If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{9} \) = 4\(\frac{1}{9}\) 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. 170 small cakes are needed for the party so \( \frac{170}{57} \) = 2\(\frac{56}{57}\) 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 + 3 = 8 cooks.

By buying two shirts, Charlie will save $47 x \( \frac{50}{100} \) = \( \frac{$47 x 50}{100} \) = \( \frac{$2350}{100} \) = $23.50 on the second shirt.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (3 + 2) ÷ 2 x 3 - 3²
P: 5 + (5) ÷ 2 x 3 - 3²
E: 5 + 5 ÷ 2 x 3 - 9
MD: 5 + \( \frac{5}{2} \) x 3 - 9
MD: 5 + \( \frac{15}{2} \) - 9
AS: \( \frac{10}{2} \) + \( \frac{15}{2} \) - 9
AS: \( \frac{25}{2} \) - 9
AS: \( \frac{25 - 18}{2} \)
\( \frac{7}{2} \)
3\(\frac{1}{2}\)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{81}} \)
\( \frac{\sqrt{49}}{\sqrt{81}} \)
\( \frac{\sqrt{7^2}}{\sqrt{9^2}} \)
\(\frac{7}{9}\)

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