Question 1

Use the Binomial Theorem to expand and simplify the expression.   $( a + 7 ) ^ { 5 }$

Accepted Answer

A)  $a ^ { 5 } + 35 a ^ { 4 } + 490 a ^ { 3 } + 343 a ^ { 2 } + 12005 a + 16807$ 
B)  $a ^ { 5 } + 35 a ^ { 4 } - 490 a ^ { 3 } + 3430 a ^ { 2 } + 12005 a + 16807$ 
C)  $a ^ { 5 } + 35 a ^ { 4 } + 490 a ^ { 3 } + 3430 a ^ { 2 } + 12005 a + 16807$ 
D)  $a ^ { 5 } + 35 a ^ { 4 } + 490 a ^ { 3 } + 3430 a ^ { 2 } + 2401 a + 16807$ 
E)  $a ^ { 5 } + 343 a ^ { 4 } + 2401 a ^ { 3 } + 49 a ^ { 2 } + 12005 a + 16807$ 
A)  $a ^ { 5 } + 35 a ^ { 4 } + 490 a ^ { 3 } + 343 a ^ { 2 } + 12005 a + 16807$ 
B)  $a ^ { 5 } + 35 a ^ { 4 } - 490 a ^ { 3 } + 3430 a ^ { 2 } + 12005 a + 16807$ 
C)  $a ^ { 5 } + 35 a ^ { 4 } + 490 a ^ { 3 } + 3430 a ^ { 2 } + 12005 a + 16807$ 
D)  $a ^ { 5 } + 35 a ^ { 4 } + 490 a ^ { 3 } + 3430 a ^ { 2 } + 2401 a + 16807$ 
E)  $a ^ { 5 } + 343 a ^ { 4 } + 2401 a ^ { 3 } + 49 a ^ { 2 } + 12005 a + 16807$

Question 2

Determine whether the sequence is geometric.If so, find the common ratio. -2, 2, 6, 10,...

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B) -2 
C) 4 
D) not geometric 
E) -4 
A)  $\frac { 1 } { 4 }$ 
B) -2 
C) 4 
D) not geometric 
E) -4

Question 3

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.   $\begin{array} { l } 
a _ { 0 } = 4 \
a _ { n } = \left( a _ { n - 1 } \right) ^ { 2 }
\end{array}$

Accepted Answer

A) 0, 4, -16, 256, -65,536, 4,294,967,296
First differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Second differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$ 
Linear 
B) 0, 4, 16, 256, 65,536, 4,294,967,296
First differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$ 
Second differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Quadratic 
C) 4, -16, 256, -65,536, 4,294,967,296, -18,446,744,073,709,600,000
First differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Second differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$
 Neither 
D) 4, 16, 256, 65,536, 4,294,967,296, 18,446,744,073,709,600,000
First differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$
 Second differences: 228, 65,040, 4,294,836,480, $2 \times 10 ^ { 19 }$ 
Neither 
E) 0, -4, 16, -256, 65,536, -4,294,967,296
First differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$ 
Second differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Quadratic 
A) 0, 4, -16, 256, -65,536, 4,294,967,296
First differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Second differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$ 
Linear 
B) 0, 4, 16, 256, 65,536, 4,294,967,296
First differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$ 
Second differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Quadratic 
C) 4, -16, 256, -65,536, 4,294,967,296, -18,446,744,073,709,600,000
First differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Second differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$
 Neither 
D) 4, 16, 256, 65,536, 4,294,967,296, 18,446,744,073,709,600,000
First differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$
 Second differences: 228, 65,040, 4,294,836,480, $2 \times 10 ^ { 19 }$ 
Neither 
E) 0, -4, 16, -256, 65,536, -4,294,967,296
First differences: 12, 240, 65,280, 4,294,901,760, $2 \times 10 ^ { 19 }$ 
Second differences: -228, 65,040, -4,294,836,480, $2 \times 10 ^ { 19 }$ 
Quadratic

Question 4

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 16 } n$

Accepted Answer

A) 18,496 
B) 8,976 
C) 1,496 
D) 272 
E) 136 
A) 18,496 
B) 8,976 
C) 1,496 
D) 272 
E) 136

Question 5

Expand the binomial by using Pascal's Triangle to determine the coefficients.   $( 2 t - s ) ^ { 5 }$

