Applied Calculus for the Managerial, Life, and Social Sciences

Problem 2

Show the interval on a number line.
$$(-2,5]$$

Tyler Moulton

Numerade Educator

Problem 3

Show the interval on a number line.
$$[-1,4)$$

Tyler Moulton

Numerade Educator

Problem 4

Show the interval on a number line.
$$\left[-\frac{6}{5},-\frac{1}{2}\right]$$

Tyler Moulton

Numerade Educator

Problem 5

Show the interval on a number line.
$$(0, \infty)$$

Tyler Moulton

Numerade Educator

Problem 6

Show the interval on a number line.
$$(0, \infty)$$

Tyler Moulton

Numerade Educator

Problem 7

Evaluate the expression.
$$27^{2 / 3}$$

Tyler Moulton

Numerade Educator

01:39

Problem 8

Evaluate the expression.
$$8^{-4 / 3}$$

Jeyasree R T

Numerade Educator

Problem 9

Evaluate the expression.
$$\left(\frac{1}{\sqrt{3}}\right)^{0}$$

Tyler Moulton

Numerade Educator

Problem 10

Evaluate the expression.
$$\left(7^{1 / 2}\right)^{4}$$

Tyler Moulton

Numerade Educator

Problem 11

Evaluate the expression.
$$\left[\left(\frac{1}{8}\right)^{1 / 3}\right]^{-2}$$

Tyler Moulton

Numerade Educator

Problem 12

Evaluate the expression.
$$\left[\left(-\frac{1}{3}\right)^{2}\right]^{-3}$$

Tyler Moulton

Numerade Educator

Problem 13

Evaluate the expression.
$$\left(\frac{7^{-5} \cdot 7^{2}}{7^{-2}}\right)^{-1}$$

Tyler Moulton

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Problem 14

Evaluate the expression.
$$\left(\frac{9}{16}\right)^{-1 / 2}$$

Tyler Moulton

Numerade Educator

01:19

Problem 15

Evaluate the expression.
$$\left(125^{2 / 3}\right)^{-1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 16

Evaluate the expression.
$$\sqrt[3]{2^{6}}$$

Tyler Moulton

Numerade Educator

Problem 17

Evaluate the expression.
$$\frac{\sqrt{32}}{\sqrt{8}}$$

Tyler Moulton

Numerade Educator

Problem 18

Evaluate the expression.
$$\sqrt[3]{\frac{-8}{27}}$$

Tyler Moulton

Numerade Educator

01:14

Problem 19

Evaluate the expression.
$$\frac{16^{5 / 8} 16^{1 / 2}}{16^{7 / 8}}$$

Tyler Moulton

Numerade Educator

Problem 20

Evaluate the expression.
$$\left(\frac{9^{-3} \cdot 9^{5}}{9^{-2}}\right)^{-1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 21

Evaluate the expression.
$$16^{1 / 4} \cdot 8^{-1 / 3}$$

Tyler Moulton

Numerade Educator

Problem 22

Evaluate the expression.
$$\frac{6^{2.5} \cdot 6^{-1.9}}{6^{-1.4}}$$

Tyler Moulton

Numerade Educator

Problem 23

Determine whether the statement is true or false. Give a reason for your choice.
$$x^{4}+2 x^{4}=3 x^{4}$$

Tyler Moulton

Numerade Educator

Problem 24

Determine whether the statement is true or false. Give a reason for your choice.
$$3^{2} \cdot 2^{2}=6^{2}$$

Tyler Moulton

Numerade Educator

Problem 25

Determine whether the statement is true or false. Give a reason for your choice.
$$x^{3} \cdot 2 x^{2}=2 x^{6}$$

Tyler Moulton

Numerade Educator

Problem 26

Determine whether the statement is true or false. Give a reason for your choice.
$$3^{3}+3=3^{4}$$

Tyler Moulton

Numerade Educator

Problem 27

Determine whether the statement is true or false. Give a reason for your choice.
$$\frac{2^{4 x}}{1^{3 x}}=2^{4 x-3 x}$$

Tyler Moulton

Numerade Educator

Problem 28

Determine whether the statement is true or false. Give a reason for your choice.
$$\frac{2^{4 x}}{1^{3 x}}=2^{4 x-3 x}$$

