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

If 53% of the town's 21,000 voters cast ballots the number of votes cast is:

(\( \frac{53}{100} \)) x 21,000 = \( \frac{1,113,000}{100} \) = 11,130

The mayor got 72% of the votes cast which is:

(\( \frac{72}{100} \)) x 11,130 = \( \frac{801,360}{100} \) = 8,014 votes.

Christine scored 85% on the test meaning she earned 85% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.85 = 204 points. Each question is worth 4 points so she got \( \frac{204}{4} \) = 51 questions right.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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