Deck 1: Fundamental Concepts of Algebra

Question 1

The lowest recorded January temperature for a city is $- 15 ^ { \circ } \mathrm { F }$ and the highest recorded temperature is $68 ^ { \circ } F.$ Find the distance between the numbers to determine the range of temperatures for January.

A) $- 30 ^ { \circ } \mathrm { F }$
B) $- 83 ^ { \circ } \mathrm { F }$
C) $- 53 ^ { \circ } \mathrm { F }$
D) $- 15 ^ { \circ } \mathrm { F }$
E) $83 ^ { \circ } F$

Answer 1

$83 ^ { \circ } F$

Question 2

Use inequality notation to describe the set. n is positive

A)n $\le$ $\infty$
B)n $\lt$ $\infty$
C)n $\le$ 0
D)n $\ge$ 0
E)n $\gt$ 0

Answer 2

n $\gt$ 0

Question 3

Use inequality notation to describe the set. m is at least -8 but less than 15

A)15 $\le$ m $\lt$ -8
B)15 $\lt$ m $\le$ -8
C)-8 $\le$ m $\lt$ 15
D)-8 $\le$ m $\le$ 15
E)-8 $\lt$ m $\lt$ 15

Answer 3

-8 $\le$ m $\lt$ 15

Question 4

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. 2, -3

A)2 < -3
B)2 > -3

Question 5

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. $- \frac { 7 } { 10 } , \frac { 1 } { 17 }$

A) $- \frac { 7 } { 10 } < \frac { 1 } { 17 }$
B) $- \frac { 7 } { 10 } > \frac { 1 } { 17 }$

Question 6

Approximate the numbers and place the correct symbol (< or >) between them.

A)-3 < 3.75
B)-3 < -3.25
C)-3 < 3.25
D)-3 > 3.25
E)-3 > 3.75

Question 7

Determine which numbers in the set are integers. $0.77,4 , - 8 \pi , 0,6.0 , - 8$

A) $4,0,6.0 , - 8$
B) $0.77,4,0,6.0 , - 8$
C) $4,0$
D) $4 , - 8 \pi , 0 , - 8$
E) $4,0 , - 8$

Question 8

Give a verbal description of the subset of real numbers represented by the inequality. 1 $\lt$ x $\le$ 8

A)all real numbers less than 1 and greater than 8
B)all real numbers between 1 and 8 not including 1 or 8
C)all real numbers between 1 and 8, including 1 but not including 8
D)all real numbers between 1 and 8, including 8 but not including 1
E)all real numbers between 1 and 8, including 1 and 8

Question 9

Determine which numbers in the set are irrational numbers. $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$

A) $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$
B) $\frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$
C) $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 9.090990999 \ldots , 5 \pi$
D) $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$
E) $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 5 \pi$

Question 10

Evaluate the expression. $| 3 - 7 |$

A)4
B)-4
C)10
D)-10
E)21

Question 11

Which graph represents the inequality? $- 2 < x \leq 5$

A) -2 5
B) -2 5
C) -2 5
D) -2 5
E) -2 5

Question 12

The quality control inspector for a tire factory is testing the rim diameter of various tires. A tire is rejected if its rim diameter varies too much from its expected measure. The diameter should not differ by more than 0.1 inch or by more than $0.1 \%$ of the expected diameter measure. Find the widest range of allowable values for the actual diameter if the expected diameter is 14.000 inches. Round to the nearest thousandth.

A)between 13.900 inches and 14.014 inches
B)between 13.986 inches and 14.100 inches
C)between 13.986 inches and 14.014 inches
D)between 13.900 inches and 14.000 inches
E)between 13.900 inches and 14.100 inches

Question 13

Determine which numbers in the set are rational numbers. $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \sqrt { 5 } , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$

A) $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , 4.070070007 \ldots$
B) $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$
C) $16 , \sqrt { 5 } , \frac { 7 } { 2 } , \sqrt { 81 }$
D) $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , \sqrt { 81 }$
E) $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \frac { 7 } { 2 }$

Question 14

Use absolute value notation to describe the situation. w is more than two units from -7.

