7-5 n)^{2}$

Answer: $49-70 n+25 n^{2}$

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Question: Solve each equation by completing the square: $x^{2}+10 x-57=4$

Answer: $-5+\sqrt{86},-5-\sqrt{86}$

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Question: State the excluded values for $\frac{b^{2}+12 b+32}{b^{2}+4 b-32}$

Answer: $-8,4$

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Question: Solve the proportion: $\frac{7}{x-1}=\frac{4}{x-6}$

Answer: $x=\frac{38}{3}$

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Question: Solve: $-5(x+7)=4(-8 x-2)$

Answer: 1

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Question: Find the product: $6(4 x-1)(4 x+1)$

Answer: $96 x^{2}-6$

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Question: Solve the equation: $0=-6 v$

Answer: 0

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Question:
Solve the following system of equations by elimination:
$-7 x+4 y=-4$
$10 x-8 y=-8$

Answer: $(4,6)$

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Question: Solve the equation $\mathrm{V}=\frac{\pi r^{2} h}{3}$ for $\mathrm{h}$.

Answer: $h=\frac{3 v}{\pi r^{2}}$

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Question: Solve the equation: $340=20 n$

Answer: 17

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Question: Simplify. Your answer should contain only positive expontents: $\left(\frac{2 a^{2} b^{3}}{a^{-1}}\right)^{4}$

Answer: $16 a^{12} b^{12}$

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Question: Simplify: $\frac{x+1}{x^{2}+8 x+7}$

Answer: $\frac{1}{x+7}$

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Question: Solve the following equation: $2 x^{4}-5 x^{2}+2=0$

Answer: $\pm \sqrt{2}, \pm \frac{\sqrt{2}}{2}$

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Question: A goldsmith combined an alloy that costs $\$ 4.30$ per ounce with an alloy that costs $\$ 1.80$ per ounce. How many ounces of each were used to make a mixture of 200 oz costing $\$ 2.50$ per ounce?

Answer: 56,144

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Question: A father is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63 years, find the present age of the father.

Answer: 45

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Question: Solve: $-55=8+7(k-5)$

Answer: -4

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Question: Solve the equation $\frac{\mathrm{ym}}{b}=\frac{c}{d}$ for $\mathrm{y}$.

Answer: $y=\frac{\mathrm{cb}}{\mathrm{dm}}$

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Question: Simplify. Your answer should contain only positive expontents: $2 a^{-2} b^{-3} \cdot\left(2 a^{0} b^{4}\right)^{4}$

Answer: $\frac{32 b^{13}}{a^{2}}$

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Question: Solve: $4 b^{2}-15 b+56=3 b^{2}$

Answer: 8,7

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Question: Find a quadratic equation with the solutions $\pm 2 \sqrt{3}$.

Answer: $x^{2}-12=0$

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Question: Solve the equation: $16^{-3 p}=64^{-3 p}$

Answer: 0

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Question: Simplify: $4 \cdot 4^{4} \cdot 4^{4}$

Answer: $4^{9}$

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Question: Find the missing numerator to build up the denominator: $\frac{x-4}{x+2}=\frac{?}{x^{2}+5 x+6}$

Answer: $x^{2}-x-12$

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Question: Solve the absolute value equation: $|n|=7$

Answer: $7,-7$

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Question: Find the slope of a line perpendicular to the given line: $x+2 y=8$

Answer: 2

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Question:
Solve the following systems of equation:
$3 x+2 y=z+2$
$y=1-2 x$
$3 z=-2 y$

Answer: $\left(\frac{2}{7}, \frac{3}{7},-\frac{2}{7}\right)$

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Question: Evaluate the expression: $(-4)+(-1)$

Answer: -5

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Question: Evaluate $\left(5 p-5 p^{4}\right)-\left(8 p-8 p^{4}\right)$.

Answer: $11 b+19$

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Question: Add or subtract the rational expressions and simplify: $\frac{7}{x y^{2}}+\frac{3}{x^{2} y}$

Answer: $\frac{7 x+3 y}{x^{2} y^{2}}$

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Question: Solve the equation $\mathrm{x}+5 \mathrm{y}=3$ for $\mathrm{x}$.

Answer: $x=3-5 y$

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Question: Simplify: $5 \sqrt{32}$

Answer: $20 \sqrt{2}$

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Question: A sink is $\frac{1}{4}$ full when both the faucet and the drain are opened. The faucet alone can fill the sink in 6 minutes, while it takes 8 minutes to empty it with the drain. How long will it take to fill the remaining $\frac{3}{4}$ of the sink?

Answer: $18 \mathrm{~min}$

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Question: Solve the equation for $x$: $\frac{3 x-1}{x+6}-\frac{2 x-3}{x-3}=\frac{-3 x^{2}}{x^{2}+3 x-18}$

Answer: $\frac{7}{4}$

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Question: Simplify and write the answer in scientific notation: $\frac{2.4 \times 10^{-6}}{6.5 \times 10^{0}}$

Answer: $3.692 \times 10^{-7}$

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Question: Combine the following radicals: $\sqrt[4]{a^{2} b c^{2}} \sqrt[5]{a^{2} b^{3} c}$

Answer: $\sqrt[20]{a^{18} b^{17} c^{14}}$

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Question: Solve: $n^{2}+4 n=12$

Answer: $2,-6$

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Question: Solve the following equation: $\left(x^{2}+x\right)^{2}-8\left(x^{2}+x\right)+12=0$

Answer: $-3, \pm 2,1$

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Question: Solve: $\sqrt{2 x+2}=3+\sqrt{2 x-1}$

Answer: no solution

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Question: Solve the equation: $x-7=-26$

Answer: -19

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Question: Solve the equation: $5^{2 n}=5^{-n}$

