Question 1

Find the specified nth term in the expansion of the binomial.   $( x - 8 y ) ^ { 5 } , n = 3$

Accepted Answer

A)  $640 x ^ { 5 } y ^ { 3 }$ 
B)  $640 x ^ { 3 } y ^ { 2 }$ 
C)  $640 x ^ { 2 } y ^ { 2 }$ 
D)  $640 x ^ { 3 } y ^ { 3 }$ 
E)  $640 x ^ { 2 } y ^ { 3 }$ 
A)  $640 x ^ { 5 } y ^ { 3 }$ 
B)  $640 x ^ { 3 } y ^ { 2 }$ 
C)  $640 x ^ { 2 } y ^ { 2 }$ 
D)  $640 x ^ { 3 } y ^ { 3 }$ 
E)  $640 x ^ { 2 } y ^ { 3 }$

Question 2

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible? ​

Accepted Answer

A) 33,522,128,640 
B) 33,523,128,640 
C) 33,522,628,640 
D) 33,572,128,640 
E) 33,532,128,640 
A) 33,522,128,640 
B) 33,523,128,640 
C) 33,522,628,640 
D) 33,572,128,640 
E) 33,532,128,640

Question 3

Find pk + 1 for the given pk.   $p _ { k } = \frac { 6 } { k ( k + 1 ) }$

Accepted Answer

A)  $p _ { k + 1 } = \frac { 2 } { k ( k + 2 ) }$ 
B)  $p _ { k + 1 } = \frac { 6 } { ( k + 1 ) ( k + 1 ) }$ 
C)  $p _ { k + 1 } = \frac { 6 } { ( k + 1 ) ( k + 2 ) }$ 
D)  $p _ { k + 1 } = \frac { 6 } { ( k + 2 ) ( k + 6 ) }$ 
E)  $p _ { k + 1 } = \frac { 6 } { k ( k + 2 ) }$ 
A)  $p _ { k + 1 } = \frac { 2 } { k ( k + 2 ) }$ 
B)  $p _ { k + 1 } = \frac { 6 } { ( k + 1 ) ( k + 1 ) }$ 
C)  $p _ { k + 1 } = \frac { 6 } { ( k + 1 ) ( k + 2 ) }$ 
D)  $p _ { k + 1 } = \frac { 6 } { ( k + 2 ) ( k + 6 ) }$ 
E)  $p _ { k + 1 } = \frac { 6 } { k ( k + 2 ) }$

Question 4

Find the sum of the indicated terms of the geometric sequence. ​
6, 18, 54 ...(to 8 terms)
​

Accepted Answer

A) s = 19,686 
B) s = 19,692 
C) s = 19,680 
D) s = 19,674 
E) none of the above 
A) s = 19,686 
B) s = 19,692 
C) s = 19,680 
D) s = 19,674 
E) none of the above

Question 5

You are given the probability that an event will happen.Find the probability that the event will not happen.   $P ( E ) = \frac { 1 } { 5 }$

Accepted Answer

A)  $\frac { 9 } { 5 }$ 
B)   $\frac { 3 } { 5 }$ 
C)   $\frac { 1 } { 5 }$ 
D)  $\frac { 2 } { 5 }$ 
E)  $\frac { 4 } { 5 }$ 
A)  $\frac { 9 } { 5 }$ 
B)   $\frac { 3 } { 5 }$ 
C)   $\frac { 1 } { 5 }$ 
D)  $\frac { 2 } { 5 }$ 
E)  $\frac { 4 } { 5 }$

Question 6

Evaluate: ${ } _ { 15 } P _ { 5 }$

Accepted Answer

A) 32,760 
B) 75 
C) undefined 
D) 360,360 
E) 3,003 
A) 32,760 
B) 75 
C) undefined 
D) 360,360 
E) 3,003

Question 7

Determine whether the sequence is arithmetic.If so, find the common difference.  
 4,8, 5.4, 6, 6.6, 7.2, ...

