Question 1

Write a formula for the nth term of the geometric sequence.
-$8,4,2,1 , \ldots$

Accepted Answer

A)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ 
B)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n }$ 
C)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 8 - \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ 
B)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n }$ 
C)  $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 8 - \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$

Question 2

Solve the problem.
-A traffic light at an intersection has a 120-sec cycle. The light is green for 80 sec, yellow for 5 sec, and red for 35 sec.
a. When a motorist approaches the intersection, find the probability that the light will be red.
(Assume that the color of the light is defined as the color when the car is 100 ft from the Intersection. This is the approximate distance at which the driver makes a decision to stop or go.)
b. If a motorist approaches the intersection twice during the day, find the probability that the light
Will be red both times.

Accepted Answer

A)  a. $\frac { 7 } { 24 }$; b. $\frac { 7 } { 48 }$ 
B)  a. $\frac { 7 } { 24 } ;$ b. $\frac { 49 } { 576 }$ 
C)  a. $\frac { 1 } { 3 } ;$ b. $\frac { 1 } { 9 }$ 
D)  a. $\frac { 1 } { 3 }$; b. $\frac { 1 } { 6 }$ 
A)  a. $\frac { 7 } { 24 }$; b. $\frac { 7 } { 48 }$ 
B)  a. $\frac { 7 } { 24 } ;$ b. $\frac { 49 } { 576 }$ 
C)  a. $\frac { 1 } { 3 } ;$ b. $\frac { 1 } { 9 }$ 
D)  a. $\frac { 1 } { 3 }$; b. $\frac { 1 } { 6 }$

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The Fundamental ________of ________indicates that if one event can occur in m different ways, and a second event can occur in n different ways, then the two events can occur in sequence in________different ways.

Accepted Answer

Principle;

Question 4

Evaluate.
-$${ } _ { 11 } C _ { 8 }$$

Accepted Answer

A)  88 
B)  6,652,800 
C)  990 
D)  165 
A)  88 
B)  6,652,800 
C)  990 
D)  165

Question 5

Find the sum of the geometric series, if possible.
-$$24 - 12 + 6 - 3 + \ldots$$

Accepted Answer

A)  48 
B)  15 
C)  Sum does not exist 
D)  16 
A)  48 
B)  15 
C)  Sum does not exist 
D)  16

Question 6

Choose the one alternative that best completes the statement or answers the question.
Determine which of the following can represent the probability of an event?
-$$104 \% , 0.04,0.46 , - \frac { 4 } { 5 }$$

Accepted Answer

A)  $104 \% , 0.46$ 
B)  $104 \% , - \frac { 4 } { 5 }$ 
C)  $0.04,0.46$ 
D)  $0.04 , - \frac { 4 } { 5 }$ 
A)  $104 \% , 0.46$ 
B)  $104 \% , - \frac { 4 } { 5 }$ 
C)  $0.04,0.46$ 
D)  $0.04 , - \frac { 4 } { 5 }$

Question 7

Using calculus, we can show that $$( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } + \ldots , \text { for } | x | < 1$$ This
formula can be used to evaluate binomial expressions raised to noninteger exponents. Use the first four
terms of this infinite series to approximate the given expression. Round to 3 decimal places if necessary.
-$$( 1.3 ) ^ { 4 / 3 }$$

Accepted Answer

A)  1.423 
B)  1.416 
C)  1.419 
D)  1.422 
A)  1.423 
B)  1.416 
C)  1.419 
D)  1.422

Question 8

Expand the binomial by using the binomial theorem.
-$$\left( x ^ { 5 } + y \right) ^ { 6 }$$

Accepted Answer

A)  $x ^ { 30 } + y ^ { 6 }$ 
B)  $x ^ { 30 } + 6 x ^ { 25 } y + 15 x ^ { 20 } y ^ { 2 } + 20 x ^ { 15 } y ^ { 3 } + 15 x ^ { 10 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
C)  $x ^ { 11 } + 6 x ^ { 10 } y + 15 x ^ { 9 } y ^ { 2 } + 20 x ^ { 8 } y ^ { 3 } + 15 x ^ { 7 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
D)  $x ^ { 6 } + 6 x ^ { 5 } y + 15 x ^ { 4 } y ^ { 2 } + 20 x ^ { 3 } y ^ { 3 } + 15 x ^ { 2 } y ^ { 4 } + 6 x y ^ { 5 } + y ^ { 6 }$ 
A)  $x ^ { 30 } + y ^ { 6 }$ 
B)  $x ^ { 30 } + 6 x ^ { 25 } y + 15 x ^ { 20 } y ^ { 2 } + 20 x ^ { 15 } y ^ { 3 } + 15 x ^ { 10 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
C)  $x ^ { 11 } + 6 x ^ { 10 } y + 15 x ^ { 9 } y ^ { 2 } + 20 x ^ { 8 } y ^ { 3 } + 15 x ^ { 7 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
D)  $x ^ { 6 } + 6 x ^ { 5 } y + 15 x ^ { 4 } y ^ { 2 } + 20 x ^ { 3 } y ^ { 3 } + 15 x ^ { 2 } y ^ { 4 } + 6 x y ^ { 5 } + y ^ { 6 }$

Question 9

Solve the problem.
-Suppose a contest has 11 participants. In how many different ways can first through fifth place be awarded?

