Consider a lottery game that is played by drawing four white balls out of a drum of 59 white balls (numbered 1–59) and one red ball out of a drum of 28 red balls (numbered 1–28). The jackpot is won by matching all four white balls in any order and the red ball. (a) Find the possible number of winning numbers. winning number(s)

(b) Find the possible number of winning numbers if the jackpot is won by matching all four white balls in order and the red ball. winning number(s)

Amonument at a park is in the shape of a right square pyramid. a diagram of the pyramid and its net are shown. what is the surface area of the monument? enter the answer in the box. m²

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

When a valve is open 281 gallons of water go through it in one hour the number of gallons that would go through in 94 hours is