Consider a weighted voting system with six players ( P 1 through P 6 ). a. Find the total number of coalitions in this weighted voting system. b. How many coalitions in this weighted voting system do not include P 1 ( Hint: Think of all the possible coalitions of the remaining players.) c. How many coalitions in this weighted voting system do not include P 3 ? [ Hint: Is this really different from (b)?] d. How many coalitions in this weighted voting system do not include P 1 and P 3 ? e. How many coalitions in this weighted voting system include both P 1 and P 3 ? [ Hint: Use your answers for (a) and (d).]
Consider a weighted voting system with six players ( P 1 through P 6 ). a. Find the total number of coalitions in this weighted voting system. b. How many coalitions in this weighted voting system do not include P 1 ( Hint: Think of all the possible coalitions of the remaining players.) c. How many coalitions in this weighted voting system do not include P 3 ? [ Hint: Is this really different from (b)?] d. How many coalitions in this weighted voting system do not include P 1 and P 3 ? e. How many coalitions in this weighted voting system include both P 1 and P 3 ? [ Hint: Use your answers for (a) and (d).]
Write an equation for the polynomial graphed below. It will probably be easiest to leave your "a" value as a
fraction.
8
7
+
9+
H
6
5
4
3
+ 3
2
1
(-30)
(-1,0)
(1,0)
(3,0)
+
-5
-4
-3
-2
2
3
4
7 2
-1
-2
3 (0,-3)
f(x) =
456
-4
-5
-6+
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