Question 1

Solve the problem.
-Suppose that $P ( A ) = 0.24$ and $P ( B ) = 0.68$, find $P ( A \cap B )$ if $A$ and $B$ are mutually exclusive.

Accepted Answer

A)  $0.1632$ 
B)  $0.92$ 
C)  $0.7568$ 
D)  0 
A)  $0.1632$ 
B)  $0.92$ 
C)  $0.7568$ 
D)  0

Question 2

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio.
-$5 , \frac { 5 } { 4 } , \frac { 5 } { 9 } , \frac { 5 } { 16 } , \ldots$

Accepted Answer

A)  yes, $\frac { 5 } { 4 }$ 
B)  yes, 4 
C)  no 
D)  yes, $\frac { 1 } { 4 }$ 
A)  yes, $\frac { 5 } { 4 }$ 
B)  yes, 4 
C)  no 
D)  yes, $\frac { 1 } { 4 }$

Question 3

Find the indicated term or coefficient of the binomial expansion.
-$$\text { Find the coefficient of } y ^ { 4 } \text { in the expansion of } ( y + 5 ) ^ { 9 }$$

Accepted Answer

A) 78,750 
B) 393,750 
C) 3125 
D) 126 
A) 78,750 
B) 393,750 
C) 3125 
D) 126

Question 4

Solve the problem.
-How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Accepted Answer

A) 45,360 
B) 15,120 
C) 90,000 
D) 59,049 
A) 45,360 
B) 15,120 
C) 90,000 
D) 59,049

Question 5

Solve the problem.
-How many 9-symbol codes can be formed using 5 different symbols? Repeated symbols are allowed.

Accepted Answer

A) 1,953,125 
B) 15,120 
C) 3024 
D) 126 
A) 1,953,125 
B) 15,120 
C) 3024 
D) 126

Question 6

Write the first four terms of the recursive sequence.
-$a _ { 1 } = 2 , a _ { n } = \frac { a _ { n } - 1 } { n + 1 }$ for $n \geq 2$

Accepted Answer

A)  $2 , \frac { 2 } { 3 } , \frac { 1 } { 6 } , \frac { 1 } { 30 }$ 
B)  $2,2,1 , \frac { 1 } { 3 }$ 
C)  $2,2 , \frac { 2 } { 3 } , \frac { 1 } { 6 }$ 
D)  $2,1 , \frac { 1 } { 3 } , \frac { 1 } { 12 }$ 
A)  $2 , \frac { 2 } { 3 } , \frac { 1 } { 6 } , \frac { 1 } { 30 }$ 
B)  $2,2,1 , \frac { 1 } { 3 }$ 
C)  $2,2 , \frac { 2 } { 3 } , \frac { 1 } { 6 }$ 
D)  $2,1 , \frac { 1 } { 3 } , \frac { 1 } { 12 }$

Question 7

Find the probability.
-A bag contains 8 red marbles, 5 blue marbles, and 9 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Accepted Answer

A)  $\frac { 9 } { 22 }$ 
B)  $\frac { 4 } { 11 }$ 
C)  $\frac { 5 } { 22 }$ 
D)  $\frac { 5 } { 13 }$ 
A)  $\frac { 9 } { 22 }$ 
B)  $\frac { 4 } { 11 }$ 
C)  $\frac { 5 } { 22 }$ 
D)  $\frac { 5 } { 13 }$

Question 8

Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.
-$$S _ { n } : 1 \cdot 8 + 2 \cdot 8 + 3 \cdot 8 + \ldots + 8 n = \frac { 8 n ( n + 1 ) } { 2 }$$

Accepted Answer

None

Question 9

The first several terms of a sequence are given. Find the indicated partial sum.
-$$- 32,64 , - 128,256 , \ldots ; S _ { 5 }$$

Accepted Answer

A) 672 
B) -512 
C) - 480 
D) - 352 
A) 672 
B) -512 
C) - 480 
D) - 352

Question 10

Find the general term of the arithmetic sequence.
-$6.9,7.7,8.5,9.3,10.1 , \ldots$

Accepted Answer

A)  $a _ { n } = 0.8 n + 6.1$ 
B)  $a _ { n } = 0.7 n + 6.1$ 
C)  $a _ { n } = 0.8 n + 5.9$ 
D)  $a _ { n } = 0.8 n + 6.9$ 
A)  $a _ { n } = 0.8 n + 6.1$ 
B)  $a _ { n } = 0.7 n + 6.1$ 
C)  $a _ { n } = 0.8 n + 5.9$ 
D)  $a _ { n } = 0.8 n + 6.9$