A) $| w + 7 |$ $\gt$ 2
B) $| w + 7 |$ $\le$ 2
C) $| w + 7 |$ $\lt$ 2
D) $| w - 7 |$ $\gt$ 2
E) $| w - 7 |$ $\ge$ 2

Question 15

Use absolute value notation to describe the situation. The distance between u and -4 is no less than 6.

A) $| u - 4 |$ $\ge$ 6
B) $| u - 4 |$ $\le$ 6
C) $| u - 4 |$ $\lt$ 6
D) $| u + 4 |$ $\gt$ 6
E) $| u + 4 |$ $\ge$ 6

Question 16

Write the following expression without absolute value symbols. $| 6 | - | 3 |$

A)9
B)-9
C)3
D)0
E)-3

Question 17

Place the correct symbol (<, >, or =) between the pair of real numbers. $- | 3 |$ $- | - 3 |$

A) $- | 3 | < - | - 3 |$
B) $- | 3 | > - | - 3 |$
C) $- | 3 | = - | - 3 |$

Question 18

Place the correct symbol (<, >, or =) between the pair of real numbers. $- ( - 3 )$ $- 3$

A) $- ( - 3 ) < - 3$
B) $- ( - 3 ) > - 3$
C) $- ( - 3 ) = - 3$

Question 19

Approximate the numbers and place the correct symbol (< or >) between them.

A) $2 \frac { 1 } { 2 } < - 4$
B) $- 2 \frac { 1 } { 2 } > - 4$
C) $2 \frac { 1 } { 2 } > 4$
D) $1 \frac { 1 } { 2 } > - 4$
E) $2 \frac { 1 } { 2 } < 4$

Question 20

Determine which numbers in the set are natural numbers. $- 13,6,11 , \sqrt { 49 } , 0 , - 9 , \sqrt { 65 }$

A) $6,11 , \sqrt { 49 } , 0 , \sqrt { 65 }$
B) $6,11 , \sqrt { 49 }$
C) $6,11,0$
D) $6,11$
E) $- 13,6,11,0 , - 9$

Question 21

Evaluate the expression for the given value of x. $- 4 x ^ { 0 }$ x = 5

A)0
B)-4
C)4
D)20
E)-20

Question 22

Identify the rule of algebra illustrated by the statement. -9r - 3r = (-9 - 3)r

A)associative property of addition
B)commutative property of addition
C)associative property of multiplication
D)commutative property of multiplication
E)distributive property

Question 23

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

A)3
B)-18
C)-729
D) $- \frac { 1 } { 729 }$
E) $\frac { 1 } { 729 }$

Question 24

The percent of people in a research study that have a particular health risk is 44.5%. The total number of people in the study is 14,677. How many people have the health risk?

A)1614 people
B)14,677 people
C)21,208 people
D)6531 people
E)8146 people

Question 25

Identify the terms of the algebraic expression below. $6 x ^ { 2 } - 6 x + 5$

A) $6,$ $- 6,$ and $5$
B) $6 x ^ { 2 }$ and $- 6 x$
C) $6 x ^ { 2 }$ and $5$
D) $- 6 x$ and $5$
E) $6 x ^ { 2 },$ $- 6 x,$ and $5$

Question 26

Evaluate the expression for the given value of x. $- x ^ { 4 }$ x = -2

A)8
B) $\frac { 1 } { 16 }$
C) $- \frac { 1 } { 16 }$
D)-16
E)16

Question 27

Identify the rules of algebra illustrated from left to right by the following statement. (n + 6) - 6 = n + (6 - 6) = n + 0 = n

A)commutative property of addition; additive inverse property; additive identity property
B)associative property of addition; additive inverse property; additive identity property
C)commutative property of addition; additive identity property; additive inverse property
D)associative property of addition; additive identity property; additive inverse property
E)distributive property; additive identity property; additive inverse property

