"You have a jar of red marbles and blue marbles." At each time step, you draw a marble, and you note the color of the marble. Then, you dilute the proportion of the opposite-colored marbles by a factor of γ, where 0 < γ < 1. (For example: if you pick a red marble, then the proportion of blue marbles is reduced by a factor of γ.) If p is the fraction of marbles that started off as red, what is the expected proportion of red marbles at time n?

What is the frequency of the sinusoidal graph?

Which property was used to simplify the expression? 3c+9 +4c=3c+4c+9

Atravel agent is booking a trip to england, scotland, ireland, and france for a group of senior citizens. the agent sent surveys to the group, asking which countries they would like to visit, in order, and created the shown preference schedule (e = england, i = ireland, s = scotland, f = france). which country is the condorcet winner? number of votes 15 12 16 19 1st f e e i 2nd e s i s 3rd s i s e 4th i f f f 1. scotland 2. england 3. france 4.ireland