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Find the probability.
71)
A 6-sided die is rolled. What is the probability of rolling a number less than 2?
71)
A)
1
3
B)
1
6
C)
1
9
D)
5
6
Use the formula for the sum of the first n terms of a geometric sequence.
72)
Find the sum of the first 14 terms of the geometric sequence: -2, -6, -18, -54, -162, . . .
72)
A)
-4,782,968
B)
-4,782,966
C)
-4,782,931
D)
-4,782,988
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.
73)
Find a9 when a1=2, r = - 2.
73)
A)
512
B)
516
C)
-14
D)
-1024
Find the probability.
74)
What is the probability that a card drawn from a deck of 52 cards is not a 5?
74)
A)
9
10
B)
12
13
C)
1
10
D)
1
13
Find the indicated sum.
75)
5
i =2
(3i - 4)
75)
A)
26
B)
17
C)
24
D)
22
Find the probability.
76)
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card will
have a value of 4 and be a face card?
76)
A)
3
13
B)
4
13
C)
1
13
D)
0
Solve the problem.
77)
A deposit of $11,000 is made in an account that earns 8% interest compounded quarterly. The
balance in the account after n quarters is given by the sequence
an=11,000(1 +0.08
4)n, n = 1, 2, 3, ...
Find the balance in the account after five years by computing a20
77)
A)
$12,144.89
B)
$6195.74
C)
$16,345.42
D)
$7429.74
Find the common difference for the arithmetic sequence.
78)
697, 688, 679, 670, . . .
78)
A)
-9
B)
697
C)
9
D)
-697
Solve the problem.
79)
Ms. Patterson proposes to give her daughter Claire an allowance of $0.20 on the first day of her
13-day vacation, $0.40 on the second day, $0.80 on the third day, and so on. Find the allowance
Claire would receive on the last day of her vacation.
79)
A)
$1638.40
B)
$2.60
C)
$819.20
D)
$4096.20
Find the probability.
80)
A lottery game contains 27 balls numbered 1 through 27. What is the probability of choosing a ball
numbered 28?
80)
A)
1
27
B)
27
C)
1
D)
0
Solve the problem.
81)
A game spinner has regions that are numbered 1 through 8. If the spinner is used twice, what is the
probability that the first number is a 3 and the second is a 5?
81)
A)
1
64
B)
1
8
C)
5
8
D)
1
16
Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
82)
22+32+42+ . . . +72
82)
A)
7
k = 0
k2
B)
7
k =3
(k - 1)2
C)
i
k =2
k2
D)
7
k =2
k2
Solve the problem.
83)
A church has 9 bells in its bell tower. Before each church service 3 bells are rung in sequence. No
bell is rung more than once. How many sequences are there?
83)
A)
504
B)
120,960
C)
84
D)
60,480
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.
84)
Find a8 when a1=6, r =3.
84)
A)
27
B)
39,366
C)
13,126
D)
13,122
Find the probability.
85)
One digit from the number 7,636,886 is written on each of seven cards. What is the probability of
drawing a card that shows 7 or 8?
85)
A)
6
7
B)
3
7
C)
7
7
D)
2
7
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.
86)
Find a9 when a1= - 2, r = - 3.
86)
A)
-26
B)
-13,118
C)
39,366
D)
-13,122
Find the probability.
87)
What is the probability that the arrow will land on an odd number?
87)
A)
1
B)
0
C)
3
5
D)
2
5
Find the indicated sum.
88)
8
i =4
8
88)
A)
32
B)
240
C)
208
D)
40
Write a formula for the general term (the nth term) of the geometric sequence.
89)
0.007, 0.07, 0.7, 7, . . .
89)
A)
an=7(0.1)n
B)
an=7(10)n
C)
an=0.007(10)n - 1
D)
an=0.07(10)n - 1
Use the formula for the sum of the first n terms of a geometric sequence to solve.
90)
Find the sum of the first 11 terms of the geometric sequence: 1
5, -2
5, 4
5, -8
5, 16
5, . . . .
90)
A)
677
5
B)
683
5
C)
138
D)
681
5
Find the probability.
91)
A bag contains 6 blue marbles, 8 green marbles, and 7 red marbles. One marble is drawn from the
bag. What is the probability that the marble drawn is not blue?
91)
A)
2
5
B)
2
7
C)
5
2
D)
5
7
92)
A card is drawn from a deck of 52 cards. What is the probability that it is a 4 or a club?
92)
A)
2
13
B)
25
26
C)
4
13
D)
17
52
Write a formula for the general term (the nth term) of the geometric sequence.
