Seven-digit telephone numbers are not allowed to begin with $0$ or $1$. I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to either the next three digits or the last three digits. For example, I can remember $389$-$3892$ and $274$-$9274$. How many seven-digit telephone numbers can I remember

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?

Two language majors, anna and megan, took exams in two languages. anna scored 85 on both exams. megan scored 74 on the first exam and 85 on the second exam. overall, student scores on the first exam had a mean of 82 and a standard deviation of 4, and the second exam scores had a mean of 71 and a standard deviation of 13. a) to qualify for language honors, a major must maintain at least an 85 average across all language courses taken. so far, which of anna and megan qualify? b) which student's overall performance was better?

An energy drink company claims that its product increases students' memory levels. to support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. the missing component in this study is a .