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Chapter 11: Problem 50
A single die is rolled twice. Find the probability of rolling a 5 the first time and a 1 the second time.
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Explaining the Concepts The president of a large company with \(10,000\) employees is considering mandatory cocaine testing for every employee. The test that would be used is \(90 \%\) accurate, meaning that it will detect \(90 \%\) of the cocaine users who are tested, and that \(90 \%\) of the nonusers will test negative. This also means that the test gives \(10 \%\) false positive. Suppose that \(1 \%\) of the employees actually use cocaine. Find the probability that someone who tests positive for cocaine use is, indeed, a user. Hint: Find the following probability fraction: the number of employees who test positive and are cocaine users the number of employees who test positive This fraction is given by $$ 90 \% \text { of } 1 \% \text { of } 10,000 $$ the number who test positive who actually use cocaine plus the number who test positive who do not use cocaine What does this probability indicate in terms of the percentage of employees who test positive who are not actually users? Discuss these numbers in terms of the issue of mandatory drug testing. Write a paper either in favor of or against mandatory drug testing, incorporating the actual percentage accuracy for such tests.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.
You are now 25 years old and would like to retire at age 55 with a retirement fund of \(\$ 1,000,000 .\) How much should you deposit at the end of each month for the next 30 years in an IRA paying \(10 \%\) annual interest compounded monthly to achieve your goal? Round up to the nearest dollar.
Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was \(\$ 656\) million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to \(46 .\) Use this information to solve Exercises \(27-30 .\) Express all probabilities as fractions. A player wins a minimum award of \(\$ 150\) by correctly matching three numbers drawn from white balls \((1 \text { through } 56\) ) and matching the number on the gold Mega Ball \((1 \text { through } 46)\) What is the probability of winning this consolation prize?
Use a right triangle to write \(\cos \left(\tan ^{-1} x\right)\) as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x . \text { (Section } 5.7, \text { Example } 9)\)
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