Solve the problem. Round to the nearest hundredth of a percent if needed.
157)
In 1999 the stock market took big swings up and down. A survey of 1000 adult investors asked how
often they tracked their portfolio. The table shows the investor responses. What is the probability
that an adult investor tracks his or her portfolio daily?
How frequently? Response
Daily 234
Weekly 282
Monthly 276
Couple times a year 146
Don’t track 62
157)
A)
24.95%
B)
23.40%
C)
28.20%
D)
27.60%
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
158)
(3x – 1)5
158)
A)
243x5– 405x4+ 270x3– 90x2+ 15x – 1
B)
243x5– 81x4+ 27x3– 9x2+ 3x – 1
C)
243x5+ 15x4– 90x3– 90x2+ 15x – 1
D)
(9x2– 6x + 1)5
Find the sum of the infinite geometric series, if it exists.
159)
–30 – 6 –6
5–6
25 – . . .
159)
A)
–186
5
B)
–75
2
C)
15
2
D)
does not exist
Find the probability.
160)
Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a
ticket from the box, what is the probability that you will draw 7, 8, or 6?
160)
A)
1
10
B)
3
10
C)
1
7
D)
1
8
Write the first five terms of the geometric sequence.
161)
an= – 4an–1; a1= – 2
161)
A)
–4, –8, –32, –128, –512
B)
–2, 8, –32, 128, –512
C)
8, –32, 128, –512, 2048
D)
–2, –6, –10, –14, –18
The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the
sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
162)
an=3n2
162)
A)
geometric, r =3
B)
arithmetic, d =3
C)
geometric, r =3
2
D)
neither
Find the probability.
163)
A 6–sided die is rolled. What is the probability of rolling a number that is even and a 5?
163)
A)
1
6
B)
0
C)
1
D)
1
2
Use the formula for the sum of the first n terms of a geometric sequence to solve.
164)
Find the sum of the first six terms of the geometric sequence: 5, 20, 80, . . . .
164)
A)
6825
B)
20,832
C)
105
D)
1365
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.
165)
Find a6 when a1=3200, r = – 1
2.
165)
A)
–10
B)
100
C)
–100
D)
–50
Use the formula for the sum of the first n terms of a geometric sequence to solve.
166)
Find the sum of the first four terms of the geometric sequence: –3, –6, –12, . . . .
166)
A)
45
B)
– 45
C)
– 15
D)
–21
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
167)
5
i = 1
3·2i
167)
A)
42
B)
22
C)
186
D)
255
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
168)
(4x – 4y)3
168)
A)
64x3– 192x2y + 192xy2– 64y3
B)
16x3y – 32x2y2+ 16xy3
C)
16x3y – 16x2y2+ 16xy3
D)
64x3– 64x2y + 64xy2– 64y3
Solve the problem.
169)
To train for a race, Will begins by jogging 12 minutes one day per week. He increases his jogging
time by 6 minutes each week. Write the general term of this arithmetic sequence, and find how
many whole weeks it takes for him to reach a jogging time of one hour.
169)
A)
an=6n +6; 9 weeks
B)
an=6n +6; 8 weeks
C)
an=6n +12; 9 weeks
D)
an=6n +12; 8 weeks
Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
170)
a + 1 +a + 2
2+ . . . +a +4
4
170)
A)
4
i = 0
a + i
i
B)
4
i = 1
a + i
i
C)
n
i = 0
a + i
i
D)
n
i = 1
a + i
i
Write a formula for the general term (the nth term) of the geometric sequence.
171)
1
5, –1
10 , 1
20 , –1
40 , . . .
171)
A)
an=1
5–1
2(n – 1)
B)
an=1
2–1
5
n – 1
C)
an=1
5
n – 1
–3
10
D)
an=1
5–1
2
n – 1
Write the first three terms in the binomial expansion, expressing the result in simplified form.
