First, solve for \( \left|b + 7\right| \):

\( \left|b + 7\right| \) + 8 = 5
\( \left|b + 7\right| \) = 5 - 8
\( \left|b + 7\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (b + 7) must equal - 3 or --3 for \( \left|b + 7\right| \) to equal -3:

So, b = -4 or b = -10.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{9}} \)
\( \frac{\sqrt{81}}{\sqrt{9}} \)
\( \frac{\sqrt{9^2}}{\sqrt{3^2}} \)
\( \frac{9}{3} \)
3

The amount of flour you need is (2\(\frac{7}{8}\) - \(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{23}{8} \) - \( \frac{5}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups

The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.

You have 2 out of the total of 100 raffle tickets sold so you have a (\( \frac{2}{100} \)) x 100 = \( \frac{2 \times 100}{100} \) = \( \frac{200}{100} \) = 2% chance to win the raffle.