Edward is making a rectangular picture frame. he wants the perimeter of the frame to be no more than 96 inches. he also wants the length of the frame to be greater than or equal to the square of 4 inches less than its width. create a system of inequalities to model the above situation and use it to determine how many of the solutions are viable. a.) part of the solution region includes a negative length; therefore, all solutions are not viable for the given situation. b.) no part of the solution region is viable because the length or width cannot be negative. c.) the entire solution region is viable. d.) part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.

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?

Aswimming pool had 2.5 million liters of water in it. some water evaporated, and then the pool only had 22 million liters of water in it. what percent of the water evaporated?

Michael is training for a marathon. in his first week he plans to run 8miles. what path should he take