Given the function g(x) = b(−5x + 1)6 − a , where a ≠ 0 and b ≠ 0 are constants.

a. find g′(x) and g′′(x).

b. prove that g is monotonic (this means that either g always increases or g always decreases).

c. show that the x-coordinate(s) of the location(s) of the relative extrema are independent of a and b.

The lengths of nails produced in a factory are normally distributed with a mean of 4.91 centimeters and a standard deviation of 0.05 centimeters. find the two lengths that separate the top 4% and the bottom 4%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

Which shows the correct solution of the equation 1/2a+2/3b=50, when b=30?

About 9% of th population is hopelessly romantic. if 2 people are randomly selected from the population, what is the probability that at least 1 person is hopelessly romantic?