Question 28

Evaluate $\frac { p ^ { 2 } + q ^ { 2 } } { p + q }$ when $p = - 12$ and $q = 9 .$

A)-3
B)9
C)441
D)-75
E)-147

Question 29

Evaluate the expression for the given value of x. expression: $\frac { x + 4 } { x - 4 }$ value: x = -4

A) $- \frac { 1 } { 4 }$
B) $\frac { 1 } { 4 }$
C)0
D)not possible since numerator is 0
E)not possible since denominator is 0

Question 30

Evaluate $3 r ^ { 3 } s ^ { 2 }$ when $r = 2$ and $s = 3.$

A)216
B)18
C)324
D)5832
E)72

Question 31

Evaluate the expression for the given value of x. $8 x ^ { - 3 }$ x = 5

A) $\frac { 8 } { 125 }$
B) $- \frac { 8 } { 125 }$
C) $- \frac { 1 } { 120 }$
D)120
E)-120

Question 32

Write the rational expression in simplest form. $\frac { 120 v ^ { 4 } } { 15 v ^ { 5 } }$

A) $\frac { 8 v ^ { 4 } } { v ^ { 5 } } , \quad v \neq 0$
B) $\frac { 40 v } { 5 } , v \neq 0$
C) $\frac { 24 } { 3 v } , \quad v \neq 0$
D) $\frac { 8 } { v } , \quad v \neq 0$
E) $\frac { 40 } { 5 v } , \quad v \neq 0$

Question 33

Evaluate the expression for the given value of x. $3 x ^ { 3 }$ x = -2

A)-18
B) $\frac { 1 } { 24 }$
C) $- \frac { 1 } { 24 }$
D)-24
E)24

Question 34

Simplify the expression. $6 z ^ { 6 } \left( 4 z ^ { 8 } \right) ^ { 3 }$

A) $72 z ^ { 17 }$
B) $384 z ^ { 17 }$
C) $384 z ^ { 30 }$
D) $24 z ^ { 30 }$
E) $72 z ^ { 30 }$

Question 35

Evaluate the expression. $2 ^ { - 1 } + 3 ^ { - 2 }$

A) $\frac { 2 } { 11 }$
B) $\frac { 11 } { 18 }$
C) $- \frac { 2 } { 11 }$
D) $- \frac { 11 } { 18 }$
E)-8

Question 36

Evaluate the expression. $\frac { 5 ^ { - 4 } } { 5 ^ { - 6 } }$

A) $\frac { 2 } { 3 }$
B) $- \frac { 1 } { 25 }$
C) $\frac { 1 } { 25 }$
D)25
E)-25

Question 37

Evaluate the expression for the given value of x. expression: $6 x ^ { 2 } - 2 x + 5$ value: x = -3

A)-25
B)65
C)-43
D)61
E)-29

Question 38

Simplify the expression below. $3 ^ { n } \cdot 3 ^ { 2 n }$

A) $3 ^ { 2 n ^ { 2 } }$
B) $9 ^ { 3 n }$
C) $27 ^ { n }$
D) $6 ^ { 3 n }$
E) $9 ^ { n ^ { 2 } }$

Question 39

Simplify the expression. $\left( \frac { 4 } { v } \right) ^ { 2 } \left( \frac { 2 } { v } \right) ^ { 3 }$

A) $\frac { 48 } { v ^ { 5 } }$
B) $\frac { 128 } { v ^ { 5 } }$
C) $\frac { 128 } { v ^ { 6 } }$
D) $\frac { 48 } { v ^ { 6 } }$
E) $\frac { 24 } { v ^ { 6 } }$

Question 40

Identify the rules of algebra illustrated from left to right by the following statement. $\frac { 1 } { 3 } ( 3 t ) = \left( \frac { 1 } { 3 } \cdot 3 \right) t = 1 \cdot t = t$

