Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. After a long time has passed, you record the number of balls in each container every second. In 10,000 s, you find 80 times when all the balls were in one container (either one) and the other container was empty. Required:
a. How many balls are there?
b. What is the most likely number of balls to be found in one of the containers?

In trapezoid efgh, m∠hef=(4x2+16)∘ and m∠gfe=(5x2+12)∘. find the value of x so that efgh is isosceles.

What is the location of point g, which partitions the directed line segment from d to f into a 5: 4 ratio? –1 0 2 3

I've been working on this for a few days and i just don't understand, it's due in a few hours. you. the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α.part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part bsuppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i. e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case. part cnow try a numerical problem. what is the direction of the vector w = < -1, 6 > ?