93)
7, 21, 63, 189, 567, . . .
93)
A)
an=7(3n)
B)
an=a1+3n
C)
an=7(3)n - 1
D)
an=7(3)n
Provide an appropriate response.
94)
Find the indicated sum:
5
i = 1
(i2+ 10) .
94)
A)
105
B)
54
C)
42
D)
80
Solve the problem.
95)
A new exhibit is scheduled to open at the local museum. Museum officials expect that 8000 people
will visit the exhibit in its first week, and that the number of visitors will drop by 40 people per
week after the first week during the first 6 months. Find the total number of visitors expected in the
exhibit's first 7 weeks.
95)
A)
47,400 visitors
B)
39,400 visitors
C)
55,160 visitors
D)
54,920 visitors
Write a formula for the general term (the nth term) of the geometric sequence.
96)
-5, -15, -45, -135, -405, . . .
96)
A)
an= - 5(3n)
B)
an= - 5(3)n
C)
an= - 5(3)n - 1
D)
an=a1+3n
Find the common ratio for the geometric sequence.
97)
4, 12, 36, 108, 324, . . .
97)
A)
not geometric
B)
8
C)
1
3
D)
3
D)
Find the indicated sum.
98)
7
i =4
2i
98)
A)
22
B)
14
C)
30
D)
44
Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
99)
a1= - 16; d =3
99)
A)
-4, -7, -10, -13, -16
B)
-16, -13, -10, -7, -4
C)
-10, -7, -4, -1, 2
D)
-10, -13, -16, -19, -22
Find the sum of the infinite geometric series, if it exists.
100)
1
2- 2 +8- . . .
100)
A)
32,768
B)
does not exist
C)
1
10
D)
- 8192
Find the common difference for the arithmetic sequence.
101)
8, 11, 14, 17, . . .
101)
A)
3
B)
9
C)
8
D)
2.25
Solve the problem.
102)
A quiz consisting of six multiple-choice questions has four answer choices for each question, with
one correct answer per question. If a person guesses at every question, what is the probability of
answering all six questions correctly?
102)
A)
1
1296
B)
1
4096
C)
1
24
D)
1
4
103)
A theater has 26 rows with 25 seats in the first row, 30 in the second row, 35 in the third row, and so
forth. How many seats are in the theater?
103)
A)
2340 seats
B)
4680 seats
C)
2275 seats
D)
4550 seats
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
104)
1, 5, 9, 13 , 17 , . . .
104)
A)
an= n +4; a20 =24
B)
an=4n -3; a20 =77
C)
an=4n + 3; a20 =83
D)
an=3n -4; a20 =56
Evaluate the given binomial coefficient.
105)
222
2
105)
A)
222!
220!
B)
49,062
C)
220
D)
24,531
Solve the problem.
106)
From the 8 books that Greg recently bought but not read, he plans to take 3 with him on vacation.
How many different sets of 3 books can he take?
106)
A)
56 different sets of 3 books
B)
336 different sets of 3 books
C)
13,440 different sets of 3 books
D)
6720 different sets of 3 books
Write a formula for the general term (the nth term) of the geometric sequence.
107)
2, -6, 18, -54, 162, . . .
107)
A)
an=a1- 3n
B)
an=2(-3n)
C)
an=2(-3)n - 1
D)
an=2(-3)n
Use the formula for the sum of the first n terms of a geometric sequence to solve.
108)
Find the sum of the first five terms of the geometric sequence: -3, -12, -48, . . . .
108)
A)
1023
B)
-63
C)
- 1023
D)
- 341
Evaluate the given binomial coefficient.
109)
10
2
109)
A)
1
B)
10
C)
0
D)
45
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.
110)
Among the students with brown eyes, find the probability of selecting a female.
Brown Blue Green
Male 28 18 4
Female 20 14 16
110)
A)
1
2
B)
7
12
C)
5
12
D)
1
5
Solve the problem.
111)
Domenica invests $250 each quarter in a fixed-interest mutual fund paying annual interest of 6.5%
compounded quarterly. How much will her account have in it at the end of 5 years? (Round to the
nearest dollar.)
111)
A)
$5982
B)
$5853
C)
$1423
D)
$17,514
Find the probability.
112)
A bag contains 8 red marbles, 4 blue marbles, and 1 green marble. What is the probability of
choosing a marble that is not blue when one marble is drawn from the bag?
112)
A)
13
9
B)
4
13
C)
9
D)
9
13
Solve the problem.
