The area of a right triangle is 50. One of its angles is 45o. Find the lengths of the sides and hypotenuse of the triangle.?
The triangle is right and the size one of its angles is 45 degrees; the third angle has a size 45 degrees and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse. Area = (1/2)x2 = 50 , solve for x: x = 10 We now use Pythagora to find H: x2 + x2 = H2 Solve for H: H = 10 sqrt(2)
The survey carried out to delineate natural features, such as hills, rivers, forests and man- made features, such as towns, villages, buildings, roads, transmission lines and canals is classified as?
Topographic survey is carried out to delineate natural features.
You have 50 red marbles, 50 blue marbles and 2 jars. One of the jars is chosen at random and then one marble will be chosen from that jar at random. How would you maximize the chance of drawing a red marble? What is the probability of doing so? All 100 marbles should be placed in the jars.
What if you put a single red marble in one jar and the rest of the marbles in the other jar? This way, you are guaranteed at least a 50% chance of getting a red marble (since one marble picked at random, doesn’t leave any room for choice). Now that you have 49 red marbles left in the other jar, you have a nearly even chance of picking a red marble (49 out of 99). So let’s calculate the total probability. P( red marble ) = P( Jar 1 ) * P( red marble in Jar 1 ) + P( Jar 2 ) * P( red marble in Jar 2 ) P( red marble ) = 0.5 * 1 + 0.5 * 49/99 P( red marble ) = 0.7474 Thus, we end up with ~75% chance of picking a red marble.