Algebra Exam 8

Write the first four terms of the following sequence whose general term is given. an = 3n + 2

 

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A. 4, 6, 10, 14

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B. 6, 9, 12, 15

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C. 5, 8, 11, 14

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D. 7, 8, 12, 15

 

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?

 

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A. 32,957,326 selections

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B. 22,957,480 selections

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C. 28,957,680 selections

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D. 225,857,480 selections

 

 

A club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

 

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A. 650 ways

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B. 720 ways

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C. 830 ways

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D. 675 ways

 

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 . . .

 

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A. 1045

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B. 2108

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C. 10478

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D. 2049

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

 

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A. 20 ways

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B. 30 ways

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C. 10 ways

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D. 15 ways

 

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

 

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A. x8 + 8×6 y + 24×4 y2 + 32×2 y3 + 16y4

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B. x8 + 8×6 y + 20×4 y2 + 30×2 y3 + 15y4

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C. x8 + 18×6 y + 34×4 y2 + 42×2 y3 + 16y4

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D. x8 + 8×6 y + 14×4 y2 + 22×2 y3 + 26y4

 

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

 

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A. ≈ 0.31

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B. ≈ 0.42

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C. ≈ 0.45

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D. ≈ 0.41

 

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

 

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A. 4, 15, 35, 453

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B. 4, 11, 15, 13

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C. 4, 11, 25, 53

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D. 3, 19, 22, 53

 

Use the Binomial Theorem to expand the following binomial and express the result in simplified form. (2×3 – 1)4

 

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A. 14×12 – 22×9 + 14×6 – 6×3 + 1

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B. 16×12 – 32×9 + 24×6 – 8×3 + 1

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C. 15×12 – 16×9 + 34×6 – 10×3 + 1

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D. 26×12 – 42×9 + 34×6 – 18×3 + 1

 

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 __________.”

 

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A.

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

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B.

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

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C.

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

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D.

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

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

 

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A. ≈ 0.07

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B. ≈ 0.02

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C. ≈ 0.01

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D. ≈ 0.001

 

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

 

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A. 40, 30, 20, 0, -20, -10

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B. 60, 40, 30, 0, -15, -10

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C. 20, 10, 0, 0, -15, -20

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D. 30, 20, 10, 0, -10, -20

 

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

 

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A. 3, 9, 27, 81

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B. 4, 10, 23, 91

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C. 5, 9, 17, 31

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D. 4, 10, 22, 41

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

 

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A. 865

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B. 955

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C. 678

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D. 895

 

Use the Binomial Theorem to find a polynomial expansion for the following function. f1(x) = (x – 2)4

 

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A. f1(x) = x4 – 5×3 + 14×2 – 42x + 26

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B. f1(x) = x4 – 16×3 + 18×2 – 22x + 18

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C. f1(x) = x4 – 18×3 + 24×2 – 28x + 16

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D. f1(x) = x4 – 8×3 + 24×2 – 32x + 16

 

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

 

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A. -4, 9, -25, 31

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B. -5, 9, -27, 41

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C. -2, 8, -17, 81

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D. -3, 9, -27, 81

 

The following are defined using recursion formulas. Write the first four terms of each sequence.  a1 = 7 and an = an-1 + 5 for n ≥ 2

 

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A. 8, 13, 21, 22

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B. 7, 12, 17, 22

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C. 6, 14, 18, 21

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D. 4, 11, 17, 20

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

 

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A. 365/365 * 365/364 * 363/365 ≈ 0.98

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B. 365/364 * 364/365 * 363/364 ≈ 0.99

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C. 365/365 * 365/363 * 363/365 ≈ 0.99

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D. 365/365 * 364/365 * 363/365 ≈ 0.99

 

Write the first six terms of the following arithmetic sequence. an = an-1 – 0.4, a1 = 1.6

 

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A. 1.6, 1.2, 0.8, 0.4, 0, -0.4

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B. 1.6, 1.4, 0.9, 0.3, 0, -0.3

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C. 1.6, 2.2, 1.8, 1.4, 0, -1.4

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D. 1.3, 1.5, 0.8, 0.6, 0, -0.6

 

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 . . .

 

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A. 531,440

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B. 535,450

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C. 535,445

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D. 431,440

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