Question 1

You are given the probability that an event will happen.Find the probability that the event will not happen.   $P ( E ) = 0.18$

Accepted Answer

A) 0.88 
B) 0.89 
C) 0.82 
D) 0.87 
E) 0.18 
A) 0.88 
B) 0.89 
C) 0.82 
D) 0.87 
E) 0.18

Question 2

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​
An = 135 - 5n
​

Accepted Answer

A) 110, 115, 120, 125, 130Arithmetic sequenced = -5 
B) 105, 110, 115, 120, 125Arithmetic sequenced = 5 
C) 130, 125, 120, 115, 110Arithmetic sequenced = 5 
D) 130, 125, 120, 115, 110Arithmetic sequenced = -5 
E) 125, 120, 115, 110, 105Arithmetic sequenced = 5 
A) 110, 115, 120, 125, 130Arithmetic sequenced = -5 
B) 105, 110, 115, 120, 125Arithmetic sequenced = 5 
C) 130, 125, 120, 115, 110Arithmetic sequenced = 5 
D) 130, 125, 120, 115, 110Arithmetic sequenced = -5 
E) 125, 120, 115, 110, 105Arithmetic sequenced = 5

Question 3

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$

Accepted Answer

A)  $\frac { 4 } { 15 }$ 
B) 0 
C) 1 
D)  $\frac { 11 } { 15 }$ 
E)  $\frac { 11 } { 30 }$ 
A)  $\frac { 4 } { 15 }$ 
B) 0 
C) 1 
D)  $\frac { 11 } { 15 }$ 
E)  $\frac { 11 } { 30 }$

Question 4

Write the first five terms of the arithmetic sequence. ​
A1 = 5, d = 7
​

Accepted Answer

A) 5, 12, 19, 26, 33 
B) 12, 19, 26, 33, 40 
C) 5, -2, -9, -16, -23 
D) 5, 12, 17, 22, 27 
E) 5, 35, 245, 1715, 12005 
A) 5, 12, 19, 26, 33 
B) 12, 19, 26, 33, 40 
C) 5, -2, -9, -16, -23 
D) 5, 12, 17, 22, 27 
E) 5, 35, 245, 1715, 12005

Question 5

Ten people are boarding an aircraft.Two have tickets for first class and board before those in the economy class.In how many ways can the ten people board the aircraft? ​

Accepted Answer

A) 240 
B) 48 
C) 80,640 
D) 12 
E) 1,440 
A) 240 
B) 48 
C) 80,640 
D) 12 
E) 1,440

Question 6

The figure shows the results of a recent survey in which 1011 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability that the adult will give the U.S.public schools an A
 ( $a = 3 \%$ , $b = 11 \%$ , $c = 19 \%$ )

Accepted Answer

A)  $\frac { 100 } { 3 }$ 
B)  $\frac { 3 } { 100 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 3 } { 50 }$ 
E) 100 
A)  $\frac { 100 } { 3 }$ 
B)  $\frac { 3 } { 100 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 3 } { 50 }$ 
E) 100

Question 7

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order. ​

Accepted Answer

A) 6 
B) 2 
C) 10 
D) 8 
E) 4 
A) 6 
B) 2 
C) 10 
D) 8 
E) 4

Question 8

Use the Binomial Theorem to expand and simplify the expression.   $( x + 6 ) ^ { 4 }$

Accepted Answer

A)  $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$ 
B)  $x ^ { 4 } - 24 x ^ { 3 } - 216 x ^ { 2 } + 864 x + 1296$ 
C)  $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x - 1296$ 
D)  $x ^ { 4 } + 36 x ^ { 3 } - 216 x ^ { 2 } + 864 x - 1296$ 
E)  $x ^ { 4 } + 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$ 
A)  $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$ 
B)  $x ^ { 4 } - 24 x ^ { 3 } - 216 x ^ { 2 } + 864 x + 1296$ 
C)  $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x - 1296$ 
D)  $x ^ { 4 } + 36 x ^ { 3 } - 216 x ^ { 2 } + 864 x - 1296$ 
E)  $x ^ { 4 } + 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$

Question 9

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards.  
The card is a 7 or lower.(Aces are low.)

Accepted Answer

A)  $\frac { 7 } { 52 }$ 
B)  $\frac { 13 } { 7 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 51 } { 52 }$ 
E)  $\frac { 7 } { 13 }$ 
A)  $\frac { 7 } { 52 }$ 
B)  $\frac { 13 } { 7 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 51 } { 52 }$ 
E)  $\frac { 7 } { 13 }$

Question 10

Use the Binomial Theorem to expand and simplify the expression.   $( y - 3 ) ^ { 3 }$

Accepted Answer

A)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y + 27$ 
B)  $y ^ { 3 } - 9 y ^ { 2 } + 27 y - 27$ 
C)  $y ^ { 3 } - 9 y ^ { 2 } - 27 y - 27$ 
D)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y - 27$ 
E)  $y ^ { 3 } + 9 y ^ { 2 } - 9 y + 27$ 
A)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y + 27$ 
B)  $y ^ { 3 } - 9 y ^ { 2 } + 27 y - 27$ 
C)  $y ^ { 3 } - 9 y ^ { 2 } - 27 y - 27$ 
D)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y - 27$ 
E)  $y ^ { 3 } + 9 y ^ { 2 } - 9 y + 27$

Question 11

Find the sum of the infinite geometric series.  $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$

Accepted Answer

A) 91 
B) 92 
C) 88 
D) 89 
E) 90 
A) 91 
B) 92 
C) 88 
D) 89 
E) 90

Question 12

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither.  
A1 = 0
An = an - 1 + 5

Accepted Answer

A) 0, 5, 10, 15, 20, 25
First differences: 0, 0, 0, 0
Second differences: 5, 5, 5, 5, 5
Quadratic 
B) 0, 5, 10, 15, 20, 25
First differences: 5, 5, 5, 5, 5
Second differences: 0, 0, 0, 0
Linear 
C) 0, 5, 10, 15, 20, 25
First differences: 5, 5, 5, 5, 5
Second differences: -1, -1, -1, -1
Quadratic 
D) 0, 5, 10, 15, 20, 25
First differences: 5, 5, 5, 5, 5
Second differences: 0, 0, 0, 0
Quadratic 
E) 0, 5, 10, 15, 20, 25
First differences: 0, 0, 0, 0
Second differences: 5, 5, 5, 5, 5
Linear 
A) 0, 5, 10, 15, 20, 25
First differences: 0, 0, 0, 0
Second differences: 5, 5, 5, 5, 5
Quadratic 
B) 0, 5, 10, 15, 20, 25
First differences: 5, 5, 5, 5, 5
Second differences: 0, 0, 0, 0
Linear 
C) 0, 5, 10, 15, 20, 25
First differences: 5, 5, 5, 5, 5
Second differences: -1, -1, -1, -1
Quadratic 
D) 0, 5, 10, 15, 20, 25
First differences: 5, 5, 5, 5, 5
Second differences: 0, 0, 0, 0
Quadratic 
E) 0, 5, 10, 15, 20, 25
First differences: 0, 0, 0, 0
Second differences: 5, 5, 5, 5, 5
Linear

Question 13

Find the sum of the infinite geometric series.   $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$

Accepted Answer

A)  $\frac { 8 } { 9 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { 9 } { 10 }$ 
E)  $\frac { 9 } { 8 }$ 
A)  $\frac { 8 } { 9 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { 9 } { 10 }$ 
E)  $\frac { 9 } { 8 }$

Question 14

You are given the probability that an event will happen.Find the probability that the event will not happen.  $P ( E ) = \frac { 6 } { 7 }$

Accepted Answer

A)  $\frac { 6 } { 7 }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 3 } { 7 }$ 
E)  $\frac { 1 } { 7 }$ 
A)  $\frac { 6 } { 7 }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 3 } { 7 }$ 
E)  $\frac { 1 } { 7 }$

Question 15

Find the sum of the indicated terms of the geometric sequence.   $\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }$

Accepted Answer

A) s = 65,535 
B) s = 65,538 
C) s = 65,532 
D) s = 65,541 
E) s = 262,140 
A) s = 65,535 
B) s = 65,538 
C) s = 65,532 
D) s = 65,541 
E) s = 262,140

Question 16

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.8$

Accepted Answer

A) 1 
B) 0.2 
C) 0.1 
D) 0.8 
E) 0 
A) 1 
B) 0.2 
C) 0.1 
D) 0.8 
E) 0

Question 17

Use a graphing utility to graph the first 10 terms of the sequence.(Assume that n begins with 1.) You may need to adjust the graphing window to the sizes indicated below to answer the question. ​
​an = -0.4n + 12
​

