The life in hours of a battery is known to be approximately normally distributed with standard deviation σ = 1.25 hours. a random sample of 10 batteries has a mean life of x =40.5hours. a. is there evidence to support the claim that battery life exceeds 40 hours? use α = 0.05. b. what is the p-value for the test in part (a)? c. what is the β-error for the test in part (a) if the true mean life is 42 hours? d. what sample size would be required to ensure that β does not exceed 0.10 if the true mean life is 44 hours? e. explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life.

The average hourly earnings for a construction worker is projected to be $24.50 in 2012. jason wants to join the construction work force after he graduates in 2012. his friend tells him that average hourly earnings for construction workers will rise by 2% from 2009 to 2012. based on the data below, assuming that the projected hourly earnings are correct, is jason’s friend’s statement accurate? construction industry - average hourly earnings, 2000-2009 a. his friend’s statement is accurate. the average hourly earnings will increase by 2%. b. his friend’s statement is not accurate. the percent increase will be more than 2% c. his friend’s statement is not accurate. the percent increase will be less than 2% d. his friend’s statement is not accurate. the average hourly earnings will decrease

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. which function could heather be writing? fx) = x2 + 36x + 12 = x2 - 36x - 12 f(x) = -x + 12x + 36 f(x) = -x? - 12x - 36

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.