Discrete math 1. Let A = {1, 3, 12, 35}, B = {3, 7, 12, 20), and C = {x | x is a prime number}. List theEelements of the following sets. Are any of the sets below disjoint from any of theothers? Are any of the sets below subsets of any others?(a) An B.(b) (A u B) - C(c) AU (B-C)

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Answered: 1. Let A = {1, 3, 12, 35}, B = {3, 7,…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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The first test a doctor would order to determine whether a person is infected with HIV (the virus that causes AIDS) is the ELISA test. It detects antibodies and antigens for HIV. A study in Statistical Science by J. Gastwirth estimated that, if the person is actually infected with HIV, this test produces a positive result 97.7% of the time. If a person is not infected with HIV, the test result is negative 92.6% of the time. According the the US Centers for Disease Control (CDC), an estimated 1.1 million Americans out of a population of 321 million were infected with HIV in 2015. Using the information above, determine the probability that a randomly selected person whose ELISA test is positive actually is infected with HIV? a. What is the probability that a randomly selected American is infected with HIV? b. Using the answer to part (a) and the conditional probabilities of positive and negative ELISA test results, fill out the contingency table below: ELISA Test Result…
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Essentials of DISCRETE MATHEMATICS
Reading is fundamental to a teenager's ability to perform well in school. Assume a researcher is interested in the ability of the number of books read over the summer to predict ACT Reading scores. Using a random sample of 10 random high school students the researchers recorded the number of books read over the summer and the students' ACT Reading scores. Books Read (X) ACT Score (Y) (X- Xmean) (Y - Ymean) (X-Xmean)(Y-Ymean) (X-Xmean)? (Y - Ymean)? 2 16 -5.4 -14.9 81 29 221 2 19 -5.4 -11.9 64 29 141 3 17 -4.4 -13.9 61 20 192 4 25 -3.4 -5.9 20 12 34 21 -3.4 -9.9 34 12 97 24 -1.4 -6.9 10 2 47 6 21 -1.4 -9.9 14 2 97 8 24 0.6 -6.9 -4 47 7 27 -0.4 -3.9 2 15 10 22 2.6 -8.9 -23 7 78 Total 52 216 259.1 113.3 969.3 МEAN 7.4 30.9 a. Identify the regression line using the number of books read to predict ACT Reading score. Use a = .05 to evaluate the quality of the prediction of the regression line. b. What is the predicted ACT Reading score when 5 books are read?
Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table. Reaction Within 5 Minutes After 5 Minutes Row Total NoneMildStrong 4025543 64323113 466378156 Column Total 500 500 1000 Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.) (d) P(N and…
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I need help with the part B-1 of this question

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1. Let A = {1, 3, 12, 35}, B = {3, 7, 12, 20), and C = {x | x is a prime number}. List the elements of the following sets. Are any of the sets below disjoint from any of the others? Are any of the sets below subsets of any others? (a) An B. (b) (A u B) - C (c) AU (B-C)