In proof testing of circuit boards, the probability that anyparticular diode will fail is 0.01.Suppose a circuit board contains 200 diodes. 1. How manydiodes would you expect to fail, and what is the standarddeviation of the number that are expected to fail?
2. What is the (approximate) probability that atleast four diodes will fail on a randomly selected board?
3. If five boards are shipped to a particularcustomer, how likely is it that at least four of them willwork properly? (A board works properly only if all its diodes work)

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Aplane takes off from an airport and flies to town a, located d1 = 215 km from the airport in the direction 20.0° north of east. the plane then flies to town b, located d2 = 230 km at 30.0° west of north from town a. use graphical methods to determine the distance and direction from town b to the airport. (enter the distance in km and the direction in degrees south of west.)

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island