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:

\( \frac{6!}{2!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{6 \times 5 \times 4 \times 3}{1} \)
\( 6 \times 5 \times 4 \times 3 \)
360

If 80% of the town's 30,000 voters cast ballots the number of votes cast is:

(\( \frac{80}{100} \)) x 30,000 = \( \frac{2,400,000}{100} \) = 24,000

The mayor got 64% of the votes cast which is:

(\( \frac{64}{100} \)) x 24,000 = \( \frac{1,536,000}{100} \) = 15,360 votes.

The equation for this sequence is:

a_n = a_n-1 + 3

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
a₆ = 13 + 3
a₆ = 16

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{135mi}{15mph} \)
9 hours

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{45\sqrt{30}}{9\sqrt{6}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{30}{6}} \)
5 \( \sqrt{5} \)