A)associative property of multiplication; multiplicative inverse property; multiplicative identity property
B)commutative property of multiplication; multiplicative inverse property; multiplicative identity property
C)associative property of multiplication; multiplicative identity property; multiplicative inverse property
D)commutative property of multiplication; multiplicative identity property; multiplicative inverse property
E)distributive property; multiplicative identity property; multiplicative inverse property

Question 41

Change the following number from scientific notation to decimal notation. $2.61 \times 10 ^ { - 3 }$

A)0.261
B)0.00261
C)2.61
D)26.1
E)0.0261

Question 42

Simplify the following radical expression. $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$

A) $4 p q \sqrt [ 3 ] { 6 p q ^ { 2 } }$
B) $4 p ^ { 3 } q ^ { 2 } \sqrt [ 3 ] { 6 q }$
C) $6 p q ^ { 2 } \sqrt [ 3 ] { 4 p q }$
D) $4 \sqrt [ 3 ] { 6 p q ^ { 2 } }$
E) $4 p ^ { 2 } q \sqrt [ 3 ] { 6 p q }$

Question 43

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 16 } { \sqrt [ 3 ] { 4 } }$

A) $4 \sqrt [ 3 ] { 4 }$
B) $4 \sqrt [ 3 ] { 16 }$
C) $4 \sqrt { 4 }$
D) $16 \sqrt [ 3 ] { 4 }$
E) $4$

Question 44

Write the following number in scientific notation. 22,100,000

A) $2.21 \times 10 ^ { 5 }$
B) $2.21 \times 10 ^ { 6 }$
C) $2.21 \times 10 ^ { 7 }$
D) $2.21 \times 10 ^ { - 7 }$
E) $2.21 \times 10 ^ { - 5 }$

Question 45

The average yearly cost of tuition, fees, and room and board at private four-year colleges in the United States was $20,805 for the academic year 1998/1999 and $24,817 for the academic year 2002/2003. Find the average yearly rate of inflation over this five-year period. Round to the nearest hundredth of a percent.

A)3.47%
B)3.77%
C)3.59%
D)3.68%
E)4.03%

Question 46

Rationalize the denominator. Then simplify your answer. $\frac { 15 } { \sqrt { 33 } }$

A) $\frac { 75 } { 11 }$
B) $\frac { 10 } { 11 }$
C) $\frac { 5 \sqrt { 33 } } { 11 }$
D) $\frac { \sqrt { 495 } } { 33 }$
E) $\frac { 2 \sqrt { 12 } } { 33 }$

Question 47

Evaluate the expression without using a calculator. $- \left( \frac { 1 } { 125 } \right) ^ { - 2 / 3 }$

A) $\frac { 1 } { 25 }$
B) $- \frac { 2 } { 375 }$
C) $\frac { 2 } { 375 }$
D)25
E)-25

Question 48

Write the number in decimal notation. One bushel equals approximately 3.524* 101 liters.

A)35.24
B)3524
C)352.4
D)-35.24
E)3.524

Question 49

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 4 } { \sqrt { 7 } + \sqrt { 6 } }$

A) $4 ( \sqrt { 7 } + \sqrt { 6 } )$
B) $4 ( \sqrt { 7 } - \sqrt { 6 } )$
C) $4 ( \sqrt { 6 } - \sqrt { 7 } )$
D) $\frac { 16 } { 13 }$
E) $\frac { 4 } { 13 }$

Question 50

Write each number in the expression below in scientific notation. Perform the operation and write your answer in scientific notation. $\frac { 242,000,000 } { 440 }$

A) $5.5 \times 10 ^ { 8 }$
B) $5.5 \times 10 ^ { 7 }$
C) $55 \times 10 ^ { 4 }$
D) $5.5 \times 10 ^ { 5 }$
E) $5.5 \times 10 ^ { 4 }$

Question 51

Write the number in scientific notation. One minute is about 0.000099 week.

A)0.99 *10-4
B)99 * 10-6
C)9.9 * 10-5
D)9.9* 10-6
E)0.000099* 10-5

Question 52

The compound interest formula can be rewritten as $P = \frac { A } { ( 1 + r / n ) ^ { n t } }$ Find the principal amount $P$ that could have been invested on the day you were born at 4.5% annual interest compounded monthly to make you a millionaire on your 21st birthday.