Accepted Answer

A)  55,440 
B)  39,916,680 
C)  161,051 
D)  462 
A)  55,440 
B)  39,916,680 
C)  161,051 
D)  462

Question 10

Write the first five terms of the geometric sequence.
-Write the first five terms of the geometric sequence.
$$a _ { 1 } = - 6 , r = - 2$$

Accepted Answer

A)  $- 6 , - 8 , - 10,9 , - 14$ 
B)  $- 2,12 , - 72,432 , - 2,592$ 
C)  $- 6,12 , - 24,48 , - 96$ 
D)  $- 2 , - 8 , - 14 , - 20,10$ 
A)  $- 6 , - 8 , - 10,9 , - 14$ 
B)  $- 2,12 , - 72,432 , - 2,592$ 
C)  $- 6,12 , - 24,48 , - 96$ 
D)  $- 2 , - 8 , - 14 , - 20,10$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-For two independent events A and B, P(A and
B) = .

Accepted Answer

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

Question 12

Use mathematical induction to prove the given statement for all positive integers n.
-$$\sum _ { i = 1 } ^ { n } 2 i = n ( n + 1 )$$

Accepted Answer

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

Question 13

Solve the problem.
-Rafael received an inheritance of $27,000. He saves $13,700 and then spends $13,300 of the money on college tuition, books, and living expenses for school. If the money is respent over and over
Again in the community an infinite number of times, at a rate of 62%, determine the total amount
Spent.

Accepted Answer

A)  $21,452 
B)  $43,548 
C)  $35,000 
D)  $71,053 
A)  $21,452 
B)  $43,548 
C)  $35,000 
D)  $71,053

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The________ ________ of an experiment is the set of all possible outcomes.

Accepted Answer

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

Question 15

Expand the binomial by using the binomial theorem.
-$$( x + y - 9 ) ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } y - 27 x ^ { 2 } + 3 x y ^ { 2 } - 54 x y + 243 x + y ^ { 3 } - 27 y ^ { 2 } + 243 y - 729$ 
B)  $x ^ { 2 } + 2 x y - 18 x + y ^ { 2 } - 18 y + 81$ 
C)  $x ^ { 3 } + y ^ { 3 } - 729$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } y + 27 x ^ { 2 } + 3 x y ^ { 2 } + 54 x y - 243 x + y ^ { 3 } + 27 y ^ { 2 } - 243 y + 729$ 
A)  $x ^ { 3 } + 3 x ^ { 2 } y - 27 x ^ { 2 } + 3 x y ^ { 2 } - 54 x y + 243 x + y ^ { 3 } - 27 y ^ { 2 } + 243 y - 729$ 
B)  $x ^ { 2 } + 2 x y - 18 x + y ^ { 2 } - 18 y + 81$ 
C)  $x ^ { 3 } + y ^ { 3 } - 729$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } y + 27 x ^ { 2 } + 3 x y ^ { 2 } + 54 x y - 243 x + y ^ { 3 } + 27 y ^ { 2 } - 243 y + 729$

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If S is a sample space with equally likely outcomes and E is an event within the sample space, then
P(E) is computed by the formula $P ( E ) = \frac { \square } { \square }$

Accepted Answer

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

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Alex has 6 shirts, 7 pairs of pants, and 3 pairs of shoes. How many outfits can he wear?

Accepted Answer

A)  5,766 outfits 
B)  126 outfits 
C)  3 outfits 
D)  16 outfits 
A)  5,766 outfits 
B)  126 outfits 
C)  3 outfits 
D)  16 outfits

Question 18

Use the provided sums to evaluate the given expression.
-$\sum _ { i = 1 } ^ { 40 } i = 820$ and $\sum _ { i = 1 } ^ { 40 } i ^ { 2 } = 22,140 ;$ evaluate $\sum _ { i = 1 } ^ { 40 } \left( 5 i ^ { 2 } + 9 i \right)$

Accepted Answer

A)  118,080 
B)  22,960 
C)  111,520 
D)  203,360 
A)  118,080 
B)  22,960 
C)  111,520 
D)  203,360

Question 19

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An arithmetic sequence is a linear function whose domain is the set of ________integers.

