Recent content by obafgkmrns

There are a discrete number of bacteria in each 1 ml sample. The probability of finding 0, 1, 2 ... bacteria in any given sample has a binomial distribution. n is the total number of bacteria present in the solution, and taking 5 samples allows one to estimate p and thereby estimate the...

The 'counting' refers to the number of bacteria colonies in each petri dish, with each colony presumed to have arisen from a single bacterium. The number of bacteria in each 1 ml sample actually has a binomial distribution, but if there are many bacteria present, a Poisson distribution is a...

Interesting problem! Fiddling with pencil & paper and looking for patterns suggests that for n integers, the answer involves sums of triangle numbers, T(n) = n(n+1)/2, but I don't see a good way to get there from simple combinetrics.

There's no doubt that they move -- supernova remnants will have some trace of the original star's proper motion, for example. The problem is that nebulae all lie at large distances (the Gum Nebula, one of the nearest, is about 700 parsecs off), and they are all, well, nebulous. That makes any...

Sounds like your actual pique is that Romney's rich, you're not, and you want the Government to rectify the situation.

When you make an investment, you take on a risk of losing every penny of it. Under U.S. tax code, you can deduct only $3,000 per year of such losses, making large investments rather hazardous. Taxing capital gains at a lower rate than ordinary income somewhat ameliorates that hazard and...

I take it that you object to church contributions. If you actually believe the Government should receive that cash, run for office and get the law changed.

Romney gave 14% of his income to charity in 2010, and the 2011 estimate is 19%. Seems generous enough to me.

MathWorld discusses it: http://mathworld.wolfram.com/SincFunction.html

Nope. It would be appropriate only if the lower end of the pipe were sealed and there were no flow. Because the flow is discharging freely into the atmosphere, the pressure at the bottom of the pipe is 1 atmosphere.

You're making it too difficult. The pressure is simply 14.7 psi. Think about what the pressure inside the stream is a fraction of an inch after leaving the pipe. The pressure in the stream a fraction of an inch before leaving the pipe must be the same. The flow inside the pipe will adjust...

y = 1 + (cos(x) + 1)^2 is a fair fit.

I'm seeing regions of differing refractive index. Those regions are composed chiefly of, well, air.

To tell the truth, that bothered me as well when I first encountered the concept. The professor was confused as to why I even asked the question. Consider a function f(x,y). Is there any problem with defining partial derivatives with respect to x and y? What if, unbeknownst to you, y is...

Perhaps you argue that we similarly can't see water or glass?