A ladder is leaning against a building. The ladder forms an angle of 77° with the ground. The distance from the base of the ladder to the base of the building is 8 feet.

Nikolas calculated the volume of the prism. his work is shown below.

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?

Tim has obtained a 3/27 balloon mortgage. after the initial period, he decided to refinance the balloon payment with a new 30-year mortgage. how many years will he be paying for his mortgage in total?