Find a simplified weighted voting system which is equivalent to
[8: 9, 3, 2, 1] and
[20: 8, 6, 3, 2, 1].

The explanation is as follows:

Step-by-step explanation:

(a) [8: 9, 3, 2, 1]

q = 8

Here, coalition is as follows:

[P1, P2, P3, P4] = [9, 3, 2, 1]

for the above coalition, the combined weight is

[P1, P2, P3, P4] = 9+3+2+1 = 15 ⇒ combined weight

For simplified weighted voting system;

q = combined weight ⇒ both the terms have to be equal for a simplified weighted voting system.

But, here 8 ≠ 15

∴ It is not a simplified weighted voting system.

(b) [20: 8, 6, 3, 2, 1]

q = 20

Here, coalition is as follows:

[P1, P2, P3, P4, P5] = [8, 6, 3, 2, 1]

for the above coalition, the combined weight is

[P1, P2, P3, P4, P5] = 8+6+3+2+1 = 20 ⇒ combined weight

For simplified weighted voting system;

q = combined weight

Since,  20 = 20

∴ It is a simplified weighted voting system.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer   download the app called socratic on your phoner:

step-by-step explanation: