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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (5 + 2) ÷ 2 x 5 - 2²
P: 5 + (7) ÷ 2 x 5 - 2²
E: 5 + 7 ÷ 2 x 5 - 4
MD: 5 + \( \frac{7}{2} \) x 5 - 4
MD: 5 + \( \frac{35}{2} \) - 4
AS: \( \frac{10}{2} \) + \( \frac{35}{2} \) - 4
AS: \( \frac{45}{2} \) - 4
AS: \( \frac{45 - 8}{2} \)
\( \frac{37}{2} \)
18\(\frac{1}{2}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{35}{100} \) = \( \frac{35 x 10}{100} \) = \( \frac{350}{100} \) = 3 shots

The center makes 30% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{3}{\frac{30}{100}} \) = 3 x \( \frac{100}{30} \) = \( \frac{3 x 100}{30} \) = \( \frac{300}{30} \) = 10 shots

to make the same number of shots as the guard and thus score the same number of points.

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 19 people needing transportation leaving 19 - 15 = 4 who will have to find other transportation.