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Hope you are doing well? Please see the attached and provide solutions. As usual, i am expecting 100/100.  please don't disappoint me. Take your time and provide correct answers only. A+ answers please. Thank you!

 

 

 

Question 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 = - 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 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 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?
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

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