Solve the problem.
230)
In how many ways can Susan arrange 8 books into 5 slots on her bookshelf?
230)
A)
6720
B)
672
C)
336
D)
112
Find the probability.
231)
Two 6–sided dice are rolled. What is the probability that the sum of the two numbers on the dice
will be greater than 9?
231)
A)
6
B)
1
12
C)
1
6
D)
1
4
Find the common ratio for the geometric sequence.
232)
1, –3, 9, –27, 81, . . .
232)
A)
–3
B)
–1
3
C)
–4
D)
3
Find the term indicated in the expansion.
233)
(x2+y4)6; 3rd term
233)
A)
90x8y8
B)
15x8y8
C)
90x6y6
D)
15x6y6
Solve the problem.
234)
One card is randomly selected from a deck of 52 cards. What is the probability that it is a picture
card (Jack, Queen, King) or a diamond?
234)
A)
7
52
B)
39
52
C)
11
26
D)
25
52
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
235)
a1=9; d = – 2
235)
A)
7, 5, 3, 1, –1
B)
9, 7, 4, 3, 1
C)
9, 7, 5, 3, 1
D)
11, 9, 7, 5, 3
Find the sum of the infinite geometric series, if it exists.
236)
i = 1
12(–0.8)i – 1
236)
A)
60
B)
20
3
C)
– 60
D)
–20
3
Find the term indicated in the expansion.
237)
(2x + 3y)12; 4th term
237)
A)
1,013,760x3y9
B)
1,520,640x3y9
C)
1,013,760x9y4
D)
3,041,280x9y3
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
238)
Find the sum of the first four terms of the arithmetic sequence: 8, 15, 22, . . . .
238)
A)
60
B)
45
C)
148
D)
74
Find the term indicated in the expansion.
239)
(x + 2y)9; 4th term
239)
A)
672x3y6
B)
336x3y6
C)
336x6y4
D)
672x6y3
62
Find the common ratio for the geometric sequence.
240)
1, 1
4, 1
16 , 1
64 , 1
256, . . .
240)
A)
1
4
B)
1
30
C)
4
D)
30
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
241)
Find 1+3+5+7+ . . ., the sum of the first 50 positive odd integers.
241)
A)
2500
B)
2446
C)
2504
D)
2450
Find the probability.
242)
Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 4. What is the
probability that a 4 is drawn from A followed by a 2 from B?
242)
A)
5
12
B)
1
24
C)
1
12
D)
1
6
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
243)
5
i = 1
3(–3)i
243)
A)
–549
B)
–63
C)
–1845
D)
72
Solve the problem.
244)
To save for retirement, you decide to deposit $2000 into an IRA at the end of each year for the next
35 years. If the interest rate is 5% per year compounded annually, find the value of the IRA after 35
years. (Round to the nearest dollar.)
244)
A)
$170,134
B)
$9032
C)
$1,311,760
D)
$180,641
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
245)
Find a140 when a1=14, d =3.
245)
A)
434
B)
431
C)
–403
D)
–406
Write the first three terms in the binomial expansion, expressing the result in simplified form.
246)
(x + 2)18
246)
A)
x18 + 36x17 + 1224x16
B)
x18 + 34x17 + 1224x16
C)
x18 + 36x17 + 612x16
D)
x18 + 34x17 + 612x16
Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
247)
a1=6; r =2
247)
A)
2, 12, 72, 432, . . .
B)
12, 24, 48, 96, . . .
C)
6, 8, 10, 12, . . .
D)
6, 12, 24, 48, . . .
Write the first four terms of the sequence whose general term is given.
248)
an=n
n2+ 2
248)
A)
1
3, 3
11 , 2
9, 5
27
B)
1
3, 1
3, 3
8, 2
5
C)
1
2, 1
3, 3
8, 2
5
D)
1
3, 1
3, 3
11 , 2
9
Solve the problem.
249)
There are 5 roads leading from Bluffton to Hardeeville, 7 roads leading from Hardeeville to
Savannah, and 4 roads leading from Savannah to Macon. How many ways are there to get from
Bluffton to Macon?
249)
A)
140 ways
B)
35 ways
C)
16 ways
D)
280 ways
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
250)
9+13 +17 +21 + . . . +41
250)
A)
10
k = 1
4k +1
B)
32
k = 0
4k +1
C)
32
k = 2
4k +1
D)
10
k = 2
4k +1
Find the indicated sum.
251)
4
i = 1
–1
3
i
251)
A)
40
81
B)
20
81
C)
–20
81
D)
–16
81
Evaluate the given binomial coefficient.
252)
10
2
252)
A)
45
B)
22
C)
1,814,400
D)
5
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
253)
a1=7
4, d =5
4
253)
A)
7
4, 1
4, –1
4, –1
2, –13
20
B)
7
4, 3, 17
4, 11
2, 27
4
C)
7
4, 1
2, –3
4, – 2, –13
4
D)
7
4, 3
2, 17
12 , 11
8, 27
20
Write the first three terms in the binomial expansion, expressing the result in simplified form.
