In one community, 78\%78%78, percent of the over 400{,}000400,000400, comma, 000 people who speak Spanish are native speakers. Suppose a politician took monthly random samples of 757575 people in the community who speak Spanish and calculated the proportion \hat p p ^ p, with, hat, on top of people from each sample who were native Spanish speakers. What will be the shape of the sampling distribution of \hat p p ^ p, with, hat, on top?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 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)