Consider a triangle where two sides have fixed lengths 12 cm and 14 cm. suppose the two sides are initially at an angle of α = 2π 3 and that they are closing together so that the angle between them is decreasing at a rate of π 12 radians per second. what is the rate at which the area of the triangle is decreasing when α = π 4 ?

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560