If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 36 large cakes are needed for the party so \( \frac{36}{8} \) = 4\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 12 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 12 x 4 = 48 small cakes during that time. 370 small cakes are needed for the party so \( \frac{370}{48} \) = 7\(\frac{17}{24}\) 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 5 + 8 = 13 cooks.

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

\( \frac{2}{6} \) x \( \frac{4}{7} \) = \( \frac{2 x 4}{6 x 7} \) = \( \frac{8}{42} \) = \(\frac{4}{21}\)

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5

First, solve for \( \left|a - 5\right| \):

\( \left|a - 5\right| \) + 8 = -8
\( \left|a - 5\right| \) = -8 - 8
\( \left|a - 5\right| \) = -16

The value inside the absolute value brackets can be either positive or negative so (a - 5) must equal - 16 or --16 for \( \left|a - 5\right| \) to equal -16:

So, a = 21 or a = -11.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)