Tyler Moulton

Numerade Educator

Problem 29

Determine whether the statement is true or false. Give a reason for your choice.
$$\frac{1}{4^{-3}}=\frac{1}{64}$$

Tyler Moulton

Numerade Educator

01:31

Problem 30

Determine whether the statement is true or false. Give a reason for your choice.
$$\frac{4^{3 / 2}}{2^{4}}=\frac{1}{2}$$

Tyler Moulton

Numerade Educator

Problem 31

Determine whether the statement is true or false. Give a reason for your choice.
$$\left(1.2^{1 / 2}\right)^{-1 / 2}=1$$

Tyler Moulton

Numerade Educator

Problem 32

Determine whether the statement is true or false. Give a reason for your choice.
$$5^{2 / 3} \cdot(25)^{2 / 3}=25$$

Tyler Moulton

Numerade Educator

Problem 33

Rewrite the expression using positive exponents only.
$$(x y)^{-2}$$

Tyler Moulton

Numerade Educator

Problem 34

Rewrite the expression using positive exponents only.
$$3 s^{1 / 3} \cdot s^{-7 / 3}$$

Tyler Moulton

Numerade Educator

Problem 35

Rewrite the expression using positive exponents only.
$$\frac{x^{-1 / 3}}{x^{1 / 2}}$$

Tyler Moulton

Numerade Educator

01:25

Problem 36

Rewrite the expression using positive exponents only.
$$\sqrt{x^{-1}} \cdot \sqrt{9 x^{-3}}$$

Tyler Moulton

Numerade Educator

Problem 37

Rewrite the expression using positive exponents only.
$$12^{0}(s+t)^{-3}$$

Tyler Moulton

Numerade Educator

Problem 38

Rewrite the expression using positive exponents only.
$$(x-y)\left(x^{-1}+y^{-1}\right)$$

Tyler Moulton

Numerade Educator

Problem 39

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\frac{x^{7 / 3}}{x^{-2}}$$

Tyler Moulton

Numerade Educator

01:18

Problem 40

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\left(49 x^{-2}\right)^{-1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 41

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\left(x^{2} y^{-3}\right)\left(x^{-5} y^{3}\right)$$

Tyler Moulton

Numerade Educator

Problem 42

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\frac{5 x^{6} y^{3}}{2 x^{2} y^{7}}$$

Tyler Moulton

Numerade Educator

Problem 43

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\frac{x^{3 / 4}}{x^{-1 / 4}}$$

Tyler Moulton

Numerade Educator

Problem 44

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\left(\frac{x^{3} y^{2}}{z^{2}}\right)^{2}$$

Tyler Moulton

Numerade Educator

01:27

Problem 45

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\left(\frac{x^{3}}{-27 y^{-6}}\right)^{-2 / 3}$$

Tyler Moulton

Numerade Educator

Problem 46

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\left(\frac{e^{x}}{e^{x-2}}\right)^{-1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 47

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\left(\frac{x^{-3}}{y^{-2}}\right)^{2}\left(\frac{y}{x}\right)^{4}$$

Tyler Moulton

Numerade Educator

Problem 48

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\frac{\left(r^{n}\right)^{4}}{r^{5-2 n}}$$

Tyler Moulton

Numerade Educator

Problem 49

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\sqrt[3]{x^{-2}} \cdot \sqrt{4 x^{5}}$$

Tyler Moulton

Numerade Educator

Problem 50

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\sqrt{81 x^{6} y^{-4}}$$

Tyler Moulton

Numerade Educator

Problem 51

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$-\sqrt[4]{16 x^{4} y^{8}}$$

Tyler Moulton

Numerade Educator

01:01

Problem 52

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\sqrt[3]{x^{3 a+b}}$$

Tyler Moulton

Numerade Educator

Problem 53

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\sqrt[6]{64 x^{8} y^{3}}$$

Tyler Moulton

Numerade Educator

Problem 54

Simplify the expression. (Assume that $x, y, r, s,$ and $t$ are positive.)
$$\sqrt[3]{27 r^{6}} \cdot \sqrt{s^{2} t^{4}}$$

Tyler Moulton

Numerade Educator

Problem 55

Use the fact that $2^{1 / 2} \approx 1.414$ and $3^{1 / 2} \approx 1.732$ to evaluate the expression without using a calculator.
$$2^{3 / 2}$$

