Latoya scored 78% on the test meaning she earned 78% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.78 = 210 points. Each question is worth 3 points so she got \( \frac{210}{3} \) = 70 questions right.

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{48} \) = \( \frac{\frac{36}{12}}{\frac{48}{12}} \) = \( \frac{3}{4} \)

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

4\( \sqrt{7} \) x 5\( \sqrt{8} \)
(4 x 5)\( \sqrt{7 \times 8} \)
20\( \sqrt{56} \)

Now we need to simplify the radical:

20\( \sqrt{56} \)
20\( \sqrt{14 \times 4} \)
20\( \sqrt{14 \times 2^2} \)
(20)(2)\( \sqrt{14} \)
40\( \sqrt{14} \)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $300
i = 0.07 x $300
i = $21

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