If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{20} \) = 1\(\frac{9}{10}\) 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. 300 small cakes are needed for the party so \( \frac{300}{56} \) = 5\(\frac{5}{14}\) 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 + 6 = 8 cooks.

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:

-8y⁴ x 5y⁶
(-8 x 5)y^{(4 + 6)}
-40y¹⁰

49% of the water consumption is industrial use and 24% is personal use so (49% - 24%) = 25% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{25}{100} \) x 10,000 gallons = 2,500 gallons.

The equation for this sequence is:

a_n = a_n-1 + 4(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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).