Tyler Moulton

Numerade Educator

Problem 56

Use the fact that $2^{1 / 2} \approx 1.414$ and $3^{1 / 2} \approx 1.732$ to evaluate the expression without using a calculator.
$$8^{1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 57

Use the fact that $2^{1 / 2} \approx 1.414$ and $3^{1 / 2} \approx 1.732$ to evaluate the expression without using a calculator.
$$9^{3 / 4}$$

Tyler Moulton

Numerade Educator

Problem 58

Use the fact that $2^{1 / 2} \approx 1.414$ and $3^{1 / 2} \approx 1.732$ to evaluate the expression without using a calculator.
$$6^{1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 59

Use the fact that $10^{1 / 2} \approx 3.162$ and $10^{1 / 3} \approx 2.154$ to evaluate the expression without using a calculator.
$$10^{3 / 2}$$

Tyler Moulton

Numerade Educator

Problem 60

Use the fact that $10^{1 / 2} \approx 3.162$ and $10^{1 / 3} \approx 2.154$ to evaluate the expression without using a calculator.
$$1000^{3 / 2}$$

Tyler Moulton

Numerade Educator

Problem 61

Use the fact that $10^{1 / 2} \approx 3.162$ and $10^{1 / 3} \approx 2.154$ to evaluate the expression without using a calculator.
$$10^{2.5}$$

Tyler Moulton

Numerade Educator

Problem 62

Use the fact that $10^{1 / 2} \approx 3.162$ and $10^{1 / 3} \approx 2.154$ to evaluate the expression without using a calculator.
$$(0.0001)^{-1 / 3}$$

Tyler Moulton

Numerade Educator

Problem 63

Rationalize the denominator.
$$\frac{3}{2 \sqrt{x}}$$

Tyler Moulton

Numerade Educator

Problem 64

Rationalize the denominator.
$$\frac{3}{\sqrt{x y}}$$

Tyler Moulton

Numerade Educator

Problem 65

Rationalize the denominator.
$$\frac{2 y}{\sqrt{3 y}}$$

Tyler Moulton

Numerade Educator

Problem 66

Rationalize the denominator.
$$\frac{5 x^{2}}{\sqrt{3 x}}$$

Tyler Moulton

Numerade Educator

00:44

Problem 67

Rationalize the denominator.
$$\frac{1}{\sqrt[3]{x}}$$

Prashansha Kaushik

Numerade Educator

Problem 68

Rationalize the denominator.
$$\sqrt{\frac{2 x}{y}}$$

Tyler Moulton

Numerade Educator

Problem 69

Rationalize the numerator.
$$\frac{2 \sqrt{x}}{3}$$

Tyler Moulton

Numerade Educator

Problem 70

Rationalize the numerator.
$$\frac{\sqrt[3]{x^{2}}}{24}$$

Tyler Moulton

Numerade Educator

Problem 71

Rationalize the numerator.
$$\sqrt{\frac{2 y}{x}}$$

Tyler Moulton

Numerade Educator

Problem 72

Rationalize the numerator.
$$\sqrt[3]{\frac{2 x}{3 y}}$$

Tyler Moulton

Numerade Educator

Problem 73

Rationalize the numerator.
$$\frac{\sqrt[3]{x^{2} z}}{y}$$

Tyler Moulton

Numerade Educator

01:19

Problem 74

Rationalize the numerator.
$$\frac{\sqrt[3]{x^{2} y}}{2 x}$$

Tyler Moulton

Numerade Educator

Problem 75

Perform the indicated operations and/or simplify each expression.
$$\left(7 x^{2}-3 x+5\right)+\left(2 x^{2}+5 x-4\right)$$

Tyler Moulton

Numerade Educator

Problem 76

Perform the indicated operations and/or simplify each expression.
$$\left(3 x^{2}+5 x y+2 y\right)+\left(4-3 x y-2 x^{2}\right)$$

Tyler Moulton

Numerade Educator

Problem 77

Perform the indicated operations and/or simplify each expression.
$$\left(5 y^{2}-2 y+1\right)-\left(y^{2}-3 y-7\right)$$

Tyler Moulton

Numerade Educator

Problem 78

Perform the indicated operations and/or simplify each expression.
$$3(2 a-b)-4(b-2 a)$$

Tyler Moulton

Numerade Educator

Problem 79

Perform the indicated operations and/or simplify each expression.
$$x-\{2 x-[-x-(1-x)]\}$$

