James asked his boy scout friends to name their favorite New York sports team. He made a list to display the results. 1/4 of the boys named the “Giants” 1/6 of the boys named the “Mets” 3/8 of the boys named the “Yankees” The rest of the boys in the scout troop named the “Rangers” What fractional part of the students in the troop named the “Rangers” as their favorite New York sports team?

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?

Which expressions are equivalent to k/2 choose 2 answers: a k-2 b 2/k c 1/2k d k/2 e k+k

Evaluate cos2θ for cosθ = square root of 3/2