# Tutor profile: Trey S.

## Questions

### Subject: SAT II Mathematics Level 2

I have two fair dice. What is the probability that I roll the dice and do not get the same number on each?

One way to think about this problem is to find the probability that each pair of "doubles" can occur. We know that there are 36 total combinations of two dice rolls (6 x 6). Each pair of "doubles" is one unique combination of a dice throw. Thus, there are 6 combinations of doubles. To find the probability we divide the number of combinations of doubles by the total number of outcomes. 6/36 = 1/6 which is the probability that we get the SAME number on each die. However, the question asked us to find the probability that we do NOT get the same number on each die. Thus to find the opposite probability we take 1 minus the probability we calculated to get 1 - 1/6 = 5/6 -- the probability we do NOT roll doubles.

### Subject: SAT II Mathematics Level 1

Alice, Bob and Eve go to a local restaurant on a Friday night. Alice spends $8.25 buying a burger, fries, and playing 6 songs on the juke box. Bob spends $3.50 on fries and 5 songs on the juke box. Eve spends $7 on a burger and 10 songs. What is the cost of queuing one song on the juke box at this restaurant?

After reading through this question we see that we have three unknowns -- the cost of a burger, fries, and a song request -- and three equations. Thus, we can solve for the value of each of the variables by setting up a system. $$8.25 = B + F + 6S $$ $$3.50 = F + 5S$$ $$7 = B + 10S$$ We can subtract the first two equations to eliminate the variable for fries. $$4.75 = B + S$$ We can subtract this equation from the last equation from above to have one equation with just the cost of a song as its only variable. $$2.25 = 9S$$ Lastly, we divide by 9 to get the cost of one song, which the question is asking for. $$.25 = S$$

### Subject: Calculus

$$ \int_0^6 x^2+3x-4\mathrm{d}x $$

We will use the power rule for integration to evaluate this definite integral. Think of it as "undoing" a derivative. $$ \int_0^6 x^2+3x-4\mathrm{d}x = \dfrac{x^3}{3} + \dfrac{3x^2}{2}-4x \Big|_0^6$$ All that is left is plugging in our limits on integration. We evaluate the expression at the top number, and then subtract away the value at the bottom. $$ 72 + 54 - 24 - (0 + 0 + 0) = 102 $$

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