Tutor profile: Cameron A.

Kourtney and Kim are roommates and they split their time between making pizza and brewing kombucha. Kourtney takes 4 hours to brew a gallon of kombucha and 2 hours to make a pizza. Kim takes 6 hours to brew a gallon of kombucha and 4 hours to make a pizza. What is each roommate’s opportunity cost of making pizza? Who has the absolute advantage in making pizza? Who has the comparative advantage in making pizza?

Kourtney's opportunity cost of making a pizza is 1/2 gallon of kombucha, because she could brew 1/2 gallon in the time (2 hours) it takes her to make a pizza. Kim's opportunity cost of making a pizza is 2/3 gallon of kombucha, because she could brew 2/3 of a gallon in the time (4 hours) it takes her to make a pizza. Kourtney has an absolute advantage in making pizza because she can make one in 2 hours, while it takes Kim 4 hours. Because Kourtney's opportunity cost of making pizza is less than Kim's, Kourtney has a comparative advantage in making pizza.

For all real numbers x such that x $$\neq$$ 0, $$\frac{4}{5}+\frac{7}{x}$$ = ? A. $$\frac{11}{5x}$$ B. $$\frac{28}{5x}$$ C. $$\frac{11}{5+x}$$ D. $$\frac{7x+20}{5+x}$$ E. $$\frac{4x+35}{5x}$$

This problem might look like you'll need a super complicated solution, but it's actually just asking for something simple but in a challenging way. It's a classic ACT style question. It's actually just asking us to simplify the expression. To add the two fractions, we need a common denominator. Let's multiply the denominators (5 times x) to find this. This already eliminates some of the multiple choice options. Choices C and D are no longer options. For the numerators, let's multiple each by the common denominator: $$\frac{4}{5}*5x+\frac{7}{x}*5x$$ Simplifying gives our answer: $$\frac{4x+35}{5x}$$ (Choice E)

Given functions f(x) = 2x+1 and g(x) = $$x^2$$-4, what is the value of f(g(-3))?

This is a composition of functions problem and it'll require several steps. The last part of the question, "What is the value of f(g(-3))?" is important because it's telling us to apply one function to the results of another function. When dealing with these types of problems we need to start in the inside and then move outward. For example, if we had the composition g(f(x)), we first need to solve the f(x) (which is inside) and then solve the g(x) (which is outside). The f(x) becomes the input of the g(x). So for this problem let's solve the inside, g(-3), first. The function g(-3) equals $$(-3)^2$$- 4 which is 5. This becomes the input for the outside function, so it would be f(5). The function f(5) equals 2(5) + 1 which is 11 (our final answer).