Larry's lemons is a street vendor business that sells lemonade and lemon bars. a cup of lemonade sells for $2 and a lemon bar sells for $1.50. when all related business expenses are included, a cup of lemonade costs $0.25 to prepare and a lemon bar costs $0.20 to prepare. last monday, one of the vendors selling larry's lemons sold at least $500 worth of lemonade and lemon bars and its expenses were no more than $100. at least 150 cups of lemonade were sold. let x be the number of cups of lemonade sold last monday and y be the number of lemon bars sold last monday. which ordered pair representing a combination of cups of lemonade and lemon bars could have been sold last monday and make sense in the context of the situation?

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?