Question 1

Calculate the binomial coefficient: ${ } _ { 4 } C _ { 3 }$

Accepted Answer

A) 12 
B) 24 
C) 0 
D) 4 
E) 1 
A) 12 
B) 24 
C) 0 
D) 4 
E) 1

Question 2

Determine the number of ways a computer can randomly generate the even integers from 1 through 30. ​

Accepted Answer

A) 17 
B) 13 
C) 15 
D) 11 
E) 19 
A) 17 
B) 13 
C) 15 
D) 11 
E) 19

Question 3

Determine whether the sequence is arithmetic.If so, find the common difference.  
 5,3, 5.7, 6.1, 6.5, 6.9, ...

Accepted Answer

A) Arithmetic sequence, d = -0.4 
B) Arithmetic sequence, d = -1.6 
C) Arithmetic sequence, d = 0.8 
D) Arithmetic sequence, d = 0.4 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = -0.4 
B) Arithmetic sequence, d = -1.6 
C) Arithmetic sequence, d = 0.8 
D) Arithmetic sequence, d = 0.4 
E) Not an arithmetic sequence

Question 4

At a high school cafeteria, diners can choose one vegetable from a choice of 3 vegetables, one meat from a choice of 3 meats, one serving of bread from among 2 breads, and a dessert from among 2 desserts.How many meal configurations are possible?

Accepted Answer

A) 18 
B) 4 
C) 36 
D) 10 
E) 12 
A) 18 
B) 4 
C) 36 
D) 10 
E) 12

Question 5

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

Accepted Answer

A)  $- 5,25 , - 15,625 , - 25$ 
B)  $- 5,25 , - 125,625 , - 3125$ 
C)  $1 , - 5,25 , - 125,625$ 
D)  $- 5 , - 10 , - 15 , - 125 , - 25$ 
E)  $- 5 , - 10 , - 15 , - 20 , - 25$ 
A)  $- 5,25 , - 15,625 , - 25$ 
B)  $- 5,25 , - 125,625 , - 3125$ 
C)  $1 , - 5,25 , - 125,625$ 
D)  $- 5 , - 10 , - 15 , - 125 , - 25$ 
E)  $- 5 , - 10 , - 15 , - 20 , - 25$

Question 6

Write the first five terms of the arithmetic sequence. ​
A1 = 8, d = 8
​

Accepted Answer

A) 16, 24, 32, 40, 8 
B) 8, 16, 24, 32, 48 
C) 8, 16, 24, 32, 40 
D) 16, 24, 32, 40, 48 
E) 8, 0, 24, 32, 40 
A) 16, 24, 32, 40, 8 
B) 8, 16, 24, 32, 48 
C) 8, 16, 24, 32, 40 
D) 16, 24, 32, 40, 48 
E) 8, 0, 24, 32, 40

Question 7

Write the first five terms of the arithmetic sequence. ​
A1 = -3.6, d = -0.6
​

Accepted Answer

A) 4.2, 4.8, 5.4, 6, 6.6 
B) -3.6, -4.2, -4.8, -5.4, -6 
C) 3.6, 4.2, 4.8, 5.4, 6 
D) -4.2, -4.8, -5.4, -6, -6.6 
E) 3.6, 4.2, 4.8, 5.4, 6.6 
A) 4.2, 4.8, 5.4, 6, 6.6 
B) -3.6, -4.2, -4.8, -5.4, -6 
C) 3.6, 4.2, 4.8, 5.4, 6 
D) -4.2, -4.8, -5.4, -6, -6.6 
E) 3.6, 4.2, 4.8, 5.4, 6.6

Question 8

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = \frac { n + 11 } { n }$

Accepted Answer

A)  $11,12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 }$ 
B)  $- 12 , \frac { 13 } { 2 } , - \frac { 14 } { 3 } , \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
C)  $12 , - \frac { 13 } { 2 } , - \frac { 14 } { 3 } , - \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
D)  $12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 } , \frac { 16 } { 5 }$ 
E)  $\frac { 1 } { 12 } , \frac { 1 } { 13 } , \frac { 1 } { 14 } , \frac { 1 } { 15 } , \frac { 1 } { 16 }$ 
A)  $11,12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 }$ 
B)  $- 12 , \frac { 13 } { 2 } , - \frac { 14 } { 3 } , \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
C)  $12 , - \frac { 13 } { 2 } , - \frac { 14 } { 3 } , - \frac { 15 } { 4 } , - \frac { 16 } { 5 }$ 
D)  $12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 } , \frac { 16 } { 5 }$ 
E)  $\frac { 1 } { 12 } , \frac { 1 } { 13 } , \frac { 1 } { 14 } , \frac { 1 } { 15 } , \frac { 1 } { 16 }$

Question 9

Select the first five terms of the sequence.(Assume that n begins with 1.)    $a _ { n } = \frac { 8 } { 5 }$

