Solve the problem.
211)
After a 14% price reduction, a boat sold for $21,500. What was the boat’s price before the reduction?
(Round to the nearest cent, if necessary.)
211)
A)
$24,510.00
B)
$153,571.43
C)
$3010.00
D)
$25,000
212)
Paul has $10,000 to invest. He puts x dollars in a safe government–insured certificate of deposit
paying 4% per year. He invests the remainder of the money in noninsured corporate bonds paying
13% per year. His total interest earned at the end of the year is given by the algebraic expression
0.04x +0.13(10,000 – x). Determine the amount of interest earned at the end of the year if he invests
$3000 in the government–insured certificate of deposit.
212)
A)
$927
B)
$1030
C)
$1570
D)
$1810
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
213)
When four times a number is added to 9 times the number, the result is 52. What is the number?
213)
A)
0.8
B)
5.8
C)
–5.8
D)
4
Subtract as indicated.
214)
–2
3–1
2
214)
A)
–5
6
B)
–1
6
C)
7
6
D)
–7
6
Find –x for the given value of x.
215)
x = – 2
7
215)
A)
–7
2
B)
2
7
C)
–2
7
D)
0
Simplify the algebraic expression.
216)
[10x2– (9x2+ 9)] + [ (10x2– (–4+ 6x2)) – 9x2]
216)
A)
26x2+ 5
B)
6x2– 13
C)
–12x2– 13
D)
–4x2– 5
Solve the equation.
217)
–10x – (3x – 7) =4
217)
A)
–13
3
B)
13
3
C)
–7
11
D)
3
13
Solve the equation to determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
218)
15x +5(x + 1) =20(x + 1) –15
218)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
219)
When 2 times a number is subtracted from 7 times the number, the result is 45. What is the
number?
219)
A)
3.1
B)
9
C)
5
D)
–9
Solve the problem.
220)
There were 38,000 people at a ball game in Los Angeles. Each person paid either $11 for a reserved
seat or $4 for general admission. If the number who paid $11 for a reserved seat was x, then the
total receipts for the game are given by the algebraic expression 11x +4(38,000 – x). Find the total
receipts for the game if the number who paid $11 was 10,000.
220)
A)
$258,000
B)
$222,000
C)
$218,000
D)
$282,000
Write the English phrase as an algebraic expression. Let x represent the number.
221)
65 less than a number
221)
A)
x + 65
B)
65
C)
65x
D)
65 – x
Express the interval in set builder notation and graph the interval on a number line.
222)
[–2, 7)
222)
A)
{x –2< x 7}
B)
{x x <7}
C)
{x –2 x <7}
D)
{x –2 x 7}
Write the English phrase as an algebraic expression. Let x represent the number.
223)
8 less than 4 times a number
223)
A)
8–4x
B)
4–8x
C)
4x –8
D)
8x –4
Solve the equation. Express the solution in scientific notation.
224)
x – (9.8 ×106) =8.3 ×106
224)
A)
{1.81 ×105}
B)
{18.1 ×106}
C)
{1.81 ×107}
D)
{1.81 ×1013}
Solve the formula for the specified variable.
225)
V =1
3Bh for h
225)
A)
h =V
3B
B)
h =3V
B
C)
h =B
3V
D)
h =3B
V
Use the order of operations to simplify the expression.
226)
62– – 6+14 +1
226)
A)
–3
B)
–1
C)
15
D)
29
Provide an appropriate response.
227)
Write in scientific notation: 118,000,000,000
227)
A)
1.18 ×1010
B)
1.18 ×1012
C)
1.18 ×1011
D)
11.8 ×1011
Divide as indicated or state that the division is undefined.
228)
3
7÷ – 2
3
228)
A)
14
9
B)
–9
14
C)
9
14
D)
–2
7
Perform the indicated operation.
229)
–1
9–1
2
229)
A)
9
2
B)
2
11
C)
1
18
D)
18
Use the meaning of the symbols
and
to determine whether the statement is true or false.
230)
–22 { x | x is a natural number}
230)
A)
True
B)
False
Solve the equation.
231)
–6x – 3 = – 8+ 8x
231)
A)
–14
5
B)
5
14
C)
–2
11
D)
14
5
Evaluate.
232)
(–1)59
232)
A)
–1
B)
–59
C)
59
D)
1
Use the roster method to list the elements in the set.
233)
{x | x is an integer greater than –3}
233)
A)
{–4, –5, –6}
B)
{–2, –1, 0, . . .}
C)
{–2, –1, 0, 1}
D)
{–4, –5, –6, . . .}
Express the interval in set builder notation and graph the interval on a number line.
234)
(–, 7]
234)
A)
{x x 7}
B)
{x x >7}
C)
{x x <7}
D)
{x x 7}
Find the absolute value.
235)
|13|
235)
A)
0
B)
–13
C)
13
D)
26
Use the meaning of the symbols
and
to determine whether the statement is true or false.
236)
10
{ x | x is an irrational number}
236)
A)
True
B)
False
Express the interval in set builder notation and graph the interval on a number line.
237)
[–2, 5]
237)
A)
{x –2 x <5 }
B)
{x –2< x 5 }
C)
{x –2 x 5 }
D)
{x –2< x <5 }
D
Determine whether the statement is true or false.
238)
Some real numbers are not rational numbers.
238)
A)
True
B)
False
Simplify the expression.
239)
–4x –3(2x –7) +9
239)
A)
2x +30
B)
10x –12
C)
–10x –12
D)
–10x +30
Solve the equation.
240)
[–4(8 –9)7– (–10)] = – 2x
240)
A)
{–3}
B)
{3}
C)
{–9}
D)
{–7}
Solve the problem.
241)
The formula C =0.051x2+0.68x +4.5 can be used to approximate the number, C, (in millions) of
laptops sold over a ten–year period, where x is the number of years since the first year this
information was recorded. According to this formula, how many laptops were sold in year 6?
Round the answer to the nearest tenth of a million.
241)
A)
4.5 million
B)
8.9 million
C)
9.2 million
D)
10.4 million
67
Express the interval in set builder notation and graph the interval on a number line.
242)
[3.5, )
242)
A)
{x x 3.5}
B)
{x x 3.5}
C)
{x x >3.5}
D)
{x x <3.5}
Evaluate the expression for the given values.
243)
6x – y, for x =8 and y =2
243)
A)
46
B)
8
C)
96
D)
50
Simplify the exponential expression.
244)
xy4
x6y
–2
244)
A)
1
x8y9
B)
x10
y6
C)
1
x14y10
D)
y6
x10
Use the indicated property to write an algebraic expression equivalent to the given expression.
245)
–3· x; commutative of multiplication
245)
A)
x – (3)
B)
3– x
C)
3· x
D)
x · (–3)
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.
246)
Four times the sum of a number and nine is represented by 4x +9 and
{x x is an irrational number}
246)
A)
True
B)
False
Solve the problem.
247)
Inclusive of a 6.3% sales tax, a diamond ring sold for $2232.30. Find the price of the ring before the
tax was added. (Round to the nearest cent, if necessary.)
247)
A)
$2100
B)
$140.63
C)
$2372.93
D)
$2091.67
Subtract as indicated.
248)
12 – (–6)
248)
A)
–18
B)
–6
C)
6
D)
18
Write the expression with positive exponents only. Then simplify, if possible.
249)
x6y–9
z–8
249)
A)
x6z8
y9
B)
y9
x6z8
C)
x6z9
y8
D)
z8
x6y9
Solve the problem.
250)
E. coli is a strain of bacteria that occurs naturally and is often used in lab experiments. Under
certain conditions, the number of bacteria present in a colony is given by E =Eo·2t/30, where E is
the number of bacteria present t minutes after the beginning of an experiment, and Eo is the
number present when t = 0. If Eo is 18, how many bacteria are present after 60 minutes?
250)
A)
72 bacteria
B)
22 bacteria
C)
648 bacteria
D)
144 bacteria
Provide an appropriate response.
251)
Write in decimal notation: 9.4 ×10–7.
251)
A)
0.000094
B)
0.00000009
C)
0.00000094
D)
0.0000094
Solve.
252)
A certain store has a fax machine available for use by its customers. The store charges $2.30 to send
the first page and $0.60 for each subsequent page. The total price, P, for the faxing x pages can be
modeled by the formula P =0.60(x – 1) +2.30. Determine the number of pages that can be faxed for
$10.10.
252)
A)
4 pages
B)
14 pages
C)
59 pages
D)
17 pages
Solve the problem.
253)
Raleigh has a total of 68 coins, all of which are either dimes or nickels. If d of the coins are dimes,
then the total value of the coins (in dollars) is given by the algebraic expression 0.1d + 0.05(68 – d).
If the number of dimes is 44, determine the total value of the coins.
253)
A)
$4.65
B)
$5.60
C)
$3.90
D)
$6.05
Find –x for the given value of x.
254)
x = – 5
254)
A)
–5
B)
5
C)
5
D)
–5
Perform the indicated computation. Write the answer in scientific notation.
255)
0.000012 ×0.00004
0.00006
255)
A)
48 ×10–7
B)
8×106
C)
48 ×107
D)
8×10–6
Use the meaning of the symbols
and
to determine whether the statement is true or false.
256)
2
9
{ x | x is a rational number}
256)
A)
True
B)
False
Divide the expression using the quotient rule.
257)
–28x9y9
7x6y6
257)
A)
x3y3
B)
–4x2y2
C)
–4x2y3
D)
–4x3y3
Graph the equation.
258)
y = – 3
258)
71
A)
B)
C)
D)
Evaluate.
259)
Evaluate x2+ 2x for the value of x satisfying 2(x + 2) + – 4=2x –3(4 – x).
259)
A)
72
B)
15
C)
24
D)
35
Simplify the algebraic expression.
260)
–7[–6x2+ 9(8 – x)]
260)
A)
42x2+ 63x – 504
B)
42x2– 63x – 504
C)
42x2+ 7x – 504
D)
42x2– 9x + 72
72
Solve the equation.
261)
1
9(x – 27) –1
7(x – 7) = x – 5
261)
A)
567
65
B)
189
65
C)
63
65
D)
441
65
Simplify the exponential expression.
262)
–8x–6y11
–56x–2y–6
262)
A)
x4y5
7
B)
y17
7x4
C)
y5
7x4
D)
x4y17
7
Write the number in scientific notation.
263)
0.000000039806
263)
A)
3.9806 ×10–8
B)
3.9806 ×108
C)
3.9806 ×10–9
D)
3.9806 ×10–7
Solve the problem.
264)
The sum of the angles of a triangle is 180°. Find the three angles of the triangle if one angle is twice
the smallest angle and the third angle is 40° greater than the smallest angle.
264)
A)
35°, 70°, 75°
B)
15°, 55°, 110°
C)
15°, 30°, 135°
D)
28°, 56°, 96°
The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve.
X Y1Y2
–3 9 –3
–2 4 –1
–1 1 1
0 0 3
1 1 5
2 4 7
3 9 9
265)
At which points do the graph of Y1 and Y2 intersect?
265)
A)
(–1, 1) and (3, 9)
B)
(0, 1) and (3, 9)
C)
(0, 3) and (0, 1)
D)
(–1, 1) and (0, 3)
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.
266)
–4000
{x x is an integer} and eight less than four times a number is represented by 4x –8.
266)
A)
True
B)
False
Write the number in scientific notation.
267)
260,000
267)
A)
2.6 ×10–6
B)
2.6 ×10–5
C)
2.6 ×105
D)
2.6 ×106
Add as indicated.
268)
–1
6–8
9
268)
A)
–19
18
B)
–13
9
C)
–3
5
D)
–1
6
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.
269)
If the mass of an object is 3.89351 ×10–6 tons and its density is 6.29 ×10–5 tons per cubic foot, find
the volume of this object. (Use the formula D =M
V.)
269)
A)
6.19 ×10–2 cubic feet
B)
61.9 ×10–2cubic feet
C)
6.19 ×10–1cubic feet
D)
6.19 ×10–3cubic feet
Divide as indicated or state that the division is undefined.
270)
0
–4.3
270)
A)
Undefined
B)
–4.3
C)
4.3
D)
0
Write the expression with positive exponents only. Then simplify, if possible.
