Latoya scored 78% on the test meaning she earned 78% of the possible points on the test. There were 80 possible points on the test so she earned 80 x 0.78 = 62 points. Each question is worth 2 points so she got \( \frac{62}{2} \) = 31 questions right.

There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 19 people needing transportation leaving 19 - 16 = 3 who will have to find other transportation.

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

9\( \sqrt{5} \) x 6\( \sqrt{4} \)
(9 x 6)\( \sqrt{5 \times 4} \)
54\( \sqrt{20} \)

Now we need to simplify the radical:

54\( \sqrt{20} \)
54\( \sqrt{5 \times 4} \)
54\( \sqrt{5 \times 2^2} \)
(54)(2)\( \sqrt{5} \)
108\( \sqrt{5} \)

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