A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{2!} \)
\( \frac{4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{4 \times 3}{1} \)
\( 4 \times 3 \)
12

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 share.

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

\( \frac{5 x 11}{3 x 11} \) + \( \frac{3 x 3}{11 x 3} \)

\( \frac{55}{33} \) + \( \frac{9}{33} \)

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

\( \frac{55 + 9}{33} \) = \( \frac{64}{33} \) = 1\(\frac{31}{33}\)

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

7\( \sqrt{9} \) x 6\( \sqrt{6} \)
(7 x 6)\( \sqrt{9 \times 6} \)
42\( \sqrt{54} \)

Now we need to simplify the radical:

42\( \sqrt{54} \)
42\( \sqrt{6 \times 9} \)
42\( \sqrt{6 \times 3^2} \)
(42)(3)\( \sqrt{6} \)
126\( \sqrt{6} \)

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 $500
i = 0.04 x $500

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

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 $100
i = 0.03 x $100
i = $3