Of all the yoga students in a particular area, 20% study with patrick and 80% study with carl. we also know that 8% of the yoga students study with patrick and are female, while 66% of the students study with carl and are female. what is the probability that a randomly selected yoga student is female, given that the person studies yoga with carl? a) .35 b) .56 c) .69 d) .83

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.