Question 1

Find the first six terms of the sequence.
-$$a _ { 1 } = 9 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n } - 1 - a _ { n - 2 }$$

Accepted Answer

A)  $9,7,2 , - 7 , - 3,8$ 
B)  $9,7,5,3,1 , - 1$ 
C)  $9,7,16,23,36,59$ 
D)  $9,7 , - 2 , - 9 , - 7,2$ 
A)  $9,7,2 , - 7 , - 3,8$ 
B)  $9,7,5,3,1 , - 1$ 
C)  $9,7,16,23,36,59$ 
D)  $9,7 , - 2 , - 9 , - 7,2$

Question 2

Solve.
-There are 6 women running in a race. How many first, second, and third place possibilities can occur?

Accepted Answer

A)  20 
B)  18 
C)  120 
D)  216 
A)  20 
B)  18 
C)  120 
D)  216

Question 3

Solve.
-A sequence of yearly payments of $6000 is invested at an interest rate of 5.2%, compounded annually. What is the total amount of the annuity after 8 years?

Accepted Answer

A)  $58,706.12 
B)  $57,706.12 
C)  $56,706.12 
D)  $57,206.12 
A)  $58,706.12 
B)  $57,706.12 
C)  $56,706.12 
D)  $57,206.12

Question 4

Solve the problem.
-A game involves choosing 8 numbers from the numbers 1 through 13. In how many ways can this be done?

Accepted Answer

A)  1287 
B)  1267 
C)  51,891,840 
D)  1295 
A)  1287 
B)  1267 
C)  51,891,840 
D)  1295

Question 5

Solve.
-A pendulum bob swings $6.0 \mathrm {~cm}$ on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Accepted Answer

A)  $12.0 \mathrm {~cm}$ 
B)  $9.0 \mathrm {~cm}$ 
C)  $13.3 \mathrm {~cm}$ 
D)  $13.0 \mathrm {~cm}$ 
A)  $12.0 \mathrm {~cm}$ 
B)  $9.0 \mathrm {~cm}$ 
C)  $13.3 \mathrm {~cm}$ 
D)  $13.0 \mathrm {~cm}$

Question 6

Solve the problem.
-There are 10 different books on a table. In how many ways can 8 books be chosen?

Accepted Answer

A)  471 
B)  226,800 
C)  45 
D)  1,814,400 
A)  471 
B)  226,800 
C)  45 
D)  1,814,400

Question 7

Determine whether the infinite geometric series converges. If the series converges, determine the limit.
-$$36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots$$

Accepted Answer

A)  Diverges 
B)  Converges; - 5616 
C)  Converges; 45 
D)  Converges; 30 
A)  Diverges 
B)  Converges; - 5616 
C)  Converges; 45 
D)  Converges; 30

Question 8

Use mathematical induction to prove the statement is true for all positive integers n.
-$$\text { The integer } n ^ { 3 } + 2 n \text { is divisible by } 3 \text { for every positive integer } n \text {. }$$

Accepted Answer

Step 1: Determine if @#LAT-DLM&, and @#LAT-DLM& are true.
@#LAT-DLM& i

Question 9

Expand the binomial.
-$$( 2 x + 1 ) ^ { 5 }$$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 4 x + 1 \right) ^ { 5 }$ 
B)  $32 x ^ { 5 } + 10 x ^ { 4 } + 40 x ^ { 3 } + 40 x ^ { 2 } + 10 x + 1$ 
C)  $32 x ^ { 5 } + 16 x ^ { 4 } + 8 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 1$ 
D)  $32 x ^ { 5 } + 80 x ^ { 4 } + 80 x ^ { 3 } + 40 x ^ { 2 } + 10 x + 1$ 
A)  $\left( 4 x ^ { 2 } + 4 x + 1 \right) ^ { 5 }$ 
B)  $32 x ^ { 5 } + 10 x ^ { 4 } + 40 x ^ { 3 } + 40 x ^ { 2 } + 10 x + 1$ 
C)  $32 x ^ { 5 } + 16 x ^ { 4 } + 8 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 1$ 
D)  $32 x ^ { 5 } + 80 x ^ { 4 } + 80 x ^ { 3 } + 40 x ^ { 2 } + 10 x + 1$

Question 10

Find the coefficient of the given term in the binomial expansion.
-$x ^ { 4 }$ term, $( x - 3 ) ^ { 15 }$

Accepted Answer

A)  $- 241,805,655$ 
B)  $- 4095$ 
C)  1365 
D)  $241,805,655$ 
A)  $- 241,805,655$ 
B)  $- 4095$ 
C)  1365 
D)  $241,805,655$

Question 11

Find an explicit rule for the nth term of the arithmetic sequence.
-$$\mathrm { a } _ { 17 } = - 46 , \mathrm { a } _ { 19 } = - 144$$

Accepted Answer

A)  $a _ { n } = 738 - 49 ( n + 1 )$ 
B)  $a _ { n } = 738 - 49 ( n - 1 )$ 
C)  $a _ { n } = 738 + 49 ( n + 1 )$ 
D)  $a _ { n } = 738 - 49 ( n - 2 )$ 
A)  $a _ { n } = 738 - 49 ( n + 1 )$ 
B)  $a _ { n } = 738 - 49 ( n - 1 )$ 
C)  $a _ { n } = 738 + 49 ( n + 1 )$ 
D)  $a _ { n } = 738 - 49 ( n - 2 )$