Answer: 0

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Question: Given $w(x)=-4 x+3$, find $w(6)$

Answer: -21

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Question: Simplify: $\frac{4}{\sqrt[4]{64 m^{4} n^{2}}}$

Answer: $\frac{\sqrt[4]{4 n^{2}}}{m n}$

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Question: Simplify the expression: $\frac{5 x^{2}}{4} \cdot \frac{6}{5}$

Answer: $\frac{3 x^{2}}{2}$

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Question: Given $g(x)=4 x-4$, find $g(0)$

Answer: -4

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Question: Find product: $(9)\left(\frac{8}{9}\right)$

Answer: 8

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Question: Combine Like Terms: $n+n$

Answer: $2 n$

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Question: State the excluded values for $\frac{7 n^{2}-32 n+16}{4 n-16}$

Answer: $\frac{7 n-4}{4}$

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Question: Combine Like Terms: $m-2 m$

Answer: $-m$

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Question: Find the slope of a line parallel to the given line: $y=4 x-5$

Answer: 4

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Question: Simplify the expression: $\frac{x^{2}-6 x-7}{x+5} \cdot \frac{x+5}{x-7}$

Answer: $x+1$

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Question: Sarah worked 10 more hours than Josh. If Sarah worked $7 \mathrm{hr}$ for every $2 \mathrm{hr}$ Josh worked, how long did they each work?

Answer: J: $4 \mathrm{hr}, \mathrm{S}: 14 \mathrm{hr}$

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Question: Solve the equation: $\frac{7}{6}-\frac{4}{3} n=-\frac{3}{2} n+2\left(n+\frac{3}{2}\right)$

Answer: -1

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Question: Simplify: $\sqrt[5]{224 n^{3}}$

Answer: $2 \sqrt[5]{7 n^{3}}$

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Question: Solve the equation: $340=-17 x$

Answer: -20

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Question: Evaluate the expression: $\frac{7}{10-7 i}$

Answer: $\frac{70+49 i}{149}$

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Question: Solve the equation $a x+b=c$ for $a$.

Answer: $a=\frac{c-b}{x}$

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Question:
Solve the following systems of equation:
$x y=72$
$(x+2)(y-4)=128$

Answer: $(2,36),(-18,-4)$

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Question: Divide: $\frac{x^{2}-2 x-71}{x+8}$

Answer: $x-10+\frac{9}{x+8}$

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Question: Three campers left their campsite by canoe and paddled downstream at an average rate of $10 \mathrm{mph}$. They then turned around and paddled back upstream at an average rate of $5 \mathrm{mph}$ to return to their campsite. How long did it take the campers to canoe downstream if the total trip took $1 \mathrm{hr}$?

Answer: $\frac{1}{3}$

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Question: Find quotient: $\frac{48}{8}$

Answer: 6

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Question: Find the slope of a line parallel to the given line: $7 x+y=-2$

Answer: -7

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Question: Simplify: $-\sqrt{5}-\sqrt{5}-2 \sqrt{54}$

Answer: $-2 \sqrt{5}-6 \sqrt{6}$

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Question: Find a quadratic equation with the solutions $-9 \pm i \sqrt{5}$.

Answer: $x^{2}+18 x+86=0$

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Question: Evaluate the expression: $(-3)+(-5)$

Answer: -8

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Question: The attendance at a school concert was 578. Admission was $\$ 2.00$ for adults and $\$ 1.50$ for children. The total receipts were $\$ 985.00$. How many adults and how many children attended?

Answer: 236 adult, 342 child

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Question: Solve the equation: $5+\frac{n}{4}=4$

Answer: -4

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Question: Solve the equation: $3^{3 x-2}=3^{3 x+1}$

Answer: No solution

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Question: Evaluate using the given values: $\frac{4-(p-m)}{2}+q$; $m=4, p=6, q=6$

Answer: 7

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Question: Solve the equation $\mathrm{E}=\frac{\mathrm{mv}^{2}}{2}$ for $\mathrm{m}$.

Answer: $m=\frac{2 E}{v_{2}}$

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Question: Add or subtract the rational expressions and simplify: $\frac{t}{t-3}-\frac{5}{4 t-12}$

Answer: $\frac{4 t-5}{4(t-3)}$

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Question: Simplify: $\frac{12 n}{4 n^{2}}$

Answer: $\frac{3}{n}$

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Question: Divide: $\frac{2 x^{2}-5 x-8}{2 x+3}$

Answer: $x-4+\frac{4}{2 x+3}$

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Question: Given $h(t)=t^{2}+t$, find $h\left(t^{2}\right)$

Answer: $t^{4}+t^{2}$

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Question: Find the angle measure to the nearest degree given $\cos \mathrm{Y}=0.6157$

Answer: $52^{\circ}$

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Question: Find quotient: $\frac{-3}{2} \div \frac{13}{7}$

Answer: $-\frac{21}{26}$

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Question: Solve the equation $\mathrm{at}-\mathrm{bw}=s$ for $\mathrm{t}$.

Answer: $t=\frac{5+\mathrm{bw}}{a}$

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Question: Find product: $33(2)\left(\frac{3}{2}\right)$

Answer: 3

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Question: Solve each equation by completing the square: $n^{2}-16 n+67=4$

Answer: 9,7

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Question: Write the number in standard notation: $5 \times 10^{4}$

Answer: 50000

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Question: A motorboat leaves a harbor and travels at an average speed of $9 \mathrm{mph}$ toward a small island. Two hours later a cabin cruiser leaves the same harbor and travels at an average speed of $18 \mathrm{mph}$ toward the same island. In how many hours after the cabin cruiser leaves will the cabin cruiser be alongside the motorboat?

