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 = 0.05 x $300
i = $15

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{52} \) = \( \frac{\frac{20}{4}}{\frac{52}{4}} \) = \( \frac{5}{13} \)

To multiply terms with radicals, multiply the coefficients and radicands separately:

2\( \sqrt{6} \) x 6\( \sqrt{7} \)
(2 x 6)\( \sqrt{6 \times 7} \)
12\( \sqrt{42} \)

You have 36 out of the total of 400 raffle tickets sold so you have a (\( \frac{36}{400} \)) x 100 = \( \frac{36 \times 100}{400} \) = \( \frac{3600}{400} \) = 9% chance to win the raffle.

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