Basic Technical Mathematics with Calculus (11th Edition)
11th Edition
ISBN: 9780134437736
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 23.4, Problem 2PE
To determine
The instantaneous velocity of the moving object at the indicated time.
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
Chapter 23 Solutions
Basic Technical Mathematics with Calculus (11th Edition)
Ch. 23.1 - Determine the continuity of the function
.
Ch. 23.1 - Prob. 2PECh. 23.1 -
Find .
Ch. 23.1 -
Find .
Ch. 23.1 - Prob. 1ECh. 23.1 - Prob. 2ECh. 23.1 - Prob. 3ECh. 23.1 - Prob. 4ECh. 23.1 - Prob. 5ECh. 23.1 - Prob. 6E
Ch. 23.1 - Prob. 7ECh. 23.1 - Prob. 8ECh. 23.1 - Prob. 9ECh. 23.1 - Prob. 10ECh. 23.1 - Prob. 11ECh. 23.1 - Prob. 12ECh. 23.1 - Prob. 13ECh. 23.1 - Prob. 14ECh. 23.1 - Prob. 15ECh. 23.1 - Prob. 16ECh. 23.1 - Prob. 17ECh. 23.1 - Prob. 18ECh. 23.1 - Prob. 19ECh. 23.1 - Prob. 20ECh. 23.1 - In Exercises 21–24, graph the function and...Ch. 23.1 - Prob. 22ECh. 23.1 - Prob. 23ECh. 23.1 - Prob. 24ECh. 23.1 - Prob. 25ECh. 23.1 - Prob. 26ECh. 23.1 - Prob. 27ECh. 23.1 - Prob. 28ECh. 23.1 - Prob. 29ECh. 23.1 - Prob. 30ECh. 23.1 - Prob. 31ECh. 23.1 - Prob. 32ECh. 23.1 - Prob. 33ECh. 23.1 - Prob. 34ECh. 23.1 - Prob. 35ECh. 23.1 - Prob. 36ECh. 23.1 - Prob. 37ECh. 23.1 - Prob. 38ECh. 23.1 - Prob. 39ECh. 23.1 - Prob. 40ECh. 23.1 - Prob. 41ECh. 23.1 - Prob. 42ECh. 23.1 - Prob. 43ECh. 23.1 - Prob. 44ECh. 23.1 - Prob. 45ECh. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - Prob. 48ECh. 23.1 - Prob. 49ECh. 23.1 - Prob. 50ECh. 23.1 - Prob. 51ECh. 23.1 - Prob. 52ECh. 23.1 - Prob. 53ECh. 23.1 - Prob. 54ECh. 23.1 - Prob. 55ECh. 23.1 - Prob. 56ECh. 23.1 - Prob. 57ECh. 23.1 - Prob. 58ECh. 23.1 - Prob. 59ECh. 23.1 - A 5-Ω resistor and a variable resistor of...Ch. 23.1 - Prob. 61ECh. 23.1 - Prob. 62ECh. 23.1 - Prob. 63ECh. 23.1 - Prob. 64ECh. 23.1 - Prob. 65ECh. 23.1 - Prob. 66ECh. 23.1 - Prob. 67ECh. 23.1 - Prob. 68ECh. 23.1 - Prob. 69ECh. 23.1 - Prob. 70ECh. 23.1 - Prob. 71ECh. 23.1 - Prob. 72ECh. 23.2 - Find the slope of a line tangent to the curve of y...Ch. 23.2 - Prob. 2PECh. 23.2 - Prob. 1ECh. 23.2 - Prob. 2ECh. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - Prob. 5ECh. 23.2 - Prob. 6ECh. 23.2 - In Exercises 7–10, use the method of Example 2 to...Ch. 23.2 - Prob. 8ECh. 23.2 - Prob. 9ECh. 23.2 - Prob. 10ECh. 23.2 - Prob. 11ECh. 23.2 - Prob. 12ECh. 23.2 - Prob. 13ECh. 23.2 - Prob. 14ECh. 23.2 - Prob. 15ECh. 23.2 - Prob. 16ECh. 23.2 - Prob. 17ECh. 23.2 - Prob. 18ECh. 23.2 - Prob. 19ECh. 23.2 - Prob. 20ECh. 23.2 - Prob. 21ECh. 23.2 - Prob. 22ECh. 23.2 - Prob. 23ECh. 23.2 - Prob. 24ECh. 23.2 - Prob. 25ECh. 23.2 - Prob. 26ECh. 23.2 - In Exercises 27–30, find the point(s) where the...Ch. 23.2 - Prob. 28ECh. 23.2 - Prob. 29ECh. 23.2 - Prob. 30ECh. 23.2 - Prob. 31ECh. 23.2 - Prob. 32ECh. 23.2 - Prob. 33ECh. 23.2 - Prob. 34ECh. 23.3 - Using the definiton, find the derivative of y = 5x...Ch. 23.3 - Prob. 2PECh. 23.3 - Prob. 1ECh. 23.3 - Prob. 2ECh. 23.3 - Prob. 3ECh. 23.3 - Prob. 4ECh. 23.3 - Prob. 5ECh. 23.3 - Prob. 6ECh. 23.3 - Prob. 7ECh. 23.3 - Prob. 8ECh. 23.3 - Prob. 9ECh. 23.3 - Prob. 10ECh. 23.3 - Prob. 11ECh. 23.3 - Prob. 12ECh. 23.3 - Prob. 13ECh. 23.3 - Prob. 14ECh. 23.3 - Prob. 15ECh. 23.3 - Prob. 16ECh. 23.3 - Prob. 17ECh. 23.3 - Prob. 18ECh. 23.3 - Prob. 19ECh. 23.3 - Prob. 20ECh. 23.3 - Prob. 21ECh. 23.3 - Prob. 22ECh. 23.3 - Prob. 23ECh. 23.3 - Prob. 24ECh. 23.3 - In Exercises 25–28, find the derivative of each...Ch. 23.3 - Prob. 26ECh. 23.3 - Prob. 27ECh. 23.3 - Prob. 28ECh. 23.3 - Prob. 29ECh. 23.3 - Prob. 30ECh. 23.3 - Prob. 31ECh. 23.3 - Prob. 32ECh. 23.3 - Prob. 33ECh. 23.3 - Prob. 34ECh. 23.3 - Prob. 35ECh. 23.3 - Prob. 36ECh. 23.3 - Prob. 37ECh. 23.3 - Prob. 38ECh. 23.3 - Prob. 39ECh. 23.3 - Prob. 40ECh. 23.4 - Prob. 1PECh. 23.4 - Prob. 2PECh. 23.4 - Prob. 1ECh. 23.4 - Prob. 2ECh. 23.4 - Prob. 3ECh. 23.4 - Prob. 4ECh. 23.4 - Prob. 5ECh. 23.4 - Prob. 6ECh. 23.4 - Prob. 7ECh. 23.4 - Prob. 8ECh. 23.4 - Prob. 9ECh. 23.4 - Prob. 10ECh. 23.4 - Prob. 11ECh. 23.4 - Prob. 12ECh. 23.4 - Prob. 13ECh. 23.4 - Prob. 14ECh. 23.4 - Prob. 15ECh. 23.4 - Prob. 16ECh. 23.4 - Prob. 17ECh. 23.4 - Prob. 18ECh. 23.4 - Prob. 19ECh. 23.4 - Prob. 20ECh. 23.4 - Prob. 21ECh. 23.4 - Prob. 22ECh. 23.4 - Prob. 23ECh. 23.4 - Prob. 24ECh. 23.4 - Prob. 25ECh. 23.4 - Prob. 26ECh. 23.4 - Prob. 27ECh. 23.4 - Prob. 28ECh. 23.4 - Prob. 29ECh. 23.4 - Prob. 30ECh. 23.4 - Prob. 31ECh. 23.4 - Prob. 32ECh. 23.4 - Prob. 33ECh. 23.4 - Prob. 34ECh. 23.4 - Prob. 35ECh. 23.4 - Prob. 36ECh. 23.4 - Prob. 37ECh. 23.4 - Prob. 38ECh. 23.4 - Prob. 39ECh. 23.4 - Prob. 40ECh. 23.4 - Prob. 41ECh. 23.4 - Prob. 42ECh. 23.4 - In Exercises 27–46, find the indicated...Ch. 23.4 - Prob. 44ECh. 23.4 - Prob. 45ECh. 23.4 - Prob. 46ECh. 23.5 - Prob. 1PECh. 23.5 - Prob. 2PECh. 23.5 - Prob. 1ECh. 23.5 - Prob. 2ECh. 23.5 - Prob. 3ECh. 23.5 - Prob. 4ECh. 23.5 - Prob. 5ECh. 23.5 - Prob. 6ECh. 23.5 - Prob. 7ECh. 23.5 - Prob. 8ECh. 23.5 - Prob. 9ECh. 23.5 - Prob. 10ECh. 23.5 - Prob. 11ECh. 23.5 - In Exercises 5–20, find the derivative of each of...Ch. 23.5 - Prob. 13ECh. 23.5 - Prob. 14ECh. 23.5 - Prob. 15ECh. 23.5 - Prob. 16ECh. 23.5 - Prob. 17ECh. 23.5 - Prob. 18ECh. 23.5 - Prob. 19ECh. 23.5 - Prob. 20ECh. 23.5 - Prob. 21ECh. 23.5 - Prob. 22ECh. 23.5 - Prob. 23ECh. 23.5 - Prob. 24ECh. 23.5 - Prob. 25ECh. 23.5 - Prob. 26ECh. 23.5 - Prob. 27ECh. 23.5 - Prob. 28ECh. 23.5 - Prob. 29ECh. 23.5 - Prob. 30ECh. 23.5 - Prob. 31ECh. 23.5 - Prob. 32ECh. 23.5 - Prob. 33ECh. 23.5 - Prob. 34ECh. 23.5 - Prob. 35ECh. 23.5 - Prob. 36ECh. 23.5 - Prob. 37ECh. 23.5 - Prob. 38ECh. 23.5 - Prob. 39ECh. 23.5 - Prob. 40ECh. 23.5 - Prob. 41ECh. 23.5 - Prob. 42ECh. 23.5 - Prob. 43ECh. 23.5 - Prob. 44ECh. 23.5 - Prob. 45ECh. 23.5 - Prob. 46ECh. 23.5 - Prob. 47ECh. 23.5 - Prob. 48ECh. 23.5 - Prob. 49ECh. 23.5 - Prob. 50ECh. 23.5 - Prob. 51ECh. 23.5 - Prob. 52ECh. 23.5 - Prob. 53ECh. 23.5 - Prob. 54ECh. 23.5 - Prob. 55ECh. 23.5 - Prob. 56ECh. 23.6 - Find the derivative of . Do not multiply factors...Ch. 23.6 - Prob. 2PECh. 23.6 - Prob. 1ECh. 23.6 - Prob. 2ECh. 23.6 - Prob. 3ECh. 23.6 - Prob. 4ECh. 23.6 - Prob. 5ECh. 23.6 - Prob. 6ECh. 23.6 - Prob. 7ECh. 23.6 - Prob. 8ECh. 23.6 - Prob. 9ECh. 23.6 - Prob. 10ECh. 23.6 - Prob. 11ECh. 23.6 - Prob. 12ECh. 23.6 - Prob. 13ECh. 23.6 - Prob. 14ECh. 23.6 - Prob. 15ECh. 23.6 - Prob. 16ECh. 23.6 - Prob. 17ECh. 23.6 - Prob. 18ECh. 23.6 - Prob. 19ECh. 23.6 - Prob. 20ECh. 23.6 - Prob. 21ECh. 23.6 - Prob. 22ECh. 23.6 - Prob. 23ECh. 23.6 - Prob. 24ECh. 23.6 - Prob. 25ECh. 23.6 - Prob. 26ECh. 23.6 - Prob. 27ECh. 23.6 - Prob. 28ECh. 23.6 - Prob. 29ECh. 23.6 - Prob. 30ECh. 23.6 - Prob. 31ECh. 23.6 - Prob. 32ECh. 23.6 - Prob. 33ECh. 23.6 - Prob. 34ECh. 23.6 - Prob. 35ECh. 23.6 - Prob. 36ECh. 23.6 - Prob. 37ECh. 23.6 - Prob. 38ECh. 23.6 - Prob. 39ECh. 23.6 - Prob. 40ECh. 23.6 - Prob. 41ECh. 23.6 - Prob. 42ECh. 23.6 - Prob. 43ECh. 23.6 - Prob. 44ECh. 23.6 - In Exercises 33–58, solve the given problems by...Ch. 23.6 - Prob. 46ECh. 23.6 - Prob. 47ECh. 23.6 - Prob. 48ECh. 23.6 - Prob. 49ECh. 23.6 - Prob. 50ECh. 23.6 - Prob. 51ECh. 23.6 - Prob. 52ECh. 23.6 - Prob. 53ECh. 23.6 - Prob. 54ECh. 23.6 - Prob. 55ECh. 23.6 - Prob. 56ECh. 23.6 - Prob. 57ECh. 23.6 - Prob. 58ECh. 23.7 - Prob. 1PECh. 23.7 - Prob. 2PECh. 23.7 - Prob. 3PECh. 23.7 - Prob. 4PECh. 23.7 - Prob. 1ECh. 23.7 - Prob. 2ECh. 23.7 - Prob. 3ECh. 23.7 - Prob. 4ECh. 23.7 - Prob. 5ECh. 23.7 - Prob. 6ECh. 23.7 - Prob. 7ECh. 23.7 - Prob. 8ECh. 23.7 - Prob. 9ECh. 23.7 - Prob. 10ECh. 23.7 - Prob. 11ECh. 23.7 - Prob. 12ECh. 23.7 - Prob. 13ECh. 23.7 - Prob. 14ECh. 23.7 - Prob. 15ECh. 23.7 - Prob. 16ECh. 23.7 - Prob. 17ECh. 23.7 - Prob. 18ECh. 23.7 - Prob. 19ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 21ECh. 23.7 - Prob. 22ECh. 23.7 - Prob. 23ECh. 23.7 - Prob. 24ECh. 23.7 - Prob. 25ECh. 23.7 - Prob. 26ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 28ECh. 23.7 - Prob. 29ECh. 23.7 - Prob. 30ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 32ECh. 23.7 - Prob. 33ECh. 23.7 - Prob. 34ECh. 23.7 - Prob. 35ECh. 23.7 - Prob. 36ECh. 23.7 - Prob. 37ECh. 23.7 - Prob. 38ECh. 23.7 - Prob. 39ECh. 23.7 - Prob. 40ECh. 23.7 - Prob. 41ECh. 23.7 - Prob. 42ECh. 23.7 - Prob. 43ECh. 23.7 - Prob. 44ECh. 23.7 - Prob. 45ECh. 23.7 - Prob. 46ECh. 23.7 - Prob. 47ECh. 23.7 - Prob. 48ECh. 23.7 - Prob. 49ECh. 23.7 - Prob. 50ECh. 23.7 - Prob. 51ECh. 23.7 - Prob. 52ECh. 23.7 - Prob. 53ECh. 23.7 - Prob. 54ECh. 23.7 - Prob. 55ECh. 23.7 - Prob. 56ECh. 23.7 - Prob. 57ECh. 23.7 - Prob. 58ECh. 23.8 - Prob. 