The lifetime of a mechanical assembly in a vibration test is exponentially distributedwith a mean of 400 hours.
(a) what is the probability that an assembly on test fails in less than 100 hours?
(b) what is the probability that an assembly operates for more than 500 hours beforefailure?
(c) if an assembly has been on test for 400 hours without a failure, what is theprobability of a failure in the next 100 hours?
(d) if 10 assemblies are tested, what is the probability that at least one fails in lessthan 100 hours? assume that the assemblies fail independently.
(e) if 10 assemblies are tested, what is the probability that all have failed by 800hours? assume the assemblies fail independently.

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm. in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

"which statement is necessarily true if bd is an altitude to the hypotenuse of right ? abc? a.) ? adb? ? bdc b.) ? adb~? bdc c.) abbc=acbd d.) ? bac? ? bdc"

Suppose you can spend at most $12. create an inequality that represents this restraint. then find at least three ordered pair solutions representing the number of boxes of candy and combos you can buy