271)
1
–5–2
271)
A)
–25
B)
1
25
C)
25
D)
–1
25
Simplify the expression using the quotients–to–powers rule.
272)
a
8
3
272)
A)
a4
4096
B)
a
8
C)
a3
8
D)
a3
512
Use the indicated property to write an algebraic expression equivalent to the given expression.
273)
– (–8x +7); distributive
273)
A)
8x –7
B)
–8x –7
C)
–8x +7
D)
8x +7
Simplify the algebraic expression.
274)
9x4+ 8x4
274)
A)
16x4
B)
17x8
C)
17x4
D)
17x16
Use the indicated property to write an algebraic expression equivalent to the given expression.
275)
2· (ay); associative
275)
A)
2· (y+a)
B)
2+ (ay)
C)
(2a) ·y
D)
(ay) ÷2
Solve the equation to determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
276)
7(x + 7) =7x + 49
276)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
Determine whether the inequality is true or false.
277)
–7<7
10
277)
A)
True
B)
False
Solve the equation. Express the solution in scientific notation.
278)
x
9×109=4.3 ×107
278)
A)
{3.87 ×1017}
B)
{3.87 ×1063}
C)
{387 ×1016}
D)
{38.7 ×1017}
Use the five–step strategy for solving word problems.
279)
Sybil is having her yard landscaped. She obtained an estimate from two landscaping companies.
Company A gave an estimate of $210 for materials and equipment rental plus $55 per hour for
labor. Company B gave and estimate of $315 for materials and equipment rental plus $40 per hour
for labor. Determine how many hours of labor will be required for the two companies to cost the
same.
279)
A)
6 hours
B)
7 hours
C)
10 hours
D)
11 hours
280)
The sum of two numbers is 118. One number is 20 less than twice the other. Find the numbers.
280)
A)
68 and 50
B)
44 and 74
C)
46 and 72
D)
44 and 68
Solve the formula for the specified variable.
281)
F =
9
5C + 32 for C
281)
A)
C =5
9(F – 32)
B)
C =5
F – 32
C)
C =9
5(F – 32)
D)
C =F – 32
9
Multiply the expression using the product rule.
282)
24·23
282)
A)
212
B)
47
C)
412
D)
27
Write the English phrase as an algebraic expression. Let x represent the number.
283)
A number decreased by 41
283)
A)
41x
B)
x –41
C)
41
D)
41 – x
Perform the indicated operation.
284)
–56.8
–8
284)
A)
7.01
B)
–7.01
C)
–7.1
D)
7.1
Simplify the exponential expression.
285)
8x–5y–2z3
2xy–2z–3
–2
285)
A)
x8
16z12
B)
4x12
z12
C)
x12y4
16z12
D)
x12
16z12
Find –x for the given value of x.
286)
x =30
286)
A)
0
B)
30
C)
1
30
D)
–30
Perform the indicated computation. Write the answer in scientific notation.
287)
(3 ×108)(3.5 ×10–3)
287)
A)
10.5 ×106
B)
105 ×105
C)
1.05 ×10–24
D)
1.05 ×106
Graph the equation.
78
288)
y = – 3x + 2
288)
A)
B)
C)
D)
79
Solve.
289)
Forensic scientists use the lengths of certain bones to calculate the height of a person. When the
femur (the bone from the knee to the hip socket) is used, the following formula applies for men:
h = 69.09 + 2.24f, where h is the height and f is the length of the femur (both in centimeters). Find
the height of a man with a femur measuring 54 centimeters.
289)
A)
190.05 cm
B)
3851.82 cm
C)
123.09 cm
D)
6.74 cm
Perform the indicated computation. Write the answer in scientific notation.
290)
(4 ×10–1)(2 ×10–3)
290)
A)
80 ×10–4
B)
8×10–3
C)
8×10–4
D)
8×103
Determine whether the statement is true or false.
291)
Some real numbers are rational numbers.
291)
A)
True
B)
False
Solve the equation to determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
292)
8x + 2(–3x – 6) = – 6– 4x
292)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
Divide as indicated or state that the division is undefined.
293)
–168
–8
293)
A)
1
21
B)
–21
C)
21
D)
11