A)$243,354.47
B)$389,367.15
C)$292,025.36
D)$194,683.58
E)$316,360.81

Question 53

Rewrite the expression with positive exponents and simplify. $\left( 3 p ^ { - 3 } \right) ^ { 4 } \left( - 3 p ^ { - 2 } \right) ^ { - 1 }$

A) $\frac { 1 } { 15 p ^ { 10 } }$
B) $\frac { 15 } { p ^ { 10 } }$
C) $\frac { 36 } { p ^ { 10 } }$
D) $- \frac { 27 } { p ^ { 10 } }$
E) $- \frac { 1 } { 27 p ^ { 10 } }$

Question 54

Rewrite the expression below with positive exponents and simplify. $\left( \frac { x ^ { - 2 } y ^ { 4 } } { 2 } \right) ^ { - 3 }$

A) $\frac { x ^ { 6 } y ^ { 12 } } { 8 }$
B) $\frac { 8 y ^ { 12 } } { x ^ { 6 } }$
C) $\frac { 8 x ^ { 6 } } { y ^ { 12 } }$
D) $\frac { x ^ { 6 } } { 8 y ^ { 12 } }$
E) $\frac { y ^ { 12 } } { 8 x ^ { 6 } }$

Question 55

Simplify the radical expression. $\sqrt [ 4 ] { 243 n ^ { 19 } t ^ { - 20 } }$

A) $\frac { 3 n \sqrt [ 4 ] { 3 n ^ { 15 } } } { t \sqrt { t ^ { 16 } } }$
B) $\frac { 3 n ^ { 4 } \sqrt [ 4 ] { 3 n ^ { 3 } } } { t ^ { 5 } }$
C) $\frac { 3 n \sqrt [ 4 ] { 3 n ^ { 3 } } } { t }$
D) $\frac { 81 n ^ { 16 } \sqrt [ 4 ] { 3 n ^ { 3 } } } { t ^ { 20 } }$
E) $\frac { 81 n \sqrt [ 4 ] { 3 n ^ { 15 } } } { t \sqrt { t ^ { 16 } } }$

Question 56

Use a calculator to evaluate the expression. Write your answer in scientific notation. (Round values to three decimal places.) $\frac { 8,200,000 + 9,600,000 } { 0.077 }$

A)1.329 *108
B)1.329* 109
C)2.312 * 107
D)2.312* 109
E)2.312 * 108

Question 57

Perform the indicated operation below and write the answer in scientific notation. $\frac { \left( 4.9 \times 10 ^ { 18 } \right) \left( 6.8 \times 10 ^ { 11 } \right) } { \left( 3.4 \times 10 ^ { - 12 } \right) }$

A) $9.8 \times 10 ^ { - 5 }$
B) $9.8 \times 10 ^ { 17 }$
C) $9.8 \times 10 ^ { 5 }$
D) $9.8 \times 10 ^ { 19 }$
E) $9.8 \times 10 ^ { 41 }$

Question 58

In 1967, the movie Imitation of Christ was released and its running time was 480 minutes long. Assuming that this film's speed was 24 frames per second, approximate the total number of frames in the film. Express the answer in scientific notation rounding to two places after the decimal..

A)1.15 $\times 10 ^ { 6 }$
B)3.22 $\times 10 ^ { 6 }$
C)6.91 $\times 10 ^ { 5 }$
D)2.88 $\times 10 ^ { 4 }$
E)1.92 $\times 10 ^ { 5 }$

