The following method was proposed to estimate the number of people over the age of 50 who reside in a town of known population 100,000: "as you walk along the streets, keep a running count of the percentage of people you encounter who are over 50. do this for a few days; then multiply the per- centage you obtain by 100,000 to obtain the esti- mate." comment on this method. hint: let p denote the proportion of people in the town who are over 50. furthermore, let α1 denote the proportion of time that a person under the age of 50 spends in the streets, and let α2 be the cor- responding value for those over 50. what quantity does the method suggested estimate? when is the estimate approximately equal to p?

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?

Ricky takes out a $31,800 student loan to pay his expenses while he is in college. after graduation, he will begin making payments of $190.66 per month for the next 30 years to pay off the loan. how much more will ricky end up paying for the loan than the original value of $31,800? ricky will end up paying $ more than he borrowed to pay off the loan.

The figure below shows rectangle abcd and the triangle eca on a coordinate plane.which of the following expressions represents the perimeter of triangle of triangle eca in units