You are playing the card game High-Low with a single suit of hearts and the first five cards drawn in order are King, 7, 9, 5, and 6. What is the probability the next card is higher (than 6) and then the next card is lower (than 6)?

The triangles are similar. what is the value of x? x=

What are the domain and range of the function f(x)=2^x+1

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?