Introductory Differential Equations
5th Edition
ISBN: 9780128149485
Author: Abell, Martha L. L.
Publisher: Elsevier Science
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Chapter 1.2, Problem 6E
To determine
To sketch: The solutions of the differential equation that passes through the given points.
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Using the toddler data table in Question 1 and
appropriate probability notation, identify and
calculate the following:
a. What percentage of the toddlers are
right-handed males?
b. What percentage of the toddlers are
right-handed females?
c. Suppose that you want to see whether you
can find a relation between gender and
dominant hand. Can you compare your
answers to parts a and b to come to a
conclusion?
d. Find two events in this table that are
mutually exclusive.
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Suppose that medical researchers collect data
from an experiment comparing a new drug
to an existing drug (call this the treatment
variable), regarding whether it made
patients' symptoms improve (call this the
outcome variable). A check for independence
shows that the outcome is related to the
treatment the patients receive.
a. Are treatment and outcome independent
or dependent in this case?
b. Do the results mean that the new medi-
cine causes the symptoms to improve?
Explain your answer.
Suppose that A and B are independent and
P(A) = 0.3 and P(B) = 0.2. Find P(AUB).
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Chapter 1 Solutions
Introductory Differential Equations
Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10E
Ch. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Prob. 51ECh. 1.1 - Prob. 52ECh. 1.1 - Prob. 53ECh. 1.1 - Prob. 54ECh. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.1 - Prob. 58ECh. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.1 - Prob. 63ECh. 1.1 - Prob. 64ECh. 1.1 - Prob. 65ECh. 1.1 - Prob. 66ECh. 1.1 - Prob. 67ECh. 1.1 - Prob. 68ECh. 1.1 - Prob. 69ECh. 1.1 - Prob. 70ECh. 1.1 - Prob. 71ECh. 1.1 - Prob. 72ECh. 1.1 - Prob. 73ECh. 1.1 - Prob. 74ECh. 1.1 - Prob. 75ECh. 1.1 - Prob. 76ECh. 1.1 - Prob. 77ECh. 1.1 - Prob. 78ECh. 1.1 - Prob. 79ECh. 1.1 - Prob. 80ECh. 1.1 - Prob. 81ECh. 1.1 - Prob. 82ECh. 1.1 - Prob. 83ECh. 1.2 - Prob. 1ECh. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RE
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- Suppose that you flip a fair coin two times, and the flips are independent. a. What is the probability that you will get two heads in a row? b. What is the probability that you will get exactly one head? c. How does your answer to b change if the chance of a head is 0.75 (coin is not fair)?arrow_forwardSuppose that A and B are independent and P(A)=0.6 and P(B) = 0.2. What is P(A and B)?arrow_forwardto, and P(BIA) uses the total group general. 13 Using the bumper sticker data from the first example problem in this chapter and appro- priate probability notation, identify and calculate the following: a. Let O = older cars and B = a lot of bumper stickers. Find and interpret P(BIO). b. What percentage of the older cars have a lot of bumper stickers? c. Of the older cars, what percentage have a lot of bumper stickers? d. What's the probability that a car has a lot of bumper stickers, given its old age? (2 al dad won gangarrow_forward
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- these are the questions and solutions. Please explain and show the method of the solutionsarrow_forwardThe evolution of a population of Hippos, R(t), in hundreds, time in years, in an African National Park is given by the equation, dR dt (a) Solve the system exactly for R(t). = R(7 – R); R(0) = 3 2 (b) What happens as the time t → ∞o, i.e. what is the population a long time in the future? (c) Write an Euler scheme and compute until the population levels off (using Excel, Matlab, Octave, LibreCalc or similar). Do it twice, once with At = 0.1 and once with At = 0.05. (d) Plot all of your solutions on the same set of axes and comment.arrow_forwardfind For triangle ABC, with vertices A = (3,-1,2), B = (-5,4,-4) and C = (6, −1, −1), (a) the length of side AB, (b) the equation of the line that passes through A and B, (c) the angle at vertex B, (d) a vector perpendicular to the plane containing the triangle ABC, (e) the area of the triangle ABC. (f) the equation of a plane passing through A, B and C.arrow_forward
- Showing all working, use the row reduction method to find the inverse of B, given by 5 -1 B = -3 1 3 1 -3 2arrow_forwardConsider the matrix A, given by +63) A = 1 -3 4 -3 4 5 -105 (a) Find the determinant of the matrix, A. (b) Find all possible solutions, x, to the system Ax = b, where b is the column vector, (1,2, −4).arrow_forwardIf a (1,4,2) and b = (−1, −5,3), find |a|, a + b, 3a - 2b, a b, a x b and b × a. What is the angle between a and b?arrow_forward
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