Which of the following statements is/are true? (5 points)
i. if f '(x) exists and is nonzero for all x, then f(1) ≠ f(0)
ii. if f is differentiable for all x and f (-1) = f(1), then there is a number c, such that |c| < 1 and f '(c) = 0.
iii. if f '(c) = 0, then f has a local maximum or minimum at x = c.

i only
ii only
i and iii only
i and ii only

You’re repairing a large rectangular aquarium. the final step is to cover the glass with a protective film. the front and back of the aquarium measure 4 meters by 2 meters, and the sides of the aquarium measure 3 meters by 2 meters. how many square meters of protective film do you need? ( )

which of the following sets of data would produce the largest value for an independent-measures t statistic? the two sample means are 10 and 20 with variances of 20 and 25 the two sample means are 10 and 20 with variances of 120 and 125 the two sample means are 10 and 12 with sample variances of 20 and 25 the two sample means are 10 and 12 with variances of 120 and 125

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? why? a. the z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. b. the z score of 0 is most preferable because it corresponds to a test score equal to the mean. c. the z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. d. the z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average