How many different ways can the first twelve letters of the alphabet be arranged

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

What is the perimeter of an equilateral triangle if each side is (x+3)?

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.