Tutor profile: Sherry Z.
Subject: SAT II Mathematics Level 2
If x is a positive, even integer, y is a negative number, and z is an odd integer, what is a possible value of xyz?
If you thought of any negative even number, you're correct!! Let's take this step by step. Let's first figure out if it is positive or negative. Since x is positive and y is negative, when they are multiplied, it becomes negative. Great! step one complete. Next, let's figure out if it even or odd. Since x is even and z is odd, when they are multiplied, it has to be even. Think about it, if you double anything, it is always even. So 4 times something is just 2 doubles. Even times odd is always even. Tada! Now you know that the answer must be a negative even number.
Two 6-sided dice are tossed. What is the probability that the sum of the two dice is greater than 4?
Since each dice has 6 possibilities, that means there is a total of 6x6 = 36 possible outcomes. Of those 36 outcomes, all of them will be greater than four except for the following combinations - ( 1 ; 1 ), ( 1 ; 2 ), ( 1 ; 3 ), ( 2 ; 1 ), ( 2; 2 ), ( 3 ; 1 ). Therefore 36 - 6 = 30 possible combination that will be greater than 4. 30/36 = 5/6 probability that the sum of the two dice is greater than 4.
True or False: If F(x) is an antiderivative of f(x) and c is any constant, then F(x) + C is also an antiderivative of f(x).
True!! The opposite of an antiderivative is a derivative, so to make sure you understand why this is true, differentiate F(x) + c. This is always true because the derivative of a constant is always 0.
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