If 87% of the town's 33,000 voters cast ballots the number of votes cast is:

(\( \frac{87}{100} \)) x 33,000 = \( \frac{2,871,000}{100} \) = 28,710

The mayor got 51% of the votes cast which is:

(\( \frac{51}{100} \)) x 28,710 = \( \frac{1,464,210}{100} \) = 14,642 votes.

The amount of flour you need is (2\(\frac{1}{8}\) - 1\(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{17}{8} \) - \( \frac{12}{8} \)) cups
\( \frac{5}{8} \) cups
\(\frac{5}{8}\) cups

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-z⁶ x 8z⁶
(-1 x 8)z^{(6 + 6)}
-8z¹²

First, solve for \( \left|z - 2\right| \):

\( \left|z - 2\right| \) - 2 = -9
\( \left|z - 2\right| \) = -9 + 2
\( \left|z - 2\right| \) = -7

The value inside the absolute value brackets can be either positive or negative so (z - 2) must equal - 7 or --7 for \( \left|z - 2\right| \) to equal -7:

So, z = 9 or z = -5.

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

\( \frac{18 + 12 + 17 + 13}{4} \) = \( \frac{60}{4} \) = 15