Suppose that we wish to predict whether a given stock will issue a dividend this year ("yes" or "no") based on x, last year’s percent profit. we examine a large number of companies and discover that the mean value of x for companies that issued a dividend was x¯ = 10, while the mean for those that didn’t was x¯ = 0. in addition, the variance of x for these two sets of companies was σˆ 2 = 36. finally, 80% of companies issued dividends. assuming that x follows a normal distribution, predict the probability that a company will issue a dividend this year given that its percentage profit was x = 4 last year.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

During which interval are the persons represented by the graph not moving? a) 0 to 0.5 hrs b) 1.5 to 2 hrs c) 2 to 2.5 hrs d) 4.5 to 5 hrs

Which statement is true about an object that is moving in a circular motion due to centripetal force, f, when the radius of its circular motion is doubled? the new force then becomes equal to 2f the new force then becomes equal to f the new force then becomes equal to f/2 the new force then becomes equal to f2 the new force then becomes equal to 1/f