To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

2c³ + 1c³
(2 + 1)c³
3c³

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 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

41,000 fans x \( \frac{3}{4} \) = \( \frac{123000}{4} \) = 30,750 fans.

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

3\( \sqrt{3} \) x 5\( \sqrt{9} \)
(3 x 5)\( \sqrt{3 \times 9} \)
15\( \sqrt{27} \)

Now we need to simplify the radical:

15\( \sqrt{27} \)
15\( \sqrt{3 \times 9} \)
15\( \sqrt{3 \times 3^2} \)
(15)(3)\( \sqrt{3} \)
45\( \sqrt{3} \)

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. 20 large cakes are needed for the party so \( \frac{20}{12} \) = 1\(\frac{2}{3}\) 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. 250 small cakes are needed for the party so \( \frac{250}{60} \) = 4\(\frac{1}{6}\) 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 2 + 5 = 7 cooks.