Question 12

Find an explicit rule for the nth term of the arithmetic sequence.
-$$- 9 , - 17 , - 25 , - 33 , \ldots$$

Accepted Answer

A)  $a _ { n } = - 9 - ( - 8 ) ( n + 1 )$ 
B)  $a _ { n } = - 9 + ( - 8 ) ( n - 1 )$ 
C)  $a _ { n } = - 9 + ( - 8 ) ( n + 1 )$ 
D)  $a _ { n } = - 9 \times ( - 8 ) ( n - 1 )$ 
A)  $a _ { n } = - 9 - ( - 8 ) ( n + 1 )$ 
B)  $a _ { n } = - 9 + ( - 8 ) ( n - 1 )$ 
C)  $a _ { n } = - 9 + ( - 8 ) ( n + 1 )$ 
D)  $a _ { n } = - 9 \times ( - 8 ) ( n - 1 )$

Question 13

Write out the first five terms of the sequence.
-$$c _ { n } = \frac { n + 2 } { n }$$

Accepted Answer

A)  $3,2 , \frac { 5 } { 3 } , \frac { 3 } { 2 } , \frac { 7 } { 5 }$ 
B)  $\frac { 2 } { 8 } , \frac { 2 } { 9 } , \frac { 2 } { 10 } , \frac { 2 } { 11 } , \frac { 2 } { 12 }$ 
C)  $1,1,1,1,1$ 
D)  $\frac { 10 } { 8 } , \frac { 11 } { 9 } , \frac { 12 } { 10 } , \frac { 13 } { 11 } , \frac { 14 } { 12 }$ 
A)  $3,2 , \frac { 5 } { 3 } , \frac { 3 } { 2 } , \frac { 7 } { 5 }$ 
B)  $\frac { 2 } { 8 } , \frac { 2 } { 9 } , \frac { 2 } { 10 } , \frac { 2 } { 11 } , \frac { 2 } { 12 }$ 
C)  $1,1,1,1,1$ 
D)  $\frac { 10 } { 8 } , \frac { 11 } { 9 } , \frac { 12 } { 10 } , \frac { 13 } { 11 } , \frac { 14 } { 12 }$

Question 14

Solve.
-How many different three-number "combinations" are possible on a combination lock having 28 numbers on its dial?

Accepted Answer

A)  19,656 
B)  37,800 
C)  18,900 
D)  9828 
A)  19,656 
B)  37,800 
C)  18,900 
D)  9828

Question 15

Solve.
-If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 30 days?

Accepted Answer

A)  $\$ 0.30$ 
B)  $\$ 2.33$ 
C)  $\$ 4.65$ 
D)  $\$ 9.30$ 
A)  $\$ 0.30$ 
B)  $\$ 2.33$ 
C)  $\$ 4.65$ 
D)  $\$ 9.30$

Question 16

How many automobile license plates can be made involving 4 letters followed by 2 digits?

Accepted Answer

A)  45,697,600 
B)  457,076 
C)  45,718,100 
D)  45,687,344 
A)  45,697,600 
B)  457,076 
C)  45,718,100 
D)  45,687,344

Question 17

Use mathematical induction to prove the statement is true for all positive integers n.
-$$n \leq 2 ^ { n }$$

Accepted Answer

@#LAT-DLM&
Step 1: Determine if @#LAT-DLM&, and @#LAT-DLM& are true.
@#LAT-DLM&

Question 18

Find the sum of the arithmetic sequence.
-$40,42,44,46 , \ldots , 62$

Accepted Answer

A)  64 
B)  480 
C)  504 
D)  612 
A)  64 
B)  480 
C)  504 
D)  612

Question 19

In the "Big Bucks" lottery game, a person is to pick 5 digits from 0 to 9 in correct order. If a number can be repeated, how many ways are there to play the game?

Accepted Answer

A)  9,765,625 
B)  1,000,000 
C)  100,000 
D)  1,953,125 
A)  9,765,625 
B)  1,000,000 
C)  100,000 
D)  1,953,125

Question 20

Solve.
-In how many ways can 7 people line up for play tickets?

Accepted Answer

A)  5040 
B)  1 
C)  823,543 
D)  7 
A)  5040 
B)  1 
C)  823,543 
D)  7

Find the first six terms of the sequence. - $a _ { 1 } = 9 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n } - 1 - a _ { n - 2 }$

Solve. -There are 6 women running in a race. How many first, second, and third place possibilities can occur?

Solve. -A sequence of yearly payments of $6000 is invested at an interest rate of 5.2%, compounded annually. What is the total amount of the annuity after 8 years?

Solve the problem. -A game involves choosing 8 numbers from the numbers 1 through 13. In how many ways can this be done?

Solve. -A pendulum bob swings $6.0 \mathrm {~cm}$ on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Solve the problem. -There are 10 different books on a table. In how many ways can 8 books be chosen?

