The equation for this sequence is:

a_n = a_n-1 + 4

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
a₆ = 17 + 4
a₆ = 21

To simplify a radical, factor out the perfect squares:

\( \sqrt{12} \)
\( \sqrt{4 \times 3} \)
\( \sqrt{2^2 \times 3} \)
2\( \sqrt{3} \)

If 86% of the town's 32,000 voters cast ballots the number of votes cast is:

(\( \frac{86}{100} \)) x 32,000 = \( \frac{2,752,000}{100} \) = 27,520

The mayor got 88% of the votes cast which is:

(\( \frac{88}{100} \)) x 27,520 = \( \frac{2,421,760}{100} \) = 24,218 votes.

The amount of flour you need is (2\(\frac{1}{4}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{18}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{12}{8} \) cups
1\(\frac{1}{2}\) cups

If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 40 large cakes are needed for the party so \( \frac{40}{4} \) = 10 cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 11 x 2 = 22 small cakes during that time. 410 small cakes are needed for the party so \( \frac{410}{22} \) = 18\(\frac{7}{11}\) 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 10 + 19 = 29 cooks.