Accepted Answer

A)    ​ 
B)    
C) ​   
D)    
E)    
A)    ​ 
B)    
C) ​   
D)    
E)

Question 18

Find Pk+1 for the given Pk. $P _ { k } = \frac { 3 } { k ( k + 7 ) }$

Accepted Answer

A)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
C)  $P _ { k + 1 } = \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
D)  $P _ { k + 1 } = \frac { 3 } { k ( k + 8 ) }$ 
E)  $P _ { k + 1 } = \frac { 8 } { ( k + 1 ) ( k + 7 ) }$ 
A)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + 1$ 
B)  $P _ { k + 1 } = \frac { 3 } { k ( k + 7 ) } + \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
C)  $P _ { k + 1 } = \frac { 3 } { ( k + 1 ) ( k + 8 ) }$ 
D)  $P _ { k + 1 } = \frac { 3 } { k ( k + 8 ) }$ 
E)  $P _ { k + 1 } = \frac { 8 } { ( k + 1 ) ( k + 7 ) }$

Question 19

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = \frac { 50 } { n ^ { 2 / 3 } }$

Accepted Answer

A)  $- 50 , \frac { 50 } { \sqrt [ 3 ] { 4 } } , - \frac { 50 } { \sqrt [ 3 ] { 9 } } , \frac { 50 } { \sqrt [ 3 ] { 16 } } , - \frac { 50 } { \sqrt [ 3 ] { 25 } }$ 
B)  $50 , - \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 9 } } , - \frac { 50 } { \sqrt [ 3 ] { 16 } } , \frac { 50 } { \sqrt [ 3 ] { 25 } }$ 
C)  $50 , \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 9 } } , \frac { 50 } { \sqrt [ 3 ] { 16 } } , \frac { 50 } { \sqrt [ 3 ] { 25 } }$ 
D)  $- 50 , \frac { 50 } { \sqrt [ 3 ] { 2 } } , - \frac { 50 } { \sqrt [ 3 ] { 3 } } , \frac { 50 } { \sqrt [ 3 ] { 4 } } , - \frac { 50 } { \sqrt [ 3 ] { 5 } }$ 
E)  $50 , \frac { 50 } { \sqrt [ 3 ] { 2 } } , \frac { 50 } { \sqrt [ 3 ] { 3 } } , \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 5 } }$ 
A)  $- 50 , \frac { 50 } { \sqrt [ 3 ] { 4 } } , - \frac { 50 } { \sqrt [ 3 ] { 9 } } , \frac { 50 } { \sqrt [ 3 ] { 16 } } , - \frac { 50 } { \sqrt [ 3 ] { 25 } }$ 
B)  $50 , - \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 9 } } , - \frac { 50 } { \sqrt [ 3 ] { 16 } } , \frac { 50 } { \sqrt [ 3 ] { 25 } }$ 
C)  $50 , \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 9 } } , \frac { 50 } { \sqrt [ 3 ] { 16 } } , \frac { 50 } { \sqrt [ 3 ] { 25 } }$ 
D)  $- 50 , \frac { 50 } { \sqrt [ 3 ] { 2 } } , - \frac { 50 } { \sqrt [ 3 ] { 3 } } , \frac { 50 } { \sqrt [ 3 ] { 4 } } , - \frac { 50 } { \sqrt [ 3 ] { 5 } }$ 
E)  $50 , \frac { 50 } { \sqrt [ 3 ] { 2 } } , \frac { 50 } { \sqrt [ 3 ] { 3 } } , \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 5 } }$

Question 20

Find pk + 1 for the given pk.   $p _ { k } = \frac { k ^ { 2 } } { 7 ( k + 2 ) ^ { 2 } }$

Accepted Answer

A)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 3 ( k + 8 ) ^ { 2 } }$ 
B)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 8 ( k + 8 ) ^ { 2 } }$ 
C)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 8 ( k + 3 ) ^ { 2 } }$ 
D)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 7 ( k + 3 ) ^ { 2 } }$ 
E)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 7 ( k + 8 ) ^ { 2 } }$ 
A)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 3 ( k + 8 ) ^ { 2 } }$ 
B)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 8 ( k + 8 ) ^ { 2 } }$ 
C)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 8 ( k + 3 ) ^ { 2 } }$ 
D)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 7 ( k + 3 ) ^ { 2 } }$ 
E)  $p _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 7 ( k + 8 ) ^ { 2 } }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.18$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 135 - 5n

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$

Write the first five terms of the arithmetic sequence. A₁ = 5, d = 7

Ten people are boarding an aircraft.Two have tickets for first class and board before those in the economy class.In how many ways can the ten people board the aircraft?

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order.

Use the Binomial Theorem to expand and simplify the expression. $( x + 6 ) ^ { 4 }$

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards. The card is a 7 or lower.(Aces are low.)

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 3 }$

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₁ = 0 A_n = an_{- 1} + 5

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 6 } { 7 }$

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.8$

Use a graphing utility to graph the first 10 terms of the sequence.(Assume that n begins with 1.) You may need to adjust the graphing window to the sizes indicated below to answer the question. a_n = -0.4n + 12

Find Pk₊₁ for the given P_k. $P _ { k } = \frac { 3 } { k ( k + 7 ) }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { 50 } { n ^ { 2 / 3 } }$

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { k ^ { 2 } } { 7 ( k + 2 ) ^ { 2 } }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=0.18P ( E ) = 0.18P(E)=0.18

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​ An = 135 - 5n ​

You are given the probability that an event will not happen.Find the probability that the event will happen. P(E)=415P ( E ) = \frac { 4 } { 15 }P(E)=154​

Write the first five terms of the arithmetic sequence. ​ A1 = 5, d = 7 ​

Ten people are boarding an aircraft.Two have tickets for first class and board before those in the economy class.In how many ways can the ten people board the aircraft? ​

The figure shows the results of a recent survey in which 1011 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability that the adult will give the U.S.public schools an A ( a=3%a = 3 \%a=3% , b=11%b = 11 \%b=11% , c=19%c = 19 \%c=19% )

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order. ​

Use the Binomial Theorem to expand and simplify the expression. (x+6)4( x + 6 ) ^ { 4 }(x+6)4

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards. The card is a 7 or lower.(Aces are low.)

Use the Binomial Theorem to expand and simplify the expression. (y−3)3( y - 3 ) ^ { 3 }(y−3)3

Find the sum of the infinite geometric series. ∑n=0∞9(910)n\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }∑n=0∞​9(109​)n

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A1 = 0 An = an - 1 + 5

Find the sum of the infinite geometric series. ∑n=0∞(−18)n\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }∑n=0∞​(−81​)n

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=67P ( E ) = \frac { 6 } { 7 }P(E)=76​

Find the sum of the indicated terms of the geometric sequence. ∑n=1n=83(4)n−1\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }∑n=1n=8​3(4)n−1

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=0.8P ( E ) = 0.8P(E)=0.8

Use a graphing utility to graph the first 10 terms of the sequence.(Assume that n begins with 1.) You may need to adjust the graphing window to the sizes indicated below to answer the question. ​ ​an = -0.4n + 12 ​

Find Pk+1 for the given Pk. Pk=3k(k+7)P _ { k } = \frac { 3 } { k ( k + 7 ) }Pk​=k(k+7)3​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=50n2/3a _ { n } = \frac { 50 } { n ^ { 2 / 3 } }an​=n2/350​

Find pk + 1 for the given pk. pk=k27(k+2)2p _ { k } = \frac { k ^ { 2 } } { 7 ( k + 2 ) ^ { 2 } }pk​=7(k+2)2k2​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.18$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 135 - 5n

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$

Write the first five terms of the arithmetic sequence. A₁ = 5, d = 7

Ten people are boarding an aircraft.Two have tickets for first class and board before those in the economy class.In how many ways can the ten people board the aircraft?

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order.

Use the Binomial Theorem to expand and simplify the expression. $( x + 6 ) ^ { 4 }$

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 3 }$

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₁ = 0 A_n = an_{- 1} + 5

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 6 } { 7 }$

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.8$

Use a graphing utility to graph the first 10 terms of the sequence.(Assume that n begins with 1.) You may need to adjust the graphing window to the sizes indicated below to answer the question. a_n = -0.4n + 12

Find Pk₊₁ for the given P_k. $P _ { k } = \frac { 3 } { k ( k + 7 ) }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { 50 } { n ^ { 2 / 3 } }$

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { k ^ { 2 } } { 7 ( k + 2 ) ^ { 2 } }$