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. 21 large cakes are needed for the party so \( \frac{21}{8} \) = 2\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 380 small cakes are needed for the party so \( \frac{380}{80} \) = 4\(\frac{3}{4}\) 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 + 5 = 8 cooks.

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

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:

\( \frac{2!}{5!} \)
\( \frac{2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4 \times 3} \)
\( \frac{1}{60} \)

Monica scored 86% on the test meaning she earned 86% of the possible points on the test. There were 320 possible points on the test so she earned 320 x 0.86 = 276 points. Each question is worth 4 points so she got \( \frac{276}{4} \) = 69 questions right.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-5z⁶ x z⁵
(-5 x 1)z^{(6 + 5)}
-5z¹¹