Find the expected value of the winnings from a game that has the following
payout probability distribution:
Payout ($)| 0
4
6 8 10
Probability 0.45 0.3 0.1 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.

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)