Deck 14: Counting and Probability

Question 1

Simplify the expression.

Answer 1

Question 2

Use properties of real numbers to write the following expression without parentheses.

Answer 2

Question 3

Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula $D = \sqrt { 2 r h + h ^ { 2 } }$ where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 955 ft above the ground? Round the answer to one decimal place.

Answer 3

37.8 mi

Question 4

Perform the indicated operations and simplify.

Question 5

Rationalize the denominator
a) $\frac { 18 } { \sqrt { 3 } }$

b) $\frac { 7 } { \sqrt { 2 } }$

c) $\frac { 3 } { \sqrt { 6 } }$

Question 6

Evaluate the expression using
.

Question 7

Factor the trinomial.

Question 8

List the elements of the given set that are
a) natural numbers
b) integers
c) rational numbers
d) irrational numbers

$\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$

Question 9

Factor the expression.

Question 10

Evaluate the arithmetic expression.

Question 11

Use a Factoring Formula to factor the expression.

Question 12

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

Question 13

Simplify the expression and eliminate any negative exponent(s).

Question 14

Express each set in interval notation.
(a)


(b)

Question 15

Express the repeating decimal as a fraction.

Question 16

Evaluate the expression $| | - 9 | - | - 11 | |$

Question 17

Factor the expression by grouping terms.

Question 18

Simplify the expression.

Question 19

Evaluate each expression
a) $\left( \frac { 7 } { 3 } \right) ^ { 0 } 2 ^ { - 1 }$

b) $\frac { 3 ^ { - 3 } } { 4 ^ { 0 } }$

c) $\left( \frac { 1 } { 5 } \right) ^ { - 2 }$

Question 20

Simplify the expression. Assume the letters denote any real numbers.

Question 21

Evaluate the expression
.

Question 22

Evaluate each expression
a) $\left( \frac { 5 } { 3 } \right) ^ { 0 } 3 ^ { - 1 }$

b) $\frac { 3 ^ { - 3 } } { 5 ^ { 0 } }$

c) $\left( \frac { 1 } { 3 } \right) ^ { - 2 }$

Question 23

Perform the addition and simplify.

Question 24

Perform the division and simplify.

Question 25

Simplify the expression. Assume the letters denote any real numbers.

Question 26

List the elements of the given set that are
a) natural numbers
b) integers
c) rational numbers
d) irrational numbers

Question 27

Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula $D = \sqrt { 2 r h + h ^ { 2 } }$ where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 1,000 ft above the ground?

Question 28

Express each set in interval notation.
(a)

(b)

Question 29

Simplify the expression.

Question 30

Express each set in interval notation.
(a)

(b)

Question 31

Simplify the expression. Eliminate any negative exponents.

Question 32

Rationalize the denominator.

Question 33

Simplify the expression.

Question 34

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 3 } } { 1 - \frac { 1 } { x - 3 } }$

Question 35

Simplify the expression.

Question 36

Factor the trinomial.

Question 37

Perform the indicated operations and simplify.

Question 38

Perform the indicated operations and simplify.

Question 39

Perform the indicated operation and simplify.

Question 40

Simplify the expression. Assume the letters denote any real numbers.

Question 41

List the elements of the given set that are rational numbers. $\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$

A) $0 , - 8,100,22 / 7,1 . \overline { 23 } , - \frac { 1 } { 9 }$

B) $0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$

C) $0 , - 8,100,22 / 7,1 . \overline { 23 } , \sqrt [ 3 ] { 4 }$

D) $0 , - 8,100$

E) $22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$

Question 42

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

A) $- \frac { 8 } { 27 }$

B) $- \frac { 27 } { 8 }$

C) $\frac { 1 } { 8 }$

D) $\frac { 27 } { 8 }$

E) $\frac { 8 } { 27 }$

Question 43

Evaluate the expression

A) 13
B) -15
C) 0
D) 15
E) - 13

Question 44

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

Question 45

Perform the indicated operations and simplify.

Question 46

Factor the expression by grouping terms.

A)
B)
C)
D)
E)

Question 47

Use properties of real numbers to write the following expression without parentheses.

