Barker and Associates specialize in corporate law. They charge $125 an hour for researching a case, $80 an hour for consultations, and $250 an hour for writing a brief. Last week one of the attorneys spent 8 hours consulting with her client, 12 hours researching the case, and 15 hours writing the brief. What was the weighted mean hourly charge for her legal services

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?

Evaluate the following expression 1/3^2

Thee blue triangle has rotated from quadrant i to quadrant iii about the origin. describe the effects of the rotation on the coordinates of the blue triangle.