In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 3 marbles into a marble jar. when the jar has 100 or more marbles, the students have a party. right now, the the jar has 24 marbles. how could mrs. morton reward the class in order for the students to have a party?

1jessica's home town is a mid-sized city experiencing a decline in population. the following graph models the estimated population if the decline continues at the same rate. select the most appropriate unit for the measure of time that the graph represents. a. years b. hours c. days d. weeks