You have 12 out of the total of 200 raffle tickets sold so you have a (\( \frac{12}{200} \)) x 100 = \( \frac{12 \times 100}{200} \) = \( \frac{1200}{200} \) = 6% chance to win the raffle.

If 69% of the town's 12,000 voters cast ballots the number of votes cast is:

(\( \frac{69}{100} \)) x 12,000 = \( \frac{828,000}{100} \) = 8,280

The mayor got 83% of the votes cast which is:

(\( \frac{83}{100} \)) x 8,280 = \( \frac{687,240}{100} \) = 6,872 votes.

First, solve for \( \left|x - 7\right| \):

\( \left|x - 7\right| \) - 6 = 3
\( \left|x - 7\right| \) = 3 + 6
\( \left|x - 7\right| \) = 9

The value inside the absolute value brackets can be either positive or negative so (x - 7) must equal + 9 or -9 for \( \left|x - 7\right| \) to equal 9:

So, x = -2 or x = 16.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

The amount of flour you need is (3\(\frac{1}{2}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{28}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{26}{8} \) cups
3\(\frac{1}{4}\) cups