Provide an appropriate response.
83)
Rooms in a 130 unit student housing complex are fully rented at $300 per month. The
university is raising rates to produce $1920 more in monthly income from these units. Each
$10 per month increase will create two vacancies with no possibility of filling them. What
should be charged for the new rent?
83)
84)
Solve: z– 2 2z– 3
2
84)
85)
Solve: –x
3< 2
85)
86)
Evaluate
44
i=1
(i2 + 4i)
86)
87)
Evaluate
30
i=1
i2
87)
88)
The sum of 3 integers is 27. The second is 3 more than the first, and the third is two more
than twice the second integer. Find the three integers.
88)
89)
Express the sum in summation notation.
7 + 11 + 15 + 19 + 23 + 27 + … + 67
89)
16
90)
Suppose a company offers you a sales position with your choice of two methods of
determining your yearly salary. One method pays $15,000 plus a bonus of 3% of your
yearly sales. The other method pays a straight 13% commission of your sales. For what
yearly sales level is it better to choose the first method?
90)
91)
A rectangular field is twice as long as it is wide. Find the dimensions of the field if it needs
600 feet of fencing to go around the field.
91)
92)
Hooke’s Law of springs states that the force F (in pounds) required to stretch a spring x
inches beyond its natural length is F=kx, where k is the “spring constant” for a given
spring. If a certain spring has a spring constant k of 6.5 and 13 F 26, what are the
corresponding values for x?
92)
93)
A company produces a product for which the variable cost per unit is $3.50 and fixed cost
is $20,000 per year. Next year, the company wants the total cost to be $48,000. How many
units of the product should be made next year?
93)
94)
Evaluate
50
i=1
(i + 2)2
94)
95)
Solve: Three times x plus four is a number –4 units from zero.
95)
96)
Solve: x+ 4
3> 2
96)
97)
Approximately 21% of the air we breathe is oxygen. To the nearest milliliter, how many
milliliters of air contain 1 milliliter of oxygen?
97)
98)
Simplify: |3 – 8| – |8 – 3|
98)
99)
A county decides to retire some of its road construction bonds in 2 years. At that time
$4,840,000 will be required. If it presently sets aside $4,000,000, at what annual rate of
interest, compounded annually, will this money need to earn in order for its future value to
be sufficient to retire the bonds?
99)
100)
Three times x plus five is a number that is more than 4 units from zero. What are the
possible values for x?
100)
101)
A recliner costs a wholesaler $189 and her markup is 10% of her selling price. If the
retailer’s markup is 30% of his selling price for the item, what is the retailer’s selling price?
101)
Express the problem using absolute value notation.
102)
For safety reasons, the arrival time of commuter train A at a station must be at least 6
minutes different from the 6:00 P.M. arrival of train B.
102)
Provide an appropriate response.
103)
An economics instructor told his class that the demand equation for a certain product is p=
400 –q2 and its supply equation is p= 20q+ 100. If the 400 –q2 is set equal to the 20q+ 100,
then the positive solution to the resulting equation gives the “equilibrium quantity.” The
instructor asked his class to find this quantity. What answer should the class give?
103)
104)
A company produces and sells q units of its product. If the variable cost is $4/unit, fixed
costs are $4800 and the selling price is $28/unit, find the number of units the company must
produce to split even (i.e., zero profit).
104)
105)
Solve: 5 – 2x> 3
105)
106)
Solve: 2(x– 8) + 5 –42 –x
2
106)
107)
A bicycle costs a wholesaler $63 and the wholesale selling price includes a markup of 25%
of the wholesale selling price. What should be the retailer’s selling price in order to make a
profit of 30%
107)
108)
The product of two consecutive integers is 42. Find the integers.
108)
The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
109)
Write the income range for line 5 as an inequality. Write the inequality that represents the
tax owed.
109)
Provide an appropriate response.
110)
Evaluate
5
k=2
2k2
110)
111)
A person deposits $50 in a bank and in two years it increases to $56.18. If the bank
compounds interest annually, what annual rate of interest does it pay?
111)
Express the problem using absolute value notation.
