The standard form of the equation for a quadratic function is, with he vertex of the graph of the function at the point (p, q). the factored form is y=a(x-x1) (x-x2), where x1 and x2 are the x-intercepts of the graph. Express p and q in terms of x1 and x2 by expanding the factored for then completing the square. Please show work.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

Amanufacturer knows that their items have a normally distributed lifespan, with a mean if 9.1 years, and standard deviation of 2.9 years. if you randomly purchase one item, what is the probability it will last longer than 10 years?

How many dollars more is the price of a pie than the price of a doughnut at erik’s store