1PECh. 23.8 - Prob. 1ECh. 23.8 - Prob. 2ECh. 23.8 - In Exercises 3–22, find dy/dx by differentiating...Ch. 23.8 - Prob. 4ECh. 23.8 - Prob. 5ECh. 23.8 - Prob. 6ECh. 23.8 - Prob. 7ECh. 23.8 - Prob. 8ECh. 23.8 - Prob. 9ECh. 23.8 - Prob. 10ECh. 23.8 - Prob. 11ECh. 23.8 - Prob. 12ECh. 23.8 - Prob. 13ECh. 23.8 - Prob. 14ECh. 23.8 - Prob. 15ECh. 23.8 - Prob. 16ECh. 23.8 - Prob. 17ECh. 23.8 - Prob. 18ECh. 23.8 - Prob. 19ECh. 23.8 - Prob. 20ECh. 23.8 - Prob. 21ECh. 23.8 - Prob. 22ECh. 23.8 - Prob. 23ECh. 23.8 - Prob. 24ECh. 23.8 - Prob. 25ECh. 23.8 - Prob. 26ECh. 23.8 - Prob. 27ECh. 23.8 - Prob. 28ECh. 23.8 - Prob. 29ECh. 23.8 - Prob. 30ECh. 23.8 - Prob. 31ECh. 23.8 - Prob. 32ECh. 23.8 - Prob. 33ECh. 23.8 - Prob. 34ECh. 23.8 - Prob. 35ECh. 23.8 - Prob. 36ECh. 23.8 - Prob. 37ECh. 23.8 - Prob. 38ECh. 23.8 - Prob. 39ECh. 23.8 - Prob. 40ECh. 23.8 - Prob. 41ECh. 23.8 - Prob. 42ECh. 23.8 - Prob. 43ECh. 23.8 - Prob. 44ECh. 23.9 - Prob. 1PECh. 23.9 - Prob. 2PECh. 23.9 - Prob. 1ECh. 23.9 - Prob. 2ECh. 23.9 - Prob. 3ECh. 23.9 - Prob. 4ECh. 23.9 - Prob. 5ECh. 23.9 - Prob. 6ECh. 23.9 - Prob. 7ECh. 23.9 - Prob. 8ECh. 23.9 - Prob. 9ECh. 23.9 - Prob. 10ECh. 23.9 - Prob. 11ECh. 23.9 - Prob. 12ECh. 23.9 - Prob. 13ECh. 23.9 - Prob. 14ECh. 23.9 - Prob. 15ECh. 23.9 - Prob. 16ECh. 23.9 - Prob. 17ECh. 23.9 - Prob. 18ECh. 23.9 - Prob. 19ECh. 23.9 - Prob. 20ECh. 23.9 - Prob. 21ECh. 23.9 - Prob. 22ECh. 23.9 - Prob. 23ECh. 23.9 - Prob. 24ECh. 23.9 - Prob. 25ECh. 23.9 - Prob. 26ECh. 23.9 - Prob. 27ECh. 23.9 - Prob. 28ECh. 23.9 - Prob. 29ECh. 23.9 - Prob. 30ECh. 23.9 - Prob. 31ECh. 23.9 - Prob. 32ECh. 23.9 - Prob. 33ECh. 23.9 - Prob. 34ECh. 23.9 - Prob. 35ECh. 23.9 - Prob. 36ECh. 23.9 - Prob. 37ECh. 23.9 - Prob. 38ECh. 23.9 - Prob. 39ECh. 23.9 - Prob. 40ECh. 23.9 - Prob. 41ECh. 23.9 - Prob. 42ECh. 23.9 - Prob. 43ECh. 23.9 - Prob. 44ECh. 23.9 - Prob. 45ECh. 23.9 - Prob. 46ECh. 23.9 - Prob. 47ECh. 23.9 - Prob. 48ECh. 23.9 - Prob. 49ECh. 23.9 - Prob. 50ECh. 23.9 - Prob. 51ECh. 23.9 - Prob. 52ECh. 23 - Prob. 1RECh. 23 - Prob. 2RECh. 23 - Prob. 3RECh. 23 - Prob. 4RECh. 23 - Prob. 5RECh. 23 - Prob. 6RECh. 23 - Prob. 7RECh. 23 - Prob. 