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D. 431,440
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
How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
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A. 13 people |
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B. 23 people |
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C. 47 people |
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| D. 28 people
Write the first six terms of the following arithmetic sequence. an = an-1 + 6, a1 = -9
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A. -9, -3, 3, 9, 15, 21 |
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B. -11, -4, 3, 9, 17, 21 |
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C. -8, -3, 3, 9, 16, 22 |
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D. -9, -5, 3, 11, 15, 27
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
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
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
k2 + 3k + 2 = (k2 + k) + 2 ( __________ )
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A. k + 5 |
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B. k + 1 |
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C. k + 3 |
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D. k + 2
The following are defined using recursion formulas. Write the first four terms of each sequence. a1 = 3 and an = 4an-1 for n ≥ 2
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A. 3, 12, 48, 192 |
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B. 4, 11, 58, 92 |
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C. 3, 14, 79, 123 |
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| D. 5, 14, 47, 177
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
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
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?
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A. 32,317 groups |
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B. 23,330 groups |
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C. 24,310 groups |
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D. 25,410 group
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.)
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A. The first person can have any birthday in the year. The second person can have all but one birthday. |
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B. The second person can have any birthday in the year. The first person can have all but one birthday. |
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C. The first person cannot a birthday in the year. The second person can have all but one birthday. |
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D. The first person can have any birthday in the year. The second cannot have all but one birthday.
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
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
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
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. (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 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
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 |
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