Aneedle of length l is dropped on an infinite plane surface that is partitioned into rectangles by horizontal lines that are a apart and vertical lines that are b apart. suppose that the needle’s length l satisfies l < a and l < b. what is the expected number of rectangle sides crossed by the rectangle? what is the probability that the needle will cross at least one side of some rectangle?

In an experiment you are to flip a two sided coin 100 times and record 55 heads up and 45 tails up determine the theoretical and experimental probability of getting a heads up in the experiment.

The tiles below are pieces of a normal ecg tracing representing a little less than two heartbeats at a resting rate of 80 bpm. arrange the tiles in their correct order. rank from first to last. do not overlap any tiles.

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling