pLEASE show your workHomework 10
July 19, 2016
MATH 106-C01 – Quantitative Reasoning
Due date: July 20, 2016, at 10:30am
Exercise 1. Do problems 16, 18, 20, 24 and 26 from p301-302 of the textbook. Show your
work.
Exercise 2. Do problems 8,10, 12,14, 16, 18, 20 and 24 from p337 of the textbook. Show
your work.
Exercise 3. Do problem 36 from p338 of the textbook.
Exercise 4. Do problems 38, 68, 70, 72 and 76 from p338 of the textbook. Show your work.
Exercise 5. Do problems 78, 80 and 82 from p338 of the textbook. Show your work.
1
II 33
338 W CHAPTER 7 The Basic Concepts of Algebra
36. Explain in your own words how to raise a power to a
4.0 billion
15 years
power,
Convert each number from standard notation to scientific
notation.
69. 230
70. 46,500
37. Which one of the following is correct?
3 3
3-1
4-1
A.
B.
4
4-1
3
71. 0.02
72. 0.0051
(
(6)
3-1
3
3-1
3-1
C.
–
D.
Convert each number from scientific notation to standard
notation.
4
4-1
4-1
73. 6.5 X 103
74. 2.317 x 105
75. 1.52 x 10-2
76. 1.63 X 10-4
38. Which one of the following is incorrect?
A. (3r)-2 = 3-27-2
B. 3r-2 = (3r)-2
1
C. (3r) -2 =
D. (3r)-2
(3r)2
9
+2
Use scientific notation to perform each of the following com-
putations. Leave the answers in scientific notation.
0.002 X 3900
Use the product, quotient, and power rules to simplify each
expression. Write answers with only positive exponents.
Assume that all variables represent nonzero real numbers.
77.
0.009 X 600
78.
0.02
0.000013
0.0004 X 56,000
0.018 X 20,000
+12
79.
80.
39. r12.rº
40.
0.000112
300 X 0.0004
x4
840,000 X 0.03
28 X 0.0045
517
312
42.
81.
82.
0.00021 X 600
140 X 1500
313
516
3-4
43.
3-2
44.
2-4
2-3
In Exercises 83-86, write the boldface numbers in scientific
notation.
reciprocal of x (x + 0)
-1
A. r-1
1
B.
X
C.
– (0)
D. – x
X
68. Which one of the following is not in scientific notation?
B. 14 x 10-6
A. 6.02 X 1023
C. 1.4 x 10-5
D. 3.8 X 103
Associative property; product rule, mutta
43.
3-2
(1.9992 x 101) x 11
9-1
= 1.9992 x 1012
45.
9
The 2005 expenditure was about $1,999,200,000,000 (almost $2 trillion).
47. 157-12
49. (3x)2
18. -4-1
7.5 EXERCISES
51. a-3a26
17. -7-2
2-3
t>
20.
.
53.
Match the exponential expressions in Exercises 1-6 with their
equivalent expressions in choices A-F below. Choices may be
used once, more than once, or not at all.
3-2
r-4
19.
.
2.
(-4)-3
31-2
-3
3,-
2
1.
2.
5-1
22.
.
55.
3
5
r-27
3. (-3)
()
21.
4-2
(1)
(
3)2
2
5-2
4.
.
5.
6.
-2
57. 762
5
3
-3
24.
-(
15
23.
3
9
25
59. (z3)
5
A.
23
B.
C.
9
9
25
4)-2
61. -3
25.
26. 3-1 + 2-1
9
D.
5
E. none of these
F. all of these
25
63. (30
27. 4-1 + 5-1
28. 80
Evaluate each exponential expression.
65. (x
7. 54
8, 103
29. 12°
30. (-23)º
67. W
9. (-2)
10, (-5)
re
31. (-4)º
32. -2°
11. -23
12. -32
33. 30 – 40
A
34. -80 – 70
13. -(-3)^
14. -(-5)
we
68.