Question 59

Simplify the expression below. $2 ^ { 1 / 3 } \cdot 2 ^ { 11 / 3 }$

A) $8$
B) $16$
C) $32$
D) $256$
E) $16 \sqrt [ 3 ] { 2 }$

Question 60

Evaluate the expression without using a calculator. $4 ^ { - 3 / 2 }$

A)-8
B)4
C)-4
D) $\frac { 1 } { 8 }$
E) $- \frac { 1 } { 8 }$

Question 61

Identify the degree and leading coefficient of the polynomial. 5 - 3x2 - 6x

A)degree: 3 leading coefficient: -6
B)degree: 2 leading coefficient: 3
C)degree: 3 leading coefficient: 3
D)degree: 2 leading coefficient: -3
E)degree: 2 leading coefficient: 5

Question 62

Perform the indicated operation below and simplify if possible by combining like terms. Write the result in standard form. $\left( y ^ { 2 } - 9 y + 4 \right) + \left( 8 y ^ { 2 } - y + 6 \right)$

A) $- 7 y ^ { 2 } - 8 y + 10$
B) $- 7 y ^ { 2 } - 10 y + 10$
C) $9 y ^ { 2 } - 10 y - 2$
D) $9 y ^ { 2 } - 8 y + 10$
E) $9 y ^ { 2 } - 10 y + 10$

Question 63

Find the special product. (-4x + 5)(-4x - 5)

A)-8x
B)-8x2
C)16x2 - 25
D)16x2 + 25
E)16x2 - 40x - 25

Question 64

Simplify the expression below. $- 5 \sqrt { 8 } + 2 \sqrt { 32 }$

A) $8 \sqrt { 2 } - 10 \sqrt { 3 }$
B) $- 10 \sqrt { 2 } + 8 \sqrt { 3 }$
C) $12 \sqrt { 2 }$
D) $- 2 \sqrt { 2 }$
E) $10 \sqrt { 2 } + 8 \sqrt { 3 }$

Question 65

Write the polynomial in standard form.
-6 + 4x2 + 2x

Question 66

The length L of the hypotenuse of a right triangle is $L = \sqrt { x ^ { 2 } + y ^ { 2 } }$ where x and y are the lengths of the other two sides. Find the length of the hypotenuse when the other sides measure 1 unit and $\frac { 4 } { 3 }$ units.

A)1 unit
B) $\frac { \sqrt { 7 } } { 2 }$ units
C) $\frac { 25 } { 9 }$ units
D) $\frac { \sqrt { 7 } } { 3 }$ units
E) $\frac { 5 } { 3 }$ units

Question 67

Perform the operation and write the result in standard form. $- 8 x \left( 8 - 7 x ^ { 4 } \right)$

A) $56 x ^ { 5 } - 64 x$
B) $- 56 x ^ { 5 } - 64 x$
C) $- 64 x + 56 x ^ { 4 }$
D) $- 64 + 56 x ^ { 4 }$
E) $- 64 - 56 x ^ { 4 }$

Question 68

A stream of water moving at a rate of $v$ feet per second can carry particles of size $0.03 \sqrt { v }$ inches. Find the size of the largest particle that can be carried by a stream flowing at the rate of $\frac { 3 } { 5 }$ foot per second. Round to the nearest thousandth of an inch.

A)0.019 inch
B)0.023 inch
C)0.021 inch
D)0.016 inch
E)0.028 inch

Question 69

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\left( \frac { 7 } { 3 } \right) ^ { - 7 / 8 } - \left( - \frac { 12 } { 5 } \right) ^ { 1 / 3 }$

A)-0.862
B)1.536
C)-1.536
D)1.815
E)3.438

Question 70

Multiply. (2x + 2)(-7x + 6)

A)-5x + 8
B)-5x2 + 8
C)-16x + 12
D)-5x2 + 3x + 8
E)-14x2 - 2x + 12

Question 71

Find the product below. $( 2 x + 3 y ) ^ { 3 }$

A) $8 x ^ { 3 } - 36 x ^ { 2 } y - 54 x y ^ { 2 } + 27 y ^ { 3 }$
B) $8 x ^ { 3 } - 54 x ^ { 2 } y + 36 x y ^ { 2 } + 27 y ^ { 3 }$
C) $8 x ^ { 3 } + 12 x ^ { 2 } y - 18 x y ^ { 2 } - 27 y ^ { 3 }$
D) $8 x ^ { 3 } + 36 x ^ { 2 } y + 54 x y ^ { 2 } + 27 y ^ { 3 }$
E) $8 x ^ { 3 } + 12 x ^ { 2 } y + 18 x y ^ { 2 } + 27 y ^ { 3 }$

