Three tas are grading a final exam. there are a total of 60 exams to grade. (a) how many ways are there to distribute the exams among the tas if all that matters is how many exams go to each ta? (b) now suppose it matters which students' exams go to which tas. how many ways are there to distribute the exams? (c) suppose again that we are counting the ways to distribute exams to tas and it matters which students' exams go to which tas. the tas grade at different rates, so the first ta will grade 25 exams, the second ta will grade 20 exams and the third ta will grade 15 exams. how many ways are there to distribute the exams?

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?

What is the expression in factored form? -x^2 + 3x + 28 a. (x-7)(x-4) b. -(x-7)(x+4) c. (x+4)(x+7) d. -(x-4)(x+7)

What is the length of the segment, endpoints of which are intersections of parabolas y=x2? 11 4 x? 7 4 and y=? 7 8 x2+x+ 31 8 ?