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots$

Use mathematical induction to prove the statement is true for all positive integers n. - $\text { The integer } n ^ { 3 } + 2 n \text { is divisible by } 3 \text { for every positive integer } n \text {. }$

Expand the binomial. - $( 2 x + 1 ) ^ { 5 }$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 4 }$ term, $( x - 3 ) ^ { 15 }$

Find an explicit rule for the nth term of the arithmetic sequence. - $\mathrm { a } _ { 17 } = - 46 , \mathrm { a } _ { 19 } = - 144$

Find an explicit rule for the nth term of the arithmetic sequence. - $- 9 , - 17 , - 25 , - 33 , \ldots$

Write out the first five terms of the sequence. - $c _ { n } = \frac { n + 2 } { n }$

Solve. -How many different three-number "combinations" are possible on a combination lock having 28 numbers on its dial?

Solve. -If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 30 days?

How many automobile license plates can be made involving 4 letters followed by 2 digits?

Use mathematical induction to prove the statement is true for all positive integers n. - $n \leq 2 ^ { n }$

Find the sum of the arithmetic sequence. - $40,42,44,46 , \ldots , 62$

In the "Big Bucks" lottery game, a person is to pick 5 digits from 0 to 9 in correct order. If a number can be repeated, how many ways are there to play the game?

Solve. -In how many ways can 7 people line up for play tickets?

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

Find the first six terms of the sequence. - a1=9,a2=7; for n≥3,an=an−1−an−2a _ { 1 } = 9 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n } - 1 - a _ { n - 2 }a1​=9,a2​=7; for n≥3,an​=an​−1−an−2​

Solve. -There are 6 women running in a race. How many first, second, and third place possibilities can occur?

Solve. -A sequence of yearly payments of $6000 is invested at an interest rate of 5.2%, compounded annually. What is the total amount of the annuity after 8 years?

Solve the problem. -A game involves choosing 8 numbers from the numbers 1 through 13. In how many ways can this be done?

Solve. -A pendulum bob swings 6.0 cm6.0 \mathrm {~cm}6.0 cm on its first oscillation. On each subsequent oscillation the bob travels 13\frac { 1 } { 3 }31​ of the previous distance. Find the total distance the bob travels before coming to rest.

Solve the problem. -There are 10 different books on a table. In how many ways can 8 books be chosen?

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - 36+365+3625+36125+…36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots36+536​+2536​+12536​+…

Expand the binomial. - (2x+1)5( 2 x + 1 ) ^ { 5 }(2x+1)5

Find the coefficient of the given term in the binomial expansion. - x4x ^ { 4 }x4 term, (x−3)15( x - 3 ) ^ { 15 }(x−3)15

Find an explicit rule for the nth term of the arithmetic sequence. - a17=−46,a19=−144\mathrm { a } _ { 17 } = - 46 , \mathrm { a } _ { 19 } = - 144a17​=−46,a19​=−144

Find an explicit rule for the nth term of the arithmetic sequence. - −9,−17,−25,−33,…- 9 , - 17 , - 25 , - 33 , \ldots−9,−17,−25,−33,…

Write out the first five terms of the sequence. - cn=n+2nc _ { n } = \frac { n + 2 } { n }cn​=nn+2​

Solve. -How many different three-number "combinations" are possible on a combination lock having 28 numbers on its dial?

Solve. -If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 30 days?

How many automobile license plates can be made involving 4 letters followed by 2 digits?

Use mathematical induction to prove the statement is true for all positive integers n. - n≤2nn \leq 2 ^ { n }n≤2n

Find the sum of the arithmetic sequence. - 40,42,44,46,…,6240,42,44,46 , \ldots , 6240,42,44,46,…,62

In the "Big Bucks" lottery game, a person is to pick 5 digits from 0 to 9 in correct order. If a number can be repeated, how many ways are there to play the game?

Solve. -In how many ways can 7 people line up for play tickets?

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

Find the first six terms of the sequence. - $a _ { 1 } = 9 , a _ { 2 } = 7 ; \text { for } n \geq 3 , a _ { n } = a _ { n } - 1 - a _ { n - 2 }$

Solve. -A pendulum bob swings $6.0 \mathrm {~cm}$ on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Determine whether the infinite geometric series converges. If the series converges, determine the limit. - $36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots$

Expand the binomial. - $( 2 x + 1 ) ^ { 5 }$

Find the coefficient of the given term in the binomial expansion. - $x ^ { 4 }$ term, $( x - 3 ) ^ { 15 }$

Find an explicit rule for the nth term of the arithmetic sequence. - $\mathrm { a } _ { 17 } = - 46 , \mathrm { a } _ { 19 } = - 144$

Find an explicit rule for the nth term of the arithmetic sequence. - $- 9 , - 17 , - 25 , - 33 , \ldots$

Write out the first five terms of the sequence. - $c _ { n } = \frac { n + 2 } { n }$

Use mathematical induction to prove the statement is true for all positive integers n. - $n \leq 2 ^ { n }$

Find the sum of the arithmetic sequence. - $40,42,44,46 , \ldots , 62$