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

2 + (5 + 3) ÷ 4 x 2 - 4²
P: 2 + (8) ÷ 4 x 2 - 4²
E: 2 + 8 ÷ 4 x 2 - 16
MD: 2 + \( \frac{8}{4} \) x 2 - 16
MD: 2 + \( \frac{16}{4} \) - 16
AS: \( \frac{8}{4} \) + \( \frac{16}{4} \) - 16
AS: \( \frac{24}{4} \) - 16
AS: \( \frac{24 - 64}{4} \)
\( \frac{-40}{4} \)
-10

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:

\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)

First, solve for \( \left|a - 1\right| \):

\( \left|a - 1\right| \) - 6 = -1
\( \left|a - 1\right| \) = -1 + 6
\( \left|a - 1\right| \) = 5

The value inside the absolute value brackets can be either positive or negative so (a - 1) must equal + 5 or -5 for \( \left|a - 1\right| \) to equal 5:

So, a = -4 or a = 6.

To simplify a radical, factor out the perfect squares:

\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%