Do you think you will benefit from the discoveries of Archimedes’ and Pascal’s Principles?

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.

1.in one challenge on the titan games, competitors have to lift 200 pounds up a long ramp. angel is able to move the weight in 42 seconds. anthony gets it done in only 38 seconds. which statement is true? angel has more power than anthony. angel does more work than anthony. anthony does more work than angel. anthony has more power than angel. 2.a mountain climber exerts 41,000 j of work to climb a cliff. how much power does the climber need if she wants to finish in only 500 seconds? power = work / time 20,500,000 watts 82 watts 0.0122 watts 41,500 watts 3.your family is moving to a new apartment. while lifting a box 83 joules of work is done to put the box on a truck, you exert an upward force of 75 n for 3 s. how much power is required to do this? (hint: you only need two of the 3 numbers given! ) power = work / time 249 watts 25 watts 2075 watts 27.7 watts

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