172)
(x – 3 )17
172)
A)
x17 – 51 x16 – 1224x15
B)
x17 + 51 x16 – 1224 x15
C)
x17 + 51 x16 + 1224x15
D)
x17 – 51 x16 + 1224x15
Find the indicated sum.
173)
5
i = 1
(i + 1)!
(i + 2)!
173)
A)
153
140
B)
39
20
C)
81
20
D)
547
140
Solve the problem.
174)
In how many ways can 5 volunteers be assigned to 5 booths for a charity bazaar?
174)
A)
20 ways
B)
120 ways
C)
240 ways
D)
60 ways
Find the indicated sum.
175)
4
k = 2
k(k – 7)
175)
A)
–22
B)
–3
C)
–40
D)
–34
Write the first four terms of the sequence whose general term is given.
176)
an=(–1)n(n +6)
176)
A)
–7, –8, –9, –10
B)
–7, 8, –9, 10
C)
–7, –16, –27, –40
D)
7, 8, 9, 10
45
Solve the problem.
177)
A deposit of $11,000 is made in an account that earns 7.6% interest compounded quarterly. The
balance in the account after n quarters is given by the sequence
an=11,000 1 +0.076
4
n, n = 1, 2, 3, …
Find the balance in the account after 5 years.
177)
A)
$7285.40
B)
$12,085.47
C)
$6051.40
D)
$16,027.89
If the given sequence is a geometric sequence, find the common ratio.
178)
3
2, 3
8, 3
32 , 3
128, 3
512
178)
A)
20
B)
4
C)
1
20
D)
1
4
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
179)
50
i = 1
(2i +4)
179)
A)
3175
B)
2700
C)
3000
D)
2750
Use the formula for the sum of the first n terms of a geometric sequence to solve.
180)
Find the sum of the first five terms of the geometric sequence: 3
2, 3
8, 3
32 , . . . .
180)
A)
341
B)
7
256
C)
1023
512
D)
1
64
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
181)
6
i = 1
2
3
i
181)
A)
422
729
B)
665
243
C)
211
243
D)
1330
729
Evaluate the given binomial coefficient.
182)
10
5
182)
A)
126
B)
30,240
C)
504
D)
252
Solve the problem.
183)
A person puts $29 into a bank account on January 1, $34 on February 1, $39 on March 1, and so
forth. How much has the person put into the bank account by December 30?
183)
A)
$708
B)
$1356
C)
$678
D)
$504
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.
184)
Find a10 when a1= – 5, r = – 2.
184)
A)
–23
B)
2564
C)
–5120
D)
2560
Find the probability.
185)
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 spade?
185)
A)
25
52
B)
39
52
C)
7
52
D)
11
26
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
186)
(x – 2)5
186)
A)
x5– 10x4+ 80x3– 160x2+ 80x – 2
B)
x5– 10x4+ 40x3– 80x2+ 80x – 2
C)
x5– 10x4+ 40x3– 80x2+ 80x – 32
D)
x5– 10x4+ 80x3– 160x2+ 80x – 32
Write the first four terms of the sequence whose general term is given.
187)
an=(n – 1)!
n5
187)
A)
1, 1
32 , 2
243, 3
512
B)
0, 0, 2
15 , 3
10
C)
1
5, 1
10 , 2
15 , 3
10
D)
0, 0, 2
243, 3
512
188)
an=3n
188)
A)
3, 9, 27, 81
B)
1, 8, 27, 64
C)
9, 27, 81, 243
D)
1, 3, 9, 27
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.
189)
Find a8 when a1=3,000,000, r = 0.1.
189)
A)
0.03
B)
0.3
C)
3
D)
0.003
Solve the problem.
190)
A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or
ketchup. How many different hamburgers can be concocted using any 4 of the extras?
190)
A)
210
B)
420
C)
840
D)
35
Use the formula for the sum of the first n terms of a geometric sequence to solve.