Accepted Answer

A) Arithmetic sequence, d = -0.6 
B) Arithmetic sequence, d = 7.2 
C) Arithmetic sequence, d = 1.2 
D) Arithmetic sequence, d = 0.6 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = -0.6 
B) Arithmetic sequence, d = 7.2 
C) Arithmetic sequence, d = 1.2 
D) Arithmetic sequence, d = 0.6 
E) Not an arithmetic sequence

Question 8

Find the sum of the infinite series.   $\sum _ { i = 1 } ^ { \infty } 4 \left( \frac { 1 } { 10 } \right) ^ { i }$

Accepted Answer

A)  $\frac { 4 i } { 9 }$ 
B)  $\frac { 4 } { 9 }$ 
C)  $\frac { 9 i } { 4 }$ 
D)  $- \frac { 4 i } { 9 }$ 
E)  $\frac { 9 } { 4 }$ 
A)  $\frac { 4 i } { 9 }$ 
B)  $\frac { 4 } { 9 }$ 
C)  $\frac { 9 i } { 4 }$ 
D)  $- \frac { 4 i } { 9 }$ 
E)  $\frac { 9 } { 4 }$

Question 9

Find the specified nth term in the expansion of the binomial.   $( x - 10 z ) ^ { 7 } , n = 4$

Accepted Answer

A)  $- 35,000 x ^ { 3 } z ^ { 4 }$ 
B)  $- 35,000 x ^ { 7 } z ^ { 3 }$ 
C)  $- 35,000 x ^ { 4 } z ^ { 3 }$ 
D)  $- 35,000 x ^ { 3 } z ^ { 3 }$ 
E)  $- 35,000 x ^ { 4 } z ^ { 4 }$ 
A)  $- 35,000 x ^ { 3 } z ^ { 4 }$ 
B)  $- 35,000 x ^ { 7 } z ^ { 3 }$ 
C)  $- 35,000 x ^ { 4 } z ^ { 3 }$ 
D)  $- 35,000 x ^ { 3 } z ^ { 3 }$ 
E)  $- 35,000 x ^ { 4 } z ^ { 4 }$

Question 10

Write the first five terms of the arithmetic sequence defined recursively.   $a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$

Accepted Answer

A)  $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$ 
B)  $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$ , $\frac { 7 } { 8 }$ 
C)  $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 9 } { 4 }$ , -1 
D)  $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $- \frac { 13 } { 8 }$ , -1, $\frac { 1 } { 4 }$ 
E)  $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 9 } { 4 }$ 
A)  $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$ 
B)  $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$ , $\frac { 7 } { 8 }$ 
C)  $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 9 } { 4 }$ , -1 
D)  $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $- \frac { 13 } { 8 }$ , -1, $\frac { 1 } { 4 }$ 
E)  $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 9 } { 4 }$

Question 11

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$

Accepted Answer

1) When n = 1, @#IMG-DLM& . The formula

Question 12

Find the sum. $\sum _ { i = 1 } ^ { 4 } - i + 5$

Accepted Answer

A) 1 
B) 15 
C) 10 
D) -10 
E) 9 
A) 1 
B) 15 
C) 10 
D) -10 
E) 9

Question 13

Evaluate the sum.   $\sum _ { k = 1 } ^ { 400 } 7$

Accepted Answer

A) 4 
B) 400 
C) 2,805 
D) 2,800 
E) 7 
A) 4 
B) 400 
C) 2,805 
D) 2,800 
E) 7

Question 14

How many three-digit numbers can be formed under the following condition? ​
The leading digit cannot be zero and the number must be even.
​

Accepted Answer

A) 900 
B) 450 
C) 350 
D) 400 
E) 550 
A) 900 
B) 450 
C) 350 
D) 400 
E) 550

Question 15

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { i = 1 } ^ { 7 } \left( 5 i - 8 i ^ { 3 } \right)$

