# Tutor profile: Christine C.

## Questions

### Subject: SAT

What is wrong with this sentence? Jordan likes Spider-Man, he is her favorite superhero.

The error is a $$\textbf{comma splice}$$. One rule of commas is that you can't use them to separate complete thoughts. "Jordan likes Spider-Man" and "that is her favorite superhero" can both be complete sentences, so a comma doesn't belong in between them. You can fix comma splices multiple ways. $$\textbf{Semicolon:}$$ Replace the comma with a semicolon. Ex: Jordan likes Spider-Man; he is her favorite superhero. $$\textbf{Pronoun:}$$ Use a relative pronoun after the comma. Ex: Jordan likes Spider-Man, who is her favorite superhero. $$\textbf{Conjunction:}$$ Use a conjunction after the comma. Ex: Jordan likes Spider-Man, and he is her favorite superhero. $$\textbf{Separate:}$$ Separate the clauses into two sentences. Ex: Jordan likes Spider-Man. He is her favorite superhero.

### Subject: Calculus

How do you approach an optimization problem?

$$\textbf{Step 1:}$$ Write down the given conditions and what you need to optimize. Ex: the perimeter of the rectangle, $$P$$, must be 10m, the area of the rectangle, $$A$$, must be maximized $$\textbf{Step 2:}$$ Draw a diagram if possible and define unknown variable(s). Ex: Draw a rectangle with sides of length $$x$$ and $$y$$ $$\textbf{Step 2a:}$$ If you have more than unknown, write them all in terms of one using the given conditions. Ex: $$P=2x+2y=10\Rightarrow x+y=5\Rightarrow y=5-x$$ $$\textbf{Step 3:}$$ Write what you're optimizing as a function of the unknown variable. Ex: $$A=xy\Rightarrow A(x)=x(5-x)=5x-x^2$$ $$\textbf{Step 4:}$$ Take the derivative of the function to find the absolute extreme value. Ex: $$\frac{d}{dx}(5x-x^2)=5-2x$$ and $$5-2x=0\Leftrightarrow x=\frac{5}{2}$$ therefore 2.5 is the absolute maximum of $$A(x)=5x-x^2$$ $$\textbf{Step 5:}$$ Write your conclusion. Ex: The maximum area of a rectangle with a 10m perimeter is 2.5m$$^2$$.

### Subject: Statistics

What is the difference between the probability of A and B versus the probability of A given B?

The probability of A given B, Prob(A | B), is based only on the portion of the sample in which B occurs. For example, if we define Event A as a cancelled flight and Event B as rain, Prob(A | B) is the percentage of rainy flights that are cancelled. The probability of A and B, Prob(A $$\cap$$ B), is based on the entire sample. For example, using the definitions above, Prob(A $$\cap$$ B) is the percentage of all flights that are planned to take off when it's raining and are cancelled.

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