If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 39 large cakes are needed for the party so \( \frac{39}{12} \) = 3\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 20 x 3 = 60 small cakes during that time. 450 small cakes are needed for the party so \( \frac{450}{60} \) = 7\(\frac{1}{2}\) 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 4 + 8 = 12 cooks.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{15 + 9 + 16 + 8}{4} \) = \( \frac{48}{4} \) = 12

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{3}{9} \) = \( \frac{3 x 3}{9 x 9} \) = \( \frac{9}{81} \) = \(\frac{1}{9}\)

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%