Question 1

Find the sum of the geometric series, if possible.
-$$\sum _ { i = 1 } ^ { 8 } 7 \left( \frac { 4 } { 5 } \right) ^ { i - 1 }$$

Accepted Answer

A)  $\frac { 11836867 } { 390625 }$ 
B)  $\frac { 325089 } { 78125 }$ 
C)  $\frac { 432187 } { 15625 }$ 
D)  $\frac { 2275623 } { 78125 }$ 
A)  $\frac { 11836867 } { 390625 }$ 
B)  $\frac { 325089 } { 78125 }$ 
C)  $\frac { 432187 } { 15625 }$ 
D)  $\frac { 2275623 } { 78125 }$

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The number of combinations of n elements taken r at a time is denoted by nCr and is computed by
.

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Find the indicated term of the arithmetic sequence based on the given information.
-$a _ { 1 } = - 11$ and $a _ { 16 } = 19 ;$ Find $a _ { 13 }$

Accepted Answer

A)  13 
B)  19 
C)  25 
D)  15 
A)  13 
B)  19 
C)  25 
D)  15

Question 4

An infinite________ is a function whose domain is the set of positive integers. A________sequence is a function whose domain is the set of the first n positive integers.

Accepted Answer

The answer of An infinite________ is a function whose domain...

Question 5

Solve the problem.
-Determine the number of ways that 5 students can be selected from the class of 24 to play 5 different roles in a short play.

Accepted Answer

A)  3,200,000 
B)  15,504 
C)  1,860,480 
D)  120 
A)  3,200,000 
B)  15,504 
C)  1,860,480 
D)  120

Question 6

Find the sum of the geometric series, if possible.
-$$\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 2 } \right) ^ { n - 1 }$$

Accepted Answer

A)  Sum does not exist 
B)  $- \frac { 1 } { 2 }$ 
C)  $- 2$ 
D)  $\frac { 1 } { 2 }$ 
A)  Sum does not exist 
B)  $- \frac { 1 } { 2 }$ 
C)  $- 2$ 
D)  $\frac { 1 } { 2 }$

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Two events in a sample space are ________ ________if they do not share any common elements.
That is, the two events do not overlap.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given an arithmetic sequence with first term $a _ { 1 }$ , and common difference d, the nth term is
represented by the formula $a _ { \mathrm { n } } =$ ________.

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Solve the problem.
-Find the sum of the integers from $- 60$ to 70 .

Accepted Answer

A)  8,450 
B)  655 
C)  8,515 
D)  650 
A)  8,450 
B)  655 
C)  8,515 
D)  650

Question 10

Evaluate.
-$$10 ^ { P _ { 2 } }$$

Accepted Answer

A)  90 
B)  20 
C)  45 
D)  1,814,400 
A)  90 
B)  20 
C)  45 
D)  1,814,400

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A license plate has 2 letters followed by 4 digits. How many license plates can be made if there no digit or letter may be replaced.

Accepted Answer

A)  3,276,000 
B)  6,760,000 
C)  3,407,040 
D)  6,500,000 
A)  3,276,000 
B)  6,760,000 
C)  3,407,040 
D)  6,500,000

Question 12

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given an infinite geometric series with first term a1 and common ratio r, if |r|  1\) | > 1, then the sum (does/does not) exist.

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The number of elements in event E is often denoted by________ .

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Expand the binomial by using the binomial theorem.
-$\left( x - 2 y ^ { 3 } \right) ^ { 4 }$

Accepted Answer

A)  $x ^ { 4 } - 8 x ^ { 3 } y + 24 x ^ { 2 } y ^ { 2 } - 32 x y ^ { 3 } + 16 y ^ { 4 }$ 
B)  $x ^ { 4 } - 2 x ^ { 3 } y + 4 x ^ { 2 } y ^ { 2 } - 8 x y ^ { 3 } + 16 y ^ { 4 }$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } y ^ { 3 } + 4 x ^ { 2 } y ^ { 6 } + 8 x y ^ { 9 } + 16 y ^ { 12 }$ 
D)  $x ^ { 4 } - 8 x ^ { 3 } y ^ { 3 } + 24 x ^ { 2 } y ^ { 6 } - 32 x y ^ { 9 } + 16 y ^ { 12 }$ 
A)  $x ^ { 4 } - 8 x ^ { 3 } y + 24 x ^ { 2 } y ^ { 2 } - 32 x y ^ { 3 } + 16 y ^ { 4 }$ 
B)  $x ^ { 4 } - 2 x ^ { 3 } y + 4 x ^ { 2 } y ^ { 2 } - 8 x y ^ { 3 } + 16 y ^ { 4 }$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } y ^ { 3 } + 4 x ^ { 2 } y ^ { 6 } + 8 x y ^ { 9 } + 16 y ^ { 12 }$ 
D)  $x ^ { 4 } - 8 x ^ { 3 } y ^ { 3 } + 24 x ^ { 2 } y ^ { 6 } - 32 x y ^ { 9 } + 16 y ^ { 12 }$

