If 55% of the town's 46,000 voters cast ballots the number of votes cast is:

(\( \frac{55}{100} \)) x 46,000 = \( \frac{2,530,000}{100} \) = 25,300

The mayor got 75% of the votes cast which is:

(\( \frac{75}{100} \)) x 25,300 = \( \frac{1,897,500}{100} \) = 18,975 votes.

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 18 meters so the equation becomes: 2w + 2h = 18.

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

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

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

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (4 + 3) ÷ 4 x 3 - 3²
P: 2 + (7) ÷ 4 x 3 - 3²
E: 2 + 7 ÷ 4 x 3 - 9
MD: 2 + \( \frac{7}{4} \) x 3 - 9
MD: 2 + \( \frac{21}{4} \) - 9
AS: \( \frac{8}{4} \) + \( \frac{21}{4} \) - 9
AS: \( \frac{29}{4} \) - 9
AS: \( \frac{29 - 36}{4} \)
\( \frac{-7}{4} \)
-1\(\frac{3}{4}\)

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-7b^5}{6b^2} \)
\( \frac{-7}{6} \) b^{(5 - 2)}
-1\(\frac{1}{6}\)b³