Answer: 2

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Question: A coin bank contains nickels and dimes. The number of dimes is 10 less than twice the number of nickels. The total value of all the coins is $\$ 2.75$. Find the number of each type of coin in the bank.

Answer: $15 \mathrm{n}, 20 \mathrm{~d}$

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Question: Solve the following equation: $(m-1)^{2}-5(m-1)=14$

Answer: $8,-1$

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Question: Divide: $\frac{a^{3}+15 a^{2}+49 a-55}{a+7}$

Answer: $a^{2}+8 a-7-\frac{6}{a+7}$

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Question: Find a quadratic equation with the solutions $\pm 5 i \sqrt{2}$.

Answer: $x^{2}+50=0$

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Question: Simplify and leave your answer as an improper fraction: $\frac{40}{16}$

Answer: $\frac{5}{2}$

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Question: Given $w(x)=x^{2}+4 x$, find $w(-5)$

Answer: 5

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Question: Express the repeating decimal as a fraction of integers: $-5.8 \overline{67}$

Answer: $-\frac{5809}{990}$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $-2 \pi \leq x \leq 2 \pi$: $\sin (2 x) \geq \sin (x)$

Answer: $\left[-2 \pi,-\frac{5 \pi}{3}\right] \cup\left[-\pi,-\frac{\pi}{3}\right] \cup\left[0, \frac{\pi}{3}\right] \cup\left[\pi, \frac{5 \pi}{3}\right]$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $-\pi \leq x \leq \pi$: $\sin ^{2}(x)<\frac{3}{4}$

Answer: $\left[-\pi,-\frac{\pi}{4}\right] \cup\left(0, \frac{3 \pi}{4}\right]$


Question: Evaluate the expression: $\ln \left(e^{5}\right)$

Answer: $\ln \left(e^{5}\right)=5$


Question: Solve the equation analytically: $5^{-x}=2$

Answer: $x=-\frac{\ln (2)}{\ln (5)}$


Question: Simplify the given power of $i$: $i^{15}$

Answer: $i^{15}=\left(i^{4}\right)^{3} \cdot i^{3}=1 \cdot(-i)=-i$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\sin (6 x)+\sin (x)=0$

Answer: $x=0, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}, \frac{\pi}{5}, \frac{3 \pi}{5}, \pi, \frac{7 \pi}{5}, \frac{9 \pi}{5}$


Question: Solve the equation analytically: $\log _{169}(3 x+7)-\log _{169}(5 x-9)=\frac{1}{2}$

Answer: $x=2$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\csc ^{3}(x)+\csc ^{2}(x)=4 \csc (x)+4$

Answer: $x=\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{7 \pi}{6}, \frac{3 \pi}{2}, \frac{11 \pi}{6}$


Question: Simplify the quantity $\sqrt{-25}\sqrt{-4}$

Answer: -10


Question: Solve the rational equation: $\frac{2 x+17}{x+1}=x+5$

Answer: $x=-6, x=2$


Question: The height $h$ in feet of a model rocket above the ground $t$ seconds after lift-off is given by $h(t)=-5 t^{2}+100 t$, for $0 \leq t \leq 20$. When does the rocket reach its maximum height above the ground? What is its maximum height?

Answer: The rocket reaches its maximum height of 500 feet 10 seconds after lift-off.


Question: Solve the equation: $|x|=x^{2}$

Answer: $x=-1, x=0$ or $x=1$


Question: The mirror in Carl's flashlight is a paraboloid of revolution. If the mirror is 5 centimeters in diameter and 2.5 centimeters deep, where should the light bulb be placed so it is at the focus of the mirror?

Answer: The bulb should be placed 0.625 centimeters above the vertex of the mirror. (As verified by Carl himself!)


Question: Solve the equation analytically: $6-3 \log _{5}(2 x)=0$

Answer: $x=\frac{25}{2}$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\sin (5 x)=\sin (3 x)$

Answer: $x=0, \frac{\pi}{8}, \frac{3 \pi}{8}, \frac{5 \pi}{8}, \frac{7 \pi}{8}, \pi, \frac{9 \pi}{8}, \frac{11 \pi}{8}, \frac{13 \pi}{8}, \frac{15 \pi}{8}$


Question: Write out the first four terms of the given sequence: $\left\{\frac{x^{n}}{n^{2}}\right\}_{n=1}^{\infty}$

Answer: $x, \frac{x^{2}}{4}, \frac{x^{3}}{9}, \frac{x^{4}}{16}$


Question: Solve the inequality analytically: $2^{\left(x^{3}-x\right)}<1$

Answer: $(-\infty,-1) \cup(0,1)$


Question: Find the distance $d$ between the points and the midpoint $M$ of the line segment which connects them: $(2 \sqrt{45}, \sqrt{12}),(\sqrt{20}, \sqrt{27})$.

Answer: $d=\sqrt{83}, M=\left(4 \sqrt{5}, \frac{5 \sqrt{3}}{2}\right)$


Question: Evaluate the expression: $\log _{6}\left(\frac{1}{36}\right)$

Answer: $\log _{6}\left(\frac{1}{36}\right)=-2$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\sin (2 x)=\tan (x)$

Answer: $x=0, \pi, \frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{4}, \frac{7 \pi}{4}$


Question: Convert the angle from radian measure into degree measure: $\frac{\pi}{3}$

Answer: $60^{\circ}$


Question:
Create a polynomial $f$ that is degree 5 and has the following characteristics:
- $x=6$, $x=i$, and $x=1-3i$ are zeros of $f$
- As $x \rightarrow -\infty$, $f(x) \rightarrow \infty$

Answer: $f(x)=a(x-6)(x-i)(x+i)(x-(1-3 i))(x-(1+3 i))$ where $a$ is any real number, $a<0$


Question: Convert the point from polar coordinates into rectangular coordinates: $\left(9, \frac{7 \pi}{2}\right)$

Answer: $(0,-9)$


Question: Find all of the angles which satisfy the given equation: $\cos (\theta)=-1.001$

Answer: $\cos (\theta)=-1.001$ never happens


Question: Use your calculator to help you solve the inequality: $e^{-x}-x e^{-x} \geq 0$

Answer: $(-\infty, 1]$


Question: Solve the equation or inequality: $3 x+\sqrt{6-9 x}=2$

Answer: $x=-\frac{1}{3}, \frac{2}{3}$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $0 \leq x \leq 2 \pi$: $\sec (x) \leq \sqrt{2}$

Answer: $\left[0, \frac{\pi}{4}\right] \cup\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right) \cup\left[\frac{7 \pi}{4}, 2 \pi\right]$


Question: Find the real solutions of the polynomial equation $x^{3}+x^{2}=\frac{11 x+10}{3}$.

Answer: $x= \pm \sqrt{3}$


Question: Expand the given logarithm and simplify: $\log _{\sqrt{2}}\left(4 x^{3}\right)$

Answer: $3 \log _{\sqrt{2}}(x)+4$


Question: Solve the quadratic equation $y^{2}-4 y=x^{2}-4$ for $x$.

Answer: $x= \pm(y-2)$


Question: Approximate the given value to three decimal places: $\cos (-2.01)$

Answer: $\cos (-2.01) \approx-0.425$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\cos (x) \csc (x) \cot (x)=6-\cot ^{2}(x)$

Answer: $x=\frac{\pi}{6}, \frac{7 \pi}{6}, \frac{5 \pi}{6}, \frac{11 \pi}{6}$


Question: Solve the equation analytically: $2 \log _{7}(x)=\log _{7}(2)+\log _{7}(x+12)$

Answer: $x=6$


Question: If $\theta=5^{\circ}$ and the hypotenuse has length 10 , how long is the side adjacent to $\theta$ ?

Answer: The side adjacent to $\theta$ has length $10 \cos \left(5^{\circ}\right) \approx 9.962$.


Question: Solve the equation analytically: $70+90 e^{-0.1 t}=75$

Answer: $t=\frac{\ln \left(\frac{1}{18}\right)}{-0.1}=10 \ln (18)$


Question: Solve the system of nonlinear equations: $\left\{\begin{array}{rr}y & =x^{3}+8 \\ y & =10 x-x^{2}\end{array}\right.$

Answer: $(-4,-56),(1,9),(2,16)$


Question: Evaluate the expression: $\log _{6}(216)$

Answer: $\log _{6}(216)=3$


Question: Find the real solutions of the polynomial equation $9 x^{3}=5 x^{2}+x$.

Answer: $x=0, \frac{5 \pm \sqrt{61}}{18}$


Question: Expand the given logarithm and simplify: $\log _{\frac{1}{2}}\left(\frac{4 \sqrt[3]{x^{2}}}{y \sqrt{z}}\right)$

Answer: $-2+\frac{2}{3} \log _{\frac{1}{2}}(x)-\log _{\frac{1}{2}}(y)-\frac{1}{2} \log _{\frac{1}{2}}(z)$


Question: Find the real solutions of the polynomial equation $2 x^{5}+3 x^{4}=18 x+27$.

Answer: $\left\{-\frac{1}{2}\right\} \cup[1, \infty)$


Question: Find the distance $d$ between the points and the midpoint $M$ of the line segment which connects them: $(1,2),(-3,5)$

Answer: $d=5, M=\left(-1, \frac{7}{2}\right)$


Question: Write out the first four terms of the given sequence: $a_{n}=2^{n}-1, n \geq 0$

Answer: $0,1,3,7$


Question: Write out the first four terms of the given sequence: $c_{0}=-2, c_{j}=\frac{c_{j-1}}{(j+1)(j+2)}, j \geq 1$

Answer: $-2,-\frac{1}{3},-\frac{1}{36},-\frac{1}{720}$


Question: Convert the equation from rectangular coordinates into polar coordinates: $x^{2}+y^{2}=x$

Answer: $\left(\frac{1}{3}, \pi+\arctan (2)\right)$


Question: Express the repeating decimal as a fraction of integers: $0 . \overline{7}$

Answer: $\frac{7}{9}$


Question: Solve the equation: $9 \arccos ^{2}(x)-\pi^{2}=0$

Answer: $x=-1,0$


Question: Solve the equation analytically: $\frac{150}{1+29 e^{-0.8 t}}=75$

Answer: $t=\frac{\ln \left(\frac{1}{29}\right)}{-0.8}=\frac{5}{4} \ln (29)$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $-\pi \leq x \leq \pi$: $\cos (x) \geq \sin (x)$

Answer: $\left[-\frac{3 \pi}{4}, \frac{\pi}{4}\right]$


Question: Solve the inequality analytically: $10 \log \left(\frac{x}{10^{-12}}\right) \geq 90$

Answer: $\left[10^{-3}, \infty\right)$


Question: Solve the equation analytically: $4^{2 x}=\frac{1}{2}$

Answer: $x=-\frac{1}{4}$


Question: Solve the inequality analytically: $e^{x}>53$

Answer: $(\ln (53), \infty)$


Question: Express the domain of the function using the extended interval notation: $f(x)=\csc (2 x)$

Answer: $\bigcup_{k=-\infty}^{\infty}\left(\frac{k \pi}{2}, \frac{(k+1) \pi}{2}\right)$


Question: Write the given sum as a product: $\cos (3 \theta)+\cos (5 \theta)$

Answer: $2 \cos (4 \theta) \cos (\theta)$


Question: Solve the polynomial inequality $x^{4}-9 x^{2} \leq 4 x-12$ and state your answer using interval notation.

Answer: $\{2\} \cup[4, \infty)$


Question: Convert the equation from rectangular coordinates into polar coordinates: $x=3 y+1$

Answer: $\left(10, \arctan \left(\frac{4}{3}\right)\right)$


Question: Solve the system of nonlinear equations: $\left\{\begin{aligned} x^{2}+y^{2} & =25 \\ 4 x^{2}-9 y & =0 \\ 3 y^{2}-16 x & =0\end{aligned}\right.$

Answer: $(3,4)$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $0 \leq x \leq 2 \pi$: $\cos (3 x) \leq 1$

Answer: $[0,2 \pi]$


Question: Solve the equation analytically: $3^{2 x}=5$

Answer: $x=\frac{\ln (5)}{2 \ln (3)}$


Question: Find all of the points on the $x$-axis which are 2 units from the point $(-1,1)$.

Answer: $(-1+\sqrt{3}, 0),(-1-\sqrt{3}, 0)$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $0 \leq x \leq 2 \pi$: $\sin \left(x+\frac{\pi}{3}\right)>\frac{1}{2}$

Answer: $\left(0, \frac{\pi}{3}\right] \cup\left[\frac{2 \pi}{3}, \pi\right) \cup\left(\pi, \frac{4 \pi}{3}\right] \cup\left[\frac{5 \pi}{3}, 2 \pi\right)$


Question: Simplify the quantity $-\sqrt{(-9)}$

Answer: $-3 i$


Question: Convert the equation from polar coordinates into rectangular coordinates: $\theta=\pi$

Answer: $\theta=\frac{\pi}{3}$


Question: Solve the equation analytically: $3^{(x-1)}=27$

Answer: $x=4$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $-2 \pi \leq x \leq 2 \pi$: $\cos (x) \leq \frac{5}{3}$

Answer: $[-2 \pi, 2 \pi]$


Question: Solve the equation analytically: $\log _{5}\left(18-x^{2}\right)=\log _{5}(6-x)$

Answer: $x=-3,4$


Question: Evaluate the expression: $\log _{36}\left(36^{216}\right)$

Answer: $\log _{36}\left(36^{216}\right)=216$


Question: Find the inverse of the given matrix: $B=\left[\begin{array}{rr}12 & -7 \\ -5 & 3\end{array}\right]$

Answer: $B^{-1}=\left[\begin{array}{rr}3 & 7 \\ 5 & 12\end{array}\right]$


Question: Find the domain of the function: $f(x)=\frac{\sqrt{-1-x}}{\log _{\frac{1}{2}}(x)}$

Answer: No domain


Question: Solve the equation: $|2 x-1|=x+1$

Answer: $x=0$ or $x=2$


Question: Solve the equation analytically: $e^{2 x}=e^{x}+6$

Answer: $x=\ln (3)$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\sqrt{2} \cos (x)-\sqrt{2} \sin (x)=1$

Answer: $x=\frac{\pi}{12}, \frac{17 \pi}{12}$


Question: Simplify the power of a complex number: $\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} i\right)^{4}$

Answer: -1


Question: Solve the equation analytically: $(\log (x))^{2}=2 \log (x)+15$

Answer: $x=10^{-3}, 10^{5}$


Question: Solve the rational inequality and express your answer using interval notation: $\frac{x^{2}-x-12}{x^{2}+x-6}>0$

Answer: $(-\infty,-3) \cup(-3,2) \cup(4, \infty)$


Question: Solve the following system of linear equations: $\left\{\begin{aligned} x-3 y-4 z & =3 \\ 3 x+4 y-z & =13 \\ 2 x-19 y-19 z & =2\end{aligned}\right.$

Answer: $\left(\frac{19}{13} t+\frac{51}{13},-\frac{11}{13} t+\frac{4}{13}, t\right)$ for all real numbers $t$


Question: Solve the equation analytically: $2^{4 x}=8$

Answer: $x=\frac{3}{4}$


Question: Solve the inequality analytically: $5.6 \leq \log \left(\frac{x}{10^{-3}}\right) \leq 7.1$

Answer: $\left[10^{2.6}, 10^{4.1}\right]$


Question: Use your calculator to help you solve the equation: $e^{\sqrt{x}}=x+1$

Answer: $x=0$


Question: Solve the inequality analytically: $2.3<-\log (x)<5.4$

Answer: $\left(10^{-5.4}, 10^{-2.3}\right)$


Question: Find the inverse of the matrix or state that the matrix is not invertible: $B=\left[\begin{array}{rr}12 & -7 \\ -5 & 3\end{array}\right]$

Answer: $B^{-1}=\left[\begin{array}{rr}3 & 7 \\ 5 & 12\end{array}\right]$


Question: Use the properties of logarithms to write the expression as a single logarithm: $\log _{2}(x)+\log _{\frac{1}{2}}(x-1)$

Answer: $\log _{2}\left(\frac{x}{x-1}\right)$


Question: Solve the inequality analytically: $1000(1.005)^{12 t} \geq 3000$

Answer: $\left[\frac{\ln (3)}{12 \ln (1.005)}, \infty\right)$


Question: Use the properties of logarithms to write the expression as a single logarithm: $\log _{7}(x)+\log _{7}(x-3)-2$

Answer: $\log _{7}\left(\frac{x(x-3)}{49}\right)$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\sin (2 x)=\cos (x)$

Answer: $x=\frac{\pi}{6}, \frac{\pi}{2}, \frac{5 \pi}{6}, \frac{3 \pi}{2}$


Question: If $\theta=12^{\circ}$ and the side adjacent to $\theta$ has length 4 , how long is the hypotenuse?

