Find the vector cross product of two vectors = − and = + − (b) what is the angle between the vectors?​

An insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers. the company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 2.2 miles per hour. another sample of 18 cars driven by women on the same highway gave a mean speed of 68 miles per hour with a standard deviation of 2.5 miles per hour. assume that the speeds at which all men and all women drive cars on this highway are both approximately normally distributed with unknown and unequal population standard deviations.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Imagine that you have two balloons (or, better yet, actually inflate two balloons, if possible). create static electricity around one of the balloons by rubbing it against your hair or your sweater and then bring that balloon close to the other balloon, which has not been charged. try this with at least one other object—and for variety in the discussion, avoid using an object already described by your classmates. then, for your initial post to the discussion, answer the following questions: what happened with the two balloons?