Accepted Answer

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

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Suppose that an infinite series $a _ { 1 } + a _ { 2 } + a _ { 3 } + \ldots + a _ { n }$ approaches a value L as $n \longrightarrow \infty$ . Then the series________. Otherwise, the series________ .

Accepted Answer

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

Write a formula for the nth term of the geometric sequence. - $8,4,2,1 , \ldots$

Evaluate. - ${ } _ { 11 } C _ { 8 }$

Find the sum of the geometric series, if possible. - $24 - 12 + 6 - 3 + \ldots$

Choose the one alternative that best completes the statement or answers the question. Determine which of the following can represent the probability of an event? - $104 \% , 0.04,0.46 , - \frac { 4 } { 5 }$

Expand the binomial by using the binomial theorem. - $\left( x ^ { 5 } + y \right) ^ { 6 }$

Solve the problem. -Suppose a contest has 11 participants. In how many different ways can first through fifth place be awarded?

Write the first five terms of the geometric sequence. -Write the first five terms of the geometric sequence. $a _ { 1 } = - 6 , r = - 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For two independent events A and B, P(A and B) = .

Use mathematical induction to prove the given statement for all positive integers n. - $\sum _ { i = 1 } ^ { n } 2 i = n ( n + 1 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The of an experiment is the set of all possible outcomes.

Expand the binomial by using the binomial theorem. - $( x + y - 9 ) ^ { 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If S is a sample space with equally likely outcomes and E is an event within the sample space, then P(E) is computed by the formula $P ( E ) = \frac { \square } { \square }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Alex has 6 shirts, 7 pairs of pants, and 3 pairs of shoes. How many outfits can he wear?

Use the provided sums to evaluate the given expression. - $\sum _ { i = 1 } ^ { 40 } i = 820$ and $\sum _ { i = 1 } ^ { 40 } i ^ { 2 } = 22,140 ;$ evaluate $\sum _ { i = 1 } ^ { 40 } \left( 5 i ^ { 2 } + 9 i \right)$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An arithmetic sequence is a linear function whose domain is the set of ________integers.

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

Write a formula for the nth term of the geometric sequence. - 8,4,2,1,…8,4,2,1 , \ldots8,4,2,1,…

Evaluate. - 11C8{ } _ { 11 } C _ { 8 }11​C8​

Find the sum of the geometric series, if possible. - 24−12+6−3+…24 - 12 + 6 - 3 + \ldots24−12+6−3+…

Choose the one alternative that best completes the statement or answers the question. Determine which of the following can represent the probability of an event? - 104%,0.04,0.46,−45104 \% , 0.04,0.46 , - \frac { 4 } { 5 }104%,0.04,0.46,−54​

Expand the binomial by using the binomial theorem. - (x5+y)6\left( x ^ { 5 } + y \right) ^ { 6 }(x5+y)6

Solve the problem. -Suppose a contest has 11 participants. In how many different ways can first through fifth place be awarded?

Write the first five terms of the geometric sequence. -Write the first five terms of the geometric sequence. a1=−6,r=−2a _ { 1 } = - 6 , r = - 2a1​=−6,r=−2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For two independent events A and B, P(A and B) = .

Use mathematical induction to prove the given statement for all positive integers n. - ∑i=1n2i=n(n+1)\sum _ { i = 1 } ^ { n } 2 i = n ( n + 1 )∑i=1n​2i=n(n+1)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The________ ________ of an experiment is the set of all possible outcomes.

Expand the binomial by using the binomial theorem. - (x+y−9)3( x + y - 9 ) ^ { 3 }(x+y−9)3

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Alex has 6 shirts, 7 pairs of pants, and 3 pairs of shoes. How many outfits can he wear?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An arithmetic sequence is a linear function whose domain is the set of ________integers.

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

Write a formula for the nth term of the geometric sequence. - $8,4,2,1 , \ldots$

Evaluate. - ${ } _ { 11 } C _ { 8 }$

Find the sum of the geometric series, if possible. - $24 - 12 + 6 - 3 + \ldots$

Choose the one alternative that best completes the statement or answers the question. Determine which of the following can represent the probability of an event? - $104 \% , 0.04,0.46 , - \frac { 4 } { 5 }$

Expand the binomial by using the binomial theorem. - $\left( x ^ { 5 } + y \right) ^ { 6 }$

Write the first five terms of the geometric sequence. -Write the first five terms of the geometric sequence. $a _ { 1 } = - 6 , r = - 2$

Use mathematical induction to prove the given statement for all positive integers n. - $\sum _ { i = 1 } ^ { n } 2 i = n ( n + 1 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The of an experiment is the set of all possible outcomes.

Expand the binomial by using the binomial theorem. - $( x + y - 9 ) ^ { 3 }$