Suppose a batch of steel rods produced at a steel plant have a mean length of 174 millimeters, and a standard deviation of 8 millimeters. if 188 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by more than 0.63 millimeters? round your answer to four decimal places.

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

The electric field between square plates of a parallel-plate capacitor has magnitude e. the potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. the magnitude of the electric field between the plates is now equal to a)e b)e/4 c)e/2 d)4e e)2e

Aheavy piece of hanging sculpture is suspended by a90-cm-long, 5.0 g steel wire. when the wind blows hard, the wire hums at its fundamental frequency of 80hz. what is the mass of the sculpture?