The denominator of a fraction is 7 more than the numerator. If 1 is added to the numerator and 6 is added to the denominator, the value of the fraction will be ½. Find the numerator and the denominator.

Cot(90° − x) = 1 the value of x that satisfies this equation is °. a. 60 b. 135 c. 225 d. 315

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?

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.