Question 15

Find the sum.
-$$\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$$

Accepted Answer

A)  $- 84$ 
B)  84 
C)  12 
D)  $- 12$ 
A)  $- 84$ 
B)  84 
C)  12 
D)  $- 12$

Question 16

Find the sum.
-Find the sum of the first 36 terms of the sequence. $\{ 1,8,15,22,29 , \ldots \}$

Accepted Answer

A)  4,572 
B)  9,144 
C)  4,446 
D)  9,108 
A)  4,572 
B)  9,144 
C)  4,446 
D)  9,108

Question 17

Solve the problem.
-A course in early civilization has 9 freshmen, 8 sophomores, and 12 juniors. If one student is selected at random, find the probability of the following events.
a. A junior is selected.
b. A freshman is selected.
c. A senior is selected.

Accepted Answer

A)  a. $\frac { 12 } { 29 }$
b. $\frac { 9 } { 29 }$
c. $\frac { 8 } { 29 }$ 
B)  a. $\frac { 9 } { 29 }$
b. $\frac { 12 } { 29 }$
c. 0 
C)  a. $\frac { 12 } { 29 }$
b. $\frac { 9 } { 29 }$
c. 0 
D)  a. $\frac { 9 } { 29 }$
b. $\frac { 8 } { 29 }$
c. $\frac { 12 } { 29 }$ 
A)  a. $\frac { 12 } { 29 }$
b. $\frac { 9 } { 29 }$
c. $\frac { 8 } { 29 }$ 
B)  a. $\frac { 9 } { 29 }$
b. $\frac { 12 } { 29 }$
c. 0 
C)  a. $\frac { 12 } { 29 }$
b. $\frac { 9 } { 29 }$
c. 0 
D)  a. $\frac { 9 } { 29 }$
b. $\frac { 8 } { 29 }$
c. $\frac { 12 } { 29 }$

Question 18

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An________ is a test with an uncertain outcome.

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Use mathematical induction to prove the given statement for all positive integers n.
-$$16 + 12 + 8 + \ldots + ( - 4 \mathrm { k } + 20 ) = - 2 n ( n - 9 )$$

Accepted Answer

The answer of Use mathematical induction to prove the given...

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given a geometric sequence with | $| r | < 1$ , the value of $r ^ { n } \rightarrow \quad \text { as } n \rightarrow \infty$

Accepted Answer

The answer of Write the word or phrase that best...

Find the sum of the geometric series, if possible. - $\sum _ { i = 1 } ^ { 8 } 7 \left( \frac { 4 } { 5 } \right) ^ { i - 1 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The number of combinations of n elements taken r at a time is denoted by nCr and is computed by .

Find the indicated term of the arithmetic sequence based on the given information. - $a _ { 1 } = - 11$ and $a _ { 16 } = 19 ;$ Find $a _ { 13 }$

An infinite is a function whose domain is the set of positive integers. Asequence is a function whose domain is the set of the first n positive integers.

Solve the problem. -Determine the number of ways that 5 students can be selected from the class of 24 to play 5 different roles in a short play.

Find the sum of the geometric series, if possible. - $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 2 } \right) ^ { n - 1 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Two events in a sample space are if they do not share any common elements. That is, the two events do not overlap.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given an arithmetic sequence with first term $a _ { 1 }$ , and common difference d, the nth term is represented by the formula $a _ { \mathrm { n } } =$ ________.

Solve the problem. -Find the sum of the integers from $- 60$ to 70 .

Evaluate. - $10 ^ { P _ { 2 } }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A license plate has 2 letters followed by 4 digits. How many license plates can be made if there no digit or letter may be replaced.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The number of elements in event E is often denoted by________ .

Expand the binomial by using the binomial theorem. - $\left( x - 2 y ^ { 3 } \right) ^ { 4 }$

Find the sum. - $\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$

Find the sum. -Find the sum of the first 36 terms of the sequence. $\{ 1,8,15,22,29 , \ldots \}$

Solve the problem. -A course in early civilization has 9 freshmen, 8 sophomores, and 12 juniors. If one student is selected at random, find the probability of the following events. a. A junior is selected. b. A freshman is selected. c. A senior is selected.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An________ is a test with an uncertain outcome.

