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Tutor profile: Elliott G.

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Elliott G.
Math teacher for ten years!
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Questions

Subject: Calculus

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Question:

Explain in your own words the Fundamental Theorem of Calculus.

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Elliott G.
Answer:

The Fundamental Theorem of Calculus, in my opinion, binds calculus together. It shows that if we take the derivative of a function, and then integrate it, we get the original function. For example, the derivative of x^2 is 2x. When we integrate 2x, we get x^2 + C. The converse is also true. If you integrate a function, and then take its derivative, you'll end up with the original function. For example, if we integrate 5x^4, we get get x^5. If we take the derivative of x^5, we get 5x^4. The Fundamental Theorem of Calculus shows there's a link in mathematics between area and rate of change.

Subject: Statistics

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Question:

Domestic kittens at nine weeks weigh an average of 24.5 oz. Kitten weights are normally distributed with a standard deviation of 5.25 oz. Find the probability that a kitten will weigh less than 14 oz.

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Elliott G.
Answer:

What is this problem asking? Let's look at the context. Kittens weigh an average of 24.5 oz., but it's highly likely that a kitten's not going to weigh that exact amount. Weights of kittens are "normally distributed" over a "bell curve," where most kittens weigh close to 24.5 oz, but a few weigh a lot more, or a lot less. A kitten that only weighs 14 oz seems far below average. How far? Let's find the z-score: z = (x - µ) / s x = 14, the random variable µ = 24.5, or the mean s = 5.25, or the standard deviation z = (14 - 24.5) / 5.25 z = -2 Sure enough, this kitten weighs 2 "standard deviations" below average. One could infer this kitten is pretty underweight. To find the probability, we use a "z-table," which can be found online. When we look up the value for -2, we get 0.0228. There is a 2.28% chance a kitten will weigh less than 14 oz.

Subject: Algebra

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Question:

A class grade is determined by four tests worth 20% each, a 10% homework grade, and a 10% classwork grade. Jamaal received a 90% homework grade, a 95% classwork grade, and three test scores of 98%, 72%, and 93%. What is the minimum score he'd need in order to get a 90% average in the class?

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Elliott G.
Answer:

In the problem, we know all of Jamaal's grades except for one: a test worth 20% of his grade. We want his weighted average to add up to 90%, or 0.90. When finding a weighted average, multiply each score (in decimal form) by its weight and add them together. We'll define the score Jamaal needs to get an A- as x. This means that: (0.1 * 0.9) + (0.1 * 0.95) + (0.2 * 0.98) + (0.2 * 0.72) + (0.2 * 0.93) + 0.2x = 0.90 Note that, since homework is work less than tests, we multiply his 90% homework grade by 0.1, while we multiply his 88% test grade by 0.2. Following order of operations and then solving for x, we get: 0.09 + 0.095 + 0.196 + 0.144 + 0.186 + 0.2x = 0.90 0.705 + 0.2x = 0.9 -0.705 -0.705 0.2x = 0.195 x = 0.975 Jamaal needs a 97.5% on his last test to get an A- in the class.

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