There are two urns filled with marbles, the first urn has 5 red marbles and 3 blue marbles while the second urn has 2 red marbles, 7 blue marbles, and 5 yellow marbles. You take one marble from each urn. What is the probability that the two marbles are grab are the same color?
Since both marbles must be the same color, the answer to this question is the probability that both marbles are red or that both marbles are blue. P(red) in the first urn is 5 red marbles out of 8 total marbles = 5/8. P(red) in the second urn is 2 red marbles out of 14 total marbles =2/14 = 1/7 P(red & red) is then 5/8 * 1/7 = 5/56 P(blue) in the first urn is 3 blue marbles out of 8 total = 3/8 P(blue) in the second urn is 7 blue marbles out of 14 total = 7/14 = 1/2 P(blue & blue) is then 3/8 * 1/2 = 3/16 There are no yellow marbles in the first urn so we don't have to worry about those, so the probability that both marbles are the same color is P((red & red) or (blue & blue)) which is 5/56 + 3/16 = 31/112
In the right triangle ABC where angle C is the right angle and AB is the hypotenuse, angle A is given by X. If segment BC is 24cm long and segment AB is 26cm long, what is X?
Sin(x) = Opposite / Hypotenuse, so Sin(x) = 24cm/26cm x = arcsin(0.923) x = 67.38 Degrees
A man is making a fence to surround his yard. His yard is a 10 meter by 20 meter rectangle. However, the man runs out of money after purchasing only half of the fence he needed to surround his entire yard, so he decides to only fence in half the yard instead (a 10 meter by 10 meter square). Can the man fence in half of his yard with this amount of fence? Why or why not?
No, the man cannot fence in half of his yard with half of the original amount of fence, although it may seem counter-intuitive. His yard is 10m X 20m giving a perimeter of 10m + 10m + 20m + 20m = 60m, meaning the man needs 60m of fence. However, the man ran out of money after purchasing only half of this amount, meaning he purchased 30m of fence. To surround half of the man's yard, however, he'd need to surround a 10m x 10m square which has a perimeter of 10m + 10m + 10m + 10m = 40m, so the man ends up having only 30m of fencing where he actually needs 40m, so he cannot fence his yard.