Question 72

Reduce the index of the radical. $\sqrt [ 9 ] { y ^ { 15 } }$

A) $y ^ { 6 }$
B) $\frac { 1 } { y ^ { 6 } }$
C) $\sqrt [ 3 ] { y ^ { 5 } }$
D) $\sqrt [ 6 ] { y }$
E) $\sqrt { y ^ { 6 } }$

Question 73

Write the expression as a single radical. Then simplify your answer. $\sqrt { \sqrt [ 3 ] { 14 t ^ { 7 } p } }$

A) $t \sqrt [ 4 ] { 14 t ^ { 3 } p }$
B) $t \sqrt [ 6 ] { 14 t p }$
C) $t \sqrt [ 5 ] { 14 t ^ { 2 } p }$
D) $t \sqrt [ 3 ] { 14 t ^ { 4 } p }$
E) $\sqrt [ 9 ] { 14 t ^ { 7 } p }$

Question 74

A wind chill temperature is a measure of how cold it feels outside. The wind chill temperature $W$ (in degrees Fahrenheit) is given by $W = 35.75 + 0.6215 T - 35.75 v ^ { 0.16 } + 0.4275 T v ^ { 0.16 }$ where $T$ is the actual temperature (in degrees Fahrenheit) and $v$ is the wind speed (in miles per hour). Find the wind chill temperature for the given conditions below. Actual temperature: $15 ^ { \circ } F,$ wind speed: $10$ mph

A) $- 16.0 ^ { \circ } \mathrm { F }$
B) $68.8 ^ { \circ } F$
C) $2.7 ^ { \circ } \mathrm { F }$
D) $- 5.6 ^ { \circ } F$
E) $106.0 ^ { \circ } \mathrm { F }$

Question 75

Simplify the expression below. $\left( 4 x ^ { 6 } y ^ { 6 } \right) ^ { 1 / 2 }$

A) $4 x ^ { 2 } y ^ { 3 }$
B) $2 x ^ { 6 } y ^ { 6 }$
C) $4 x ^ { 3 } y ^ { 3 }$
D) $2 x ^ { 2 } y ^ { 3 }$
E) $2 x ^ { 3 } y ^ { 3 }$

Question 76

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\sqrt [ 4 ] { 8 }$

A)1.682
B)32.000
C)2.828
D)2.000
E)12.000

Question 77

Perform the operation and write the result in standard form. $\left( 2 x ^ { 2 } + 6 \right) - \left( x ^ { 2 } - 5 x + 1 \right)$

A) $x ^ { 2 } - 5 x + 7$
B) $x ^ { 2 } + 5 x + 5$
C) $x ^ { 4 } + 5 x + 5$
D) $x ^ { 4 } - 5 x + 7$
E) $3 x ^ { 4 } - 5 x + 7$

Question 78

Perform the operation and write the result in standard form. $\left( 8 x ^ { 4 } - 6 \right) - \left( 5 x ^ { 4 } - 4 x - 9 \right)$

A) $3 x ^ { 4 } - 4 x - 15$
B) $3 x ^ { 4 } + 4 x + 3$
C) $3 x ^ { 8 } + 4 x + 3$
D) $3 x ^ { 8 } - 4 x - 15$
E) $13 x ^ { 8 } - 4 x - 15$

Question 79

Find the special product. (4x - 9)2

A)16x2 - 72x + 81
B)16x2 - 36x + 81
C)8x2 - 18
D)16x2 - 81
E)16x2 + 81

Question 80

Evaluate the following polynomial for the indicated value of the variable. $- 7 y ^ { 2 } - 9 y - 2$ , for $y = - 1$

A)0
B)2
C)14
D)16
E)-18