algebra exam 8 - norman93 only!

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Question 1 of 20

5.0 Points

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.  an = an-1 - 10, a1 = 30

 

A. an = 60 - 10n; a = -260

 

B. an = 70 - 10n; a = -50

 

C. an = 40 - 10n; a = -160

 

D. an = 10 - 10n; a = -70

Question 2 of 20

5.0 Points

Use the Binomial Theorem to expand the following binomial and express the result in simplified form. (2x3 - 1)4

 

A. 14x12 - 22x9 + 14x6 - 6x3 + 1

 

B. 16x12 - 32x9 + 24x6 - 8x3 + 1

 

C. 15x12 - 16x9 + 34x6 - 10x3 + 1

 

D. 26x12 - 42x9 + 34x6 - 18x3 + 1

Question 3 of 20

5.0 Points

Write the first six terms of the following arithmetic sequence.  an = an-1 + 6, a1 = -9

 

A. -9, -3, 3, 9, 15, 21

 

B. -11, -4, 3, 9, 17, 21

 

C. -8, -3, 3, 9, 16, 22

 

D. -9, -5, 3, 11, 15, 27

Question 4 of 20

5.0 Points

Use the Binomial Theorem to expand the following binomial and express the result in simplified form. (x2 + 2y)4

 

A. x8 + 8x6 y + 24x4 y2 + 32x2 y3 + 16y4

 

B. x8 + 8x6 y + 20x4 y2 + 30x2 y3 + 15y4

 

C. x8 + 18x6 y + 34x4 y2 + 42x2 y3 + 16y4

 

D. x8 + 8x6 y + 14x4 y2 + 22x2 y3 + 26y4

Question 5 of 20

5.0 Points

How large a group is needed to give a 0.5 chance of at least two people having the same birthday?

 

A. 13 people

 

B. 23 people

 

C. 47 people

 

D. 28 people

Question 6 of 20

5.0 Points

Write the first six terms of the following arithmetic sequence. an = an-1 - 10, a1 = 30

 

A. 40, 30, 20, 0, -20, -10

 

B. 60, 40, 30, 0, -15, -10

 

C. 20, 10, 0, 0, -15, -20

 

D. 30, 20, 10, 0, -10, -20

Question 7 of 20

5.0 Points

Write the first six terms of the following arithmetic sequence. a1 = 5/2, d = - ½

 

A. 3/2, 2, 1/2, 1, 1/4, 0

 

B. 7/2, 2, 5/2, 1 ,3/2, 0

 

C. 5/2, 2, 3/2, 1, 1/2, 0

 

D. 9/2, 2, 5/2, 1, 1/2, 0

Question 8 of 20

5.0 Points

The following are defined using recursion formulas. Write the first four terms of each sequence.   a1 = 4 and an = 2an-1 + 3 for n ≥ 2

 

A. 4, 15, 35, 453

 

B. 4, 11, 15, 13

 

C. 4, 11, 25, 53

 

D. 3, 19, 22, 53

Question 9 of 20

5.0 Points

Consider the statement "2 is a factor of n2 + 3n." If n = 1, the statement is "2 is a factor of __________." If n = 2, the statement is "2 is a factor of __________." If n = 3, the statement is "2 is a factor of __________." If n = k + 1, the statement before the algebra is simplified is "2 is a factor of __________." If n = k + 1, the statement after the algebra is simplified is "2 is a factor of __________."

 

A.

4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 8

 

B.

4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7

 

C.

4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4

 

D.

4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 6

Question 10 of 20

5.0 Points

If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.

 

A. ≈ 0.31

 

B. ≈ 0.42

 

C. ≈ 0.45

 

D. ≈ 0.41

Question 11 of 20

5.0 Points

The following are defined using recursion formulas. Write the first four terms of each sequence. a1 = 3 and an = 4an-1 for n ≥ 2

 

A. 3, 12, 48, 192

 

B. 4, 11, 58, 92

 

C. 3, 14, 79, 123

 

D. 5, 14, 47, 177

Question 12 of 20

5.0 Points

Use the formula for the sum of the first n terms of a geometric sequence to solve the following. Find the sum of the first 11 terms of the geometric sequence: 3, -6, 12, -24 . . .

 

A. 1045

 

B. 2108

 

C. 10478

 

D. 2049

Question 13 of 20

5.0 Points

You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

 

A. 32,317 groups

 

B. 23,330 groups

 

C. 24,310 groups

 

D. 25,410 groups

Question 14 of 20

5.0 Points

Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.  Find a6 when a1 = 13, d = 4

 

A. 36

 

B. 63

 

C. 43

 

D. 33

Question 15 of 20

5.0 Points

Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.  Find a200 when a1 = -40, d = 5

 

A. 865

 

B. 955

 

C. 678

 

D. 895

Question 16 of 20

5.0 Points

To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

 

A. 32,957,326 selections

 

B. 22,957,480 selections

 

C. 28,957,680 selections

 

D. 225,857,480 selections

Question 17 of 20

5.0 Points

Use the formula for the sum of the first n terms of a geometric sequence to solve the following. Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54 . . .

 

A. 531,440

 

B. 535,450

 

C. 535,445

 

D. 431,440

Question 18 of 20

5.0 Points

Write the first four terms of the following sequence whose general term is given. an = (-3)n

 

A. -4, 9, -25, 31

 

B. -5, 9, -27, 41

 

C. -2, 8, -17, 81

 

Question 19 of 20

5.0 Points

If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)

 

A. The first person can have any birthday in the year. The second person can have all but one birthday.

 

B. The second person can have any birthday in the year. The first person can have all but one birthday.

 

C. The first person cannot a birthday in the year. The second person can have all but one birthday.

 

D. The first person can have any birthday in the year. The second cannot have all but one birthday.

Question 20 of 20

5.0 Points

If three people are selected at random, find the probability that they all have different birthdays.

 

A. 365/365 * 365/364 * 363/365 ≈ 0.98

 

B. 365/364 * 364/365 * 363/364 ≈ 0.99

 

C. 365/365 * 365/363 * 363/365 ≈ 0.99

 

D. 365/365 * 364/365 * 363/365 ≈ 0.99