Question

Let S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }

S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } be the universal set. Let sets A and B be subsets of S , where: Set A = { 4 , 6 , 10 , 11 , 12 , 15 , 16 , 18 , 19 , 20 }

Set B = { 1 , 3 , 5 , 7 , 8 , 9 , 12 , 13 , 14 , 16 , 17 , 18 , 20 }

Determine the following:

n ( A ) =

n ( ¯¯¯ A ) =

n ( B ) =

n ( A ∩ B ) =

n ( A ∪ B ) =

Answer #1

A = {4, 6, 10, 11, 12, 15, 16, 18, 19, 20}

Since the number of elements in set A is 4, so

n(A) = 10

= {1, 2, 3, 5, 7, 8, 9, 13, 14, 17}

Since no of elements in set is 10, so

n() = 10

B = {1, 3, 5, 7, 8, 9, 12, 13, 14, 16, 17, 18, 20}

Since the no of elements in set B is 13, so

n(B) = 13

(A B) = { 12, 16, 18, 20}

Since no of elements in set (A B) is 4, so

n(A B) = 4

(A U B) = {1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Since no of elements in set (A U B) is 19,so

n(A U B) = 19

4. Let set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20}
set A = numbers in U that divide into 12 with no remainder,
set B = numbers in U that divide into 16 with no remainder, and set
C = the numbers in U that divide into 20 with no remainder.
a. Made a Venn diagram showing the elements of the sets U, A,...

1)Let the Universal Set, S, have 97 elements. A and B are
subsets of S. Set A contains 45 elements and Set B contains 18
elements. If Sets A and B have 1 elements in common, how many
elements are in A but not in B?
2)Let the Universal Set, S, have 178 elements. A and B are
subsets of S. Set A contains 72 elements and Set B contains 95
elements. If Sets A and B have 39 elements...

Find variance of the following stocks A,B and C:
Stock
A
B
C
1
3
19
-2
2
5
17
4
3
7
15
0
4
9
13
8
5
11
11
12
6
13
9
14
8
15
7
-8
9
17
5
16
10
19
3
20

# of text messages sent yesterday
3 8 3 18 2 1 8 1 6 13 15 14 13 9 20 12 5 9 18 18 13 2 7 6 0 0 11
12 4 13 1 19 4 12 4 11 8 18 1 15 12 6 6 12 19 12 20 12 8 12
Test the following claim:
70% of individuals that send text messages send less than 10
messages per day, α = 0.01

Test, at the 1% level of significance, whether the average
business has more than 15 employees.
Answer using excel.
Employees
14
17
17
6
8
17
21
16
6
17
11
17
15
16
20
19
6
12
17
22
20
17
11
11
9
22
17
18
21
20
26
7
16
19
18
11
21
17
25
16
22
14
14
16
18
20
21
11
19
13
6
11
19
14
18
31
13
15
17
21...

Let SS be the universal set, where:
S={1,2,3,...,28,29,30}S={1,2,3,...,28,29,30}
Let sets AA and BB be subsets of SS, where:
Set
A={1,8,13,14,16,17,20,25,27,28}A={1,8,13,14,16,17,20,25,27,28}
Set B={6,7,9,13,14,30}B={6,7,9,13,14,30}
Set
C={5,8,10,11,13,14,15,17,23,25,28}C={5,8,10,11,13,14,15,17,23,25,28}
Find the number of elements in the set (A∩B)(A∩B)
n(A∩B)n(A∩B) =
Find the number of elements in the set (B∩C)(B∩C)
n(B∩C)n(B∩C) =
Find the number of elements in the set (A∩C)(A∩C)
n(A∩C)n(A∩C) =

1)Calculate the dividend yield and the payout ratio.
2)Calculate the annual dividend growth rate for the last 10
years. Based on the annual dividend growth rate for each company,
will you forecast a constant or non-constant growth in
dividends?
Date
Dividends
12/2/10
0.31
3/3/11
0.31
6/2/11
0.31
9/1/11
0.31
12/1/11
0.36
3/1/12
0.36
5/31/12
0.36
8/30/12
0.36
12/6/12
0.42
2/28/13
0.21
5/30/13
0.21
8/29/13
0.21
12/12/13
0.24
2/27/14
0.24
5/29/14
0.24
8/28/14
0.24
8/29/14
0.24
12/11/14
0.28
2/26/15
0.28
5/28/15...

Bag
Blue
Orange
Green
Yellow
Red
Brown
Total Number of Candies
1
7
23
9
11
4
6
60
2
16
16
4
7
9
4
56
3
14
14
3
10
5
11
57
4
13
14
7
8
8
6
56
5
18
12
7
10
5
7
59
6
12
9
11
9
8
8
57
7
15
16
6
6
6
8
57
8
15
17
8
4
6
7
57
9
12
14
10
5...

Plant sizes get larger as you move from ATC-1 to ATC-4. Output
ATC-1 ATC-2 ATC-3 ATC-4 1,500 $10 15 $20 $30 2,000 8 12 17 25 2,500
9 10 15 20 3,000 12 8 13 18 3,500 15 6 11 16 4,000 18 10 9 14 4,500
20 12 7 12 5,000 24 15 11 10 5,500 29 19 13 8 6,000 35 25 15 9 In
the long run, the firm should use plant size ATC-4 for what level...

Plant sizes get larger as you move from ATC-1 to ATC-4. Output
ATC-1 ATC-2 ATC-3 ATC-4 1,500 $10 15 $20 $30 2,000 8 12 17 25 2,500
9 10 15 20 3,000 12 8 13 18 3,500 15 6 11 16 4,000 18 10 9 14 4,500
20 12 7 12 5,000 24 15 11 10 5,500 29 19 13 8 6,000 35 25 15 9
Which plant size would produce at the least cost for the
1,500-2,500 range of...

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