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Consider the following set of preference lists: Number of Voters (7) Rank 1 1 1 1 1 1 1 First C D C B E D C Second A A E D D E A Third E E D A A A E Fourth B C A E C B B Fifth D B B C B C D Calculate the winning using: a) Plurality voting b) The Borda count c) The Hare Method d) The Condorcet Method e) Sequential pairwise using the agenda A, B, C, D, E f) Find another agenda for pairwise voting that will produce a different winner than in e)
All the integrals below are understood in the sense of the Lebesgue. (1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]
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Derivative with Polar Coordinates dy/dx = (dr/dθ (sin θ) + r cos θ) / (dr/dθ (cosθ) - r sinθ) Note: Rather than trying to keep in mind this formula it would possibly be easi
Q. Suppose the probability of David coming to a party is 75% and the probability of Jason coming to a party is 85%. What is the probability that they will both come to a party, a
Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe
The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms . Ans: Let a 1 , a 2 ... and d 1 , d 2 be the I terms are Cd's of t
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An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
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