Describe the tribological differences between ordinary machine elements (such as meshing gears, cams in contact with followers, and ball bearings with inner and outer races) and elements of metalworking processes (such as forging, rolling, and extrusion, which involve workpieces in contact with tools and dies).

An urn contains four red balls, five yellow balls, and seven green balls.  You randomly select two balls without replacement.  Express your answer as a decimal rounded to four decimal places. a.)  What is the probability they are both green?  [a] b.)  What is the probability the first ball is green and the second ball is yellow?  [b]

You want to know what proportion of adults in the United States use an electric toothbrush.  How many adults have to be surveyed to estimate this proportion with a margin of error of 3% using a 95% confidence interval?

A national polling organization does a survey of  995 people to estimate the percentage of all American adults who favor a ban on the use of cell phones while driving.  In the survey, 37% said they favor such a ban.   a.)  Find a 90% confidence interval for the proportion of all American adults who favor such a ban.  Also find the margin of error.  Round your answers to four decimal places.                      90% Confidence Interval:  (  [LL]  ,  [UL]  )                    Margin of Error:   [E]   b.)  Still using a 90% confidence interval, how many should be polled to reduce the margin of error to 2%?  Use the fact that in the first poll 37% said that they favor such a ban.                  Required sample size =  [n]

An Olympic archer is able to hit the bull’s eye 75% of the time.  Suppose she shoots 25 arrows.  For a – c, express your answer as a decimal rounded to four decimal places.    a.)  What is the probability she gets exactly 19 bull’s eyes?  [a] b.)  What is the probability that she gets at most 16 bull’s eyes?  [b]   c.)   What is the probability that she gets at least 14 bull’s eyes?  [c] d.)  If she shot 25 arrows many times, what is the mean and standard deviation of how many bull’s eyes she would get?  Round to one decimal place, if appropriate.              Mean = [mean]             Standard Deviation = [sd]

Suppose in the mass-spring system, the position function is given by

Find the general solution:

Suppose we are solving in equation in the form: In each of the following parts, determine the roots of the characteristic equation given a corresponding general solution:

Suppose in a mass spring system the ODE is where

Suppose we have a mass-spring system with an external force represented by an ODE in the form