35. In order to raise a fraction to a negative power,
change the fraction to its
exponent to the
15. 7-2
16. 4-1
and change
of the original expon
7.2 EXERCISES
11. the product of 6 less than a number and 4 more than the
Decide whether each of the following translates into an
expression or an equation.
number
1. the product of a number and 6
12. the quotient of a number and 9
2. 39% of a number
13. the ratio of 25 and a nonzero number
3. Z of a number is 36.
4. 9 is 5 more than a number.
14. of a number
15. Write a few sentences describing the six steps for prob-
lem solving
5. the ratio of a number and 24
6. 48 divided by a number is 12.
(16, Which is not a valid translation of “30% of a number”?
3х
A. 0.30x B. 0.3x C.
D. 0.30
10
7. Rework Example 6, letting the variable represent the
number of quarters. Is the answer to the problem the
same?
8. Explain why 19 – x is not a correct translation of
“19 less than a number.”
Unknown Numbers Let x represent the number, write an
equation for the sentence, and then solve.
17. If 2 is added to five times a number, the result is equal to
5 more than four times the number. Find the number.
Translate each verbal phrase into a mathematical expression.
Use x to represent the unknown number,
18. If four times a number is added to 8, the result is three
times the number added to 5. Find the number.
9. a number decreased by 12
10. 7 more than a number
19. If 2 is subtracted from a number and this difference is
tripled, the result is 6 more than the number. Find the
number.
ations | 30
CHAPTER 7 The Basic Concepts of Algebra
302 III CHAPTER 7
20. If 3 is added to a number and this sum is doubled, the
26. MLB Record In the 2008 Major League Baseball season,
the Tampa Bay Rays won 33 fewer than twice as many
games as they lost. They played 162 regular season
games. How many wins and losses did the team have?
(Source: www.mlb.com)
result is 2 more than the number. Find the number.
21. The sum of three times a number and 7 more than the
number is the same as the difference between -11 and
twice the number. What is the number?
22. If 4 is added to twice a number and this sum is multi-
plied by 2, the result is the same as if the number is
multiplied by 3 and 4 is added to the product. What is
the number?
27. U.S. Senate During the 111th Congress (beginning in
2009), the U.S. Senate had a total of 98 Democrats and
Republicans. There were 18 fewer Republicans than
Democrats. How many Democrats and Republicans
were there in the Senate? (Source: World Almanac and
Book of Facts.)
bike
28. U.S. House of Representatives The total number of
Democrats and Republicans in the U.S. House of
Representatives during the 111th Congress was 435.
There were 31 more Democrats than Republicans. How
many members of each party were there? (Source:
World Almanac and Book of Facts.)
Use the methods of Examples 1 and 2 or your own method
to solve each problem.
23. Concert Revenues Bon Jovi and Bruce Springsteen had
the two top-grossing North American concert tours for
2008, together generating $415.3 million in ticket sales.
If Bruce Springsteen took in $6.1 million less than
Bon Jovi, how much did each tour generate? (Source:
www.billboard.com)
ce by bus
29. Submarine Sandwich Nagaraj Nanjappa has a party-
length sandwich that is 59 inches long and is to be cut
into three pieces. The middle piece will be 5 inches
the shortest piece, and the shortest piec
niece. Ho
II 33
338 W CHAPTER 7 The Basic Concepts of Algebra
36. Explain in your own words how to raise a power to a
4.0 billion
15 years
power,
Convert each number from standard notation to scientific
notation.
69. 230
70. 46,500
37. Which one of the following is correct?
3 3
3-1
4-1
A.
B.
4
4-1
3
71. 0.02
72. 0.0051
(
(6)
3-1
3-1
3-1
C.
–
3
4-1
D.
Convert each number from scientific notation to standard
notation.
4
4-1
73. 6.5 X 103
74. 2.317 x 105
75. 1.52 x 10-2
76. 1.63 X 10-4
38. Which one of the following is incorrect?
A. (3r)-2 = 3-27-2
B. 3r-2 = (3r)-2
1
C. (3r) -2 =
D. (3r)-2
(3r)2
9
+2
Use scientific notation to perform each of the following com-
putations. Leave the answers in scientific notation.
Use the product, quotient, and power rules to simplify each
expression. Write answers with only positive exponents.
Assume that all variables represent nonzero real numbers.
77.
0.002 X 3900
0.000013
0.009 X 600
78.
0.02
0.0004 X 56,000
+12
80.
0.018 X 20,000
300 X 0.0004
39. r12.rº
79.
40.
0.000112
x4
28 X 0.0045
517
42.
312
313
81.
82.
840,000 X 0.03
0.00021 X 600
140 X 1500
516
3-4
43.
3-2
44.
2-4
2-3
In Exercises 83-86, write the boldface numbers in scientific
notation.
reciprocal of x (x + 0)
-1
A. r-1
1
B.
X
C.
– (0)
D. – x
X
A. 6.02 X 1023
C. 1.4 x 10-5
68. Which one of the following is not in scientific notation?
B. 14 x 10-6
D. 3.8 X 103
Associative property; product rule, mutta
43.
3-2
(1.9992 x 101) x 11
9-1
= 1.9992 x 1012
45.
9
The 2005 expenditure was about $1,999,200,000,000 (almost $2 trillion).
47. 157-12
49. (3x)2
18. -4-1
7.5 EXERCISES
51. a-3a26
17. -7-2
2-3
t>
20.
.
53.
Match the exponential expressions in Exercises 1-6 with their
equivalent expressions in choices A-F below. Choices may be
used once, more than once, or not at all.
3-2
r-4
19.
.
2.
(-4)-3
31-2
-3
3,-
2
1.
2.
5-1
22.
.
55.
3
5
r-27
3. (-3)
()
21.
4-2
(1)
(
3)2
2
5-2
4.
.
5.
6.
-2
57. 762
5
3
-3
24.
-(
15
23.
3
9
25
59. (z3)
5
A.
23
B.
C.
9
9
25
4)-2
61. -3
25.
26. 3-1 + 2-1
9
D.
5
E. none of these
F. all of these
25
63. (30
27. 4-1 + 5-1
28. 80
Evaluate each exponential expression.
65. (x
7. 54
8, 103
29. 12°
30. (-23)º
67. W
9. (-2)
10, (-5)
re
31. (-4)º
32. -2°
11. -23
12. -32
33. 30 – 40
A
34. -80 – 70
13. -(-3)^
14. -(-5)
we
68.
35. In order to raise a fraction to a negative power,
change the fraction to its
exponent to the
15. 7-2
16. 4-1
and change
of the original expon
7.2 EXERCISES
11. the product of 6 less than a number and 4 more than the
Decide whether each of the following translates into an
expression or an equation.
number
1. the product of a number and 6
12. the quotient of a number and 9
2. 39% of a number
13. the ratio of 25 and a nonzero number
3. Z of a number is 36.
4. 9 is 5 more than a number.
14. of a number
15. Write a few sentences describing the six steps for prob-
lem solving
5. the ratio of a number and 24
6. 48 divided by a number is 12.
(16, Which is not a valid translation of “30% of a number”?
3х
A. 0.30x B. 0.3x C.
D. 0.30
10
7. Rework Example 6, letting the variable represent the
number of quarters. Is the answer to the problem the
same?
8. Explain why 19 – x is not a correct translation of
“19 less than a number.”
Unknown Numbers Let x represent the number, write an
equation for the sentence, and then solve.
17. If 2 is added to five times a number, the result is equal to
5 more than four times the number. Find the number.
Translate each verbal phrase into a mathematical expression.
Use x to represent the unknown number,
18. If four times a number is added to 8, the result is three
times the number added to 5. Find the number.
9. a number decreased by 12
10. 7 more than a number
19. If 2 is subtracted from a number and this difference is
tripled, the result is 6 more than the number. Find the
number.
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