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Le Z.

Experienced Tutor for High School and Undergraduate Math, Science, and Economics Courses

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Chemistry

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Question:

50 mL of 0.10 M NaOH is mixed with 150 mL of 0.20 M HCl. What is the pH of the resultant mixture?

Le Z.

Answer:

We calculate the excess [H+]: [H+] = ((150 mL)(0.20 M) - (50 mL)(0.10 M))(50 mL + 150 mL) = 0.125 M pH = -log[H+] = 0.90

Economics

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Question:

John has 2 options: a) A lottery has 30% of winning $40 and 70% of winning $80. b) The other option is to receive $60 with 100% certainty. John's personal utility function is u(x) = x^(1/2). Will he play the lottery?

Le Z.

Answer:

John's expected utility if he plays the lottery is: E(u(x)) = (0.3)($40)^(1/2) + (0.7)($80)^(1/2) = 8.15 John's expected utility if takes the $60 is: E(u(x)) = (1.0)($60)^(1/2) = 7.75 Thus, he will play the lottery

Statistics

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Question:

A manufacturer of lightbulbs has found that the lifetime hours of their lightbulbs is normally distributed with a mean of 1100 hours and standard deviation of 150 hours. 97.5% of all their manufactured lightbulbs will last at least how many hours?

Le Z.

Answer:

You should realize that 97.5% indicates 2 standard deviations from the mean. And this would be 2 standard deviations BELOW the mean, because we are talking about the top 97.5% of the dataset. Thus, 1100 - 2(150) = 800 hours.

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