Five partners ( P 1 , P 2 , P 3 , P 4 , and P 5 ) jointly own the Gaussian Electric Company. P 1 owns 15 shares of the company, P 2 owns 12 shares, P 3 and P 4 each owns 10 shares and P 5 owns 3 shares, with the usual agreement that one share equals one vote. Describe the partnership as a weighted voting system using the standard notation [ q : w 1 , w − { 2 } , ... , w N ] if a . decisions in the partnership are made by simple majority. b . decisions in the partnership require two-thirds of the votes.
Five partners
(
P
1
,
P
2
,
P
3
,
P
4
, and
P
5
)
jointly own the Gaussian Electric Company.
P
1
owns 15 shares of the company,
P
2
owns 12 shares,
P
3
and
P
4
each owns 10 shares and
P
5
owns 3 shares, with the usual agreement that one share equals one vote. Describe the partnership as a weighted voting system using the standard notation
[
q
:
w
1
,
w
−
{
2
}
,
...
,
w
N
]
if
a. decisions in the partnership are made by simple majority.
b. decisions in the partnership require two-thirds of the votes.
Expert Solution
To determine
a)
To describe:
The partnership as a weighted voting system where decisions in the partnership are made by simple majority.
Answer to Problem 1E
Solution:
The partnership as a weighted voting system by simple majority is given as,
[26:15,12,10,10,3]
Explanation of Solution
Given:
In the Gaussian Electric Company, P1 owns 15 shares of the company, P2 owns 12 shares, P3 and P4 each owns 10 shares and P5 owns 3 shares, with the usual agreement that one share equals one vote.
Procedure:
A given number of votes are controlled by each player in a formal voting arrangement, it is said to be weighted voting system.
Calculation:
The total share of the company is 100%. The distribution of shares of the company gives the number of votes owned by P1, P2, P3, P4 and P5.15% shares are owned by P1, and it represents 15 votes of the company. 12% shares are owned by P2, and it represents 12 votes of the company. 10% shares are owned by P3, which is 10 votes of the company. 10% shares are owned by P4, which is 10 votes of the company and 3% shares are owned by P5, which is 3 votes of the company.
Total number of votes is given by,
15+12+10+10+3=50
The simple majority is considered to be more than 50% of the total number of votes.
Majority is given by,
502+1=25+1=26
The standard notation of weighted voting system where decisions in the partnership are made by simple majority is given as,
[26:15,12,10,10,3]
Conclusion:
Thus, the partnership as a weighted voting system by simple majority is given as,
[26:15,12,10,10,3]
Expert Solution
To determine
b)
To calculate:
The partnership as a weighted voting system where decisions in the partnership require two-thirds of the votes.
Answer to Problem 1E
Solution:
The partnership as a weighted voting system where decisions in the partnership require two-thirds of the votes is given as,
[34:15,12,10,10,3]
Explanation of Solution
Given:
In the Gaussian Electric Company, P1 owns 15 shares of the company, P2 owns 12 shares, P3 and P4 each owns 10 shares and P5 owns 3 shares, with the usual agreement that one share equals one vote.
Procedure:
A given number of votes are controlled by each player in a formal voting arrangement, it is said to be weighted voting system.
Calculation:
The total share of the company is 100%. The distribution of shares of the company gives the number of votes owned by P1, P2, P3, P4 and P5.15% shares are owned by P1, and it represents 15 votes of the company. 12% shares are owned by P2, and it represents 12 votes of the company. 10% shares are owned by P3, which is 10 votes of the company. 10% shares are owned by P4, which is 10 votes of the company and 3% shares are owned by P5, which is 3 votes of the company.
The standard notation of weighted voting system where decisions in the partnership require two-thirds of the votes is given as,
q=23 of 50=34
[34:15,12,10,10,3]
Conclusion:
Thus, the partnership as a weighted voting system where decisions in the partnership require two-thirds of the votes is given as,
[34:15,12,10,10,3]
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A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows.
Hours of Training
Defects per Countertop
1
5
4
1
7
0
3
3
2
5
2
4
5
1
5
2
1
8
6
2
Copy Data The estimated regression line and the standard error are given.
Defects per Countertop=6.717822−1.004950(Hours of Training)se=1.229787se=1.229787
Suppose a new employee has had 5 hours of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.
A researcher would like to determine the political preference of the nationbefore the upcoming midterm elections. From where should the researchercollect his/her data?
A. From all the voting population in the nation.B. From a sample of people living in one region.C. From a sample of people randomly chosen across the nation.D. From all the people in a randomly selected region.
Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino.Suppose that one Californian is randomly selected.In this problem, let:•C= Californians (registered voters) preferring life in prison withoutparole over the death penalty for a person convicted of first degree murder.•L= Latino Californians
Find P(C||L).
the probability their californian given their latino
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