Question 1

Find the sum of the series.
-$$\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } + 2 ) ! } { ( \mathrm { i } + 1 ) ! }$$

Accepted Answer

A)  19 
B)  $\frac { 129 } { 20 }$ 
C)  25 
D)  $\frac { 377 } { 60 }$ 
A)  19 
B)  $\frac { 129 } { 20 }$ 
C)  25 
D)  $\frac { 377 } { 60 }$

Question 2

Solve the problem.
-On a gambling boat, Gertrude tripled her bet each time she won. If her first winning bet was $4 and she won six consecutive bets, find how much she won on the sixth bet. Find the total amount she won on these six bets.

Accepted Answer

A) $2916; $1456 
B) $972; $1456 
C) $324; $484 
D) $2916; $4372 
A) $2916; $1456 
B) $972; $1456 
C) $324; $484 
D) $2916; $4372

Question 3

Find the indicated term or coefficient of the binomial expansion.
-Find the coefficient of m in the expansion of $$\left( m ^ { 2 } + \frac { 4 } { m } \right) ^ { 9 }$$

Accepted Answer

A) 32,256 
B) 1024 
C) 129,024 
D) 126 
A) 32,256 
B) 1024 
C) 129,024 
D) 126

Question 4

Solve the problem.
-Suppose that $P ( A ) = 0.22$ and $P ( B ) = 0.36$, find $P ( A \cup B )$ if $A$ and $B$ are mutually exclusive.

Accepted Answer

A)  $0.0792$ 
B)  0 
C)  $0.5008$ 
D)  $0.58$ 
A)  $0.0792$ 
B)  0 
C)  $0.5008$ 
D)  $0.58$

Question 5

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio.
-4, -12, 36, -108, 324, . . .

Accepted Answer

A) yes, -3 
B) no 
C) yes, 12 $$\text { 
D)  } y e s , - \frac { 1 } { 3 }$$ 
A) yes, -3 
B) no 
C) yes, 12 $$\text { 
D)  } y e s , - \frac { 1 } { 3 }$$

Question 6

Use the Binomial Theorem to expand the binomial.
-$$( x + 3 ) ^ { 6 }$$

Accepted Answer

A)  $x ^ { 6 } + 18 x ^ { 5 } + 135 x ^ { 4 } + 540 x ^ { 3 } + 1215 x ^ { 2 } + 1458 x + 729$ 
B)  $x ^ { 6 } + 18 x ^ { 5 } + 729 x ^ { 4 } + 60 x ^ { 3 } + 729 x ^ { 2 } + 18 x + 3$ 
C)  $x ^ { 6 } + 18 x ^ { 5 } + 108 x ^ { 4 } + 486 x ^ { 3 } + 972 x ^ { 2 } + 1458 x + 729$ 
D)  $x ^ { 6 } + 18 x ^ { 5 } + 36 x ^ { 4 } + 54 x ^ { 3 } + 36 x ^ { 2 } + 18 x + 3$ 
A)  $x ^ { 6 } + 18 x ^ { 5 } + 135 x ^ { 4 } + 540 x ^ { 3 } + 1215 x ^ { 2 } + 1458 x + 729$ 
B)  $x ^ { 6 } + 18 x ^ { 5 } + 729 x ^ { 4 } + 60 x ^ { 3 } + 729 x ^ { 2 } + 18 x + 3$ 
C)  $x ^ { 6 } + 18 x ^ { 5 } + 108 x ^ { 4 } + 486 x ^ { 3 } + 972 x ^ { 2 } + 1458 x + 729$ 
D)  $x ^ { 6 } + 18 x ^ { 5 } + 36 x ^ { 4 } + 54 x ^ { 3 } + 36 x ^ { 2 } + 18 x + 3$