254)
(x + 6)20
254)
A)
x20 + 120x19 + 6840x18
B)
x20 + 6840x19 + 6840x18
C)
x20 + 1140x19 + 6840x18
D)
x20 + 120x19 – 6840x18
Solve the problem.
255)
A student must choose 1 of 5 science electives, 1 of 6 social studies electives, and 1 of 7 language
electives. How many possible course selections are there?
255)
A)
18 course selections
B)
210 course selections
C)
420 course selections
D)
30 course selections
Does the problem involve permutations or combinations? Do not solve.
256)
From 8 names on a ballot, a committee of 3 will be elected to attend a political national convention.
How many different committees are possible?
256)
A)
permutations
B)
combinations
Find the term indicated in the expansion.
257)
(2x + 5)5; 5th term
257)
A)
2500x2
B)
15,625
C)
6250x
D)
1250x
Does the problem involve permutations or combinations? Do not solve.
258)
The matching section of an exam has 4 questions and 6 possible answers. In how many different
ways can a student answer the 4 questions, if none of the answer choices can be repeated?
258)
A)
permutations
B)
combinations
Write the first four terms of the sequence whose general term is given.
259)
an=n2– n
259)
A)
0, 3, 8, 15
B)
1, 4, 9, 16
C)
0, 2, 6, 12
D)
2, 6, 12, 20
Solve the problem.
260)
A human resource manager has 9 applicants to fill 6 different positions. Assuming that all
applicants are equally qualified for any of the 6 positions, in how many ways can this be done?
260)
A)
362,880 ways to fill the positions
B)
84 ways to fill the positions
C)
504 ways to fill the positions
D)
60,480 ways to fill the positions
Provide an appropriate response.
261)
Evaluate: 12
4 .
261)
A)
247
B)
495
C)
19,958,400
D)
3
A class is collecting data on eye color and gender. They organize the data they collected into a table. Numbers in the table
represent the number of students from the class that belong to each of the categories. Use the data to solve the problem.
Express probabilities as simplified fractions.
262)
Find the probability that a randomly selected student is male or has blue eyes.
Brown Blue Green
Male 20 14 16
Female 26 16 8
262)
A)
1
2
B)
16
25
C)
4
5
D)
33
50
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
263)
Find a8 when a1=1, d = – 3 .
263)
A)
22
B)
25
C)
–23
D)
–20
Find the probability.
264)
Two 6–sided dice are rolled. What is the probability that the sum is odd and the number on one of
the dice is a 5?
264)
A)
1
2
B)
1
6
C)
5
36
D)
1
12
68
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
265)
Find a14 when a1=20, d = – 3.
265)
A)
59
B)
–22
C)
–39
D)
–19
Solve the problem.
266)
How many 3–letter codes can be formed using the letters A, B, C, D, and E? No letter can be used
more than once.
266)
A)
10
B)
20
C)
40
D)
60
Solve the problem. Round to the nearest hundredth of a percent if needed.
267)
Measurements of the height of a group of men entering a particular college produced the following
table. What is the probability that a man entering the college is 68–69 inches tall?
Height (inches) 60–61 62–63 64–65 66–67 68–69 70–71 72–73 74–75 76+
Number 413 82 212 275 150 90 39 6
267)
A)
31.94%
B)
31.57%
C)
24.34%
D)
17.22%
Solve the problem.
268)
In a student government election, 7 seniors, 2 juniors, and 3sophomores are running for election.
Students elect four at–large senators. In how many ways can this be done?
268)
A)
19,958,400
B)
495
C)
11,880
D)
42
Use the formula for the sum of the first n terms of a geometric sequence to solve.
269)
Find the sum of the first 10 terms of the geometric sequence: 2, 6, 18, 54, 162, . . . .
269)
A)
59,028
B)
59,085
C)
59,050
D)
59,048
Use the partial sum formula to find the partial sum of the given arithmetic sequence.
270)
Find the sum of the first 15 terms of the arithmetic sequence: 3, 7, 11, 15, . . . .
270)
A)
495
B)
330
C)
465
D)
434
Solve the problem. Round to the nearest hundredth of a percent if needed.
271)
During clinical trials of a new drug intended to reduce the risk of heart attack, the following data
indicate the occurrence of adverse reactions among 1100 adult male trial members. What is the
probability that an adult male using the drug will experience nausea?
Adverse Reaction Number
Heartburn 15
Headache 13
Dizziness 9
Urinary problems 7
Nausea 20
Abdominal pain 17
271)
A)
24.69%
B)
1.55%
C)
1.82%
D)
1.69%
Find the sum of the infinite geometric series, if it exists.
