A linear function is given by the equation y=4x. Using the points x and x=1, show that the y-values increase by 4 between any two points separated by x2-x1=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?

Consider the image of klmn for the translation (x, y) → (x – 2, y – 1). what is the ordered pair of l′?

When solving a logarithm equation, how do you find the missing variable ?