If 32% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{32}{100} \)) x 44,000 = \( \frac{1,408,000}{100} \) = 14,080

The mayor got 84% of the votes cast which is:

(\( \frac{84}{100} \)) x 14,080 = \( \frac{1,182,720}{100} \) = 11,827 votes.

1

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 36 meters so the equation becomes: 2w + 2h = 36.

Putting these two equations together and solving for width (w):

2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6

Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m²

47% of the water consumption is industrial use and 22% is personal use so (47% - 22%) = 25% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{25}{100} \) x 40,000 gallons = 10,000 gallons.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-8y⁵ + 6y⁵
(-8 + 6)y⁵
-2y⁵