Accepted Answer

A)  $32 t ^ { 5 } - 80 t ^ { 4 } s + 80 t ^ { 3 } s ^ { 2 } - 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } - s ^ { 5 }$ 
B)  $32 t ^ { 5 } + 80 t ^ { 4 } s + 80 t ^ { 3 } s ^ { 2 } - 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } - s ^ { 5 }$ 
C)  $32 t ^ { 5 } - 80 t ^ { 4 } s - 80 t ^ { 3 } s ^ { 2 } - 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } - s ^ { 5 }$ 
D)  $32 t ^ { 5 } - 80 t ^ { 4 } s + 80 t ^ { 3 } s ^ { 2 } + 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } + s ^ { 5 }$ 
E)  $32 t ^ { 5 } + 80 t ^ { 4 } s - 80 t ^ { 3 } s ^ { 2 } + 40 t ^ { 2 } s ^ { 3 } - 10 t s ^ { 4 } + s ^ { 5 }$ 
A)  $32 t ^ { 5 } - 80 t ^ { 4 } s + 80 t ^ { 3 } s ^ { 2 } - 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } - s ^ { 5 }$ 
B)  $32 t ^ { 5 } + 80 t ^ { 4 } s + 80 t ^ { 3 } s ^ { 2 } - 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } - s ^ { 5 }$ 
C)  $32 t ^ { 5 } - 80 t ^ { 4 } s - 80 t ^ { 3 } s ^ { 2 } - 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } - s ^ { 5 }$ 
D)  $32 t ^ { 5 } - 80 t ^ { 4 } s + 80 t ^ { 3 } s ^ { 2 } + 40 t ^ { 2 } s ^ { 3 } + 10 t s ^ { 4 } + s ^ { 5 }$ 
E)  $32 t ^ { 5 } + 80 t ^ { 4 } s - 80 t ^ { 3 } s ^ { 2 } + 40 t ^ { 2 } s ^ { 3 } - 10 t s ^ { 4 } + s ^ { 5 }$

Question 6

Select the first five terms of the sequence defined recursively.   $a _ { 1 } = 23 , a _ { k + 1 } = a _ { k } + 3$

Accepted Answer

A)  $23,26,29,32,35$ 
B)  $26,17,29,11,8$ 
C)  $20,26,14,32,8$ 
D)  $20,17,14,11,8$ 
E)  $23,17,29,11,35$ 
A)  $23,26,29,32,35$ 
B)  $26,17,29,11,8$ 
C)  $20,26,14,32,8$ 
D)  $20,17,14,11,8$ 
E)  $23,17,29,11,35$

Question 7

Determine whether the sequence is arithmetic.If so, find the common difference. 2, 7, 12, 17, 22

Accepted Answer

A) -5 
B) -3 
C) 5 
D) not arithmetic 
E) 2 
A) -5 
B) -3 
C) 5 
D) not arithmetic 
E) 2

Question 8

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.  
A2 = -4
An = -2an - 1

Accepted Answer

A) -4, 8, -16, 32, -64, 128
First differences: 12, -24, 48, -96, 192
Second differences: -36, 72, -144, 288
Neither 
B) 0, 4, 8, 16, 32, 64
First differences: 12, 24, 48, 96, 192
Second differences: -36, 72, -144, 288
Quadratic 
C) 0, 4, -8, 16, -32, 64
First differences: -36, 72, -144, 288
Second differences: 12, 24, 48, 96, 192
Linear 
D) 0, -4, 8, -16, 32, -64
First differences: 12, 24, 48, 96, 192
Second differences: -36, 72, -144, 288
Quadratic 
E) 4, -8, 16, -32, 64, -128
First differences: -36, 72, -144, 288
Second differences: 12, 24, 48, 96, 192
Neither 
A) -4, 8, -16, 32, -64, 128
First differences: 12, -24, 48, -96, 192
Second differences: -36, 72, -144, 288
Neither 
B) 0, 4, 8, 16, 32, 64
First differences: 12, 24, 48, 96, 192
Second differences: -36, 72, -144, 288
Quadratic 
C) 0, 4, -8, 16, -32, 64
First differences: -36, 72, -144, 288
Second differences: 12, 24, 48, 96, 192
Linear 
D) 0, -4, 8, -16, 32, -64
First differences: 12, 24, 48, 96, 192
Second differences: -36, 72, -144, 288
Quadratic 
E) 4, -8, 16, -32, 64, -128
First differences: -36, 72, -144, 288
Second differences: 12, 24, 48, 96, 192
Neither