112)
The absolute value of the difference of two numbers is equal to the absolute value of the
difference of the two numbers in reverse order.
112)
Provide an appropriate response.
113)
The relationship between Fahrenheit and Celsius temperature is given by the formula
F– 32
180 =C
100. Normal body temperature is F 98.6. Find the corresponding Celsius
temperature.
113)
114)
A company manufactures hair dryers. The manufacturing cost is $9 per unit with a fixed
cost of $16,000. A hair dryer sells for $15. If the company wants to earn a profit of $50,000,
how many dryers must be sold?
114)
115)
A kitchen cabinet maker wants to establish a list price for a standard cabinet so that the
selling price gives a trade discount of 10% of the list price. If he makes a markup of 20% of
the selling price, and his cost is $144, what list price should he charge?
115)
116)
Solve: 7 – 2x< 9
116)
117)
A theater owner charges $3 for each ticket. Currently, only 100 people attend the theater
daily. The owner believes that for each $0.10 decrease per ticket, 10 more people will
attend. If this is true and the capacity of the theater is 200, what should the price of a ticket
be if the owner wants to receive $375 daily from ticket sales?
117)
Answer:
Explanation:
118)
The cost of publishing each copy of a magazine is $1.75. The revenue from dealers if $1.60
for each copy. The amount received for advertising is 10% of the amount received for all
magazines sold beyond 1,000. Find the smallest number of copies that must be sold to
break even.
118)
Answer:
Explanation:
The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
119)
Write the income range for line 2 as an inequality. Write the inequality that represents the
tax owed.
119)
Answer:
Explanation:
Provide an appropriate response.
120)
Evaluate
13
k=10
(4k + 9)
120)
Answer:
220
Explanation:
121)
A retired couple has $192,000 to invest. A safe investment yields 9.5% per year, but a
riskier investment yields 12.5% per year. How much should they invest at each rate to earn
$21,000 per year?
121)
Answer:
Explanation:
122)
A company produces a product at a cost of $6 per unit. If fixed costs are $20,000 and each
unit sells at $8, at least how many units must be sold in order to earn a profit?
122)
Answer:
Explanation:
Answer:
Explanation:
123)
Give the bounds of summation and the index of summation for
10
j=7
(j3–j2 + 6j– 1)
123)
124)
A manufacturer makes CD players. If the variable costs are $25 per player and the fixed
costs are $50,000, what is the minimum number of CD players that must be sold to make a
profit of $75,000 given that the CD players sell for $45 per player?
124)
125)
Solve: (1 –2x)2– 4(3 –x)2 5
125)
126)
Ohm’s Law in electrical theory states that V=IR, where R is the resistance (in ohms) of an
object, V is the potential difference (in volts) across the object, and I is the current (in
amperes) that flows through it. If the voltage is 220 volts, what values for the current will
result in a resistance that is less than 20 ohms?
126)
127)
Solve: a
2–a
3<a
5+ 1
127)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated sum.
128)
5
k = 3
(k2+ 7)
128)
A)
71
B)
90
C)
33
D)
45
Determine whether the given sequences are equal to each other.
129)
(k2–9) and (k + 3)(k – 3)
129)
A)
equal
B)
not equal
21
Determine the indicated term of the given recursively defined sequence.
130)
a1=4, a2=12, ak+2=ak+1+ 8; a4
130)
A)
12
B)
20
C)
36
D)
28
Solve the problem.
131)
A theater has 24 rows with 30 seats in the first row, 33 in the second row, 36 in the third row, and so
forth. How many seats are in the theater?
131)
A)
1584 seats
B)
3168 seats
C)
1548 seats
D)
3096 seats
Find the infinite sum, if possible.
132)
k=1
1
10
k–1
132)
A)
1
9
B)
10
9
C)
not possible
D)
–1
9
Write the indicated term of the given sequence.
133)
(ak) =7(3k); a2
133)
A)
63
B)
567
C)
21
D)
189
Write the first five terms of the arithmetic sequence with the given first term a and common difference d.
