A tree casts a shadow 60 feet long. At the same time, a nearby 8-foot post casts a 12- foot shadow. How tall is the tree?

Explain how you can find the missing fraction in 3 4/5 / (blank) 2 5/7. then find the missing fraction.

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?

Which of the following constants can be added to x2 - 3x to form a perfect square trinomial?