The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $300
i = 0.07 x $300

No payments were made so the total amount due is the original amount + the accumulated interest:

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 42 meters so the equation becomes: 2w + 2h = 42.

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

2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h

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

w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7

Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m²

If 79% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{79}{100} \)) x 44,000 = \( \frac{3,476,000}{100} \) = 34,760

The mayor got 52% of the votes cast which is:

(\( \frac{52}{100} \)) x 34,760 = \( \frac{1,807,520}{100} \) = 18,075 votes.

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{76} \) = \( \frac{\frac{28}{4}}{\frac{76}{4}} \) = \( \frac{7}{19} \)

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.