134)
a =12; d = – 3
134)
A)
12, 9, 6, 3, 0
B)
9, 6, 3, 0, –3
C)
12, 9, 5, 3, 0
D)
15, 12, 9, 6, 3
135)
a = – 16; d =2
135)
A)
–8, –10, –12, –14, –16
B)
–16, –14, –12, –10, –8
C)
–12, –14, –16, –18, –20
D)
–12, –10, –8, –6, –4
Write the first five terms of the geometric sequence with the given first term a and common ratio r.
136)
a =4; r =5
136)
A)
4, 20, 100, 500, 2500
B)
5, 20, 80, 320, 1280
C)
20, 100, 500, 2500, 12,500
D)
4, 9, 14, 19, 24
Find the indicated sum.
137)
4
k = 1
2k
137)
A)
20
B)
14
C)
18
D)
30
138)
4
k=1
(2k – 3)
138)
A)
5
B)
7
C)
8
D)
9
Write the first five terms of the arithmetic sequence with the given first term a and common difference d.
139)
a =21; d = – 5
139)
A)
21, 16, 11, 6, 1
B)
–21, –16, –11, –6, –1
C)
0, 21, 16, 11, 6
D)
25, 19, 13, 7, 1
Solve the problem.
140)
The population of a town is increasing by 400 inhabitants each year. If its population at the
beginning of 1990 was 22,289, what was its population at the beginning of 1997?
140)
A)
155,939 people
B)
311,878 people
C)
25,089 people
D)
24,689 people
141)
Keyana takes a job with a starting salary of $31,000 for the first year with an annual increase of
4.5% beginning in the second year. What is Keyana‘s salary, to the nearest dollar, at the end of the
seventh year?
141)
A)
$38,930
B)
$42,850
C)
$41,089
D)
$40,370
Find the indicated sum.
142)
6
k =3
9k
142)
A)
162
B)
81
C)
108
D)
54
Write the indicated term of the given sequence.
143)
a =12, 24, 36, 48; a2
143)
A)
12
B)
36
C)
2
D)
24
Find the indicated sum.
144)
5
k= 1
(k– 10)
144)
A)
–35
B)
–30
C)
–14
D)
–5
Find a general term, (ak), that fits the displayed terms of the given sequence.
145)
1, 5, 9, 13 , 17
145)
A)
(4k +3) 4
k=0
B)
(4k –3) 4
k=0
C)
(4k +3) 5
k=1
D)
(4k –3) 5
k=1
Write the first five terms of the geometric sequence with the given first term a and common ratio r.
146)
a = – 8; r = – 4
146)
A)
–8, –12, –16, –20, –24
B)
–8, 32, –128, 512, –2048
C)
–4, 32, –128, 512, –2048
D)
–8, –32, –128, 512, –2048
Find the indicated sum.
147)
4
k = 2
k(k + 4)
147)
A)
30
B)
44
C)
70
D)
65
Write the first five terms of the arithmetic sequence with the given first term a and common difference d.
148)
a =4; d =5
148)
A)
0, 4, 9, 14, 19
B)
4, 8, 12, 16, 20
C)
4, 9, 14, 19, 24
D)
9, 14, 19, 24, 29
Write the first five terms of the geometric sequence with the given first term a and common ratio r.
149)
a =6; r = – 5
149)
A)
–5, –30, 150, –750, 3750
B)
6, 30, 150, –750, 3750
C)
6, 1, –4, –9, –14
D)
6, –30, 150, –750, 3750
Solve the problem.
150)
To train for a race, Will begins by jogging 11 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.
150)
A)
ak=6k +11; 9 weeks
B)
ak=6k +5; 9 weeks
C)
ak=6k +5; 10 weeks
D)
ak=6k +11; 10 weeks
Write the first five terms of the geometric sequence with the given first term a and common ratio r.
151)
a =6; r =1
3
151)
A)
6, 19
3, 20
3, 7, 22
3
B)
6, 2, 2
3, 2
9, 2
27
C)
2, 2
3, 2
9, 2
27 , 2
81
D)
6, 18, 54, 162, 486
Answer Key
Testname: C1
27
Answer Key
Testname: C1
Answer Key
Testname: C1
Answer Key
Testname: C1