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:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

By buying two shirts, Monty will save $31 x \( \frac{50}{100} \) = \( \frac{$31 x 50}{100} \) = \( \frac{$1550}{100} \) = $15.50 on the second shirt.

So, his total cost will be
$31.00 + ($31.00 - $15.50)
$31.00 + $15.50
$46.50

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 36 meters so the equation becomes: 2w + 2h = 36.

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

2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h

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

w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6

Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m²

Latoya scored 92% on the test meaning she earned 92% of the possible points on the test. There were 200 possible points on the test so she earned 200 x 0.92 = 184 points. Each question is worth 2 points so she got \( \frac{184}{2} \) = 92 questions right.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{210mi}{70mph} \)
3 hours