Answer: The hypotenuse has length $\frac{4}{\cos \left(12^{\circ}\right)} \approx 4.089$.


Question: Find the exact value of the cosine and sine of the given angle: $\theta=\frac{10 \pi}{3}$

Answer: $\cos \left(\frac{10 \pi}{3}\right)=-\frac{1}{2}, \sin \left(\frac{10 \pi}{3}\right)=-\frac{\sqrt{3}}{2}$


Question: Let's assume for a moment that we are standing at the origin and the positive $y$-axis points due North while the positive $x$-axis points due East. Our Sasquatch-o-meter tells us that Sasquatch is 3 miles West and 4 miles South of our current position. What are the coordinates of his position? How far away is he from us? If he runs 7 miles due East what would his new position be?

Answer: (-3, -4), 5 miles, $(4,-4)$


Question: Solve the following system of linear equations: $\left\{\begin{aligned} x+y+z & =3 \\ 2 x-y+z & =0 \\ -3 x+5 y+7 z & =7\end{aligned}\right.$

Answer: $(-3,20,19)$


Question: Find the distance $d$ between the points and the midpoint $M$ of the line segment which connects them: $\left(\frac{24}{5}, \frac{6}{5}\right),\left(-\frac{11}{5},-\frac{19}{5}\right)$.

Answer: $d=\sqrt{74}, M=\left(\frac{13}{10},-\frac{13}{10}\right)$


Question: Find all of the exact solutions of the equation and then list those solutions which are in the interval $[0,2 \pi)$: $\cos (9 x)=9$

Answer: No solution


Question: Solve the equation or inequality using your calculator: $\ln \left(x^{2}+1\right) \geq 5$

Answer: $\approx(-\infty,-12.1414) \cup(12.1414, \infty)$


Question: Find the exact value of the cosine and sine of the given angle: $\theta=\pi$

Answer: $\cos (\pi)=-1, \sin (\pi)=0$


Question: Approximate the given value to three decimal places: $\sin \left(\pi^{\circ}\right)$

Answer: $\sin \left(\pi^{\circ}\right) \approx 0.055$


Question:
Use one matrix inverse to solve the following system of linear equations:
$\left\{\begin{aligned} 3 x+7 y & =-7 \\ 5 x+12 y & =5\end{aligned}\right.$

Answer: $\left[\begin{array}{rr}12 & -7 \\ -5 & 3\end{array}\right]\left[\begin{array}{r}-7 \\ 5\end{array}\right]=\left[\begin{array}{r}-119 \\ 50\end{array}\right]$ So $x=-119$ and $y=50$.


Question: Find the inverse of the matrix or state that the matrix is not invertible: $E=\left[\begin{array}{rrr}3 & 0 & 4 \\ 2 & -1 & 3 \\ -3 & 2 & -5\end{array}\right]$

Answer: $E^{-1}=\left[\begin{array}{rrr}-1 & 8 & 4 \\ 1 & -3 & -1 \\ 1 & -6 & -3\end{array}\right]$


Question: Use the properties of logarithms to write the expression as a single logarithm: $3-\log (x)$

Answer: $\log \left(\frac{1000}{x}\right)$


Question: Solve the following system of linear equations: $\left\{\begin{aligned} x+y+z & =4 \\ 2 x-4 y-z & =-1 \\ x-y & =2\end{aligned}\right.$

Answer: Inconsistent


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\sin (2 x)=\sin (x)$

Answer: $x=0, \frac{\pi}{3}, \pi, \frac{5 \pi}{3}$


Question: Simplify the given power of $i$: $i^{117}$

Answer: $i^{117}=\left(i^{4}\right)^{29} \cdot i=1 \cdot i=i$


Question: Write the set using interval notation: $\{x \mid x \leq-3$ or $x>0\}$

Answer: $(-\infty,-3] \cup(0, \infty)$


Question: Solve the equation: $|2-5 x|=5|x+1|$

Answer: $x=-\frac{3}{10}$


Question: Convert the angle into the DMS system and round the answer to the nearest second: $-317.06^{\circ}$

Answer: $-317^{\circ} 3^{\prime} 36^{\prime \prime} \quad


Question: Convert the angle from degree measure into radian measure, giving the exact value in terms of $\pi$: $-315^{\circ}$

Answer: $-\frac{7 \pi}{4}$


Question: Solve the equation analytically: $\log _{2}\left(x^{3}\right)=\log _{2}(x)$

Answer: $x=1$


Question: Solve the following system of linear equations: $\left\{\begin{aligned} 4 x-y+z & =5 \\ 2 y+6 z & =30 \\ x+z & =5\end{aligned}\right.$

Answer: $(-3 t+4,-6 t-6,2, t)$ for all real numbers $t$


Question: Evaluate the expression: $\log \left(\frac{1}{1000000}\right)$

Answer: $\log \frac{1}{1000000}=-6$


Question: Find all of the exact solutions of the equation and then list those solutions which are in the interval $[0,2 \pi)$: $\sin ^{2}(x)=\frac{3}{4}$

Answer: $x=\frac{\pi}{3}+\pi k$ or $x=\frac{2 \pi}{3}+\pi k ; x=\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{4 \pi}{3}, \frac{5 \pi}{3}$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $-2 \pi \leq x \leq 2 \pi$: $\cos (2 x) \leq \sin (x)$

Answer: $\left[-\frac{11 \pi}{6},-\frac{7 \pi}{6}\right] \cup\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \cup,\left\{-\frac{\pi}{2}, \frac{3 \pi}{2}\right\}$


Question: Evaluate the expression: $\log \left(\sqrt[3]{10^{5}}\right)$

Answer: $\log \left(\sqrt[3]{10^{5}}\right)=\frac{5}{3}$


Question: Solve the equation analytically: $e^{x}-3 e^{-x}=2$

Answer: $x=\ln (3)$


Question: Express the repeating decimal as a fraction of integers: $0 . \overline{13}$

Answer: $\frac{13}{99}$


Question: Write out the first four terms of the given sequence: $\left\{\frac{\ln (n)}{n}\right\}_{n=1}^{\infty}$

Answer: $0, \frac{\ln (2)}{2}, \frac{\ln (3)}{3}, \frac{\ln (4)}{4}$


Question: Solve the equation analytically: $3^{(x-1)}=\left(\frac{1}{2}\right)^{(x+5)}$

Answer: $x=\frac{\ln (3)+5 \ln \left(\frac{1}{2}\right)}{\ln (3)-\ln \left(\frac{1}{2}\right)}=\frac{\ln (3)-5 \ln (2)}{\ln (3)+\ln (2)}$


Question: Solve the polynomial inequality $(x-1)^{2} \geq 4$ and state your answer using interval notation.

Answer: $(-\infty,-\sqrt[3]{3}) \cup(\sqrt[3]{2}, \infty)$


Question: Convert the equation from rectangular coordinates into polar coordinates: $(x+2)^{2}+y^{2}=4$

Answer: $\left(15,2 \pi-\arctan \left(\frac{3}{4}\right)\right)$


Question: Expand the given logarithm and simplify: $\log \left(\frac{100 x \sqrt{y}}{\sqrt[3]{10}}\right)$

Answer: $\frac{5}{3}+\log (x)+\frac{1}{2} \log (y)$


Question: Suppose the cost, in thousands of dollars, to produce $x$ hundred LCD TVs is given by $C(x)=200 x+25$ for $x \geq 0$. Find and simplify an expression for the profit function $P(x)$. (Remember: Profit $=$ Revenue - Cost.)

Answer: $p(t)=-t^{2}(3-5 t)\left(t^{2}+t+4\right)$


Question: Solve the quadratic equation $x^{2}-10 y^{2}=0$ for $x$.

Answer: $x= \pm y \sqrt{10}$


Question: Write the set using interval notation: $\{x \mid x \neq 2,-2\}$

Answer: $(-\infty,-2) \cup(-2,2) \cup(2, \infty)$


Question: Use the properties of logarithms to write the expression as a single logarithm: $\log (x)-\frac{1}{3} \log (z)+\frac{1}{2} \log (y)$

Answer: $\log \left(\frac{x \sqrt{y}}{\sqrt[3]{z}}\right)$


Question: Determine if the given sequence is arithmetic, geometric or neither. If it is arithmetic, find the common difference $d$; if it is geometric, find the common ratio $r$: $2,22,222,2222, \ldots$

Answer: neither


Question: Solve the equation analytically: $\frac{100 e^{x}}{e^{x}+2}=50$

Answer: $x=\ln (2)$


Question: Convert the point from polar coordinates into rectangular coordinates: $\left(2, \pi-\arctan \left(\frac{1}{2}\right)\right)$

Answer: $\left(-\frac{4 \sqrt{5}}{5}, \frac{2 \sqrt{5}}{5}\right)$


Question: Find all of the exact solutions of the equation and then list those solutions which are in the interval $[0,2 \pi)$: $\cos (3 x)=\frac{1}{2}$

Answer: $x=\frac{\pi}{9}+\frac{2 \pi k}{3}$ or $x=\frac{5 \pi}{9}+\frac{2 \pi k}{3} ; x=\frac{\pi}{9}, \frac{5 \pi}{9}, \frac{7 \pi}{9}, \frac{11 \pi}{9}, \frac{13 \pi}{9}, \frac{17 \pi}{9}$


Question: Solve the equation: $4-|x|=3$

Answer: $x=-1$ or $x=1$


Question: Evaluate the expression: $\log _{5}\left(3^{\log _{3}(5)}\right)$

Answer: $\log _{5}\left(3^{\log _{3} 5}\right)=1$


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\tan (x)=\sec (x)$

Answer: No solution


Question: Solve the equation, giving the exact solutions which lie in $[0,2 \pi)$: $\cot ^{4}(x)=4 \csc ^{2}(x)-7$

Answer: $x=\frac{\pi}{6}, \frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{6}, \frac{7 \pi}{6}, \frac{5 \pi}{4}, \frac{7 \pi}{4}, \frac{11 \pi}{6}$


Question: Express the domain of the function using the extended interval notation: $f(x)=\sqrt{2-\sec (x)}$

Answer: $\bigcup_{k=-\infty}^{\infty}\left\{\left[\frac{(6 k-1) \pi}{3}, \frac{(6 k+1) \pi}{3}\right] \cup\left(\frac{(4 k+1) \pi}{2}, \frac{(4 k+3) \pi}{2}\right)\right\}$


Question: A local pizza store offers medium two-topping pizzas delivered for $\$ 6.00$ per pizza plus a $\$ 1.50$ delivery charge per order. On weekends, the store runs a 'game day' special: if six or more medium two-topping pizzas are ordered, they are $\$ 5.50$ each with no delivery charge. Write a piecewise-defined linear function which calculates the $\operatorname{cost} C$ (in dollars) of $p$ medium two-topping pizzas delivered during a weekend.

Answer: $C(p)=\left\{\begin{array}{rll}6 p+1.5 & \text { if } & 1 \leq p \leq 5 \\ 5.5 p & \text { if } & p \geq 6\end{array}\right.$


Question: Rewrite the sum using summation notation: $-\ln (3)+\ln (4)-\ln (5)+\cdots+\ln (20)$

Answer: $\sum_{k=3}^{20}(-1)^{k} \ln (k)$


Question: Find all of the exact solutions of the equation and then list those solutions which are in the interval $[0,2 \pi)$: $\cot (2 x)=-\frac{\sqrt{3}}{3}$

Answer: $x=\frac{\pi}{3}+\frac{\pi k}{2} ; x=\frac{\pi}{3}, \frac{5 \pi}{6}, \frac{4 \pi}{3}, \frac{11 \pi}{6}$


Question: Convert the angle into decimal degrees and round the answer to three decimal places: $502^{\circ} 35^{\prime}$

Answer: $502.583^{\circ}$


Question: Expand the binomial: $\left(x-x^{-1}\right)^{4}$

Answer: $\left(x-x^{-1}\right)^{4}=x^{4}-4 x^{2}+6-4 x^{-2}+x^{-4}$


Question: Convert the angle from radian measure into degree measure: $\frac{5 \pi}{3}$

Answer: $300^{\circ}$


Question: Solve the inequality. Express the exact answer in interval notation, restricting your attention to $-2 \pi \leq x \leq 2 \pi$: $\cot (x) \geq 5$

Answer: $(-2 \pi, \operatorname{arccot}(5)-2 \pi] \cup(-\pi, \operatorname{arccot}(5)-\pi] \cup(0, \operatorname{arccot}(5)] \cup(\pi, \pi+\operatorname{arccot}(5)]$


Question: Write out the first four terms of the given sequence: $F_{0}=1, F_{1}=1, F_{n}=F_{n-1}+F_{n-2}, n \geq 2$ (This is the famous Fibonacci Sequence)

Answer: $1,1,2,3$


Question: If $\theta=59^{\circ}$ and the side opposite $\theta$ has length 117.42 , how long is the hypotenuse?

Answer: The hypotenuse has length $\frac{117.42}{\sin \left(59^{\circ}\right)} \approx 136.99$.


Question: Solve the given inequality: $6 \operatorname{arccot}(7 x) \geq \pi$

Answer: $\left(-\infty, \frac{\sqrt{3}}{7}\right]$


Question: Use the properties of logarithms to write the expression as a single logarithm: $\log _{2}(x)+\log _{2}(y)-\log _{2}(z)$

Answer: $\log _{2}\left(\frac{x y}{z}\right)$


Question: Carl can stuff 6 envelopes per minute. Find a linear function $E$ that represents the total number of envelopes Carl can stuff after $t$ hours, assuming he doesn't take any breaks.

Answer: $E(t)=360 t, t \geq 0$.


Question: Solve the equation analytically: $3^{7 x}=81^{4-2 x}$

Answer: $x=\frac{16}{15}$


Question: The height $h$ in feet of a model rocket above the ground $t$ seconds after lift-off is given by $h(t)=-5 t^{2}+100 t$, for $0 \leq t \leq 20$. When does the rocket reach its maximum height above the ground? What is its maximum height?

Answer: $\left[-\frac{1}{3}, 4\right]$


Question: Simplify the given power of $i$: $i^5$

Answer: $i^{5}=i^{4} \cdot i=1 \cdot i=i$


Question: Solve the equation or inequality using your calculator: $\ln \left(-2 x^{3}-x^{2}+13 x-6\right)<0$

Answer: $\approx(-3.0281,-3) \cup(0.5,0.5991) \cup(1.9299,2)$


Question: Solve the equation: $|7 x-1|+2=0$

Answer: no solution


Question: Evaluate the expression: $36^{\log _{36}(216)}$

Answer: $36^{\log _{36}(216)}=216$


Question: Find all of the exact solutions of the equation and then list those solutions which are in the interval $[0,2 \pi)$: $2 \cos \left(x+\frac{7 \pi}{4}\right)=\sqrt{3}$

Answer: $x=-\frac{19 \pi}{12}+2 \pi k$ or $x=\frac{\pi}{12}+2 \pi k ; x=\frac{\pi}{12}, \frac{5 \pi}{12}$


Question: Determine whether or not the equation represents $y$ as a function of $x$: $x^{3}+y^{3}=4$

Answer: Function


Question: Solve the equation or inequality using your calculator: $\ln (x)=\sqrt[4]{x}$

Answer: $x \approx 4.177, x \approx 5503.665$


Question: Solve the rational inequality and express your answer using interval notation: $\frac{x^{4}-4 x^{3}+x^{2}-2 x-15}{x^{3}-4 x^{2}} \geq x$

Answer: $[-3,0) \cup(0,4) \cup[5, \infty)$


Question: Find the real solutions of the polynomial equation $x^{4}+2 x^{2}=15$.

Answer: $x=-\frac{3}{2}, \pm \sqrt{3}$


Question: Use the properties of logarithms to write the expression as a single logarithm: $4 \ln (x)+2 \ln (y)$

Answer: $\ln \left(x^{4} y^{2}\right)$


Question: Find the domain of the function: $f(x)=\ln \left(x^{2}+1\right)$

Answer: $(-\infty, \infty)$


Question: Solve the equation analytically: $3 \ln (x)-2=1-\ln (x)$

Answer: $x=e^{3 / 4}$


Question: Find the distance $d$ between the points and the midpoint $M$ of the line segment which connects them: $(0,0),(x, y)$

Answer: $d=\sqrt{x^{2}+y^{2}}, M=\left(\frac{x}{2}, \frac{y}{2}\right)$


Question: Find an equation for the parabola which fits the given criteria: Focus $(10,1)$, directrix $x=5$

Answer: $(y-1)^{2}=10\left(x-\frac{15}{2}\right)$


Question: Express the domain of the function using the extended interval notation: $f(x)=\frac{\cos (x)}{\sin (x)+1}$

Answer: $\bigcup_{k=-\infty}^{\infty}\left(\frac{(4 k-1) \pi}{2}, \frac{(4 k+3) \pi}{2}\right)$