Tutor profile: Sarah G.

Ginny wants to go straight from college to her house. Ginny's college is 15 kilometers north of the library. The library is 7 kilometers east of Ginny's house. Assuming there are roads going straight between each location, how far must Ginny drive to get from her college to her house?

To solve this, we can either use the distance formula or Pythagorean theorem (as the former is derived from the latter). We can set up an equation using Pythagorean theorem like so: $( 15^{2}+7^{2}=d^{2}\\ 225+49 =d^{2}\\ 274=d^{2}\\ d\approx16.56 $) Therefore, Ginny must drive 16.56km to get straight home from college. Note that we took the square root of both sides of the equation for the last step.

Jimmy wants you to play a game. It costs $1 to play. He tells you that you have a 10% chance of winning $10, 5% of winning $50, and 1% chance of winning $100. Otherwise, you lose and win nothing. Is this game in your favor? (Note: If you win, you do not have your initial $1 cost replaced.)

This question is asking you for the expected value, or expected winnings, from this game. First, you have a $$100-10-5-1=84\%$$ chance of losing. Then, we can derive the following equation for our expected value: $(E[X]=.84(-1)+.10(9)+.05(49)+.01(99) $) The winnings are subtracted by $$1$$ since we are subtracting the cost to play in the first place. When we solve this equation, we get $$E[X]=3.5$$. This means that if we were to play this game many times, we should, on average, earn $$\$ 3.50$$. This does not mean we will earn exactly this much over many trials, but over many, many games, we're likely to get close. So, yes, this game is in our favor, especially if we were to play it many times.

Jeremy invested $1000 total into two different investments. The first investment earned 4% interest and the second, 8% interest. Over the course of 1 year, he earned $60 in interest. How much money did he invest into each investment?

Let $$P$$ be the amount of money invested into the first investment. This means he invested $$1000-P$$ into the second investment. Recall that $$I=Prt$$ is the formula for calculating interest from principal (initial investment), interest rate, and time. This means that $$P\cdot 0.04\cdot 1$$ is the interest generated from the first investment and $$(1000-P)\cdot 0.08\cdot 1$$ corresponds to the second investment. This means that if we add both of these expressions together, they must equal $$\$ 60$$, the total interest. We set up the following equation: $(P\cdot 0.04\cdot 1 + (1000-P)\cdot 0.08\cdot 1 = 60 $) Then we solve for $$P$$. $( 0.04P + 80-0.08P=60 \\ 80 - 0.04P = 60 \\ -0.04P = -20 \\ P=500 $) Therefore, Jeremy invested $$\$ 500$$ into the first investment and $$1000-500=\$500$$ into the second investment.