Accepted Answer

A) -784 
B) -3,136 
C) 4,200 
D) 5,600 
E) -6,132 
A) -784 
B) -3,136 
C) 4,200 
D) 5,600 
E) -6,132

Question 16

Find the sum of the finite geometric sequence.  
  $\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }$

Accepted Answer

A)   $\frac { 1,225,723 } { 262,144 }$ 
B)   $\frac { 141,361 } { 262,144 }$ 
C)   $\frac { 1,068,259 } { 262,144 }$ 
D)   $- \frac { 1,225,723 } { 262,144 }$ 
E)   $- \frac { 1,068,259 } { 262,144 }$ 
A)   $\frac { 1,225,723 } { 262,144 }$ 
B)   $\frac { 141,361 } { 262,144 }$ 
C)   $\frac { 1,068,259 } { 262,144 }$ 
D)   $- \frac { 1,225,723 } { 262,144 }$ 
E)   $- \frac { 1,068,259 } { 262,144 }$

Question 17

Determine the number of ways a computer can randomly generate the integer that is divisible by 3 from 1 through 42.

Accepted Answer

A) 18 
B) 12 
C) 10 
D) 16 
E) 14 
A) 18 
B) 12 
C) 10 
D) 16 
E) 14

Question 18

Use a calculator to find the sum.Round to four decimal places. $\sum _ { k = 4 } ^ { 12 } \frac { - 1 } { k + 2 }$

Accepted Answer

A) -0.9682 
B) -2.2516 
C) -0.0714 
D) -0.8968 
E) -1.7516 
A) -0.9682 
B) -2.2516 
C) -0.0714 
D) -0.8968 
E) -1.7516

Question 19

The first two terms of the arithmetic sequence are given.Find the indicated term.   $a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =$

Accepted Answer

A) -3 
B) 69 
C) 76 
D) 83 
E) -4 
A) -3 
B) 69 
C) 76 
D) 83 
E) -4

Question 20

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$

Accepted Answer

A) 0.87 
B) 0.13 
C) 0.065 
D) 0 
E) 1 
A) 0.87 
B) 0.13 
C) 0.065 
D) 0 
E) 1

Find the specified nth term in the expansion of the binomial. $( x - 8 y ) ^ { 5 } , n = 3$

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible?

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { 6 } { k ( k + 1 ) }$

Find the sum of the indicated terms of the geometric sequence. 6, 18, 54 ...(to 8 terms)

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 1 } { 5 }$

Evaluate: ${ } _ { 15 } P _ { 5 }$

Determine whether the sequence is arithmetic.If so, find the common difference. 4,8, 5.4, 6, 6.6, 7.2, ...

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 4 \left( \frac { 1 } { 10 } \right) ^ { i }$

Find the specified nth term in the expansion of the binomial. $( x - 10 z ) ^ { 7 } , n = 4$

Write the first five terms of the arithmetic sequence defined recursively. $a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$

Find the sum. $\sum _ { i = 1 } ^ { 4 } - i + 5$

Evaluate the sum. $\sum _ { k = 1 } ^ { 400 } 7$

How many three-digit numbers can be formed under the following condition? The leading digit cannot be zero and the number must be even.

Find the sum using the formulas for the sums of powers of integers. $\sum _ { i = 1 } ^ { 7 } \left( 5 i - 8 i ^ { 3 } \right)$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }$

Determine the number of ways a computer can randomly generate the integer that is divisible by 3 from 1 through 42.

Use a calculator to find the sum.Round to four decimal places. $\sum _ { k = 4 } ^ { 12 } \frac { - 1 } { k + 2 }$

The first two terms of the arithmetic sequence are given.Find the indicated term. $a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =$ $The first two terms of the arithmetic sequence are given.Find the indicated term. a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$

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

Find the specified nth term in the expansion of the binomial. (x−8y)5,n=3( x - 8 y ) ^ { 5 } , n = 3(x−8y)5,n=3

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible? ​

Find pk + 1 for the given pk. pk=6k(k+1)p _ { k } = \frac { 6 } { k ( k + 1 ) }pk​=k(k+1)6​

Find the sum of the indicated terms of the geometric sequence. ​ 6, 18, 54 ...(to 8 terms) ​

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=15P ( E ) = \frac { 1 } { 5 }P(E)=51​

Evaluate: 15P5{ } _ { 15 } P _ { 5 }15​P5​

Determine whether the sequence is arithmetic.If so, find the common difference. 4,8, 5.4, 6, 6.6, 7.2, ...

