Solve the problem.A committee is selected to vote yes or no on a proposed location for a new parts distribution center. The committee is composed of three people who live in (A)bbeytown, five people who live in (B)arnsborough, six people who live in (C)hatterville, eight people who live in (D)itherburgh, and nine people who live in (E)lkington. At least 23 votes are required for a decision, and the committee members will vote in blocs according to their places of residence. List all winning coalitions, and identify those blocs that are critical to each of the winning coalitions.
A. {A, B, C, D, E}, {B, C, D, E}, {A, C, D, E}, {A, B, D, E}, {A, B, C, E}, {C, D, E} ;
Only D and E are critical to {A, B, C, D, E} ;
Only C, D, and E are critical to {B, C, D, E} ;
Only C, D, and E are critical to {A, C, D, E} ;
A, B, D, and E are critical to {A, B, D, E} ;
A, B, C, and E are critical to {A, B, C, E} ;
C, D, and E are critical to {C, D, E} ;
B. {A, B, C, D, E}, {B, C, D, E}, {A, C, D, E}, {A, B, D, E}, {A, B, C, E}, {C, D, E} ;
Only E is critical to {A, B, C, D, E} ;
Only C, D, and E are critical to {B, C, D, E} ;
Only C, D, and E are critical to {A, C, D, E} ;
A, B, D, and E are critical to {A, B, D, E} ;
A, B, C, and E are critical to {A, B, C, E} ;
C, D, and E are critical to {C, D, E} ;
C. {A, B, C, D, E}, {B, C, D, E}, {A, C, D, E}, {A, B, D, E}, {A, B, C, E}, {C, D, E} ;
Only E is critical to {A, B, C, D, E} ;
Only C, D, and E are critical to {B, C, D, E} ;
Only C, D, and E are critical to {A, C, D, E} ;
Only B, D, and E are critical to {A, B, D, E} ;
Only B, C, and E are critical to {A, B, C, E} ;
C, D, and E are critical to {C, D, E} ;
D. {B, C, D, E}, {A, C, D, E}, {A, B, D, E}, {A, B, C, E}, {C, D, E} ;
Only C, D, and E are critical to {B, C, D, E} ;
Only C, D, and E are critical to {A, C, D, E} ;
A, B, D, and E are critical to {A, B, D, E} ;
A, B, C, and E are critical to {A, B, C, E} ;
C, D, and E are critical to {C, D, E} ;
Answer: B
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Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability.Three coins are tossed, and the number of heads is noted.
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Perform the indicated operation. ?
A. -
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Identify the following as rational or irrational. If the number is rational, find the root exactly. If the number is irrational, approximate the number to the nearest thousandth when necessary.
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