The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
135)
During which two hour period did the temperature increase the most?
135)
A)
10 a.m. to 12 p.m.
B)
9 a.m. to 11 a.m.
C)
10 a.m. to 11 a.m.
D)
12 p.m. to 2 p.m.
Solve the problem.
136)
It is known that one–fourth of all aluminum cans distributed will be recycled each year, thus the
number of cans still in use (recycled) after t years is N = P(1
4)t, where P is the number of cans
produced in a year. If a beverage company distributes 290,000 new cans in a given year, how many
of these cans are still in use after 2 years?
136)
A)
72,500 cans
B)
36,250 cans
C)
18,125 cans
D)
4,640,000 cans
Write the number in scientific notation.
137)
30,795
137)
A)
3.0795 × 101
B)
3.0795 × 10–4
C)
3.0795 × 104
D)
3.0795 × 105
Graph the equation.
41
138)
y =1
x
138)
A)
B)
C)
D)
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
139)
50% of what number is 71?
139)
A)
1420
B)
14.2
C)
35.5
D)
142
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
140)
–0.4> – 0.4 and –73+4
140)
A)
True
B)
False
Simplify the expression using the quotients–to–powers rule.
141)
–4p
q
2
141)
A)
16p2
q2
B)
16p
q2
C)
–8p
q
D)
–8p2
q2
Graph the equation.
142)
y =x3+ 1
142)
43
A)
B)
C)
D)
Add as indicated.
143)
–9.1 +8.6
143)
A)
0.5
B)
–17.7
C)
–0.5
D)
17.7
Divide the expression using the quotient rule.
144)
–45x11y10z5
5x6y4z4
144)
A)
–9x5y6z
B)
–9x4y5z
C)
–9x5y6
D)
x5y6z
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.
145)
A particle is observed moving at 6.62 ×103 meters per second. Find the distance the particle would
travel in 6.85 ×10–7 seconds.
145)
A)
4.53 ×10–4 meters
B)
4.53 ×10–2 meters
C)
0.45 ×10–3 meters
D)
4.53 ×10–3 meters
Find –x for the given value of x.
146)
x =13
146)
A)
13
B)
0
C)
1
13
D)
–13
Determine whether the inequality is true or false.
147)
1>3
147)
A)
True
B)
False
Multiply the expression using the product rule.
148)
x8·x5
148)
A)
x40
B)
13x
C)
40x
D)
x13
Solve the equation to determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
149)
6x + 1 + 8x + 7 =7x + 7x + 5
149)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
45
Write the English phrase as an algebraic expression. Let x represent the number.
150)
The sum of a number and 87
150)
A)
87
B)
87 – x
C)
87x
D)
87 + x
Simplify the exponential expression.
151)
–4x11
2x5
151)
A)
–2x6
B)
x6
C)
–2x5
D)
x5
Write the English phrase as an algebraic expression. Let x represent the number.
152)
The quotient of 72 and a number
152)
A)
x –72
B)
x
72
C)
72 – x
D)
72
x
Express the interval in set builder notation and graph the interval on a number line.
153)
(–, 2.5]
153)
A)
{x x 2.5}
B)
{x x >2.5}
C)
{x x 2.5}
D)
{x x <2.5}
Divide as indicated or state that the division is undefined.
154)
–7.5
0
154)
A)
Undefined
B)
0
C)
7.5
D)
–7.5
Find the absolute value.
155)
–|–8|
155)
A)
0
B)
–8
C)
8
D)
16
Evaluate the expression for the given values.
156)
(x + 3y)2 , for x =2, y =2
156)
A)
64
B)
8
C)
25
D)
16
Provide an appropriate response.
157)
Currently, the world population of a certain species is approximately 4.7 ×108. By some
projections, this population will be 5 times as big in 30 years. Express the population 30 years from
now in scientific notation.
157)
A)
235 ×108
B)
23.5 ×109
C)
2.35 ×109
D)
2.35 ×1016
Use the indicated property to write an algebraic expression equivalent to the given expression.
158)
3+ x; commutative
158)
A)
x + 3
B)
–x – 3
C)
3– x
D)
x – 3
47
Simplify the exponential expression.
159)
y–9·y2
159)
A)
1
y18
B)
1
y11
C)
1
y7
D)
y11
Provide an appropriate response.
160)
Use the roster method to list the elements in the set: {x|x is an integer greater than –6}.
160)
A)
{–5, –4, –3, . . .}
B)
{–7, –8, –9, . . .}
C)
{–6, –5, –4, –3, . . .}
D)
{–5, –4, –3, –2}
A
Add as indicated.
161)
–6+ 16
161)
A)
–22
B)
10
C)
22
D)
–10
B
Use the roster method to list the elements in the set.
162)
{x | x is a whole number between 5 and 9}
162)
A)
{6, 7, 8}
B)
{5, 6, 7, 8}
C)
{5, 6, 7, 8, 9}
D)
{6, 7, 8, 9}
A
Evaluate.
163)
(–5)3
163)
A)
–125
B)
–2
C)
–15
D)
125
A
C
Use the meaning of the symbols
and
to determine whether the statement is true or false.
164)
8
{ x | x is a real number}
164)
A)
True
B)
False
Subtract as indicated.
165)
–15 – (–5)
165)
A)
20
B)
–20
C)
10
D)
–10
Multiply as indicated.
166)
34(–50)
166)
A)
1700
B)
–1800
C)
–1734
D)
–1700
Divide as indicated or state that the division is undefined.
167)
–40
4
167)
A)
–1
10
B)
–20
C)
10
D)
–10
Write the number in scientific notation.
168)
34,000,000
168)
A)
3.4 × 10–7
B)
3.4 × 107
C)
3.4 × 106
D)
3.4 × 10–6
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.
169)
A business projects next year’s profits to be $8,000,000. Write this number in scientific notation.
169)
A)
8.00 ×106
B)
8.00 ×10–7
C)
8.00 ×107
D)
8.00 ×105
Graph the equation.
170)
y =3|x|
170)
A)
B)
C)
D)
Perform the indicated computation. Write the answer in scientific notation.
171)
8,000,000,000
0.00002
171)
A)
6×1014
B)
6×1013
C)
4×1014
D)
4×1013
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
172)
–20,000
{x x is a whole number} and twelve less than twice a number is represented by 2x –12.
172)
A)
True
B)
False
Evaluate.
173)
– – 9
5
3
173)
A)
729
125
B)
–27
5
C)
–729
125
D)
93
5
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
174)
26
{1, 2, 3, ....} and {1}
{1, 2, 3, 4}
174)
A)
True
B)
False
B)
C)
D)
Express the interval in set builder notation and graph the interval on a number line.
175)
(5.5, )
175)
A)
{x x <5.5}
B)
{x x >5.5}
C)
{x x 5.5}
D)
{x x 5.5}
Solve the equation.
176)
x
4–x
7=6
176)
A)
56
B)
{28}
C)
{42}
D)
{24}
Write the expression with positive exponents only. Then simplify, if possible.
177)
(–5)–2
177)
A)
25
B)
–1
25
C)
1
25
D)
–25
Multiply the expression using the product rule.
178)
x·x9
178)
A)
2x9
B)
x10
C)
2x10
D)
x9
Multiply as indicated.
179)
(–45)(38)
179)
A)
–1710
B)
–1810
C)
–17,100
D)
–1748
Determine whether the inequality is true or false.
180)
–78 < 0
180)
A)
True
B)
False
A
Solve the equation. If the solution set is or (–, ), classify the equation as an inconsistent equation or an identity.
181)
7(x + 1) + 17 =9x –2(x – 3)
181)
A)
( , ); identity
B)
{11}
C)
; inconsistent equation
D)
{23}
C
Simplify the expression using the products to powers rule.
182)
(4x–7y4z–2)–3
182)
A)
x21z6
64y12
B)
y7
–12x10z5
C)
x21z6
–12y–12
D)
y7
64x10z5
A
Determine whether the inequality is true or false.
183)
–10 10
183)
A)
True
B)
False
B
A
Use the roster method to list the elements in the set.
184)
{x x is a natural number less than 7}
184)
A)
{0, 1, 2, 3, 4, 5, 6}
B)
{1, 2, 3, 4, 5, 6}
C)
{1, 2, 3, 4, 5, 6, 7}
D)
{0, 1, 2, 3, 4, 5, 6, 7}
Subtract as indicated.
185)
2
7– – 1
5
185)
A)
–2
35
B)
3
35
C)
17
35
D)
–17
35
Write the English phrase as an algebraic expression. Let x represent the number.
186)
The product of 3 and a number
186)
A)
3+ x
B)
3– x
C)
3x
D)
3
x
Find –x for the given value of x.
187)
x =1
4
187)
A)
1
4
B)
–1
4
C)
4
D)
0
Use the meaning of the symbols
and
to determine whether the statement is true or false.
188)
–6{ x | x is a whole number}
188)
A)
True
B)
False
Solve the problem.
189)
The length of a rectangular room is 2 feet longer than twice the width. If the room’s perimeter is 196
feet, what are the room’s dimensions?
189)
A)
Width =48 ft; length =50 ft
B)
Width =37 ft; length =76 ft
C)
Width =64 ft; length =132 ft
D)
Width =32 ft; length =66 ft
Use the order of operations to simplify the expression.
190)
12 + 4 · 9
32–3· 6 +10 –13
190)
A)
–16
5
B)
48
C)
16
11
D)
Undefined
Solve the formula for the specified variable.
191)
S = 2rh + 2r2 for h
191)
A)
h = 2(S – r)
B)
h =S
2r– 1
C)
h = S – r
D)
h =S – 2r2
2r
55
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
192)
What temperature was recorded at 3 p.m.?
192)
A)
77 ° F
B)
75 ° F
C)
79 ° F
D)
78 ° F
Subtract as indicated.
193)
0 – (–3)
193)
A)
3
B)
–3
C)
–3
D)
3
Simplify the expression.
194)
32 –66 ÷6·4
194)
A)
–232
B)
–12
C)
–72
D)
–231
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.
195)
A computer compiles a program in 0.000605 seconds. Write this number in scientific notation.
195)
A)
6.05 ×10–4
B)
6.05 ×103
C)
6.05 ×10–5
D)
6.05 ×10–6
Evaluate the expression for the given values.
196)
10x2+4y, for x =6, y =3
196)
A)
1200
B)
3612
C)
114
D)
372
Write the English phrase as an algebraic expression. Let x represent the number.
197)
6 more than 4 times a number
197)
A)
10x
B)
4x +6
C)
6x +4
D)
4(6 + x)
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.
198)
If the density of a substance is 2.58 ×10–6 tons per cubic foot, what would be the mass of
1.15 ×10–6 cubic feet of this substance. (Use the formula D =M
V.)
198)
A)
2.97 ×10–11 tons
B)
2.97 ×10–13 tons
C)
2.97 ×10–12 tons
D)
0.30 ×10–12 tons
199)
In a state with a population of 6,000,000 people, the average citizen spends $6,000 on housing each
year. What is the total spent on housing for the state?
199)
A)
$36 ×1010
B)
$3.6 ×109
C)
$36 ×1011
D)
$3.6 ×1010
Simplify the exponential expression.
200)
5x11
x7
200)
A)
20x
B)
625x4
C)
5x18
D)
5x4
Write the expression with positive exponents only. Then simplify, if possible.
201)
–5–3
201)
A)
–1
125
B)
125
C)
–125
D)
1
15
By definition, an “and” statement is true only when the statements before and after the “and” connective are both true.
Use this definition to determine whether the given statement is true or false.
202)
0.7> 0.7 and 14 7+7
202)
A)
True
B)
False
Write the number in scientific notation.
203)
5.96
203)
A)
5.96 ×101
B)
59.6 ×100
C)
59.6 ×10–1
D)
5.96 ×100
The bar graph shows the expenditures of one city government in a recent year.
204)
How much more is spent on Pensions than on Miscellaneous?
204)
A)
$9.8 million
B)
$8.5 million
C)
$6.9 million
D)
$5.2 million
Solve the equation.
205)
–{5(d + 2) – 6[3d – 2(3d + 8)] – 7} = – 18d + 191
205)
A)
{–58}
B)
290
41
C)
{63}
D)
105
8
Find the absolute value.
206)
–7
206)
A)
0
B)
–7
C)
7
D)
–14
Simplify the expression using the quotients–to–powers rule.
207)
p4
4
3
207)
A)
p12
64
B)
p7
64
C)
p12
4
D)
p7
4
Use the order of operations to simplify the expression.
208)
0 ÷6+9·8
208)
A)
120
B)
72
C)
Undefined
D)
78
Find –x for the given value of x.
209)
x = – 11
209)
A)
–11
B)
0
C)
11
D)
–1
11
Express the interval in set builder notation and graph the interval on a number line.
210)
[–7, 8)
210)
A)
{x –7 x 8 }
B)
{x x <8 }
C)
{x –7 x <8 }
D)
{x –7< x 8 }