James W.

Tutor for 10 years with degrees in Math, Economics, and Statistics

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Calculus

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Question:

What is the biggest result of the fundamental theorem of calculus?

James W.

Answer:

All continuous functions have antiderivatives that are also continuous.

Economics

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Question:

What is the price elasticity of demand?

James W.

Answer:

Elasticity refers to the percentage change of one variable as a result of a percentage change of another. For the price elasticity of demand, the ratio is the percentage change in quantity consumed as a result of a 1% change in price.

Statistics

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Question:

Suppose that 30% of people skip breakfast and 40% of people skip lunch. If 50% of people eat both breakfast and lunch, what is the probability that a selected person skips both breakfast and lunch?

James W.

Answer:

Let skipping breakfast be event A and skipping lunch be event B and the compliment denoted by an apostrophe. Then: Pr(A) = .30, Pr(B) = .40, Pr(A' AND B') = Pr((A OR B)') = .50, and thus Pr(A OR B) = 1 - .50 = .50 Pr(A AND B) = Pr(A) + Pr(B) - Pr(A OR B) = .30 + .40 - .50 = .20

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