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 30 meters so the equation becomes: 2w + 2h = 30.

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

2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h

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

w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5

Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m²

If 57% of the town's 9,000 voters cast ballots the number of votes cast is:

(\( \frac{57}{100} \)) x 9,000 = \( \frac{513,000}{100} \) = 5,130

The mayor got 73% of the votes cast which is:

(\( \frac{73}{100} \)) x 5,130 = \( \frac{374,490}{100} \) = 3,745 votes.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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

6z³ x 4z²
(6 x 4)z^{(3 + 2)}
24z⁵

You have 3 out of the total of 50 raffle tickets sold so you have a (\( \frac{3}{50} \)) x 100 = \( \frac{3 \times 100}{50} \) = \( \frac{300}{50} \) = 7% chance to win the raffle.