Tyler Moulton

Numerade Educator

01:35

Problem 80

Perform the indicated operations and/or simplify each expression.
$$3 x^{2}-\left\{x^{2}+1-x[x-(2 x-1)]\right\}+2$$

Tyler Moulton

Numerade Educator

Problem 81

Perform the indicated operations and/or simplify each expression.
$$\left(\frac{1}{3}-1+e\right)-\left(-\frac{1}{3}-1+e^{-1}\right)$$

Tyler Moulton

Numerade Educator

Problem 82

Perform the indicated operations and/or simplify each expression.
$$-\frac{3}{4} y-\frac{1}{4} x+100+\frac{1}{2} x+\frac{1}{4} y-120$$

Tyler Moulton

Numerade Educator

Problem 83

Perform the indicated operations and/or simplify each expression.
$$3 \sqrt{8}+8-2 \sqrt{y}+\frac{1}{2} \sqrt{x}-\frac{3}{4} \sqrt{y}$$

Tyler Moulton

Numerade Educator

Problem 84

Perform the indicated operations and/or simplify each expression.
$$\frac{8}{9} x^{2}+\frac{2}{3} x+\frac{16}{3} x^{2}-\frac{16}{x} x-2 x+2$$

Tyler Moulton

Numerade Educator

Problem 85

Perform the indicated operations and/or simplify each expression.
$$(x+8)(x-2)$$

Tyler Moulton

Numerade Educator

Problem 86

Perform the indicated operations and/or simplify each expression.
$$(5 x+2)(3 x-4)$$

Tyler Moulton

Numerade Educator

Problem 87

Perform the indicated operations and/or simplify each expression.
$$(a+5)^{2}$$

Tyler Moulton

Numerade Educator

Problem 88

Perform the indicated operations and/or simplify each expression.
$$(3 a-4 b)^{2}$$

Tyler Moulton

Numerade Educator

Problem 89

Perform the indicated operations and/or simplify each expression.
$$(x+2 y)^{2}$$

Tyler Moulton

Numerade Educator

Problem 90

Perform the indicated operations and/or simplify each expression.
$$(6-3 x)^{2}$$

Tyler Moulton

Numerade Educator

Problem 91

Perform the indicated operations and/or simplify each expression.
$$(2 x+y)(2 x-y)$$

Tyler Moulton

Numerade Educator

Problem 92

Perform the indicated operations and/or simplify each expression.
$$(3 x+2)(2-3 x)$$

Tyler Moulton

Numerade Educator

Problem 93

Perform the indicated operations and/or simplify each expression.
$$\left(2 x^{2}-1\right)\left(3 x^{2}\right)+\left(x^{2}+3\right)(4 x)$$

Tyler Moulton

Numerade Educator

Problem 94

Perform the indicated operations and/or simplify each expression.
$$\left(x^{2}-1\right)(2 x)-x^{2}(2 x)$$

Tyler Moulton

Numerade Educator

01:34

Problem 95

Perform the indicated operations and/or simplify each expression.
$$6 x\left(\frac{1}{2}\right)\left(2 x^{2}+3\right)^{-1 / 2}(4 x)+6\left(2 x^{2}+3\right)^{1 / 2}$$

Tyler Moulton

Numerade Educator

Problem 96

Perform the indicated operations and/or simplify each expression.
$$\left(x^{1 / 2}+1\right)\left(\frac{1}{2} x^{-1 / 2}\right)-\left(x^{1 / 2}-1\right)\left(\frac{1}{2} x^{-1 / 2}\right)$$

Tyler Moulton

Numerade Educator

Problem 97

Perform the indicated operations and/or simplify each expression.
$$100\left(-10 t e^{-0.1 t}-100 e^{-0.1 t}\right)$$

Tyler Moulton

Numerade Educator

Problem 98

Perform the indicated operations and/or simplify each expression.
$$2(t+\sqrt{t})^{2}-2 t^{2}$$

Tyler Moulton

Numerade Educator

Problem 99

Factor out the greatest common factor from each expression.
$$4 x^{5}-12 x^{4}-6 x^{3}$$

Tyler Moulton

Numerade Educator

Problem 100

Factor out the greatest common factor from each expression.
$$4 x^{2} y^{2} z-2 x^{5} y^{2}+6 x^{3} y^{2} z^{2}$$

