You enter a special kind of chess tournament, in which you play one game with each of three opponents, but you get to choose the order in which you play your opponents, knowing the probability of a win against each. You win the tournament if you win two games in a row, and you want to maximize the probability of winning.
Show that it is optimal to play the weakest opponent second and that the order of playing the other two opponents does not matter.

Which of the following is true about the graph of f(x)=7^x. select all that apply. a= it intercepts the x axis b=it intercepts both axis c=it intercepts neither d=it intercepts the y axis

Identify the expression equivalent to 4(x + x + 7) − 2x + 8 − 4 by substituting x = 1 and x = 2.

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.