8RECh. 23 - Prob. 9RECh. 23 - Prob. 10RECh. 23 - Prob. 11RECh. 23 - Prob. 12RECh. 23 - Prob. 13RECh. 23 - Prob. 14RECh. 23 - Prob. 15RECh. 23 - Prob. 16RECh. 23 - Prob. 17RECh. 23 - Prob. 18RECh. 23 - Prob. 19RECh. 23 - Prob. 20RECh. 23 - In Exercises 21–28, use the definition to find the...Ch. 23 - Prob. 22RECh. 23 - Prob. 23RECh. 23 - Prob. 24RECh. 23 - Prob. 25RECh. 23 - Prob. 26RECh. 23 - Prob. 27RECh. 23 - Prob. 28RECh. 23 - Prob. 29RECh. 23 - Prob. 30RECh. 23 - Prob. 31RECh. 23 - Prob. 32RECh. 23 - Prob. 33RECh. 23 - Prob. 34RECh. 23 - Prob. 35RECh. 23 - Prob. 36RECh. 23 - Prob. 37RECh. 23 - Prob. 38RECh. 23 - Prob. 39RECh. 23 - Prob. 40RECh. 23 - Prob. 41RECh. 23 - Prob. 42RECh. 23 - Prob. 43RECh. 23 - Prob. 44RECh. 23 - Prob. 45RECh. 23 - Prob. 46RECh. 23 - Prob. 47RECh. 23 - Prob. 48RECh. 23 - Prob. 49RECh. 23 - Prob. 50RECh. 23 - Prob. 51RECh. 23 - Prob. 52RECh. 23 - Prob. 53RECh. 23 - Prob. 54RECh. 23 - Prob. 55RECh. 23 - Prob. 56RECh. 23 - Prob. 57RECh. 23 - Prob. 58RECh. 23 - Prob. 59RECh. 23 - Prob. 60RECh. 23 - Prob. 61RECh. 23 - Prob. 62RECh. 23 - Prob. 63RECh. 23 - Prob. 64RECh. 23 - If $5000 is invested at interest rate i,...Ch. 23 - The temperature T (in °C) of a rotating machine...Ch. 23 - Prob. 67RECh. 23 - Prob. 68RECh. 23 - Prob. 69RECh. 23 - Prob. 70RECh. 23 - Prob. 71RECh. 23 - Prob. 72RECh. 23 - Prob. 73RECh. 23 - Prob. 74RECh. 23 - Prob. 75RECh. 23 - Prob. 76RECh. 23 - Prob. 77RECh. 23 - Prob. 78RECh. 23 - Prob. 79RECh. 23 - Prob. 80RECh. 23 - Prob. 81RECh. 23 - Prob. 82RECh. 23 - Prob. 83RECh. 23 - Prob. 84RECh. 23 - Prob. 85RECh. 23 - Prob. 86RECh. 23 - Prob. 87RECh. 23 - Prob. 88RECh. 23 - Prob. 89RECh. 23 - Prob. 90RECh. 23 - Prob. 91RECh. 23 - Prob. 92RECh. 23 - Prob. 93RECh. 23 - Prob. 94RECh. 23 - Prob. 95RECh. 23 - Prob. 96RECh. 23 - Prob. 97RECh. 23 - Prob. 98RECh. 23 - In Exercises 53–98, solve the given problems.
99....Ch. 23 - Prob. 1PTCh. 23 - Prob. 2PTCh. 23 - Prob. 3PTCh. 23 - Prob. 4PTCh. 23 - Prob. 5PTCh. 23 - Prob. 6PTCh. 23 - Prob. 7PTCh. 23 - Prob. 8PTCh. 23 - Prob. 9PTCh. 23 - Prob. 10PT
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