191)
Find the sum of the first 11 terms of the geometric sequence: 1
6, –1
2, 3
2, –9
2, 27
2, . . . .
191)
A)
44285
6
B)
44287
6
C)
22147
3
D)
44281
6
Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of
summation.
192)
4+9
2+5+11
2+ . . . +10
192)
A)
12
k =8
k
2
B)
20
k =8
k
2
C)
20
k = 2
k
2
D)
20
k = 1
k
2
Write the first four terms of the sequence whose general term is given.
193)
an= – 2
3
n
193)
A)
2
3, –2
6, 2
9, –2
12
B)
–2
3, 4
9, –8
27 , 16
81
C)
–2
3, –4
9, –8
27 , –16
81
D)
–2
3, 2
6, –2
9, –2
12
Solve the problem.
194)
A basketball player signs a contract with a starting salary of $830,000 per year and an annual
increase of 4.5% beginning in the second year. What will the athlete’s salary be, to the nearest
dollar, in the seventh year?
194)
A)
$1,083,233
B)
$1,081,650
C)
$1,080,876
D)
$1,079,554
Use the formula for the sum of the first n terms of a geometric sequence to solve.
195)
Find the sum of the first five terms of the geometric sequence: 4
3, 16
3, 64
3, . . . .
195)
A)
1363
15
B)
1364
3
C)
1364
15
D)
1363
3
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
196)
(x + 2y)3
196)
A)
x3+ 8y3
B)
x3+ 2x2y + 4xy + 4xy2+ 8y2+ 8y3
C)
x3+ 6x2y + 12xy2+ 8y3
D)
3x +6y
Write the first four terms of the sequence whose general term is given.
197)
an=2(2n – 1)
197)
A)
2, 6, 10, 14
B)
–2, 2, 6, 10
C)
1, 3, 5, 7
D)
2, 4, 6, 8
Find the sum of the infinite geometric series, if it exists.
198)
i = 1
4(–0.4)i – 1
198)
A)
–20
3
B)
20
7
C)
20
3
D)
–20
7
199)
1
4–1
2+1– . . .
199)
A)
– 32
B)
1
12
C)
64
D)
does not exist
D)
Does the problem involve permutations or combinations? Do not solve.
200)
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?
200)
A)
permutations
B)
combinations
Write the first three terms in the binomial expansion, expressing the result in simplified form.
201)
(x + 2) 19
201)
A)
x19 + 36 x18 + 1368x17
B)
x19 + 38 x18 + 684 x17
C)
x19 + 38 x18 + 1368x17
D)
x19 + 36 x18 + 684 x17
D)
Find the indicated sum.
202)
4
i = 1
2i
202)
A)
20
B)
18
C)
14
D)
30
D)
D)
Does the problem involve permutations or combinations? Do not solve.
203)
From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention.
How many different committees are possible?
203)
A)
permutations
B)
combinations
Solve the problem.
204)
Lisa has 4 skirts, 10 blouses, and 4 jackets. How many 3–piece outfits can she put together
assuming any piece goes with any other?
204)
A)
320 possible outfits
B)
40 possible outfits
C)
160 possible outfits
D)
18 possible outfits
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
205)
(x + 4)4
205)
A)
x4+ 4x3+ 96x2+ 128x + 256
B)
x4+ 16x3+ 96x2+ 16x + 256
C)
x4+ 16x3+ 96x2+ 256x + 256
D)
x4+ 16x3+ 128x2+ 256x + 256
Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of
summation.
206)
a + ar + ar2+ . . . + ar14
206)
A)
14
k = 0
(ar)k
B)
14
k = 1
ark
C)
15
k = 1
ark
D)
14
k = 0
ark
Solve the problem.
207)
A church has 9 bells in its bell tower. Before each church service 5 bells are rung in sequence. No
bell is rung more than once. How many sequences are there?
207)
A)
126
B)
15,120
C)
6048
D)
3024