Tyler Moulton

Numerade Educator

Problem 101

Factor out the greatest common factor from each expression.
$$7 a^{4}-42 a^{2} b^{2}+49 a^{3} b$$

Tyler Moulton

Numerade Educator

Problem 102

Factor out the greatest common factor from each expression.
$$3 x^{2 / 3}-2 x^{1 / 3}$$

Tyler Moulton

Numerade Educator

Problem 103

Factor out the greatest common factor from each expression.
$$e^{-x}-x e^{-x}$$

Tyler Moulton

Numerade Educator

Problem 104

Factor out the greatest common factor from each expression.
$$2 y e^{x y^{2}}+2 x y^{3} e^{x y^{2}}$$

Tyler Moulton

Numerade Educator

Problem 105

Factor out the greatest common factor from each expression.
$$2 x^{-5 / 2} y^{2}-\frac{3}{2} x^{-3 / 2}$$

Tyler Moulton

Numerade Educator

01:18

Problem 106

Factor out the greatest common factor from each expression.
$$\frac{1}{2}\left(\frac{2}{3} u^{3 / 2}-2 u^{1 / 2}\right)$$

Tyler Moulton

Numerade Educator

Problem 107

Factor each expression completely.
$$6 a c+3 b c-4 a d-2 b d$$

Tyler Moulton

Numerade Educator

Problem 108

Factor each expression completely.
$$3 x^{3}-x^{2}+3 x-1$$

Tyler Moulton

Numerade Educator

Problem 109

Factor each expression completely.
$$4 a^{2}-b^{2}$$

Tyler Moulton

Numerade Educator

Problem 110

Factor each expression completely.
$$12 x^{2}-3 y^{2}$$

Tyler Moulton

Numerade Educator

Problem 111

Factor each expression completely.
$$10-14 x-12 x^{2}$$

Tyler Moulton

Numerade Educator

Problem 112

Factor each expression completely.
$$x^{2}-2 x-15$$

Tyler Moulton

Numerade Educator

Problem 113

Factor each expression completely.
$$3 x^{2}-6 x-24$$

Tyler Moulton

Numerade Educator

Problem 114

Factor each expression completely.
$$3 x^{2}-4 x-4$$

Tyler Moulton

Numerade Educator

01:19

Problem 115

Factor each expression completely.
$$12 x^{2}-2 x-30$$

Tyler Moulton

Numerade Educator

Problem 116

Factor each expression completely.
$$(x+y)^{2}-1$$

Tyler Moulton

Numerade Educator

Problem 117

Factor each expression completely.
$$9 x^{2}-16 y^{2}$$

Tyler Moulton

Numerade Educator

01:32

Problem 118

Factor each expression completely.
$$8 a^{2}-2 a b-6 b^{2}$$

Christopher Stanley

Numerade Educator

01:25

Problem 119

Factor each expression completely.
$$x^{6}+125$$

Christopher Stanley

Numerade Educator

00:34

Problem 120

Factor each expression completely.
$$x^{3}-27$$

Ankit Gupta

Numerade Educator

Problem 121

Perform the indicated operations and simplify each expression.
$$\left(x^{2}+y^{2}\right) x-x y(2 y)$$

Tyler Moulton

Numerade Educator

Problem 122

Perform the indicated operations and simplify each expression.
$$2 k r(R-r)-k r^{2}$$

Tyler Moulton

Numerade Educator

Problem 123

Perform the indicated operations and simplify each expression.
$$2(x-1)(2 x+2)^{3}[4(x-1)+(2 x+2)]$$

Tyler Moulton

Numerade Educator

01:44

Problem 124

Perform the indicated operations and simplify each expression.
$$5 x^{2}\left(3 x^{2}+1\right)^{4}(6 x)+\left(3 x^{2}+1\right)^{5}(2 x)$$

Christopher Stanley

Numerade Educator

01:41

Problem 125

Perform the indicated operations and simplify each expression.
$$4(x-1)^{2}(2 x+2)^{3}(2)+(2 x+2)^{4}(2)(x-1)$$

Christopher Stanley

Numerade Educator

01:23

Problem 126

Perform the indicated operations and simplify each expression.
$$\left(x^{2}+1\right)\left(4 x^{3}-3 x^{2}+2 x\right)-\left(x^{4}-x^{3}+x^{2}\right)(2 x)$$

