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 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{80}{15} \) = 5\(\frac{1}{3}\)

So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.

If a single cook can bake 2 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 2 x 3 = 6 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{6} \) = 6\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 460 small cakes are needed for the party so \( \frac{460}{33} \) = 13\(\frac{31}{33}\) 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 7 + 14 = 21 cooks.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

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

4c⁴ x 3c⁴
(4 x 3)c^{(4 + 4)}
12c⁸