Exam 9: Discrete Mathematics

Use mathematical induction to prove the statement is true for all positive integers n. - $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

(Essay)

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Question 41

Solve. -How many ways can a president, vice-president, and secretary be chosen from a club with 9 members?

(Multiple Choice)

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Question 42

A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 4 audio systems. How many ways are there to order this model of car?

(Multiple Choice)

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Question 43

Solve the problem. -There are 11 essay questions on a test. Students must select 3 questions to write essays on. In how many ways can the 3 questions be chosen?

(Multiple Choice)

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Question 44

Write out the first five terms of the sequence. - $a _ { n } = 2 n - 1$

(Multiple Choice)

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Question 45

Expand the binomial. - $( 4 x + 2 y ) ^ { 4 }$

(Multiple Choice)

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Question 46

Write the sum using summation notation, assuming the suggested pattern continues. - $2 - 4 + 8 - 16 + \ldots$

(Multiple Choice)

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Question 47

Express the rational number as a fraction of integers. - $0.91919191 \ldots$

(Multiple Choice)

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Question 48

Express the rational number as a fraction of integers. - $1.5050505 \ldots$

(Multiple Choice)

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Question 49

Find an explicit rule for the nth term of the arithmetic sequence. - $- 20 , - 14 , - 8 , - 2 , \ldots$

(Multiple Choice)

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Question 50

Solve the problem. -How many ways are there to choose 9 books from a collection of 12 different books?

(Multiple Choice)

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Question 51

How many automobile license plates can be made involving 3 letters followed by 4 digits, if letters cannot be repeated ( used more than once ) but digits can be repeated ?

(Multiple Choice)

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Question 52

Solve. -An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

(Multiple Choice)

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Question 53

Tell whether permutations or combinations are being described. -4 dishwashers are ranked for performance by an independent laboratory.

(Multiple Choice)

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Question 54

Solve the problem. -How many committees of 5 people can be selected from 9 men and 8 women if the committee must have 3 men and 2 women?

(Multiple Choice)

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Question 55

Find the sum of the arithmetic sequence. - $13,15,17,19 , \ldots , 31$

(Multiple Choice)

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Question 56

Find the coefficient of the given term in the binomial expansion. - $x ^ { 6 } y ^ { 7 }$ term, $( x + y ) ^ { 13 }$

(Multiple Choice)

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Question 57

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $\frac { 1 } { 4096 } + \frac { 1 } { 512 } + \frac { 1 } { 64 } + \frac { 1 } { 8 } + \ldots$

(Multiple Choice)

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Question 58

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $\frac { 1 } { 462 } + \frac { 1 } { 66 } + \frac { 7 } { 66 } + \frac { 49 } { 66 } + \ldots$

(Multiple Choice)

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Question 59

Find an explicit rule for the nth term of the sequence. -The second and fifth terms of a geometric sequence are $- 16$ and 128 , respectively.

(Multiple Choice)

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Question 60

Use mathematical induction to prove the statement is true for all positive integers n. - $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

Solve. -How many ways can a president, vice-president, and secretary be chosen from a club with 9 members?

A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 4 audio systems. How many ways are there to order this model of car?

Solve the problem. -There are 11 essay questions on a test. Students must select 3 questions to write essays on. In how many ways can the 3 questions be chosen?

Write out the first five terms of the sequence. - $a _ { n } = 2 n - 1$

Expand the binomial. - $( 4 x + 2 y ) ^ { 4 }$

Write the sum using summation notation, assuming the suggested pattern continues. - $2 - 4 + 8 - 16 + \ldots$

Express the rational number as a fraction of integers. - $0.91919191 \ldots$

Express the rational number as a fraction of integers. - $1.5050505 \ldots$

Find an explicit rule for the nth term of the arithmetic sequence. - $- 20 , - 14 , - 8 , - 2 , \ldots$

Solve the problem. -How many ways are there to choose 9 books from a collection of 12 different books?

How many automobile license plates can be made involving 3 letters followed by 4 digits, if letters cannot be repeated ( used more than once ) but digits can be repeated ?

Solve. -An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Tell whether permutations or combinations are being described. -4 dishwashers are ranked for performance by an independent laboratory.

Solve the problem. -How many committees of 5 people can be selected from 9 men and 8 women if the committee must have 3 men and 2 women?

