Question 1

A company spent $$66,700 on health insurance out of total sales of 569$$,400. What percent of total sales was spent on health insurance? Round to the nearest tenth of a percent.

Accepted Answer

$$11.7\%$$

Question 2

Solve for $$x$$: $$4x + \dfrac{3}{2} + 1 = -4x$$

Accepted Answer

$$-\dfrac{3}{4}$$

Question 3

A rectangular lot has a perimeter of $$90$$ meters. If the length is $$7$$ meters more than the width, what is the length of the lot?

Accepted Answer

$$26 m$$

Question 4

Walt invested $$10,000 in $$two accounts: one at $$10\%$$ and the other at $$9\%. If he $$earned $$960 in $$interest, how much did he invest at $$9\%$$?

Accepted Answer

$$4,000$$

Question 5

A car radiator contains $$70$$ liters of $$20\%$$ antifreeze solution. How many liters should be drained and replaced with pure antifreeze to obtain a $$40\%$$ solution?

Accepted Answer

$$17.5$$ liters

Question 6

In a chemistry lab, $$7$$ liters of a $$4\%$$ silver iodide solution must be mixed with a $$10\%$$ solution to get a $$6\%$$ solution. How many liters of the $$10\%$$ solution are needed?

Accepted Answer

$$3.5$$ liters

Question 7

A convention manager has $$48$$ bills totaling $$\1320$, made up of 20$'s and 50$'s. How many 50$-dollar bills does she have?

Accepted Answer

$$12$$

Question 8

Bert and Brenda are $$18 km $$apart and walk toward each other. Bert walks at $$3 km/h $$and they meet in $$4$$ hours. What is Brenda's speed?

Accepted Answer

$$1.5$$\ 	ext{km/h}$

Question 9

A boat travels $$78$$ miles downstream and $$39$$ miles upstream in the same time. If the stream's speed is $$4$$ mph, what is the speed of the boat in still water?

Accepted Answer

$$12$$\ 	ext{mph}$

Question 10

The sum of three consecutive odd integers is $$267. $$What is the smallest of these integers?

Accepted Answer

$$87$$

Question 11

Find the slope of the line passing through the points $$(1, -9)$$ and $$(-1, -3).$$

Accepted Answer

$$-3$$

Question 12

Simplify the expression $$\dfrac{17r$$^{-1}$$(r^3)^5$}{19(r$$^{-4}$$)^{-1}$$}$ so that no negative exponents appear.

Accepted Answer

$$\dfrac{17r$$^{10}$$}{19}$$

Question 13

Factor the trinomial $$u^2 - 2uv$$ - $$35v^2$$ completely.

Accepted Answer

$$(u + 5v)(u - 7v)$$

Question 14

Express the rational expression $$\dfrac{y^2$ - 2y - 35}{y^2$ + 14y + 45} in $$lowest terms.

Accepted Answer

$$\dfrac{y - 7}{y + 9}$$

Question 15

A plane flies $$460$$ miles with the wind and $$300$$ miles against the wind in the same time. If the wind speed is $$28$$ mph, what is the speed of the plane in still air?

Accepted Answer

$$133$$\ 	ext{mph}$

Question 16

Simplify the radical $$-\sqrt{500k^7$q^8$$}$, assuming all variables are positive real numbers.

Accepted Answer

$$-10k^3q^4$

Question 17

Find the domain and range of the function $$f(x) = -5x^2$ - 3.$$

Accepted Answer

Domain: $$(-\infty, \infty)$$; range: $$(-\infty, -3)$$

Question 18

Which of the following relations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$y^2 = 4x$; domain: $$[0, \infty)$$

Question 19

Solve for $$x$$ using the quadratic formula: $$3x(x + 3) = 1.$$

Accepted Answer

$$x = \dfrac{-9 \pm \sqrt{93}}{6}$$

College Algebra Final Exam Review: Step-by-Step Guidance

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