Rosencrantz chooses a coin from guildenstern's collection of one hundred pennies and promptly tosses six heads in a row. while rhapsodizing over his good luck, he learns that four of the pennies were two-headed. the probability that rosencrantz chose one of the two-headed pennies given that he flipped six heads in a row can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m + n$.

Leo is going to use a random number generator 4 0 0 400 times. each time he uses it, he will get a 1 , 2 , 3 , 4 , 1,2,3,4, or 5 5. what is the best prediction for the number of times that leo will get an odd number?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

Ateam has p points. p = 3w + d w = wins d = draws a) a football team has 5 wins and 3 draws. how many points does the team have?