X= y2 - 1
2x - y = 4
which of the following equations could be the result of using substitution to solve the system?
2y² - y - 5 = 0
2y² - y - 6 = 0
2y² - 2y - 5 = 0

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Aquality characteristic of new iphone x made at the amsterdam plant at apple computers has a manufacturing specification (in mm) of 0.200 +/- .07. historical data indicates that if the quality characteristic takes on values greater than 0.27 or smaller than 0.13 the component fails at a cost of20.19. based on these data: determine the taguchi loss function (must show work) calculate an estimated loss for a quality characteristic of .30 calculate an estimated loss for quality characteristic of .40.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.