Question 11

Find the indicated term of the arithmetic sequence.
-6.1, 5.5, 4.9, . . . ; $$\text { a9 }$$

Accepted Answer

A) 1.9 
B) 1.31 
C) 1.3 
D) 0.7 
A) 1.9 
B) 1.31 
C) 1.3 
D) 0.7

Question 12

Use the Binomial Theorem to expand the binomial.
-$$( x + 5 y ) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }$ 
B)  $x ^ { 4 } + 20 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } + 20 x y ^ { 3 } + 625 y ^ { 4 }$ 
C)  $x ^ { 4 } + 5 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } + 250 x y ^ { 3 } + 625 y ^ { 4 }$ 
D)  $x ^ { 4 } + 20 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } + 500 x y ^ { 3 } + 625 y ^ { 4 }$ 
A)  $x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }$ 
B)  $x ^ { 4 } + 20 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } + 20 x y ^ { 3 } + 625 y ^ { 4 }$ 
C)  $x ^ { 4 } + 5 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } + 250 x y ^ { 3 } + 625 y ^ { 4 }$ 
D)  $x ^ { 4 } + 20 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } + 500 x y ^ { 3 } + 625 y ^ { 4 }$

Question 13

Find the general term of the arithmetic sequence.
-$- 1 , - 7 , - 13 , - 19 , - 25 , \ldots$

Accepted Answer

A)  $a _ { n } = - 11 - 6 n$ 
B)  $a _ { n } = 5 - 6 n$ 
C)  $a _ { n } = 6 n - 5$ 
D)  $a _ { n } = - 5 - 6 n$ 
A)  $a _ { n } = - 11 - 6 n$ 
B)  $a _ { n } = 5 - 6 n$ 
C)  $a _ { n } = 6 n - 5$ 
D)  $a _ { n } = - 5 - 6 n$

Question 14

Solve the problem.
-If the odds that it will rain are 1 to 8, what is the probability of rain?

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 8 } { 9 }$ 
D)  $8 : 9$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 8 } { 9 }$ 
D)  $8 : 9$

Question 15

Use Pascal's triangle to expand the binomial.
-$$( c - x ) ^ { 6 }$$

Accepted Answer

A)  $c ^ { 6 } - 8 c ^ { 5 } x + 17 c ^ { 4 } x ^ { 2 } - 22 c ^ { 3 } x ^ { 3 } + 17 c ^ { 2 } x ^ { 4 } - 8 c x ^ { 5 } + x ^ { 6 }$ 
B)  $c ^ { 6 } - 6 c ^ { 5 } x - 30 c ^ { 4 } x ^ { 2 } + 120 c ^ { 3 } x ^ { 3 } + 360 c ^ { 2 } x ^ { 4 } - 720 c x ^ { 5 } - 720 x ^ { 6 }$ 
C)  $c ^ { 6 } - x ^ { 6 }$ 
D)  $c ^ { 6 } - 6 c ^ { 5 } x + 15 c ^ { 4 } x ^ { 2 } - 20 c ^ { 3 } x ^ { 3 } + 15 c ^ { 2 } x ^ { 4 } - 6 c x ^ { 5 } + x ^ { 6 }$ 
A)  $c ^ { 6 } - 8 c ^ { 5 } x + 17 c ^ { 4 } x ^ { 2 } - 22 c ^ { 3 } x ^ { 3 } + 17 c ^ { 2 } x ^ { 4 } - 8 c x ^ { 5 } + x ^ { 6 }$ 
B)  $c ^ { 6 } - 6 c ^ { 5 } x - 30 c ^ { 4 } x ^ { 2 } + 120 c ^ { 3 } x ^ { 3 } + 360 c ^ { 2 } x ^ { 4 } - 720 c x ^ { 5 } - 720 x ^ { 6 }$ 
C)  $c ^ { 6 } - x ^ { 6 }$ 
D)  $c ^ { 6 } - 6 c ^ { 5 } x + 15 c ^ { 4 } x ^ { 2 } - 20 c ^ { 3 } x ^ { 3 } + 15 c ^ { 2 } x ^ { 4 } - 6 c x ^ { 5 } + x ^ { 6 }$

Question 16

Find the indicated term or coefficient of the binomial expansion.
-$$\text { Find the coefficient of } x ^ { 2 } \text { in the expansion of } ( 3 x + 2 ) 10 \text {. }$$

Accepted Answer

A) 658,948 
B) 34,560 
C) 103,680 
D) 51,840 
A) 658,948 
B) 34,560 
C) 103,680 
D) 51,840

Question 17

Write the first five terms of the geometric sequence with the given information.
-The first term is 4 and the common ratio is 3.