Question 7

Use Pascal's triangle to expand the binomial.
-$$( 3 x + 4 ) ^ { 4 }$$

Accepted Answer

A)  $81 x ^ { 3 } + 432 x ^ { 2 } + 864 x + 768$ 
B)  $81 x ^ { 4 } + 432 x ^ { 3 } + 864 x ^ { 2 } + 768 x + 256$ 
C)  $324 x ^ { 4 } + 1728 x ^ { 3 } + 864 x ^ { 2 } + 3072 x + 256$ 
D)  $81 x ^ { 4 } + 256 x ^ { 4 }$ 
A)  $81 x ^ { 3 } + 432 x ^ { 2 } + 864 x + 768$ 
B)  $81 x ^ { 4 } + 432 x ^ { 3 } + 864 x ^ { 2 } + 768 x + 256$ 
C)  $324 x ^ { 4 } + 1728 x ^ { 3 } + 864 x ^ { 2 } + 3072 x + 256$ 
D)  $81 x ^ { 4 } + 256 x ^ { 4 }$

Question 8

The general term of a sequence is given. Find the indicated partial sum.
-$$a _ { n } = 5 n - 2 ; S _ { 5 }$$

Accepted Answer

A) 65 
B) 85 
C) 100 
D) 55 
A) 65 
B) 85 
C) 100 
D) 55

Question 9

Find the probability.
-A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Accepted Answer

A)  $\frac { 6 } { 13 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  $\frac { 13 } { 6 }$ 
D)  6 
A)  $\frac { 6 } { 13 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  $\frac { 13 } { 6 }$ 
D)  6

Question 10

Solve the problem.
-Mary finds 9 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a must?

Accepted Answer

A) 3024; 1680 
B) 7560; 840 
C) 126; 70 
D) 15,120; 1680 
A) 3024; 1680 
B) 7560; 840 
C) 126; 70 
D) 15,120; 1680

Question 11

Solve the problem.
-How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 6 midfield players, and 9 defensive players?

Accepted Answer

A) 21,772,800 
B) 25,200 
C) 119 
D) 352,716 
A) 21,772,800 
B) 25,200 
C) 119 
D) 352,716

Question 12

Write the statements SS1U1B11S1U1B0, SS1U1B12S1U1B0, and SS1U1B13S1U1B0 and determine if each statement is true.
-$$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

Accepted Answer

\[\begin{array}{l}
\mathrm { S } _ { 1 }

Question 13

Find the indicated sum.
-Find the sum of the first 837 even positive integers.

Accepted Answer

A) 699,732 
B) 701,406 
C) 702,244 
D) 700,569 
A) 699,732 
B) 701,406 
C) 702,244 
D) 700,569

Question 14

Find the probability.
-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

Accepted Answer

A)  $\frac { 1 } { 18 }$ 
B)  3 
C)  $\frac { 5 } { 18 }$ 
D)  $\frac { 1 } { 12 }$ 
A)  $\frac { 1 } { 18 }$ 
B)  3 
C)  $\frac { 5 } { 18 }$ 
D)  $\frac { 1 } { 12 }$

Question 15

The general term of a sequence is given. Find the indicated partial sum.
-$$a _ { 1 } = 4 , a _ { n } = a _ { n } - 1 + 6 \text { for } n \geq 2 ; S _ { 5 }$$

Accepted Answer

A) 100 
B) 80 
C) 85 
D) 55 
A) 100 
B) 80 
C) 85 
D) 55

Question 16

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
-$$2 ^ { 2 } + 4 ^ { 3 } + 6 ^ { 4 } + \ldots + 16 ^ { 9 }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 8 } ( 2 \mathrm { i } ) ^ { \mathrm { i } + 1 }$ 
B)  $\sum _ { i = 1 } ^ { 8 } 2 ( i - 1 ) ^ { i + 1}$ 
C)  $\sum _ { i = 1 } ^ { 8 } ( 2 i ) ^ { i }$ 
D)  $\sum _ { i = 1 } ^ { 8 } 2 i ^ { 2 i - 1 }$ 
A)  $\sum _ { i = 1 } ^ { 8 } ( 2 \mathrm { i } ) ^ { \mathrm { i } + 1 }$ 
B)  $\sum _ { i = 1 } ^ { 8 } 2 ( i - 1 ) ^ { i + 1}$ 
C)  $\sum _ { i = 1 } ^ { 8 } ( 2 i ) ^ { i }$ 
D)  $\sum _ { i = 1 } ^ { 8 } 2 i ^ { 2 i - 1 }$

Question 17

Find the indicated term or coefficient of the binomial expansion.
-Find the 4 th term of the expansion of $( s - t ) ^ { 6 }$.

Accepted Answer

A)  $- 20 \mathrm {~s} ^ { 3 } \mathrm { t } ^ { 3 }$ 
B)  $s ^ { 2 } t ^ { 4 }$ 
C)  $- s ^ { 3 } t ^ { 3 }$ 
D)  $15 s ^ { 2 } t ^ { 4 }$ 
A)  $- 20 \mathrm {~s} ^ { 3 } \mathrm { t } ^ { 3 }$ 
B)  $s ^ { 2 } t ^ { 4 }$ 
C)  $- s ^ { 3 } t ^ { 3 }$ 
D)  $15 s ^ { 2 } t ^ { 4 }$

Question 18

Solve the problem.
-$\frac { 1 } { 25 },$ the odds against a direct hit?

Accepted Answer

A) 25 : 1 
B) 1: 25 
C) 24 : 1 
D) 23 : 1 
A) 25 : 1 
B) 1: 25 
C) 24 : 1 
D) 23 : 1

Question 19

Solve the problem.
-A collection of dimes is arranged in a triangular array with 15 coins in the base row, 14 in the next, 13 in the next, and so on with 1 dime in the last row. Find the value of the collection.

Accepted Answer

A) $1.20 
B) $24.00 
C) $12.00 
D) $6.00 
A) $1.20 
B) $24.00 
C) $12.00 
D) $6.00

Question 20

Write the statements SS1U1B1kS1U1B0 and SS1U1B1kS1U1B0+1.
-$$S _ { n } : 2 \text { is a factor of } n ^ { 2 } + 3 n$$

Accepted Answer

@#LAT-DLM& is a factor of @#LAT-DLM&
@#LAT-DLM& is a factor

Find the sum of the series. - $\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } + 2 ) ! } { ( \mathrm { i } + 1 ) ! }$

Solve the problem. -On a gambling boat, Gertrude tripled her bet each time she won. If her first winning bet was $4 and she won six consecutive bets, find how much she won on the sixth bet. Find the total amount she won on these six bets.

Find the indicated term or coefficient of the binomial expansion. -Find the coefficient of m in the expansion of $\left( m ^ { 2 } + \frac { 4 } { m } \right) ^ { 9 }$

Solve the problem. -Suppose that $P ( A ) = 0.22$ and $P ( B ) = 0.36$ , find $P ( A \cup B )$ if $A$ and $B$ are mutually exclusive.

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. -4, -12, 36, -108, 324, . . .

Use the Binomial Theorem to expand the binomial. - $( x + 3 ) ^ { 6 }$

Use Pascal's triangle to expand the binomial. - $( 3 x + 4 ) ^ { 4 }$

The general term of a sequence is given. Find the indicated partial sum. - $a _ { n } = 5 n - 2 ; S _ { 5 }$

Find the probability. -A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Solve the problem. -Mary finds 9 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a must?

Solve the problem. -How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 6 midfield players, and 9 defensive players?

Write the statements S₁, S₂, and S₃ and determine if each statement is true. - $S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$

Find the indicated sum. -Find the sum of the first 837 even positive integers.

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

The general term of a sequence is given. Find the indicated partial sum. - $a _ { 1 } = 4 , a _ { n } = a _ { n } - 1 + 6 \text { for } n \geq 2 ; S _ { 5 }$

Rewrite the series using summation notation. Use 1 as the lower limit of summation. - $2 ^ { 2 } + 4 ^ { 3 } + 6 ^ { 4 } + \ldots + 16 ^ { 9 }$

Find the indicated term or coefficient of the binomial expansion. -Find the 4 th term of the expansion of $( s - t ) ^ { 6 }$ .

Solve the problem. - $\frac { 1 } { 25 },$ the odds against a direct hit?

Solve the problem. -A collection of dimes is arranged in a triangular array with 15 coins in the base row, 14 in the next, 13 in the next, and so on with 1 dime in the last row. Find the value of the collection.

Write the statements S_k and S_k+1. - $S _ { n } : 2 \text { is a factor of } n ^ { 2 } + 3 n$

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

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Exam 9: Sequences and Series; Counting and Probability

Find the sum of the series. - ∑i=15(i+2)!(i+1)!\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } + 2 ) ! } { ( \mathrm { i } + 1 ) ! }∑i=15​(i+1)!(i+2)!​