A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 15mph \times 3h \)
45 miles

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 $1,000
i = 0.07 x $1,000

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

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 3}{2 x 3} \) - \( \frac{8 x 1}{6 x 1} \)

\( \frac{15}{6} \) - \( \frac{8}{6} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{15 - 8}{6} \) = \( \frac{7}{6} \) = 1\(\frac{1}{6}\)