A radioactive isotope decays exponentially at a rate of 0.0119% each year.

How long will it take 500 g of the isotope to decay to 150 g? Round your answer to the nearest whole number.

It will take about years for 500 g of the radioactive isotope to decay to 150 g.

The half-life for a radioactive isotope is the amount of time it takes for the isotope to reach half its initial value. What is the half-life of the given radioactive isotope? Round your answer to the nearest whole number.

The half-life of the given radioactive isotope is about years.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.