You are standing at a certain distance from a building that is 20 meters tall. the angle of elevation that the top of the building makes with your feet is 45°. if you walk 6 meters toward the building, the angle of elevation changes to °.

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?

George writes the mixed number as sum and uses the distributive property 1/2.-2/5=1/2-2+2/5=1/2

Julia bought 7 hats a week later half of all her hats were destroyed in a fire. there are now only 12 hats left with how many did she start