If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{16} \) = 1\(\frac{7}{16}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 260 small cakes are needed for the party so \( \frac{260}{56} \) = 4\(\frac{9}{14}\) 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 2 + 5 = 7 cooks.

First, solve for \( \left|a + 8\right| \):

\( \left|a + 8\right| \) + 8 = 9
\( \left|a + 8\right| \) = 9 - 8
\( \left|a + 8\right| \) = 1

The value inside the absolute value brackets can be either positive or negative so (a + 8) must equal + 1 or -1 for \( \left|a + 8\right| \) to equal 1:

So, a = -9 or a = -7.

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:

\( \frac{4!}{6!} \)
\( \frac{4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5} \)
\( \frac{1}{30} \)

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

7b⁶ + 2b⁶
(7 + 2)b⁶
9b⁶