First, solve for \( \left|a + 4\right| \):

\( \left|a + 4\right| \) - 2 = 4
\( \left|a + 4\right| \) = 4 + 2
\( \left|a + 4\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (a + 4) must equal + 6 or -6 for \( \left|a + 4\right| \) to equal 6:

So, a = -10 or a = 2.

You have 15 out of the total of 300 raffle tickets sold so you have a (\( \frac{15}{300} \)) x 100 = \( \frac{15 \times 100}{300} \) = \( \frac{1500}{300} \) = 5% chance to win the raffle.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{56\sqrt{63}}{8\sqrt{9}} \)
\( \frac{56}{8} \) \( \sqrt{\frac{63}{9}} \)
7 \( \sqrt{7} \)

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{9} \) ÷ \( \frac{2}{6} \) = \( \frac{4}{9} \) x \( \frac{6}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{9} \) x \( \frac{6}{2} \) = \( \frac{4 x 6}{9 x 2} \) = \( \frac{24}{18} \) = 1\(\frac{1}{3}\)

If a single cook can bake 4 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 4 x 2 = 8 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{8} \) = 2\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 11 x 2 = 22 small cakes during that time. 280 small cakes are needed for the party so \( \frac{280}{22} \) = 12\(\frac{8}{11}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 13 = 16 cooks.