(a) Explanation Given: The awards 4 points, 3 points, 2 points, and 1 points for first, second, third, and forth place respectively. The preference table is shown below. Categories Cat Looks Eyes Size Attitude A 4 3 2 3 B 2 4 1 2 C 1 1 4 4 D 3 2 3 1 Voting method use: Borda Count Method: 1. Voters rank the candidates from the most favorable to the least favorable. 2. Each last place vote is rewarded one point, each next to last place vote is rewarded two points, each third place from the last place is rewarded three points, and so forth. 3. The candidate receiving the most points is the winner of the election. Calculation: Given that the 4, 3, 2 and 1 points represent the first, second, third and fourth places for each cat. Use the given preference table to obtain the total number of votes for each Cat... (b) To determine To find: The cat which wins the election by using a Borda count method that awards 5 points, 3 points, 1 points, and 0 points for first, second, third, and forth place respectively, in each category.

A Survey of Mathematics with Applications (10th Edition) - Standalone book

10th Edition

ISBN: 9780134112107

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 14.1, Problem 44E

(a)

To determine

To find: The cat which wins the election by using the Borda count method.

(b)

To determine

To find: The cat which wins the election by using a Borda count method that awards 5 points, 3 points, 1 points, and 0 points for first, second, third, and forth place respectively, in each category.

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Chapter 14.1, Problem 43E

Chapter 14.1, Problem 45E

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Consider the cones K = = {(x1, x2, x3) | € R³ : X3 ≥√√√2x² + 3x² M = = {(21,22,23) (x1, x2, x3) Є R³: x3 > + 2 3 Prove that M = K*. Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix A.

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Chapter 14 Solutions

A Survey of Mathematics with Applications (10th Edition) - Standalone book

Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 5E Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Plurality Three candidates are running for mayor...Ch. 14.1 - Prob. 10E

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The cat which wins the election by using the Borda count method.

Solution Summary: The author explains the Borda count method used to find the cat which wins the election with 11 points.