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:

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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (2 + 2) ÷ 2 x 4 - 4²
P: 2 + (4) ÷ 2 x 4 - 4²
E: 2 + 4 ÷ 2 x 4 - 16
MD: 2 + \( \frac{4}{2} \) x 4 - 16
MD: 2 + \( \frac{16}{2} \) - 16
AS: \( \frac{4}{2} \) + \( \frac{16}{2} \) - 16
AS: \( \frac{20}{2} \) - 16
AS: \( \frac{20 - 32}{2} \)
\( \frac{-12}{2} \)
-6

The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

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

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0007371 in scientific notation is 7.371 x 10^-4