Use mathematical induction to prove the given statement for all positive integers n. - $16 + 12 + 8 + \ldots + ( - 4 \mathrm { k } + 20 ) = - 2 n ( n - 9 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a geometric sequence with | $| r | < 1$ , the value of $r ^ { n } \rightarrow \quad \text { as } n \rightarrow \infty$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Review of Prerequisites

Filters

Exam 8: Sequences, Series, Induction, and Probability

Find the sum of the geometric series, if possible. - ∑i=187(45)i−1\sum _ { i = 1 } ^ { 8 } 7 \left( \frac { 4 } { 5 } \right) ^ { i - 1 }∑i=18​7(54​)i−1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The number of combinations of n elements taken r at a time is denoted by nCr and is computed by .

Find the indicated term of the arithmetic sequence based on the given information. - a1=−11a _ { 1 } = - 11a1​=−11 and a16=19;a _ { 16 } = 19 ;a16​=19; Find a13a _ { 13 }a13​

An infinite________ is a function whose domain is the set of positive integers. A________sequence is a function whose domain is the set of the first n positive integers.

Solve the problem. -Determine the number of ways that 5 students can be selected from the class of 24 to play 5 different roles in a short play.

Find the sum of the geometric series, if possible. - ∑n=1∞(32)n−1\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 2 } \right) ^ { n - 1 }∑n=1∞​(23​)n−1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Two events in a sample space are ________ ________if they do not share any common elements. That is, the two events do not overlap.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given an arithmetic sequence with first term a1a _ { 1 }a1​ , and common difference d, the nth term is represented by the formula an=a _ { \mathrm { n } } =an​= ________.

Solve the problem. -Find the sum of the integers from −60- 60−60 to 70 .

Evaluate. - 10P210 ^ { P _ { 2 } }10P2​

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -A license plate has 2 letters followed by 4 digits. How many license plates can be made if there no digit or letter may be replaced.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The number of elements in event E is often denoted by________ .

Expand the binomial by using the binomial theorem. - (x−2y3)4\left( x - 2 y ^ { 3 } \right) ^ { 4 }(x−2y3)4

Find the sum. - ∑j=16(−1)j(4j)\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )∑j=16​(−1)j(4j)

Find the sum. -Find the sum of the first 36 terms of the sequence. {1,8,15,22,29,…}\{ 1,8,15,22,29 , \ldots \}{1,8,15,22,29,…}

Solve the problem. -A course in early civilization has 9 freshmen, 8 sophomores, and 12 juniors. If one student is selected at random, find the probability of the following events. a. A junior is selected. b. A freshman is selected. c. A senior is selected.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An________ is a test with an uncertain outcome.

Use mathematical induction to prove the given statement for all positive integers n. - 16+12+8+…+(−4k+20)=−2n(n−9)16 + 12 + 8 + \ldots + ( - 4 \mathrm { k } + 20 ) = - 2 n ( n - 9 )16+12+8+…+(−4k+20)=−2n(n−9)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a geometric sequence with | ∣r∣<1| r | < 1∣r∣<1 , the value of rn→ as n→∞r ^ { n } \rightarrow \quad \text { as } n \rightarrow \inftyrn→ as n→∞

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Review of Prerequisites

Filters

Find the sum of the geometric series, if possible. - $\sum _ { i = 1 } ^ { 8 } 7 \left( \frac { 4 } { 5 } \right) ^ { i - 1 }$

Find the indicated term of the arithmetic sequence based on the given information. - $a _ { 1 } = - 11$ and $a _ { 16 } = 19 ;$ Find $a _ { 13 }$

An infinite is a function whose domain is the set of positive integers. Asequence is a function whose domain is the set of the first n positive integers.

Find the sum of the geometric series, if possible. - $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { 2 } \right) ^ { n - 1 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Two events in a sample space are if they do not share any common elements. That is, the two events do not overlap.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given an arithmetic sequence with first term $a _ { 1 }$ , and common difference d, the nth term is represented by the formula $a _ { \mathrm { n } } =$ ________.

Solve the problem. -Find the sum of the integers from $- 60$ to 70 .

Evaluate. - $10 ^ { P _ { 2 } }$

Expand the binomial by using the binomial theorem. - $\left( x - 2 y ^ { 3 } \right) ^ { 4 }$

Find the sum. - $\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$

Find the sum. -Find the sum of the first 36 terms of the sequence. $\{ 1,8,15,22,29 , \ldots \}$

Use mathematical induction to prove the given statement for all positive integers n. - $16 + 12 + 8 + \ldots + ( - 4 \mathrm { k } + 20 ) = - 2 n ( n - 9 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a geometric sequence with | $| r | < 1$ , the value of $r ^ { n } \rightarrow \quad \text { as } n \rightarrow \infty$