Find the sum of the infinite series. ∑i=1∞4(110)i\sum _ { i = 1 } ^ { \infty } 4 \left( \frac { 1 } { 10 } \right) ^ { i }∑i=1∞​4(101​)i

Find the specified nth term in the expansion of the binomial. (x−10z)7,n=4( x - 10 z ) ^ { 7 } , n = 4(x−10z)7,n=4

Write the first five terms of the arithmetic sequence defined recursively. a1=78,an+1=an−58a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }a1​=87​,an+1​=an​−85​

Use mathematical induction to prove the formula for every positive integer n.Show all your work. +6+11+16+21+…+(5n+1)=n2(5n+7)+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )+6+11+16+21+…+(5n+1)=2n​(5n+7)

Find the sum. ∑i=14−i+5\sum _ { i = 1 } ^ { 4 } - i + 5∑i=14​−i+5

Evaluate the sum. ∑k=14007\sum _ { k = 1 } ^ { 400 } 7∑k=1400​7

How many three-digit numbers can be formed under the following condition? ​ The leading digit cannot be zero and the number must be even. ​

Find the sum using the formulas for the sums of powers of integers. ∑i=17(5i−8i3)\sum _ { i = 1 } ^ { 7 } \left( 5 i - 8 i ^ { 3 } \right)∑i=17​(5i−8i3)

Find the sum of the finite geometric sequence. ∑n=110(−34)n−1\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }∑n=110​(−43​)n−1

Determine the number of ways a computer can randomly generate the integer that is divisible by 3 from 1 through 42.

Use a calculator to find the sum.Round to four decimal places. ∑k=412−1k+2\sum _ { k = 4 } ^ { 12 } \frac { - 1 } { k + 2 }∑k=412​k+2−1​

The first two terms of the arithmetic sequence are given.Find the indicated term. a1=−1,a2=6,a11=a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =a1​=−1,a2​=6,a11​=

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=0.87P ( E ) = 0.87P(E)=0.87

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

Find the specified nth term in the expansion of the binomial. $( x - 8 y ) ^ { 5 } , n = 3$

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible?

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { 6 } { k ( k + 1 ) }$

Find the sum of the indicated terms of the geometric sequence. 6, 18, 54 ...(to 8 terms)

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 1 } { 5 }$

Evaluate: ${ } _ { 15 } P _ { 5 }$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 4 \left( \frac { 1 } { 10 } \right) ^ { i }$

Find the specified nth term in the expansion of the binomial. $( x - 10 z ) ^ { 7 } , n = 4$

Write the first five terms of the arithmetic sequence defined recursively. $a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$

Find the sum. $\sum _ { i = 1 } ^ { 4 } - i + 5$

Evaluate the sum. $\sum _ { k = 1 } ^ { 400 } 7$

How many three-digit numbers can be formed under the following condition? The leading digit cannot be zero and the number must be even.

Find the sum using the formulas for the sums of powers of integers. $\sum _ { i = 1 } ^ { 7 } \left( 5 i - 8 i ^ { 3 } \right)$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 10 } \left( - \frac { 3 } { 4 } \right) ^ { n - 1 }$

Use a calculator to find the sum.Round to four decimal places. $\sum _ { k = 4 } ^ { 12 } \frac { - 1 } { k + 2 }$

The first two terms of the arithmetic sequence are given.Find the indicated term. $a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =$ $The first two terms of the arithmetic sequence are given.Find the indicated term. a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$