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

\( \frac{45\sqrt{49}}{9\sqrt{7}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{49}{7}} \)
5 \( \sqrt{7} \)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 share.

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

\( \frac{4 x 3}{8 x 3} \) - \( \frac{5 x 2}{12 x 2} \)

\( \frac{12}{24} \) - \( \frac{10}{24} \)

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

\( \frac{12 - 10}{24} \) = \( \frac{2}{24} \) = \(\frac{1}{12}\)

By buying two shirts, Damon will save $40 x \( \frac{20}{100} \) = \( \frac{$40 x 20}{100} \) = \( \frac{$800}{100} \) = $8.00 on the second shirt.

So, his total cost will be
$40.00 + ($40.00 - $8.00)
$40.00 + $32.00
$72.00

If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{15} \) = 2\(\frac{7}{15}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 19 x 3 = 57 small cakes during that time. 270 small cakes are needed for the party so \( \frac{270}{57} \) = 4\(\frac{14}{19}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 5 = 8 cooks.

You have 2 out of the total of 50 raffle tickets sold so you have a (\( \frac{2}{50} \)) x 100 = \( \frac{2 \times 100}{50} \) = \( \frac{200}{50} \) = 5% chance to win the raffle.