Krystal is creating a square garden with a walkway around it. The walkway will be one-quarter as wide as the garden. The are of the garden is 144 square feet. A rough sketch, probably not to scale, is below.
Question 2
How wide is the path surrounding the garden? Make sure to label!
Question 3
What is the area of the walkway surrounding the garden (NOT including the garden)?
Question 4
At Krystal’s old residence, she only had room for a garden with an area of 64 square feet. What is the relative change from that residence to the new one? Reminder: the garden at the new residence has an area of 144 square feet. Round to the nearest 10th of a percent if necessary. Include a negative sign if applicable. Remember to label!
There are 19 armies in a hush, and 25 hushes in a grue.
Question 5
How many armies are in a grue? armies
Question 6
A machine processes at a rate of 4.7 gures per day. How many armies per minute would that be? Round to the nearest hundredth if necessary. grues/minute
Question 7
Diann only has 2/3 of a cup of flour, but wants to make a recipe that would normally require 1 cup of flour. The recipe originally called for 1 cup sugar, 1 T baking powder, and 1/2 cup milk. How much of these should she use in the adjusted recipe?
Reminder: 16 Tablespoons (T) = 1 cup (c), and 3 teaspoons (t) = 1 Tablespoon (T)
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Sugar |
|
|
Baking Powder |
|
|
Milk |
Use the preference schedule for a student body president election, with candidates Anderson, Thornton, and Underhill
|
13 |
11 |
4 |
1 |
|
|
1st |
U |
T |
T |
A |
|
2nd |
T |
U |
A |
U |
|
3rd |
A |
A |
U |
T |
Question 8
How many people voted in the election?
Question 9
What is the minimum number of votes a candidate needs to have a majority in this election?
Question 10
Is there a majority candidate in this election? If so, who?
Underhill
Anderson
There is no majority candidate.
Thornton
Question 11
Who wins by the Plurality Method?
Thornton
Anderson
Underhill
Question 12
Who wins by Plurality with Elimination?
Underhill
Anderson
Thornton
Find the points for each candidate using the Borda Count method, and indicate who wins.
Points for Anderson:
Points for Thornton:
Points for Underhill:
Winner:
Question 14
Find the points each candidate earns via Copeland’s Method, and indicate who the winner is
Points for Anderson:
Points for Thornton:
Points for Underhill:
Winner:
Question 15
Is there a Condorcet Candidate for this election? If so, who?
There is no Condorcet Candidate.
Underhill is the Condorcet Candidate
Anderson is the Condorcet Candidate
Thornton is the Condorcet Candidate
Question 16
If Anderson won, which of the fairness criteria would be violated? Say “none” if applicable. Explain your answer
Question 17
Find the Banzhaf Power Indices for each player in the system below. Round to the nearest tenth of a percent if necessary.
{19 : 9, 7, 4, 2, 1}
Hint: There are 5 winning coalitions.
Player 1:
Player 2:
Player 3:
Player 4:
Player 5:
Find the Shapley Shubik power distirbution for the system below. Round to the nearest tenth of a percent if necessary.
{12: 11, 2, 1}
The sequential coalitions for three players are given below:
< P1, P2, P3 > < P1, P3, P2 > < P2, P1, P3 >
< P2, P3, P1 > < P3, P1, P2 > < P3, P2, P1 >
Player 1:
Player 2:
Player 3:
Question 19
In the system {5: 7, 1, 1, 1} , Player 1 is blank , and Players 2, 3, and 4 are each blank
In the system {12: 5, 5, 2, 2, 2, 2, 2}, Player 1 is blank , Player 2 is blank , and each of the rest of the players is blank
the Shapley Shubik Power Index None of These a Dictator the Quota the Banzhaf Power Index a Dummy Player a Player with Veto Power a Weight
Question 20
What values of the quota would be reasonable for this voting system: { q : 9, 7, 4, 2, 1} Explain.
Give a list or range of values {e.g. 1, 2, 3, 4 or “from 1 to 4”}
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