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PbAF 499 Homework Assignment #1
Page 1 of 9
PbAf 499, Summer 2011
Homework Assignment #1, Due 6/30
On this homework assignment, I will be grading the starred questions.
Calculate the following. In the case of fractions, reduce them to their simplest
possible forms.
PbAF 499 Homework Assignment #1
1.
53

1 3
2. * 5 
3

1 3
3.
53
3
1
4.
22

222
5.
22
2
22
6.
1 2
 
2 3
7.
1 2
 
2 3
8.
1 2
 
2 3
9.
1 2
 
2 3
10.
5 2 52


2 7 35
11. *
12.
27 52


5  2 35
27 52


5  2 35
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PbAF 499 Homework Assignment #1
13 .
12  10 8  12


74
37  3
14 .
12  10 8  12


74
37  3
15 .
12  10 8  12


74
37  3
16 .
2 3
 
5 7
17 .
2 3
 
5 7
18 .
2 3
 
5 7
19 .
2 3
 
5 7
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PbAF 499 Homework Assignment #1
Page 4 of 9
Simplify the following fractions as much as possible.
20.
48

60
21.
27

99
22.
49

56
23. *
8

24
24.
11

13
25.
16

25
26.
81

99
27.
40

88
28.
24

68
29.
6  12

33
30.
89

43
Calculate the following percentage changes using the first number as the base.
31.*
32.
Population increases from 120,000 to 135,000.
Average house price increases from $180,000 to $210,000.
PbAF 499 Homework Assignment #1
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33.
Hourly wage increases from $6.25 to $6.75.
34.
Weight decreases from 170 pounds to 160 pounds
35.
The price of a pound of rice falls from $0.30 to $0.25.
36.
Rainfall decreases from 135 inches per year to 120 inches per year.
37.
The number of miles biked in one year falls from 2100 to 1800.
38.
The number of students in a graduating class falls from 675 to 625.
39.
The number of commuters on the Burke-Gilman trail rises from 1600 to 1700.
40.
Average class size rises from 25 to 30 students.
Calculate the following percentage changes using the average of the two numbers as
the base.
41.*
Population increases from 120,000 to 135,000.
42.
Average house price increases from $180,000 to $210,000.
43.
Hourly wage increases from $6.25 to $6.75.
44.
Weight decreases from 170 pounds to 160 pounds
45.
The price of a pound of rice falls from $0.30 to $0.25.
46.
Rainfall decreases from 135 inches per year to 120 inches per year.
47.
The number of miles biked in one year falls from 2100 to 1800.
48.
The number of students in a graduating class falls from 675 to 625.
49.
The number of commuters on the Burke-Gilman trail rises from 1600 to 1700.
50.
Average class size rises from 25 to 30 students.
Calculate the price elasticity in each case. When calculating the percentage change,
use the average of the two numbers as the base.
51.
Price rises by 10% and the quantity demanded falls by 5%.
52.
Price falls by 35% and the quantity demanded rises by 7%.
53.*
54.
The price rises from 25 to 30 and the quantity demanded falls from 60 to 50.
The price rises from 33 to 35 and the quantity demanded falls from 80 to 75.
PbAF 499 Homework Assignment #1
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55.
The price falls from 69 to 64 and the quantity demanded rises from 800,000 to
820,000.
56.
Price falls by 100% and quantity demanded rises by 50%.
57.
Price rises by 3.5% and quantity demanded falls by 7%.
58.
Price falls from $3.00 to $2.50 and quantity demanded rises from 500,000 to
600,000.
59.
Price falls from $35.00 to $33.00 and the quantity demanded rises from 7.5
million tons to 8.0 million tons.
60.
Price rises from $6.40 to $6.90 and the quantity demanded falls from 820 to
800.
PbAF 499 Homework Assignment #1
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Calculate the following sums. Use the following data points where necessary:
X1=5
X2=12
X3=18
X4=8
X5=7
10
61. *
i 
i 1
10
62.
i
2
i 1
5
63.
X
i 1
i
5
64.
X
2
i
i 1
5
65.
 X
i
 10 
 X
i
 10 
 X
2
i
 Xi 
X
2
i
i 1
5
66.
i 1
5
67.
2
i 1
5
68.

i 1

69.
1
2
i 1

70.
1
2
i 0
i
i
 Xi 
Xi
PbAF 499 Homework Assignment #1
Page 8 of 9
Calculate the following fractions:
71. *
72!

68!
72.
22!

20!
73.
5!

3!
74.
28!

23! 5!
75.
56!

50! 6!
76.
20! 4!

18!
77.
98!

94! 4!
78.
115!

112! 3!
In a lotto drawing, the number of possible outcomes is
n!
x! n - x!
where n is the number of balls in the machine and x is the number actually drawn.
79. Calculate the number of possible combinations in a lotto where 7 balls are
chosen from 40.
80. Calculate the number of possible combinations in a lotto where 33 balls are
chosen from 40.
81. To see why we define 0!=1, calculate the number of possible combinations in a
lotto where 0 balls are chosen from 80.
82. Alternatively, calculate the number of possible combinations in a lotto where 80
balls are chosen from 80.
PbAF 499 Homework Assignment #1
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83.* Calculate the number of possible combinations in a lotto where 7 balls are
chosen from 49. How does it compare to the number when 7 are chosen from 40?
84.
Why are all lottos run like the one in #79 rather than the one in #80?
The average or mean of a sample of data is defined as:
n
X

i 1
Xi

n
n

i 1
1
1
Xi 
n
n
n
X
i
i 1
Calculate the means of the following data sets.
85.
X1=5, X2=12, X3=18, X4=8, X5=7
86.
X1=5, X2=12, X3=18, X4=8, X5=7, X6=10
87.
X1=5, X2=12, X3=18, X4=8, X5=7, X6=22
88.*
X1=5, X2=12, X3=18, X4=8, X5=7, X6=0
Break the following numbers down into their prime factors.
89.*
68=
90.
24=
91.
18=
92.
72=
93.
85=
94.
56=
95.
128=
96.
48=
97.*
97=
98.
100=
99.
41=
100.
42=