In making the decision to return to school for an MBA, prospective students desire to know the time it will take to recoup their investment (forgone wages plus tuition and other direct costs). The time it will take to recoup their investment is normally distributed. You are in charge of estimating this time for a brochure advertising an MBA program at UCLA. You randomly sample 20 past UCLA MBA students and find that the sample average is 3.61 years with a standard deviation of 0.63 years. To estimate the mean number of years required to recoup an investment in a UCLA MBA to within 2 months (0.17 years) with 80% confidence, the sample size should be approximately

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?

Type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. consider the given table.

State one method by which you can recognize a perfect square trinomial.