Accepted Answer

A) 4, 7, 10, 13, 16 
B) 3, 12, 48, 192, 768 
C) 4, 12, 36, 108, 324 
D) 12, 36, 108, 324, 972 
A) 4, 7, 10, 13, 16 
B) 3, 12, 48, 192, 768 
C) 4, 12, 36, 108, 324 
D) 12, 36, 108, 324, 972

Question 18

Find the sum of the geometric series.
-$$4 - 8 + 16 - 32 + 64 - \ldots + 4 \cdot ( - 2 ) ^ { 11 }$$

Accepted Answer

A)  $- 5453$ 
B)  $- 5462$ 
C)  $- 5460$ 
D)  $- 5466$ 
A)  $- 5453$ 
B)  $- 5462$ 
C)  $- 5460$ 
D)  $- 5466$

Question 19

Write the statements SS1U1B11S1U1B0, SS1U1B12S1U1B0, and SS1U1B13S1U1B0 and determine if each statement is true.
-$$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

Accepted Answer

The answer of Write the statements SS1U1B11S1U1B0, SS1U1B12S1U1B0, and SS1U1B13S1U1B0...

Question 20

Write the statements SS1U1B1kS1U1B0 and SS1U1B1kS1U1B0+1.
-$$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

Accepted Answer

\[\begin{array} { l } 
\mathrm { S } _ {

Solve the problem. -Suppose that $P ( A ) = 0.24$ and $P ( B ) = 0.68$ , find $P ( A \cap B )$ if $A$ and $B$ are mutually exclusive.

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. - $5 , \frac { 5 } { 4 } , \frac { 5 } { 9 } , \frac { 5 } { 16 } , \ldots$

Find the indicated term or coefficient of the binomial expansion. - $\text { Find the coefficient of } y ^ { 4 } \text { in the expansion of } ( y + 5 ) ^ { 9 }$

Solve the problem. -How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Solve the problem. -How many 9-symbol codes can be formed using 5 different symbols? Repeated symbols are allowed.

Write the first four terms of the recursive sequence. - $a _ { 1 } = 2 , a _ { n } = \frac { a _ { n } - 1 } { n + 1 }$ for $n \geq 2$

Find the probability. -A bag contains 8 red marbles, 5 blue marbles, and 9 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n. - $S _ { n } : 1 \cdot 8 + 2 \cdot 8 + 3 \cdot 8 + \ldots + 8 n = \frac { 8 n ( n + 1 ) } { 2 }$

The first several terms of a sequence are given. Find the indicated partial sum. - $- 32,64 , - 128,256 , \ldots ; S _ { 5 }$

Find the general term of the arithmetic sequence. - $6.9,7.7,8.5,9.3,10.1 , \ldots$

Find the indicated term of the arithmetic sequence. -6.1, 5.5, 4.9, . . . ; $\text { a9 }$

Use the Binomial Theorem to expand the binomial. - $( x + 5 y ) ^ { 4 }$

Find the general term of the arithmetic sequence. - $- 1 , - 7 , - 13 , - 19 , - 25 , \ldots$

Solve the problem. -If the odds that it will rain are 1 to 8, what is the probability of rain?

Use Pascal's triangle to expand the binomial. - $( c - x ) ^ { 6 }$

Find the indicated term or coefficient of the binomial expansion. - $\text { Find the coefficient of } x ^ { 2 } \text { in the expansion of } ( 3 x + 2 ) 10 \text {. }$

Write the first five terms of the geometric sequence with the given information. -The first term is 4 and the common ratio is 3.

Find the sum of the geometric series. - $4 - 8 + 16 - 32 + 64 - \ldots + 4 \cdot ( - 2 ) ^ { 11 }$

Write the statements S₁, S₂, and S₃ and determine if each statement is true. - $S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

Write the statements S_k and S_k+1. - $S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -Suppose that P(A)=0.24P ( A ) = 0.24P(A)=0.24 and P(B)=0.68P ( B ) = 0.68P(B)=0.68 , find P(A∩B)P ( A \cap B )P(A∩B) if AAA and BBB are mutually exclusive.

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. - 5,54,59,516,…5 , \frac { 5 } { 4 } , \frac { 5 } { 9 } , \frac { 5 } { 16 } , \ldots5,45​,95​,165​,…

Find the indicated term or coefficient of the binomial expansion. - Find the coefficient of y4 in the expansion of (y+5)9\text { Find the coefficient of } y ^ { 4 } \text { in the expansion of } ( y + 5 ) ^ { 9 } Find the coefficient of y4 in the expansion of (y+5)9