12 Questions
In the context of the text, what is the approximate probability that no two people in a group of seven have the same birthday?
0.056
When finding the limit of (sin 3x) / (sin 4x) as x approaches 0, what is the result?
1
If a shipment of 12 television sets contains 3 defective sets, in how many ways can a hotel purchase 5 sets and receive at least 2 of the defective sets?
240 ways, 110 ways
For x = 2 sin θ and y = cos 2θ, what is d²y/dx²?
-cot θ / cos θ
What is the probability of getting either two heads or three heads when six fair coins are tossed at once?
0.35
In the federal prison, if 3/5 of the inmates are male and 5/8 are female or 25 years of age or older, what is the probability of selecting a female inmate who is at least 25 years old?
15/120
If f(a) = f(b) = 0 and f(x) is continuous on [a, b], what can be concluded about f(x)?
f(x) must be identically zero
Regarding the inequality between mean and variance of the Binomial distribution, which statement is true?
Mean < Variance
If a student is randomly chosen from the class and found to have earned an A, what is the probability that he or she is a junior?
0.48
What is the derivative of y = (x + 1)ln²(x + 1) with respect to x?
2ln(x + 1) + 4ln²(x + 1)
What is the probability that a student arranges the cards in the order blue, red, yellow, and green, given that they have 6 color options and choose randomly?
1/540
What is the integral of (2x + 1)/(4 + x²) dx?
(1/2) tan¯¹ (x/2) + C
Calculate the probability of a randomly chosen student, who received an A, being a senior based on the given numbers of juniors, seniors, and graduate students who received an A in the course.
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