Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b. The area of the base of the cube, B, is square units. The volume of the cube is cubic units. The height of each pyramid, h, is . Therefore, b = 2h. There are square pyramids with the same base and height that exactly fill the given cube. Therefore, the volume of one pyramid is or One-thirdBh.

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?

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

50 will mark show all use the linear combination method to solve the system of equations. explain each step of your solution. if steps are not explained, you will not receive credit for that step. 2x+9y= -26 -3x-7y=13