To subtract these radicals together their radicands must be the same:

5\( \sqrt{32} \) - 9\( \sqrt{2} \)
5\( \sqrt{16 \times 2} \) - 9\( \sqrt{2} \)
5\( \sqrt{4^2 \times 2} \) - 9\( \sqrt{2} \)
(5)(4)\( \sqrt{2} \) - 9\( \sqrt{2} \)
20\( \sqrt{2} \) - 9\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

54% of the water consumption is industrial use and 21% is personal use so (54% - 21%) = 33% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 40,000 gallons = 13,200 gallons.

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

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. 38 large cakes are needed for the party so \( \frac{38}{8} \) = 4\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 18 x 2 = 36 small cakes during that time. 130 small cakes are needed for the party so \( \frac{130}{36} \) = 3\(\frac{11}{18}\) 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 + 4 = 9 cooks.