A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

33,000 fans x \( \frac{3}{4} \) = \( \frac{99000}{4} \) = 24,750 fans.

There are 4 3-passenger taxis available so that's 4 x 3 = 12 total seats. There are 17 people needing transportation leaving 17 - 12 = 5 who will have to find other transportation.

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

2 + (2 + 4) ÷ 3 x 2 - 5²
P: 2 + (6) ÷ 3 x 2 - 5²
E: 2 + 6 ÷ 3 x 2 - 25
MD: 2 + \( \frac{6}{3} \) x 2 - 25
MD: 2 + \( \frac{12}{3} \) - 25
AS: \( \frac{6}{3} \) + \( \frac{12}{3} \) - 25
AS: \( \frac{18}{3} \) - 25
AS: \( \frac{18 - 75}{3} \)
\( \frac{-57}{3} \)
-19

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-4z⁴ - 3z⁴
(-4 - 3)z⁴
-7z⁴