113)
A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it
swings only 64% as far as on the previous swing. What is the length of the arc after 11 swings?
Round to two decimal places.
113)
A)
0.38 in.
B)
0.92 in.
C)
0.59 in.
D)
512.00 in.
Find the probability.
114)
A 6-sided die is rolled. What is the probability of rolling a number that is even and a 5?
114)
A)
1
6
B)
1
C)
0
D)
1
2
115)
Given the sequence 7, 8, 9, 10 ... 44, what is the probability that a number in the sequence is even or
that it is greater than 12 and less then 29?
115)
A)
53
74
B)
53
76
C)
35
38
D)
27
38
Use the formula for the sum of the first n terms of an arithmetic sequence.
116)
Find
44
i = 1
(5i - 3) .
116)
A)
5038
B)
5192
C)
4818
D)
4708
Solve the problem.
117)
The bar graph below shows a company's yearly profits from 2003 to 2011. Let an represent the
company's profit, in millions, in year n, where n = 1 corresponds to 2003, n = 2 corresponds to 2004,
and so on.
Find
9
i =4
ai
117)
A)
$549.6 million
B)
$167.9 million
C)
$502.1 million
D)
$491.7 million
118)
Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a
monthly raise of $190 during her first year on the job. Find the general term of this arithmetic
sequence and her monthly salary at the end of her first year.
118)
A)
an=3000 +190n; $5090
B)
an=3000 +190n; $5280
C)
an=2810 +190(n - 1); $4900
D)
an=2810 +190n; $5090
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
119)
2+4+6+ . . . +18
119)
A)
9
i = 1
i2
B)
9
i = 0
2i
C)
9
i = 1
2i2
D)
9
i = 1
2i
32
Find the probability.
120)
Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be
3?
120)
A)
1
2
B)
17
18
C)
2
D)
1
18
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.
121)
Find a4 when a1=6, r =5.
121)
A)
750
B)
3750
C)
90
D)
125
If the probability an event will occur is p and the probability it will not occur is q, then each term in the expansion of
(p +
q)n represents a probability.
122)
The probability that a person in the general population suffers from anxiety is 0.25. If five people
from the general population are randomly selected, the probability that three of them will suffer
from anxiety is the third term of the binomial expansion of
5 people from the general
population are selected.
(0.25 +0.75)5.
Probability a person in
the general population
suffers from anxiety
Probability a person in the
general population does
not suffer from anxiety
What is this probability? Round the answer to four decimal places.
122)
A)
0.0879
B)
0.3516
C)
0.2637
D)
0.0659
Solve the problem.
123)
The following table shows a country's population from 2009 to 2012:
Year 2009 2010 2011 2012
Population in millions 10.20 10.71 11.25 11.81
Divide the population for each year by the population in the preceding year. Use this ratio to write
the general term of the geometric sequence describing the country's population growth n years after
2008. Then estimate the country's population, in millions, in 2018.
123)
A)
an=10.20(1.04)n - 1; 18.75 million
B)
an=10.20(1.05)n - 1; 16.61 million
C)
an=10.20(1.05)n - 1; 15.82 million
D)
an=10.20(1.04)n - 1; 17.53 million
Evaluate the given binomial coefficient.
124)
12
6
124)
A)
462
B)
924
C)
665,280
D)
1848
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
125)
5
i = 1
2·3i
125)
A)
726
B)
1230
C)
24
D)
87
Write the first four terms of the sequence whose general term is given.
126)
an=3(4n - 3)
126)
A)
3, 6, 9, 12, 15
B)
-9, 3, 15, 27, 39
C)
1, 5, 9, 13, 17
D)
3, 15, 27, 39, 51
Find the indicated sum.
127)
5
i = 3
(i2- 3)
127)
A)
15
B)
41
C)
40
D)
3
Evaluate the expression.
128)
1 -4P2
6P4
128)
A)
29
30
B)
1
30
C)
31
30
D)
3
5
Write the first four terms of the sequence whose general term is given.
129)
an=3n
(n +3)!
129)
A)
3
4, 9
5, 9
2, 81
7
B)
1
8, 3
40 , 3
80 , 9
560
C)
3
7, 9
8, 3, 81
10
D)
1
8, 3
40 , 3
40 , 9
280
Solve the problem. Round to the nearest hundredth of a percent if needed.
130)
The table below represents the number of deaths per 100 cases for an illness having a median
mortality of four years and a right-skewed distribution over time. What is the probability of living
more than 12 years after diagnosis of the disease?