272)
2–1
2+1
8–1
32 + . . .
272)
A)
3
2
B)
–1
2
C)
8
5
D)
does not exist
273)
i = 1
5
4–1
4
i – 1
273)
A)
5
4
B)
1
C)
does not exist
D)
1
5
Evaluate the given binomial coefficient.
274)
110
108
274)
A)
647,460
B)
5995
C)
55
54
D)
5995
108
Find the common ratio for the geometric sequence.
275)
36, 18, 9, 4.5, 2.25, . . .
275)
A)
2
B)
–0.5
C)
0.5
D)
2.25
Find the sum of the infinite geometric series, if it exists.
276)
i = 1
1
2
1
4
i – 1
276)
A)
1
3
B)
2
3
C)
does not exist
D)
1
2
277)
i = 1
15(3 )i – 1
277)
A)
15
B)
240
C)
does not exist
D)
–4
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
278)
Find a4 when a1=2000, r = – 1
2.
278)
A)
250
B)
–250
C)
–25
D)
–125
Solve the problem.
279)
A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or
ketchup. How many different hamburgers can be concocted using any 3 of the extras?
279)
A)
35
B)
105
C)
840
D)
210
Find the common ratio for the geometric sequence.
280)
6, 0.6, 0.06, 0.006, . . .
280)
A)
0.6
B)
0.1
C)
1
D)
0.01
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence
with the given first term, a1, and common difference, d.
281)
Find a 37 when a1=3, d =4
3.
281)
A)
–139
3
B)
– 45
C)
157
3
D)
51
72
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
282)
4
5+5
6+6
7+7
8+ . . . +16
17
282)
A)
16
k =5
k
k + 1
B)
16
k =5
k + 1
k
C)
16
k =4
k
k + 1
D)
16
k =4
k + 1
k
Solve the problem.
283)
A job pays a salary of 29,000 the first year. During the next 8 years, the salary increases by 6% each
year. What is the salary for the 9th year? What is the total salary over the 9–year period? Round to
the nearest cent.
283)
A)
$48,994.89; $287,043.24
B)
$46,221.59; $287,026.57
C)
$46,221.59; $333,248.16
D)
$48,994.89; $382,243.05
284)
The finite sequence whose general term is an=0.15n2–1.06n +7.74, where n = 1, 2, 3, . . ., 9 models
the total operating costs, in millions of dollars, for a company for nine consecutive years.
Find
5
i = 1
ai
284)
A)
$34.15 million
B)
$24.86 million
C)
$27.32 million
D)
$31.05 million
Find the sum of the infinite geometric series, if it exists.
285)
108 + 18 + 3 +1
2+ . . .
285)
A)
does not exist
B)
–108
5
C)
129
D)
648
5
73
Use the formula for the sum of the first n terms of a geometric sequence to solve.
286)
Find the sum of the first 14 terms of the geometric sequence: 1
6, 1
2, 3
2, 9
2, 27
2, . . . .
286)
A)
1,195,739
3
B)
1,195,741
3
C)
2,391,491
6
D)
1,195,742
3
Find the probability.
287)
A card is drawn from a deck of 52 cards. What is the probability that it is a picture card (Jack,
Queen, King) or a diamond?
287)
A)
39
52
B)
11
26
C)
25
52
D)
7
52
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
288)
2+8+18 + . . . +72
288)
A)
6
i = 1
2i2
B)
6
i = 1
i2
C)
6
i = 0
2i2
D)
6
i = 1
22i
Solve the problem.
289)
In how many ways can 5 volunteers be assigned to 5 booths for a charity bazaar?
289)
A)
60 ways
B)
120 ways
C)
240 ways
D)
20 ways
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
290)
(x2+ 5y)4
290)
A)
x4+ 20x3y + 150x2y2+ 500xy3+ 625y4
B)
x8+ 20x6y + 150x4y2+ 20x2y3+ 625y4
C)
x8+ 5x6y + 150x4y2+ 250x2y3+ 625y4
D)
x8+ 20x6y + 150x4y2+ 500x2y3+ 625y4
Write a formula for the general term (the nth term) of the sequence. Then use the formula for an to find the twelfth term
of the sequence.
291)
4, 12 , 20 , 28 , . . .
291)
A)
an=8n – 4; a12 =92
B)
an=4n –8; a12 =40
C)
an=8n –2; a12 =94
D)
an=4n –2; a12 =46
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
292)
Find a8 when a1=2000, r =1
2.
292)
A)
4007
2
B)
125
16
C)
125
32
D)
125
8
Solve the problem.
293)
A person puts $20 into a bank account on January 1, $30 on February 1, $40 on March 1, and so
forth. How much has the person put into the bank account by December 30?
293)
A)
$900
B)
$1800
C)
$780
D)
$960