Question 9

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 28 } { 40 }$

Accepted Answer

A)   $\frac { 7 } { 10 }$ 
B)  1 
C)   $\frac { 3 } { 20 }$ 
D)  0 
E)   $\frac { 3 } { 10 }$ 
A)   $\frac { 7 } { 10 }$ 
B)  1 
C)   $\frac { 3 } { 20 }$ 
D)  0 
E)   $\frac { 3 } { 10 }$

Question 10

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 3, 8, 13, 18, 23

Accepted Answer

A)  $a _ { n } = - 2 n + 5$ 
B)  $a _ { n } = ( - 1 ) ^ { n } ( 5 n - 2 )$ 
C)  $a _ { n } = 5 n$ 
D)  $a _ { n } = 5 ^ { n } - 2$ 
E)  $a _ { n } = 5 n - 2$ 
A)  $a _ { n } = - 2 n + 5$ 
B)  $a _ { n } = ( - 1 ) ^ { n } ( 5 n - 2 )$ 
C)  $a _ { n } = 5 n$ 
D)  $a _ { n } = 5 ^ { n } - 2$ 
E)  $a _ { n } = 5 n - 2$

Question 11

Use mathematical induction to solve for all positive integers n.  
A factor of $\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)$ is:

Accepted Answer

A) 7 
B) 9 
C) 8 
D) 6 
E) 3 
A) 7 
B) 9 
C) 8 
D) 6 
E) 3

Question 12

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 6.3 million in 2007 and let $a = 6.3 \%$ , $b = 20.5 \%$ , $c = 11.6 \%$ and $d = 13.3 \%$ .Find the probability that a person 25 years or older selected at random has earned a Bachelor's degree or higher.

Accepted Answer

A) 3.321 
B) 2.321 
C) 4.321 
D) 0.321 
E) 1.321 
A) 3.321 
B) 2.321 
C) 4.321 
D) 0.321 
E) 1.321

Question 13

Determine the number of ways a computer can randomly generate the integers that is divisible by 4 from 1 through 40.

Accepted Answer

A) 14 
B) 12 
C) 10 
D) 6 
E) 8 
A) 14 
B) 12 
C) 10 
D) 6 
E) 8

Question 14

Select the first five terms of the sequence.(Assume that n begins with 1.)  $a _ { n } = \left( \frac { 1 } { 5 } \right) ^ { n }$

Accepted Answer

A)  $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 15 } , \frac { 1 } { 125 } , \frac { 1 } { 25 }$ 
B)  $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 125 } , \frac { 1 } { 20 } , \frac { 1 } { 3125 }$ 
C)  $\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \frac { 1 } { 3125 }$ 
D)  $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 15 } , \frac { 1 } { 20 } , \frac { 1 } { 25 }$ 
E)  $1 , \frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 }$ 
A)  $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 15 } , \frac { 1 } { 125 } , \frac { 1 } { 25 }$ 
B)  $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 125 } , \frac { 1 } { 20 } , \frac { 1 } { 3125 }$ 
C)  $\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \frac { 1 } { 3125 }$ 
D)  $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 15 } , \frac { 1 } { 20 } , \frac { 1 } { 25 }$ 
E)  $1 , \frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 }$

Question 15

Use mathematical induction to solve for all positive integers n.   $3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?$

Accepted Answer

A)  $\frac { n } { 6 } ( 5 n + 1 )$ 
B)  $n ( 5 n + 1 )$ 
C)  $\frac { n } { 2 } ( 5 n + 1 )$ 
D)  $\frac { n } { 4 } ( 5 n + 1 )$ 
E)  $5 n + 1$ 
A)  $\frac { n } { 6 } ( 5 n + 1 )$ 
B)  $n ( 5 n + 1 )$ 
C)  $\frac { n } { 2 } ( 5 n + 1 )$ 
D)  $\frac { n } { 4 } ( 5 n + 1 )$ 
E)  $5 n + 1$

Question 16

Determine the sample space for the experiment.
Three prize winners are selected from six people: A, B, C, D, E, and F.

