Diane scored 79% on the test meaning she earned 79% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.79 = 213 points. Each question is worth 3 points so she got \( \frac{213}{3} \) = 71 questions right.

You have 3 out of the total of 50 raffle tickets sold so you have a (\( \frac{3}{50} \)) x 100 = \( \frac{3 \times 100}{50} \) = \( \frac{300}{50} \) = 6% 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 6 meters so the equation becomes: 2w + 2h = 6.

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

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

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

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

By buying two shirts, Charlie will save $25 x \( \frac{25}{100} \) = \( \frac{$25 x 25}{100} \) = \( \frac{$625}{100} \) = $6.25 on the second shirt.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120