Suppose that you have ten lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential distribution with parameter 3.

(a) What is the probability that all ten bulbs fail before time t?

(b) What is the probability that exactly k of the ten bulbs fail before time t?

(c) Suppose that nine of the bulbs have lifetimes that are exponentially distributed with parameter λ

and that the remaining bulb has a lifetime that is exponentially distributed with parameter θ (it is made by another manufacturer). What is the probability that exactly five of the ten bulbs fail before time t?

A250-n box is at rest on a frictionless horizotal floor. then a person shoves the box with a non-zero force of magnitude p. which statement best describes the relationship betweeen p and the motion of the box after it was shoved? -the box will not move when p< 250n but otherwise will accelerate at a constant rate that is directly proportional to p - the box will begin moving at a speed that is directly proportional to p, then will gradually slow to a halt -the box will move with constant velocity at a speed that is directly proportional to p -box will accelerate across the floor at a constant rate that is directly proportional to p

Aplayground slide is 8.80 ft long and makes an angle of 25.0° with the horizontal. a 63.0-kg child, initially at the top, slides all the way down to the bottom of the slide. (a) choosing the bottom of the slide as the reference configuration, what is the system's potential energy when the child is at the top and at the bottom of the slide? what is the change in potential energy as the child slides from the top to the bottom of the slide? (include the sign of the value in your answer.)

Awave that is traveling fast can be said to have a high a. frequency b. speed c. wavelength d. amplitude e. period f. none of these