Accepted Answer

A)  $- \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 }$ 
B)  $- \frac { 5 } { 8 } , \frac { 5 } { 8 } , - \frac { 5 } { 8 } , \frac { 5 } { 8 } , - \frac { 5 } { 8 }$ 
C)  $\frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 }$ 
D) 0, 1, 2, 3, 4 
E)  $\frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 }$ 
A)  $- \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 }$ 
B)  $- \frac { 5 } { 8 } , \frac { 5 } { 8 } , - \frac { 5 } { 8 } , \frac { 5 } { 8 } , - \frac { 5 } { 8 }$ 
C)  $\frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 }$ 
D) 0, 1, 2, 3, 4 
E)  $\frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 }$

Question 10

You are given the probability that an event will not happen.Find the probability that the event will happen.   $P \left( E ^ { \prime } \right) = 0.75$

Accepted Answer

A) 0.4 
B) 0.25 
C) 0.35 
D) 0.3 
E) 0.45 
A) 0.4 
B) 0.25 
C) 0.35 
D) 0.3 
E) 0.45

Question 11

Write the first five terms of the geometric sequence. $a _ { 1 } = - 5 , r = \frac { 1 } { 8 }$

Accepted Answer

A)  $- 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 }$ 
B)  $1 , - 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 }$ 
C) -5, -40, -320, -2,560, -20,480 
D) -5, 3, 11, 19, 27 
E)  $- \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 } , - \frac { 5 } { 32,768 }$ 
A)  $- 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 }$ 
B)  $1 , - 5 , - \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 }$ 
C) -5, -40, -320, -2,560, -20,480 
D) -5, 3, 11, 19, 27 
E)  $- \frac { 5 } { 8 } , - \frac { 5 } { 64 } , - \frac { 5 } { 512 } , - \frac { 5 } { 4,096 } , - \frac { 5 } { 32,768 }$

Question 12

Calculate the binomial coefficient.   $\left( \frac { 12 } { 8 } \right)$

Accepted Answer

A) 496 
B) 493 
C) 498 
D) 497 
E) 495 
A) 496 
B) 493 
C) 498 
D) 497 
E) 495

Question 13

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually. ​

Accepted Answer

A) $3261.79 
B) $3258.79 
C) $3259.79 
D) $3257.79 
E) $3260.79 
A) $3261.79 
B) $3258.79 
C) $3259.79 
D) $3257.79 
E) $3260.79

Question 14

Find the sum of the finite arithmetic sequence. ​
3 + 7 + 11 + 15 + 19 + 23 + 27
​

Accepted Answer

A) 107 
B) 109 
C) 105 
D) 1105 
E) 113 
A) 107 
B) 109 
C) 105 
D) 1105 
E) 113

Question 15

The first two terms of the arithmetic sequence are given.Find the missing term.  
A1 = 2.2, a2 = 3.6, a7 =

Accepted Answer

A) 13.4 
B) 12 
C) 16.2 
D) 9.2 
E) 10.6 
A) 13.4 
B) 12 
C) 16.2 
D) 9.2 
E) 10.6

Question 16

There are 15 patients in Dr.Ziglar's waiting room.Dr.Ziglar can see 6 patients before lunch.In how many different orders can Dr.Ziglar see 6 of the patients before lunch?

Accepted Answer

A) 90 
B) 6 
C) 1,816,214,400 
D) 3,603,600 
E) 5,005 
A) 90 
B) 6 
C) 1,816,214,400 
D) 3,603,600 
E) 5,005

Question 17

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 14 } n ^ { 3 }$

Accepted Answer

A) 6,090 
B) 105 
C) 11,025 
D) 1,015 
E) 210 
A) 6,090 
B) 105 
C) 11,025 
D) 1,015 
E) 210

Question 18

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 8.0 million in 2007 and let $a = 8.0 \%$ , $b = 19.9 \%$ and $c = 9.5 \%$ .Find the probability that a person 25 years or older selected at random has earned a Bachelor's degree or higher.

Accepted Answer

A) 0.294 
B) 1.294 
C) 4.294 
D) 2.294 
E) 3.294 
A) 0.294 
B) 1.294 
C) 4.294 
D) 2.294 
E) 3.294

Question 19

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 22 } \left( n ^ { 3 } - n \right)$

Accepted Answer

A) 22,770 
B) 3,795 
C) 63,756 
D) 256,036 
E) 64,009 
A) 22,770 
B) 3,795 
C) 63,756 
D) 256,036 
E) 64,009

Question 20

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly. ​

Accepted Answer

A) $8137.92 
B) $8135.92 
C) $8139.92 
D) $8136.92 
E) $8138.92 
A) $8137.92 
B) $8135.92 
C) $8139.92 
D) $8136.92 
E) $8138.92

Calculate the binomial coefficient: ${ } _ { 4 } C _ { 3 }$

Determine the number of ways a computer can randomly generate the even integers from 1 through 30.