Find the sum of the arithmetic sequence. - $13,15,17,19 , \ldots , 31$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 6 } y ^ { 7 }$ term, $( x + y ) ^ { 13 }$

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $\frac { 1 } { 4096 } + \frac { 1 } { 512 } + \frac { 1 } { 64 } + \frac { 1 } { 8 } + \ldots$

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $\frac { 1 } { 462 } + \frac { 1 } { 66 } + \frac { 7 } { 66 } + \frac { 49 } { 66 } + \ldots$

Find an explicit rule for the nth term of the sequence. -The second and fifth terms of a geometric sequence are $- 16$ and 128 , respectively.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 9: Discrete Mathematics

Use mathematical induction to prove the statement is true for all positive integers n. - 1⋅2+2⋅3+3⋅4+…+n(n+1)=n(n+1)(n+2)31 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }1⋅2+2⋅3+3⋅4+…+n(n+1)=3n(n+1)(n+2)​

Solve. -How many ways can a president, vice-president, and secretary be chosen from a club with 9 members?

A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 4 audio systems. How many ways are there to order this model of car?

Solve the problem. -There are 11 essay questions on a test. Students must select 3 questions to write essays on. In how many ways can the 3 questions be chosen?

Write out the first five terms of the sequence. - an=2n−1a _ { n } = 2 n - 1an​=2n−1

Expand the binomial. - (4x+2y)4( 4 x + 2 y ) ^ { 4 }(4x+2y)4

Write the sum using summation notation, assuming the suggested pattern continues. - 2−4+8−16+…2 - 4 + 8 - 16 + \ldots2−4+8−16+…

Express the rational number as a fraction of integers. - 0.91919191…0.91919191 \ldots0.91919191…

Express the rational number as a fraction of integers. - 1.5050505…1.5050505 \ldots1.5050505…

Find an explicit rule for the nth term of the arithmetic sequence. - −20,−14,−8,−2,…- 20 , - 14 , - 8 , - 2 , \ldots−20,−14,−8,−2,…

Solve the problem. -How many ways are there to choose 9 books from a collection of 12 different books?

How many automobile license plates can be made involving 3 letters followed by 4 digits, if letters cannot be repeated ( used more than once ) but digits can be repeated ?

Solve. -An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Tell whether permutations or combinations are being described. -4 dishwashers are ranked for performance by an independent laboratory.

Solve the problem. -How many committees of 5 people can be selected from 9 men and 8 women if the committee must have 3 men and 2 women?

Find the sum of the arithmetic sequence. - 13,15,17,19,…,3113,15,17,19 , \ldots , 3113,15,17,19,…,31

Find the coefficient of the given term in the binomial expansion. - x6y7x ^ { 6 } y ^ { 7 }x6y7 term, (x+y)13( x + y ) ^ { 13 }(x+y)13

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - 14096+1512+164+18+…\frac { 1 } { 4096 } + \frac { 1 } { 512 } + \frac { 1 } { 64 } + \frac { 1 } { 8 } + \ldots40961​+5121​+641​+81​+…

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - 1462+166+766+4966+…\frac { 1 } { 462 } + \frac { 1 } { 66 } + \frac { 7 } { 66 } + \frac { 49 } { 66 } + \ldots4621​+661​+667​+6649​+…

Find an explicit rule for the nth term of the sequence. -The second and fifth terms of a geometric sequence are −16- 16−16 and 128 , respectively.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Use mathematical induction to prove the statement is true for all positive integers n. - $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

Write out the first five terms of the sequence. - $a _ { n } = 2 n - 1$

Expand the binomial. - $( 4 x + 2 y ) ^ { 4 }$

Write the sum using summation notation, assuming the suggested pattern continues. - $2 - 4 + 8 - 16 + \ldots$

Express the rational number as a fraction of integers. - $0.91919191 \ldots$

Express the rational number as a fraction of integers. - $1.5050505 \ldots$

Find an explicit rule for the nth term of the arithmetic sequence. - $- 20 , - 14 , - 8 , - 2 , \ldots$

Find the sum of the arithmetic sequence. - $13,15,17,19 , \ldots , 31$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 6 } y ^ { 7 }$ term, $( x + y ) ^ { 13 }$

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $\frac { 1 } { 4096 } + \frac { 1 } { 512 } + \frac { 1 } { 64 } + \frac { 1 } { 8 } + \ldots$

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $\frac { 1 } { 462 } + \frac { 1 } { 66 } + \frac { 7 } { 66 } + \frac { 49 } { 66 } + \ldots$

Find an explicit rule for the nth term of the sequence. -The second and fifth terms of a geometric sequence are $- 16$ and 128 , respectively.