Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter 12.4, Problem 15E
To determine
To find:
The expected value for the random variable x having the given function.
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(10 points) Let f(x, y, z) = ze²²+y². Let
E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}.
Calculate the integral
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E
(12 points) Let
E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}.
(a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such
that
(x, y, z) (psin cos 0, psin sin 0, p cos) € E.
(b) (8 points) Calculate the integral
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xyz dV using spherical coordinates.
(10 points) Let f(x, y, z) = ze²²+y². Let
E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}.
Calculate the integral
y,
f(x, y, z) dV.
Chapter 12 Solutions
Calculus For The Life Sciences
Ch. 12.1 - YOUR TURN Write the elements belonging to the set...Ch. 12.1 - Prob. 2YTCh. 12.1 - Prob. 3YTCh. 12.1 - Prob. 4YTCh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - In Exercises 1-6, write true or false for each...Ch. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6E
Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - What does the notation n(A) represent?Ch. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.1 - Prob. 60ECh. 12.1 - Draw a Venn diagram and use the given information...Ch. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Prob. 73ECh. 12.1 - Prob. 74ECh. 12.1 - Prob. 77ECh. 12.1 - Prob. 78ECh. 12.1 - Prob. 79ECh. 12.1 - Military The number of female military personal in...Ch. 12.1 - Chinese New Year A survey of people attending a...Ch. 12.1 - Prob. 86ECh. 12.1 - Prob. 87ECh. 12.1 - Prob. 88ECh. 12.1 - Prob. 89ECh. 12.1 - Prob. 90ECh. 12.1 - Prob. 91ECh. 12.1 - Prob. 92ECh. 12.1 - Prob. 93ECh. 12.2 - YOUR TURN 1 Two coins are tossed, and a head or a...Ch. 12.2 - Prob. 2YTCh. 12.2 - Prob. 3YTCh. 12.2 - Prob. 4YTCh. 12.2 - Prob. 5YTCh. 12.2 - Prob. 6YTCh. 12.2 - YOUR TURN 7 Find the probability that when two...Ch. 12.2 - Prob. 8YTCh. 12.2 - Prob. 9YTCh. 12.2 - Prob. 10YTCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Write the sample space for the experiments in...Ch. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - For the experiments in Exercises 9-14, write out...Ch. 12.2 - Prob. 12ECh. 12.2 - For the experiments in Exercises 9-14,write out...Ch. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - EXERCISES Decide whether the events in Exercises...Ch. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - EXERCISES Two dice are rolled. Find the...Ch. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - The numbers 1, 2, 3, 4, and 5 are written on slips...Ch. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - EXERCISES Which of Exercises 5964are examples of...Ch. 12.2 - EXERCISES Which of Exercises 5964are examples of...Ch. 12.2 - Prob. 61ECh. 12.2 - Prob. 62ECh. 12.2 - Which of Exercises 59-64 are examples of empirical...Ch. 12.2 - Which of Exercises 59-64 are examples of empirical...Ch. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prob. 68ECh. 12.2 - Prob. 69ECh. 12.2 - Prob. 70ECh. 12.2 - Prob. 71ECh. 12.2 - Prob. 72ECh. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Prob. 79ECh. 12.2 - Prob. 80ECh. 12.2 - The following description of the classic Linda...Ch. 12.2 - Prob. 82ECh. 12.2 - Prob. 83ECh. 12.2 - Prob. 84ECh. 12.2 - Body Types A study on body types gave the...Ch. 12.2 - Prob. 86ECh. 12.2 - Prob. 87ECh. 12.2 - Prob. 88ECh. 12.2 - Prob. 89ECh. 12.2 - Doctor VisitThe probability that a visit to a...Ch. 12.2 - Shoulder InjuriesAmong a large group of patients...Ch. 12.2 - Prob. 92ECh. 12.2 - Prob. 93ECh. 12.2 - Prob. 94ECh. 12.2 - Prob. 95ECh. 12.2 - Prob. 96ECh. 12.2 - Book of Odds The following table gives the...Ch. 12.2 - Prob. 98ECh. 12.2 - Prob. 99ECh. 12.2 - Civil War Estimates of the Confederate Armys...Ch. 12.2 - Prob. 101ECh. 12.2 - Prob. 103ECh. 12.2 - Prob. 104ECh. 12.2 - Refugees In a refugee camp in southern Mexico it...Ch. 12.2 - Prob. 106ECh. 12.2 - Chinese New Year Exercise 83 of the previous...Ch. 12.2 - Prob. 108ECh. 12.3 - Your turn 1 In example 2, find P(A|F). EXAMPLE 2...Ch. 12.3 - Prob. 2YTCh. 12.3 - Prob. 3YTCh. 12.3 - YOUR TURN At a local college, 4/5 of the students...Ch. 12.3 - Prob. 6YTCh. 12.3 - Prob. 7YTCh. 12.3 - YOUR TURN 8 The probability that a student will...Ch. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - If two fair dices are rolled, find the...Ch. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - If two cards are drawn without replacement from an...Ch. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Decide whether the following pairs of events are...Ch. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Another friend asks you to explain how to tell...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - If A and B are events such that P(A)=0.5 and...Ch. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - The following problem submitted by Daniel Hahn of...Ch. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - The following table shows frequencies for...Ch. 12.3 - Prob. 49ECh. 12.3 - Prob. 51ECh. 12.3 - Breast Cancer To explain why the chance of a woman...Ch. 12.3 - Cigarette Smokers The following table gives a...Ch. 12.3 - Prob. 55ECh. 12.3 - Prob. 56ECh. 12.3 - Prob. 57ECh. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - Prob. 61ECh. 12.3 - Prob. 62ECh. 12.3 - Seat Belt Effectiveness A federal study showed...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.3 - Working Women A survey has shown that 52 of the...Ch. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Prob. 69ECh. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Drivers License Test The Motor Vehicle Department...Ch. 12.3 - Prob. 74ECh. 12.3 - Studying A teacher has found that the probability...Ch. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Alcohol Abstinence The Harvard School of Public...Ch. 12.3 - Prob. 80ECh. 12.3 - Prob. 81ECh. 12.3 - Prob. 82ECh. 12.3 - Prob. 83ECh. 12.3 - Job QualificationsOf all the people applying for a...Ch. 12.3 - Prob. 85ECh. 12.3 - Prob. 86ECh. 12.4 - Prob. 1YTCh. 12.4 - Prob. 2YTCh. 12.4 - Prob. 3YTCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 4ECh. 12.4 - Draw a histogram for the following, and shade the...Ch. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Find the expected value and standard deviation for...Ch. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Suppose a die is rolled 4 times. a. Find the...Ch. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Four slips of paper numbered 2, 3, 4, and 5 are in...Ch. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Prob. 42ECh. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.CR - Determine whether each of the following statements...Ch. 12.CR - Prob. 2CRCh. 12.CR - Prob. 3CRCh. 12.CR - Prob. 4CRCh. 12.CR - Prob. 5CRCh. 12.CR - Prob. 6CRCh. 12.CR - Prob. 7CRCh. 12.CR - Prob. 8CRCh. 12.CR - Prob. 9CRCh. 12.CR - Prob. 10CRCh. 12.CR - Prob. 11CRCh. 12.CR - Prob. 12CRCh. 12.CR - Prob. 13CRCh. 12.CR - Prob. 14CRCh. 12.CR - Prob. 15CRCh. 12.CR - Prob. 16CRCh. 12.CR - Prob. 17CRCh. 12.CR - Prob. 18CRCh. 12.CR - Prob. 19CRCh. 12.CR - Prob. 20CRCh. 12.CR - Prob. 21CRCh. 12.CR - Prob. 22CRCh. 12.CR - Prob. 23CRCh. 12.CR - Prob. 24CRCh. 12.CR - Prob. 25CRCh. 12.CR - Prob. 26CRCh. 12.CR - Prob. 27CRCh. 12.CR - Prob. 28CRCh. 12.CR - Prob. 29CRCh. 12.CR - Prob. 30CRCh. 12.CR - Prob. 31CRCh. 12.CR - Prob. 32CRCh. 12.CR - Prob. 33CRCh. 12.CR - Prob. 34CRCh. 12.CR - Prob. 35CRCh. 12.CR - Prob. 36CRCh. 12.CR - Prob. 37CRCh. 12.CR - Prob. 38CRCh. 12.CR - Prob. 39CRCh. 12.CR - Prob. 40CRCh. 12.CR - Prob. 41CRCh. 12.CR - Prob. 42CRCh. 12.CR - Prob. 43CRCh. 12.CR - Prob. 44CRCh. 12.CR - Prob. 45CRCh. 12.CR - Prob. 46CRCh. 12.CR - Prob. 47CRCh. 12.CR - Prob. 48CRCh. 12.CR - Prob. 49CRCh. 12.CR - Prob. 50CRCh. 12.CR - Prob. 51CRCh. 12.CR - Prob. 52CRCh. 12.CR - Prob. 53CRCh. 12.CR - Prob. 54CRCh. 12.CR - Prob. 55CRCh. 12.CR - Prob. 56CRCh. 12.CR - Prob. 57CRCh. 12.CR - Prob. 58CRCh. 12.CR - Prob. 59CRCh. 12.CR - Prob. 60CRCh. 12.CR - Prob. 61CRCh. 12.CR - Prob. 62CRCh. 12.CR - Prob. 63CRCh. 12.CR - Prob. 64CRCh. 12.CR - Prob. 65CRCh. 12.CR - Prob. 66CRCh. 12.CR - Prob. 67CRCh. 12.CR - Prob. 68CRCh. 12.CR - Prob. 69CRCh. 12.CR - Prob. 70CRCh. 12.CR - Prob. 71CRCh. 12.CR - Prob. 72CRCh. 12.CR - Prob. 73CRCh. 12.CR - Prob. 74CRCh. 12.CR - Prob. 75CRCh. 12.CR - Prob. 76CRCh. 12.CR - Prob. 77CRCh. 12.CR - Prob. 78CRCh. 12.CR - Prob. 79CRCh. 12.CR - Prob. 80CRCh. 12.CR - Prob. 81CRCh. 12.CR - Prob. 82CRCh. 12.CR - Prob. 83CRCh. 12.CR - Prob. 84CRCh. 12.CR - Prob. 85CRCh. 12.CR - Prob. 86CRCh. 12.CR - Prob. 87CRCh. 12.CR - Prob. 88CRCh. 12.CR - Prob. 89CRCh. 12.CR - Prob. 90CRCh. 12.CR - Prob. 91CRCh. 12.CR - Prob. 92CRCh. 12.CR - Prob. 93CRCh. 12.CR - Prob. 94CRCh. 12.CR - Prob. 97CRCh. 12.CR - Body Mass Index the results of a survey of body...Ch. 12.CR - Elections In the 2012 presidential election, over...Ch. 12.CR - Prob. 105CRCh. 12.CR - Prob. 109CRCh. 12.CR - Prob. 110CRCh. 12.CR - Prob. 112CRCh. 12.EA - Find P(H2C1).Ch. 12.EA - Prob. 2EACh. 12.EA - Prob. 3EA
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