To find the average of these 4 numbers add them together then divide by 4:

\( \frac{12 + 10 + 13 + 9}{4} \) = \( \frac{44}{4} \) = 11

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

First, solve for \( \left|b - 4\right| \):

\( \left|b - 4\right| \) + 1 = 1
\( \left|b - 4\right| \) = 1 - 1
\( \left|b - 4\right| \) = 0

The value inside the absolute value brackets can be either positive or negative so (b - 4) must equal + 0 or -0 for \( \left|b - 4\right| \) to equal 0:

So, b = 4 or b = 4.

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

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{48} \) = \( \frac{\frac{16}{16}}{\frac{48}{16}} \) = \( \frac{1}{3} \)