25. [0.14/0.22 Points] DETAILS PREVIOUS ANSWERS AUFEXC4 3.4.011. 6/100 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following statement. If I were rich, I would quit this job. (a) Write the converse of the given statement. O If I quit this job, then I am not rich. O If I quit this job, then I am rich. O If I were not rich, then I would not quit this job. O If I would not quit this job, then I would not be rich. If I were not rich, then I would quit this job. (b) Write the inverse of the given statement. O If I quit this job, then I am not rich. O If I quit this job, then I am rich. O If I were not rich, then I would not quit this job. O If I would not quit this job, then I would not be rich. O If I were not rich, then I would quit this job. (c) Write the contrapositive of the given statement. O If I quit this job, then I am not rich. O If I quit this job, then I am rich. O If I were not rich, then I would not quit this job. O If I would not quit this job, then I would not be rich. O If I were not rich, then I would quit this job. Need Help? Read It37. [0.08/0.22 Points] DETAILS PREVIOUS ANSWERS AUFEXC4 4.2.011. 2/100 Submissions Used MY NOTES ASK YOUR TEACHER A kindergarten class was surveyed to determine the children's favorite cartoon characters among Mickey Mouse, Bugs Bunny, and Scooby Doo. The students ranked the characters in order of preference; the results are shown in the preference schedule below. Rankings Mickey Mouse 1 1 2 2 3 3 Bugs Bunny 2 3 1 1 Scooby Doo 3 2 1 Number of students: 4 4 5 6 4 8 (a) How many students are in the class? x students [b) How many votes are required for a majority? * votes c) Using plurality voting, which character is the children's favorite? O Mickey Mouse O Bugs Bunny O Scooby Doo There is a tie between Mickey Mouse and Bugs Bunny. O There is a tie between Mickey Mouse and Scooby Doo. Need Help? Read It Watch It41. [-10.22 Points] AUFEXC4 4.3.012. 01100 Submissions Used ASK YOUR TEACHER The weighted voting systems for the voters A, B, C, are given in the form {(12 W1, w , W3, W4, ..., wn}. The weight of vuterA is W1, the weight of voter B is \"'2' the weight of voter C is "'3' and six on. Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If= nnt possible, enter IMPOSSIBLE.) {83: 54-, 36, 25, 17} em: = E see: = E 3..., = E see) : Z Need Help? 43. [0.071022 Points] PREVIOUS ANSWERS AUFEXC4 4.3.023. 3/1 00 Submissions Used ASK YOUR TEACHER At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {5: 4, 3, 1}. [n this voting system, the head coach A has a weight of 4, the assistant coach B has a weight of 3, and thejunior varsity coach C has a weight of l. (a) Compute the Banzhaf power index for each of the coaches. (Round your answers to the nearest hundredth.) am = |:l mm = |:| me: = |:l (b) Explain why it seems reasonable that the assistant coach and the junior varsity coach have the same Banzhaf power index in this voting system. Q The weightings for the minor coaches are different, so are their critical votes. 0 As to forming a winning coalition, the two minor coaches are the same. 0 Winning coalitions often include support of different weight. Need Help? Submit Amwer 44. [0.131054 Points] DETAILS PREVIOUS ANSWERS AUFEXC4 4.3.027. 21100 Submissions Used MY NOTES ASK YOUR TEACHER Consider the weighted voting system {1.1: B, 3, 3, 2}, with q an integer and 9 S q S 16. (a) For what values of q is there a dummy? (Enter your answers as a commaseparated list.) X (h) For what values ofq do all voters have the same power? (Enter your answers as a commaseparated list.) X (c) If a voter is a dummy for a given quota, must the voter be a dummy for all larger quotas? 0 Yes G) No I Need new W 42. [010.22 Points] PREVIOUS ANSWERS AUFEXCd 4.3.019. 3/100 Submissions Used ASK YOUR TEACHER A voter who has a weight that is greater than or equal to the quota is called a dictator. In a weighted voting system, the dictator has all the power. A voter who is never a critical Voter has no power and is referred to as a dummy. This term is not meant to be a comment on the voter's intellectual powers. It just indicates that the voter has no ability to inuence an election. Identify any dictator and all dummies for the given weighted voting system. [Select all that apply.) {22: 22, 7, 4, 3, 2} Dictators: : the person with 22 votes 7 the person with 7 votes the person with 4 votes the person with 3 votes the person with 2 votes none of these Dummies: _ the person with 22 votes _ the person with 7 votes the person with 4 votes the person with 3 votes the person with 2 votes : none of these Need Help? SubmilAnswer l