My birthday is coming up and I want to make goodie bags for my friends. My mom bought 30 cupcakes and 40 bags of chips. I want each goodie bag to have the same number of cupcakes and chips. What is the most amount of friends I can invite?

Restrictions on f(x) = 1/x+5 and g(x) = x-2

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?

What ratio is proportional to 18/21