Determine whether the sequence is arithmetic.If so, find the common difference. 5,3, 5.7, 6.1, 6.5, 6.9, ...

At a high school cafeteria, diners can choose one vegetable from a choice of 3 vegetables, one meat from a choice of 3 meats, one serving of bread from among 2 breads, and a dessert from among 2 desserts.How many meal configurations are possible?

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

Write the first five terms of the arithmetic sequence. A₁ = 8, d = 8

Write the first five terms of the arithmetic sequence. A₁ = -3.6, d = -0.6

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { n + 11 } { n }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { 8 } { 5 }$

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.75$

Write the first five terms of the geometric sequence. $a _ { 1 } = - 5 , r = \frac { 1 } { 8 }$

Calculate the binomial coefficient. $\left( \frac { 12 } { 8 } \right)$

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually.

Find the sum of the finite arithmetic sequence. 3 + 7 + 11 + 15 + 19 + 23 + 27

The first two terms of the arithmetic sequence are given.Find the missing term. A₁ = 2.2, a₂ = 3.6, a₇ =

There are 15 patients in Dr.Ziglar's waiting room.Dr.Ziglar can see 6 patients before lunch.In how many different orders can Dr.Ziglar see 6 of the patients before lunch?

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 14 } n ^ { 3 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 22 } \left( n ^ { 3 } - n \right)$

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly.

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

Calculate the binomial coefficient: 4C3{ } _ { 4 } C _ { 3 }4​C3​

Determine the number of ways a computer can randomly generate the even integers from 1 through 30. ​

Determine whether the sequence is arithmetic.If so, find the common difference. 5,3, 5.7, 6.1, 6.5, 6.9, ...

At a high school cafeteria, diners can choose one vegetable from a choice of 3 vegetables, one meat from a choice of 3 meats, one serving of bread from among 2 breads, and a dessert from among 2 desserts.How many meal configurations are possible?

Select the first five terms of the sequence.(Assume that n begins with 1.) an=(−5)na _ { n } = ( - 5 ) ^ { n }an​=(−5)n

Write the first five terms of the arithmetic sequence. ​ A1 = 8, d = 8 ​

Write the first five terms of the arithmetic sequence. ​ A1 = -3.6, d = -0.6 ​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=n+11na _ { n } = \frac { n + 11 } { n }an​=nn+11​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=85a _ { n } = \frac { 8 } { 5 }an​=58​

You are given the probability that an event will not happen.Find the probability that the event will happen. P(E′)=0.75P \left( E ^ { \prime } \right) = 0.75P(E′)=0.75

Write the first five terms of the geometric sequence. a1=−5,r=18a _ { 1 } = - 5 , r = \frac { 1 } { 8 }a1​=−5,r=81​

Calculate the binomial coefficient. (128)\left( \frac { 12 } { 8 } \right)(812​)

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually. ​

Find the sum of the finite arithmetic sequence. ​ 3 + 7 + 11 + 15 + 19 + 23 + 27 ​

The first two terms of the arithmetic sequence are given.Find the missing term. A1 = 2.2, a2 = 3.6, a7 =

There are 15 patients in Dr.Ziglar's waiting room.Dr.Ziglar can see 6 patients before lunch.In how many different orders can Dr.Ziglar see 6 of the patients before lunch?

Find the sum using the formulas for the sums of powers of integers. ∑n=114n3\sum _ { n = 1 } ^ { 14 } n ^ { 3 }∑n=114​n3

Find the sum using the formulas for the sums of powers of integers. ∑n=122(n3−n)\sum _ { n = 1 } ^ { 22 } \left( n ^ { 3 } - n \right)∑n=122​(n3−n)

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly. ​

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

Calculate the binomial coefficient: ${ } _ { 4 } C _ { 3 }$

Determine the number of ways a computer can randomly generate the even integers from 1 through 30.

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

Write the first five terms of the arithmetic sequence. A₁ = 8, d = 8

Write the first five terms of the arithmetic sequence. A₁ = -3.6, d = -0.6

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { n + 11 } { n }$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { 8 } { 5 }$

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.75$

Write the first five terms of the geometric sequence. $a _ { 1 } = - 5 , r = \frac { 1 } { 8 }$

Calculate the binomial coefficient. $\left( \frac { 12 } { 8 } \right)$

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually.

Find the sum of the finite arithmetic sequence. 3 + 7 + 11 + 15 + 19 + 23 + 27

The first two terms of the arithmetic sequence are given.Find the missing term. A₁ = 2.2, a₂ = 3.6, a₇ =

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 14 } n ^ { 3 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 22 } \left( n ^ { 3 } - n \right)$

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly.