Betty scored 83% on the test meaning she earned 83% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.83 = 200 points. Each question is worth 4 points so she got \( \frac{200}{4} \) = 50 questions right.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{4}} \)
\( \frac{\sqrt{49}}{\sqrt{4}} \)
\( \frac{\sqrt{7^2}}{\sqrt{2^2}} \)
\( \frac{7}{2} \)
3\(\frac{1}{2}\)

The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 the greatest factor 20 and 48 have in common.

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 $600
i = 0.01 x $600

No payments were made so the total amount due is the original amount + the accumulated interest:

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