1 of 20 5.0 Points Use the Binomial Theorem to find a polynomial expansion for the following function. f1(x) = (x - 2)4 A. f1(x) = x4 - 5x3 + 14x2 - 42x + 26 B. f1(x) = x4 - 16x3 + 18x2 - 22x + 18 C. f1(x) = x4 - 18x3 + 24x2 - 28x + 16 D. f1(x) = x4 - 8x3 + 24x2 - 32x + 16 Question 2 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 3 of 20 5.0 Points Write the first six terms of the following arithmetic sequence. a1 = 5/2, d = - 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 4 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 5 of 20 5.0 Points A club with ten members is to choose three officerspresident, 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? A. 650 ways B. 720 ways C. 830 ways D. 675 ways Question 6 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 Question 7 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 8 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 9 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 10 of 20 5.0 Points k2 + 3k + 2 = (k2 + k) + 2 ( __________ ) A. k + 5 B. k + 1 C. k + 3 D. k + 2 Question 11 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 12 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 13 of 20 5.0 Points An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done? A. 20 ways B. 30 ways C. 10 ways D. 15 ways Question 14 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 15 of 20 5.0 Points Write the first four terms of the following sequence whose general term is given. an = 3n + 2 A. 4, 6, 10, 14 B. 6, 9, 12, 15 C. 5, 8, 11, 14 D. 7, 8, 12, 15. Question 16 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 D. -3, 9, -27, 81 Question 17 of 20 5.0 Points 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 A. 8, 13, 21, 22 B. 7, 12, 17, 22 C. 6, 14, 18, 21 D. 4, 11, 17, 20. Question 18 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 19 of 20 5.0 Points Write the first four terms of the following sequence whose general term is given. an = 3n A. 3, 9, 27, 81 B. 4, 10, 23, 91 C. 5, 9, 17, 31 D. 4, 10, 22, 41 Question 20 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