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Calculus an Applied Approach

Ron Larson, David C, Falvo

Chapter 0

Precalculus Review - all with Video Answers

Educators

Section 1

The Real Number Line and Order

00:25

Problem 1

In Exercises determine whether the real number is rational or irrational.
$$0.25$$

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00:21

Problem 2

In Exercises determine whether the real number is rational or irrational.
$$-3678$$

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00:24

Problem 3

In Exercises determine whether the real number is rational or irrational.
$$\frac{3 \pi}{2}$$

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00:20

Problem 4

In Exercises determine whether the real number is rational or irrational.
$$3 \sqrt{2}-1$$

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00:18

Problem 5

In Exercises determine whether the real number is rational or irrational.
$$4.3 \overline{451}$$

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00:21

Problem 6

In Exercises determine whether the real number is rational or irrational.
$$\frac{22}{7}$$

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00:16

Problem 7

In Exercises determine whether the real number is rational or irrational.
$$\sqrt[3]{64}$$

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00:17

Problem 8

In Exercises determine whether the real number is rational or irrational.
$$0 . \overline{8177}$$

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00:19

Problem 9

In Exercises determine whether the real number is rational or irrational.
$$\sqrt[3]{60}$$

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00:17

Problem 10

In Exercises determine whether the real number is rational or irrational.
$$2 e$$

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01:00

Problem 11

In Exercises determine whether each given value of $x$ satisfies the inequality.
$$
\begin{array}{l}{5 x-12>0} \\ {\text { (a) } x=3 \quad \text { (b) } x=-3 \quad \text { (c) } x=\frac{5}{2}}\end{array}
$$

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01:07

Problem 12

In Exercises determine whether each given value of $x$ satisfies the inequality.
$$
\begin{array}{l}{x+1<\frac{x}{3}} \\ {\text { (a) } x=0 \quad \text { (b) } x=4 \quad \text { (c) } x=-4}\end{array}
$$

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01:20

Problem 13

In Exercises determine whether each given value of $x$ satisfies the inequality.
$$
\begin{array}{l}{0<\frac{x-2}{4}<2} \\ {\text { (a) } x=4 \quad \text { (b) } x=10 \quad \text { (c) } x=0}\end{array}
$$

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01:27

Problem 14

In Exercises determine whether each given value of $x$ satisfies the inequality.
$$
\begin{array}{l}{-1<\frac{3-x}{2} \leq 1} \\ {\text { (a) } x=0 \quad \text { (b) } x=1 \quad \text { (c) } x=5}\end{array}
$$

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00:36

Problem 15

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
x-5 \geq 7
$$

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00:34

Problem 16

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
2 x>3
$$

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00:53

Problem 17

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
4 x+1<2 x
$$

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00:36

Problem 18

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
2 x+7<3
$$

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01:03

Problem 19

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
4-2 x<3 x-1
$$

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00:59

Problem 20

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
x-4 \leq 2 x+1
$$

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00:51

Problem 21

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
-4<2 x-3<4
$$

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00:33

Problem 22

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
0 \leq x+3<5
$$

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00:58

Problem 23

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
\frac{3}{4}>x+1>\frac{1}{4}
$$

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00:52

Problem 24

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
-1<-\frac{x}{3}<1
$$

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00:58

Problem 25

$$
\frac{x}{2}+\frac{x}{3}>5
$$

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00:56

Problem 26

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
\frac{x}{2}-\frac{x}{3}>5
$$

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02:49

Problem 27

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
2 x^{2}-x<6
$$

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02:14

Problem 28

In Exercises $15-28,$ solve the inequality and sketch the graph of the solution on the real number line.
$$
2 x^{2}+1<9 x-3
$$

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00:49

Problem 29

Use inequality notation to describe the subset of real numbers.
A company expects its earnings per share $E$ for the next quarter to be no less than $\$ 4.10$ and no more than $\$ 4.25$.

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00:49

Problem 30

Use inequality notation to describe the subset of real numbers.
The estimated daily oil production $p$ at a refinery is greater than 2 million barrels but less than 2.4 million barrels.

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00:32

Problem 31

Use inequality notation to describe the subset of real numbers.
According to a survey, the percent $p$ of Americans that now conduct most of their banking transactions online is no more than $40 \% .$

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00:22

Problem 32

Use inequality notation to describe the subset of real numbers.
The net income $I$ of a company is expected to be no less than $\$ 239$ million.

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01:23

Problem 33

Physiology The maximum heart rate of a person in normal health is related to the person's age by the equation
$r=220-A$
where $r$ is the maximum heart rate in beats per minute and $A$ is the person's age in years. Some physiologists recommend that during physical activity a person should strive to increase his or her heart rate to at least $60 \%$ of the maximum heart rate for sedentary people and at most $90 \%$ of the maximum heart rate for highly fit people. Express as an interval the range of the target heart rate for a 20 -year-old.

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01:34

Problem 34

Profit The revenue for selling $x$ units of a product is $R=115.95 x,$ and the cost of producing $x$ units is
$C=95 x+750 .$ To obtain a profit, the revenue must be greater than the cost. For what values of $x$ will this product return a profit?

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02:40

Problem 35

Sales A doughnut shop at a shopping mall sells a dozen doughnuts for $\$ 220$ . Beyond the fixed cost (for rent, utilities, and insurance) of $\$ 220$ per day, it costs $\$ 2.75$ for enough materials (flour, sugar, etc.) and labor to produce each dozen doughnuts. If the daily profit varies between $\$ 60$ and $\$ 270,$ between what levels (in dozens) do the daily sales vary?

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01:05

Problem 36

Annual Operating costs A utility company has a fleet of vans. The annual operating cost $C$ (in dollars) of each van is estimated to be $C=0.35 m+2500$, where $m$ is the number of miles driven. The company wants the annual operating cost of each van to be less than $\$ 13,000$. To do this, $m$ must be less than what value?

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02:02

Problem 37

Determine whether each statement is true or false, given $a<b$.
(a) $-2 a < -2 b$
(b) $a+2 < b+2$
(c) $6 a < 6 b$
(d) $\frac{1}{a} < \frac{1}{b}$

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02:01

Problem 38

Determine whether each statement is true or false, given $a<b$.
(a) $a-4 < b-4$
(b) $4-a < 4-b$
(c) $-3 b < -3 a$
(d) $\frac{a}{4} < \frac{b}{4}$

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