Years after Diagnosis Number deaths
1-215
3-435
5-616
7-8 9
9-10 6
11-12 4
13-14 2
15+13
130)
A)
13.00%
B)
15.00%
C)
19.00%
D)
85.00%
Find the probability.
131)
A game spinner has regions that are numbered 1 through 8. If the spinner is used twice, what is the
probability that the first number is a 3 and the second is a 6?
131)
A)
1
64
B)
2
3
C)
9
64
D)
1
16
Solve the problem.
132)
A lottery game is set up so that each player chooses four different numbers from 1 to 14. If the four
numbers match the four numbers drawn in the lottery, the player wins (or shares) the top cash
prize. What is the probability of winning the prize with 50 different lottery tickets?
132)
A)
1
1001
B)
50
1001
C)
100
1001
D)
1
50,050
Write the first four terms of the sequence whose general term is given.
133)
an=4n
133)
A)
4, 16, 64, 256
B)
1, 4, 16, 64
C)
1, 16, 81, 256
D)
16, 64, 256, 1024
Find the probability.
134)
One digit from the number 7,646,336 is written on each of seven cards. What is the probability of
drawing a card that shows 7, 6, or 4?
134)
A)
2
7
B)
4
7
C)
5
7
D)
3
7
Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
135)
a1=8, d = - 0.4
135)
A)
an=8n - 8.4; a20 =151.6
B)
an= - 0.4n + 8.4; a20 =0.4
C)
an=8n - 0.4; a20 =159.6
D)
an= - 0.4n + 8; a20 =0
Provide an appropriate response.
136)
Express 0.45 in fractional notation.
136)
A)
9
200
B)
9
20
C)
5
11
D)
500
11
Solve the problem. Round to the nearest hundredth of a percent if needed.
137)
During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On
average, 11.8 days have afternoon thunderstorms. What is the probability that a randomly selected
day in July will not have a thunderstorm?
137)
A)
61.94%
B)
88.20%
C)
38.06%
D)
60.67%
Write the first four terms of the sequence whose general term is given.
138)
an=3
5
n
138)
A)
3
5, 9
25 , 27
125, 81
625
B)
3
5, 3
10 , 3
15 , 3
20
C)
1, 9
25 , 27
125, 81
625
D)
1, 3
5, 9
25 , 27
125
Find the indicated sum.
139)
4
k = 1
(-1)k(k + 1)
139)
A)
-14
B)
2
C)
14
D)
6
Write a formula for the general term (the nth term) of the geometric sequence.
140)
1
5, -1
20 , 1
80 , -1
320, . . .
140)
A)
an=1
5-1
4(n - 1)
B)
an=1
4-1
5
n - 1
C)
an=1
5
n - 1
-1
4
D)
an=1
5-1
4
n - 1
Find the sum of the infinite geometric series, if it exists.
141)
-15 - 5 -5
3-5
9- . . .
141)
A)
15
2
B)
does not exist
C)
-65
3
D)
-45
2
Find the probability.
142)
A card is drawn from a deck of 52 cards. What is the probability that it is a club or that it is greater
than 2 and less than 10?
142)
A)
17
26
B)
31
52
C)
37
52
D)
41
52
Express the repeating decimal as a fraction in lowest terms.
143)
0.426
143)
A)
19
125
B)
142
333
C)
213
500
D)
152
333
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
144)
(x + 7)5
144)
A)
x5+ 35x4+ 980x3+ 6860x2+ 12,005x + 16,807
B)
x5+ 35x4+ 980x3+ 6860x2+ 12,005x + 7
C)
x5+ 35x4+ 490x3+ 3430x2+ 12,005x + 7
D)
x5+ 35x4+ 490x3+ 3430x2+ 12,005x + 16,807
39
Write out the first three terms and the last term of the arithmetic sequence.
145)
50
i=1
-3i
145)
A)
-3+9-27 + . . . -450
B)
-3-6-9- . . . -150
C)
-3-9-27 - . . . -450
D)
-1 -3-6- . . . -150
Write the first four terms of the sequence whose general term is given.
146)
an=(-1)n(n +4)
146)
A)
-5, -6, -7, -8
B)
-5, -12, -21, -32
C)
5, 6, 7, 8
D)
-5, 6, -7, 8
Find the probability.
147)
A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has
an even number when one ball is drawn from the bag?
147)
A)
7
B)
15
7
C)
2
15
D)
7
15
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
148)
8
i = 1
2
5
i
148)
A)
155,994
390,625
B)
130,123
78,125
C)
77,997
78,125
D)
260,246
390,625
