ΔHFG is dilated by a scale factor of 2 with the center of dilation at point F. Then, it is reflected over line a to create ΔEFI. Based on these transformations, which statement is true? Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F. segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI segment FG = segment FI, segment FH = segment FE, and segment HG = segment EI; ΔHFG ~ ΔEFI segment FG = one half segment FE, segment FH = one half segment FI, and segment HG = one halfsegment EI; ΔHFG ~ ΔIFE segment FG = segment FE, segment FH = segment FI and segment HG = segment EI; ΔHFG ~ ΔIFE

Which interval for the graphed function contains the local maximum? [–3, –2] [–2, 0] [0, 2] [2, 4]

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?

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.