If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 27 large cakes are needed for the party so \( \frac{27}{6} \) = 4\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 10 x 2 = 20 small cakes during that time. 490 small cakes are needed for the party so \( \frac{490}{20} \) = 24\(\frac{1}{2}\) 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 5 + 25 = 30 cooks.

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{420mi}{70mph} \)
6 hours

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

49,000 fans x \( \frac{2}{3} \) = \( \frac{98000}{3} \) = 32,667 fans.

To subtract these radicals together their radicands must be the same:

2\( \sqrt{80} \) - 4\( \sqrt{5} \)
2\( \sqrt{16 \times 5} \) - 4\( \sqrt{5} \)
2\( \sqrt{4^2 \times 5} \) - 4\( \sqrt{5} \)
(2)(4)\( \sqrt{5} \) - 4\( \sqrt{5} \)
8\( \sqrt{5} \) - 4\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-5c^9}{9c^4} \)
\( \frac{-5}{9} \) c^{(9 - 4)}
-\(\frac{5}{9}\)c⁵