The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. if g(x) is obtained by shifting f(x) down by 7 units, then what is the value of k?

The number of 8th graders who responded to a poll of 6th grade and 8 th graders was one fourtg of the number of 6th graders whi responded if a total of 100 students responddd to the poll how many of the students responded were 6 th graders

In a certain city, the hourly wage of workers on temporary employment contracts is normally distributed. the mean is $15 and the standard deviation is $3. what percentage of temporary workers earn less than $12 per hour? a. 6% b. 16% c. 26% d. 36%

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?