Over time, the number of original basic words in a language tends to decrease as words become obsolete or are replaced with new words. for a certain language proportion of words that remain after t millennia is a random variable that is exponentially distributed with a = 0.247. complete parts (a) and (b)
a. find the life expectancy and standard deviation of a word from this language.
what is the life expectancy?
4.05 millennia
what is the standard deviation?
4.05 millennia
b. what is the probability that a randomly chosen word from this language will remain after 2000 years?
(round to four decimal places as needed)

1. gar principles or "the principles"are intended to do what? a. foster an awareness of the hierarchical structure of the organization b. explain the best method of implementing biometric security techniques c. foster an awareness of the importance of good employee training d. foster an awareness of getting upper level management on board in understanding the need to implement an ig program e. foster an awareness of good record keeping principles

Who is not spending wisely? erika goes shopping and saves her receipts. she totals how much she spent and writes it down. mia needs to buy a new pair of shoes because she joined the soccer team. she looks at newspaper ads to find the best price. lauren has been thinking about getting a puppy for a long time. she walks by the pet store at the mall and decides to get a puppy. erin makes a purchase online using a credit card. she knows that she can pay the entire bill when it arrives.

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?