Charlie (c) has 75 more pencils than Kate (k). Together, they have 135 pencils. How many pencils does Kate have? * ​

Which of the expressions (on the photo document i inserted) together represent all solutions to the following equation? 8cos(12x)+4=-4 *the answer should be in degrees.* > i would like for someone to explain the process to find the solutions for this.

Question 5 spring semester final exam math evaluate

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?