Accepted Answer

S = {ABC, ABD, ABE, ABF, ACD,

Question 17

Use a calculator to find the sum.Round to four decimal places. $\sum _ { k = 3 } ^ { 9 } \frac { 3 } { k + 1 }$

Accepted Answer

A) 5.7869 
B) 8.7869 
C) 0.3 
D) 3.2869 
E) 2.9869 
A) 5.7869 
B) 8.7869 
C) 0.3 
D) 3.2869 
E) 2.9869

Question 18

A college needs two additional faculty members: a chemist and a statistician.In how many ways can these positions be filled if there are three applicants for the chemistry position and four applicants for the statistics position?

Accepted Answer

A) 10 
B) 11 
C) 16 
D) 14 
E) 12 
A) 10 
B) 11 
C) 16 
D) 14 
E) 12

Question 19

Simplify the factorial expression. $\frac { 12 ! } { 9 ! }$

Accepted Answer

A)  $11880 
B)  1320 
C)   $\frac { 4 } { 3 }$ 
D)  132 
E)  $17160 
A)  $11880 
B)  1320 
C)   $\frac { 4 } { 3 }$ 
D)  132 
E)  $17160

Question 20

Select the first five terms of the sequence.(Assume that n begins with 1.)  $a _ { n } = \frac { 8 ^ { n } } { 3 ^ { n } }$

Accepted Answer

A)  $\frac { 8 } { 27 } , \frac { 64 } { 9 } , \frac { 512 } { 3 } , \frac { 4,096 } { 9 } , \frac { 32,768 } { 27 }$ 
B)   $\frac { 8 } { 9 } , \frac { 64 } { 27 } , \frac { 512 } { 81 } , \frac { 4,096 } { 243 } , \frac { 32,768 } { 3 }$ 
C)  $\frac { 64 } { 3 } , \frac { 512 } { 9 } , \frac { 4,096 } { 27 } , \frac { 32,768 } { 81 } , \frac { 8 } { 243 }$ 
D)  $\frac { 3 } { 8 } , \frac { 9 } { 64 } , \frac { 27 } { 512 } , \frac { 81 } { 4,096 } , \frac { 243 } { 32,768 }$ 
E)  $\frac { 8 } { 3 } , \frac { 64 } { 9 } , \frac { 512 } { 27 } , \frac { 4,096 } { 81 } , \frac { 32,768 } { 243 }$ 
A)  $\frac { 8 } { 27 } , \frac { 64 } { 9 } , \frac { 512 } { 3 } , \frac { 4,096 } { 9 } , \frac { 32,768 } { 27 }$ 
B)   $\frac { 8 } { 9 } , \frac { 64 } { 27 } , \frac { 512 } { 81 } , \frac { 4,096 } { 243 } , \frac { 32,768 } { 3 }$ 
C)  $\frac { 64 } { 3 } , \frac { 512 } { 9 } , \frac { 4,096 } { 27 } , \frac { 32,768 } { 81 } , \frac { 8 } { 243 }$ 
D)  $\frac { 3 } { 8 } , \frac { 9 } { 64 } , \frac { 27 } { 512 } , \frac { 81 } { 4,096 } , \frac { 243 } { 32,768 }$ 
E)  $\frac { 8 } { 3 } , \frac { 64 } { 9 } , \frac { 512 } { 27 } , \frac { 4,096 } { 81 } , \frac { 32,768 } { 243 }$

Use the Binomial Theorem to expand and simplify the expression. $( a + 7 ) ^ { 5 }$

Determine whether the sequence is geometric.If so, find the common ratio. -2, 2, 6, 10,...

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. =4 =

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 16 } n$

Expand the binomial by using Pascal's Triangle to determine the coefficients. $( 2 t - s ) ^ { 5 }$

Select the first five terms of the sequence defined recursively. $a _ { 1 } = 23 , a _ { k + 1 } = a _ { k } + 3$

Determine whether the sequence is arithmetic.If so, find the common difference. 2, 7, 12, 17, 22

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. A₂ = -4 A_n = -2an_{- 1}

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 28 } { 40 }$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 3, 8, 13, 18, 23

Use mathematical induction to solve for all positive integers n. A factor of $\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)$ is:

Determine the number of ways a computer can randomly generate the integers that is divisible by 4 from 1 through 40.