Carson Merrill

Numerade Educator

Problem 128

Perform the indicated operations and simplify each expression.
$$\left(x^{2}-4\right)\left(x^{2}+4\right)(2 x+8)-\left(x^{2}+8 x-4\right)\left(4 x^{3}\right)$$

Carson Merrill

Numerade Educator

Problem 129

Find the real roots of each equation by factoring.
$$x^{2}+x-12=0$$

Tyler Moulton

Numerade Educator

Problem 130

Find the real roots of each equation by factoring.
$$3 x^{2}-x-4=0$$

Tyler Moulton

Numerade Educator

Problem 131

Find the real roots of each equation by factoring.
$$4 t^{2}+2 t-2=0$$

Tyler Moulton

Numerade Educator

Problem 132

Find the real roots of each equation by factoring.
$$-6 x^{2}+x+12=0$$

Tyler Moulton

Numerade Educator

Problem 133

Find the real roots of each equation by factoring.
$$\frac{1}{4} x^{2}-x+1=0$$

Tyler Moulton

Numerade Educator

Problem 134

Find the real roots of each equation by factoring.
$$\frac{1}{2} a^{2}+a-12=0$$

Tyler Moulton

Numerade Educator

Problem 135

Solve the equation by using the quadratic formula.
$$4 x^{2}+5 x-6=0$$

Tyler Moulton

Numerade Educator

Problem 136

Solve the equation by using the quadratic formula.
$$3 x^{2}-4 x+1=0$$

Tyler Moulton

Numerade Educator

Problem 137

Solve the equation by using the quadratic formula.
$$8 x^{2}-8 x-3=0$$

Tyler Moulton

Numerade Educator

Problem 138

Solve the equation by using the quadratic formula.
$$x^{2}-6 x+6=0$$

Tyler Moulton

Numerade Educator

Problem 139

Solve the equation by using the quadratic formula.
$$2 x^{2}+4 x-3=0$$

Tyler Moulton

Numerade Educator

Problem 140

Solve the equation by using the quadratic formula.
$$2 x^{2}+7 x-15=0$$

Tyler Moulton

Numerade Educator

Jake owns two gas stations. The total revenue of the first gas station for the next 12 months is projected to be $$0.2 t^{2}+150 t \quad(0 \leq t \leq 12)$$ thousand dollars $t$ months from now. The total revenue of the second gas station for the next
12 months is projected to be $$0.5 t^{2}+200 t \quad(0 \leq t \leq 12)$$ thousand dollars $t$ months from now. Find an expression that gives the total revenue realized by Jake's gas stations in month $t(0 \leq t \leq 12)$.

Christopher Stanley

Numerade Educator

01:27

Problem 142

Find an expression that gives the amount by which the revenue of the second gas station will exceed the revenue of the first gas station in month $t(0 \leq t \leq 12)$.

Carson Merrill

Numerade Educator

02:04

Problem 143

Solve the equation by using the quadratic formula.
The distribution of income in a certain city can be described by the mathematical model $y=\left(5.6 \cdot 10^{11}\right)(x)^{-1.5},$ where $y$ is the number of families with an income of
$x$ or more dollars.
a. How many families in this city have an income of 30,000 dollar or more?
b. How many families have an income of 60,000 dollar or more?
c. How many families have an income of 150,000 dollar or more?

Christopher Stanley

Numerade Educator

01:26

Problem 144

An efficiency study conducted by Elektra Electronics showed that the number of Space Commander walkie-talkies assembled by the average worker $t$ hr after starting work at 8 A.M. is $$-t^{3}+6 t^{2}+15 t \quad(0 \leq t \leq 4)$$ Factor the expression.

Willis James

Numerade Educator

Problem 145

Williams Commuter Air Service realizes a monthly revenue of $$8000 x-100 x^{2} \quad(0 \leq x \leq 80)$$ dollars when the price charged per passenger is $x$ dollars. Factor the expression.

Christopher Stanley

Numerade Educator

Problem 146

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If $b^{2}-4 a c>0,$ then $a x^{2}+b x+c=0(a \neq 0)$ has two real roots.

Christopher Stanley

Numerade Educator

00:58

Problem 147

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If $b^{2}-4 a c<0,$ then $a x^{2}+b x+c=0(a \neq 0)$ has no real roots.

Christopher Stanley

Numerade Educator