An old woman sits on a park bench and begins dropping rice on the ground at a constant rate of 7grains per second. initially, there is no rice on the ground and no pigeons are present, but after the woman has been dropping rice for 10 seconds, a pigeon shows up and begins eating rice at a constant rate of 3 grains per second. if the woman continues dropping rice at the same rate, if one new pigeon shows up every 10 seconds, if no pigeons leave, and if all pigeons eat at the same constant rate as long as there is rice on the ground, how many pigeons will be present the next time there is no rice on the ground?

James is playing his favorite game at the arcade. after playing the game 3 times, he has 8 tokens remaining. he initially had 20 tokens, and the game costs the same number of tokens each time. the number t of tokens james has is a function of g, the number of games he plays. write the function’s formula? t=

Two florida panthers were weighed. one weighs 6x+21 pounds and the two together weigh 14x+11 pounds how much does he other panther weigh alone

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?