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An unfair coin with Pr[H] = 2/3 is flipped. If the flip results in a head, then a marble is selected from an urn containing 4 red, 7 white, and 4 blue marbles. If the flip results in a tail then a marble is selected from an urn containing 1 red and 6 white marbles. If the marble selected is white, then what is the probability that a flip resulted in a head?
Permutation and combination
Using trigonometry to solve a Right triangle - Find the width of the lake.
Prove that if f(x) is even on [-a, a] and integrable on [0, a] where a>0, then f(x) is integrable on [-a, a] and Int([-a, a], f(x)dx) = 2*Int([0, a], f(x)dx).
Suppose you are going to flip a coin once. What is the set of possible outcomes for this? Suppose you are going to flip a coin twice. What is the set of possible outcomes for this?
A light-year is a measure of length equal to the distance that light travels in 1 year. Compute the conversion factor between light-years and meters, and find the distance to the star Proxima Centauri 4 1016 m in light-years.
Evaluate the coordinate of centroid using multiple integral method - Find the z- coordinate of the centroid of T
Write the expression in the standard form a + b i. First convert to rectangular form--- calculate the magnitude-- find reference angle--then the argument of z---
In a certain population of people, 20% are blue-eyed and 80% are brown-eyed. Also, 6% of the blue-eyed people are left-handed and 14%of the brown-eyed people are left-handed.
Suppose u and v are non-parallel unit vectors, a=u+sqrt(3)v and b=u-sqrt(3)v. If the angle theta between u and v are the same as that between a and b, find cos theta.
Half angle formula to find the exact value.
Show that log(r), where this is log base 10, is irrational when r is a positive rational that is not an integral power of 10
Determine the above rates in other quotation format ( i.e. if above rates are quoted indirectly,calculate direct quotation,and vice versa) Please provide your answer in proper manner ( i.e. XX per YY)
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