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \left( \frac { 1 } { 5 } \right) ^ { n }$

Use mathematical induction to solve for all positive integers n. $3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?$

Determine the sample space for the experiment. Three prize winners are selected from six people: A, B, C, D, E, and F.

Use a calculator to find the sum.Round to four decimal places. $\sum _ { k = 3 } ^ { 9 } \frac { 3 } { k + 1 }$

A college needs two additional faculty members: a chemist and a statistician.In how many ways can these positions be filled if there are three applicants for the chemistry position and four applicants for the statistics position?

Simplify the factorial expression. $\frac { 12 ! } { 9 ! }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { 8 ^ { n } } { 3 ^ { n } }$

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

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Exam 9: Sequences Series and Probability

Use the Binomial Theorem to expand and simplify the expression. (a+7)5( a + 7 ) ^ { 5 }(a+7)5

Determine whether the sequence is geometric.If so, find the common ratio. -2, 2, 6, 10,...

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. =4 =

Find the sum using the formulas for the sums of powers of integers. ∑n=116n\sum _ { n = 1 } ^ { 16 } n∑n=116​n

Expand the binomial by using Pascal's Triangle to determine the coefficients. (2t−s)5( 2 t - s ) ^ { 5 }(2t−s)5

Select the first five terms of the sequence defined recursively. a1=23,ak+1=ak+3a _ { 1 } = 23 , a _ { k + 1 } = a _ { k } + 3a1​=23,ak+1​=ak​+3

Determine whether the sequence is arithmetic.If so, find the common difference. 2, 7, 12, 17, 22

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. A2 = -4 An = -2an - 1

You are given the probability that an event will not happen.Find the probability that the event will happen. P(E)=2840P ( E ) = \frac { 28 } { 40 }P(E)=4028​

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 3, 8, 13, 18, 23

Use mathematical induction to solve for all positive integers n. A factor of (n3+7n2+6n)\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)(n3+7n2+6n) is:

Determine the number of ways a computer can randomly generate the integers that is divisible by 4 from 1 through 40.

Select the first five terms of the sequence.(Assume that n begins with 1.) an=(15)na _ { n } = \left( \frac { 1 } { 5 } \right) ^ { n }an​=(51​)n

Use mathematical induction to solve for all positive integers n. 3+8+13+18+…+(5n−2)=?3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?3+8+13+18+…+(5n−2)=?

Determine the sample space for the experiment. Three prize winners are selected from six people: A, B, C, D, E, and F.

Use a calculator to find the sum.Round to four decimal places. ∑k=393k+1\sum _ { k = 3 } ^ { 9 } \frac { 3 } { k + 1 }∑k=39​k+13​

A college needs two additional faculty members: a chemist and a statistician.In how many ways can these positions be filled if there are three applicants for the chemistry position and four applicants for the statistics position?

Simplify the factorial expression. 12!9!\frac { 12 ! } { 9 ! }9!12!​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=8n3na _ { n } = \frac { 8 ^ { n } } { 3 ^ { n } }an​=3n8n​

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

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Use the Binomial Theorem to expand and simplify the expression. $( a + 7 ) ^ { 5 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 16 } n$

Expand the binomial by using Pascal's Triangle to determine the coefficients. $( 2 t - s ) ^ { 5 }$

Select the first five terms of the sequence defined recursively. $a _ { 1 } = 23 , a _ { k + 1 } = a _ { k } + 3$

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. A₂ = -4 A_n = -2an_{- 1}

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 28 } { 40 }$

Use mathematical induction to solve for all positive integers n. A factor of $\left( n ^ { 3 } + 7 n ^ { 2 } + 6 n \right)$ is:

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \left( \frac { 1 } { 5 } \right) ^ { n }$

Use mathematical induction to solve for all positive integers n. $3 + 8 + 13 + 18 + \ldots + ( 5 n - 2 ) = ?$

Use a calculator to find the sum.Round to four decimal places. $\sum _ { k = 3 } ^ { 9 } \frac { 3 } { k + 1 }$

Simplify the factorial expression. $\frac { 12 ! } { 9 ! }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { 8 ^ { n } } { 3 ^ { n } }$