You have 9 out of the total of 150 raffle tickets sold so you have a (\( \frac{9}{150} \)) x 100 = \( \frac{9 \times 100}{150} \) = \( \frac{900}{150} \) = 6% chance to win the raffle.

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:

-2a⁵ + 7a⁵
(-2 + 7)a⁵
5a⁵

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 4 x 2 = 8 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{8} \) = 2\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 230 small cakes are needed for the party so \( \frac{230}{26} \) = 8\(\frac{11}{13}\) 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 3 + 9 = 12 cooks.

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\(\frac{1}{2}\)%