A)9y - 6x
B)9x + 6y
C)9x - 6y
D)6y - 9x
E)6x - 9y

Question 48

Simplify the expression. $\frac { \left( x ^ { 8 } y ^ { 4 } \right) ^ { 5 } \left( x ^ { 2 } y ^ { 8 } \right) ^ { - 5 } } { x ^ { 2 } y ^ { 10 } }$

A) $\frac { x ^ { 29 } } { y ^ { 30 } }$

B) $\frac { x ^ { 31 } } { y ^ { 32 } }$

C) $\frac { x ^ { 28 } } { y ^ { 31 } }$

D) $\frac { x ^ { 2 } } { y ^ { 30 } }$

E) $\frac { x ^ { 30 } } { y ^ { 28 } }$

Question 49

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 50

Factor the expression.

Question 51

Simplify the expression.

A)
B)
C)
D)
E)

Question 52

Evaluate the arithmetic expression.

Question 53

Evaluate the arithmetic expression.

Question 54

Perform the indicated operation and simplify.

Question 55

Simplify the expression.

A)
B)
C)
D)
E)

Question 56

Evaluate the arithmetic expression.

A)20
B)27
C)-36
D) 36
E) none of these

Question 57

Express the inequality in interval notation

A)
B)
C)
D)
E)

Question 58

Express the repeating decimal as a fraction.

A)
B)
C)
D)
E)none of these

Question 59

Perform the indicated operations and simplify.

A)
B)
C)
D)
E)

Question 60

Express the repeating decimal as a fraction.

Question 61

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 62

Evaluate the expression using .

A)256
B)2
C)8
D)4
E)16

Question 63

Simplify the expression. Assume the letters denote any real numbers.

A)
B)
C)
D)
E)

Question 64

List the elements of the given set that are rational numbers.

A)
B)
C)
D)
E)

Question 65

Factor the expression completely.

Question 66

Simplify the expression. $\frac { t - 4 } { t ^ { 2 } - 16 } \cdot \frac { t + 4 } { t ^ { 2 } + 16 }$

A) $\frac { 1 } { t - 16 }$

B) $\frac { 1 } { t ^ { 2 } + 16 }$

C) $t ^ { 2 } + 16$

D) $\frac { t ^ { 2 } - 4 } { t + 16 }$

E) $\frac { t ^ { 2 } + 4 } { t + 16 }$

Question 67

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$

A) $\frac { x ^ { 2 } - 14 } { ( x + 3 ) ( x + 2 ) }$

B) $\frac { x ^ { 2 } - 21 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

C) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

D) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 2 ) }$

E) $\frac { x - 2 } { ( x + 3 ) ( x + 2 ) }$

Question 68

Factor the expression completely.

A) (9x + 7)(5x - 6)
B) (9x - 7)(7x + 9)
C) (9x + 7)(7x - 9)
D) (6x + 5)(5x - 6)
E) (6x + 5)(7x - 9)

Question 69

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 70

Perform the indicated operation and simplify.

A)
B)
C)
D)
E)

Question 71

Simplify the expression.

A)
B)
C)
D)
E)

Question 72

Factor the expression completely.

A) (9x + 7)(5x - 6)
B) (6x + 5)(5x - 6)
C) (9x - 7)(7x + 9)
D) (6x + 5)(7x - 9)
E) (9x + 7)(7x - 9)

Question 73

Simplify the expression.

A)
B) 1
C)
D)
E)

Question 74

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$

A) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

B) $\frac { x - 2 } { ( x + 3 ) ( x + 2 ) }$

C) $\frac { x ^ { 2 } - 14 } { ( x + 3 ) ( x + 2 ) }$

D) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 2 ) }$

E) $\frac { x ^ { 2 } - 21 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

Question 75

Rationalize the denominator. $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$

A) $\frac { \sqrt [ 5 ] { x ^ { 3 } } } { x }$

B) $x ^ { - \frac { 2 } { 5 } }$

C) $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { x }$

D) $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$

E) $\frac { 1 } { x ^ { 2 / 5 } }$

Question 76

Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 955 ft above the ground? Round the answer to one decimal place

A) 37.8 mi
B) 73.8 mi
C)1428.8 mi
D)428.8 mi
E)none of these

Question 77

Use a Factoring Formula to factor the expression.

Question 78

Factor the expression completely.

A)
B)
C)
D)
E)

Question 79

Simplify the expression. $\frac { 1 + \frac { 1 } { x - 5 } } { 1 - \frac { 1 } { x - 5 } }$

A) $\frac { x - 6 } { x - 4 }$

B) $\frac { x - 5 } { x - 4 }$

C) $\frac { 4 - x } { 6 + x }$

D) $\frac { x - 5 } { x - 6 }$

E) $\frac { x - 4 } { x - 6 }$

Question 80

Perform the indicated operations and simplify.

A)
B)
C)
D)
E)