Joseph and his younger brother, Ryan, are taking a backpacking trip and must take a total of 12 gallons of water. Ryan will carry 4 less than half of gallons Joseph will carry. Let x be the number of gallons Joseph carries and let y be the number of gallons Ryan carries.

Alawn mower manufacturer incurs a total of 34,816 in overhead costs and 388 per lawn mower in production costs. how many lawn mowers were manufactured if the average cost of productions is 660

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

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)