Discrete Math. 1. List the members of these sets.a) {x | x is a real number such that x2 =b) {x | x is a positive integer less than 12}c) {x | x is the square of an integer and x < 100}d) {x | x is an integer such that x² =e) {x | x is a multiple of 3 A 0

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Answered: a) {x | x is a real number such that x²…

Advanced Engineering Mathematics

10th Edition

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…
Data compiled by the Highway Patrol Department regarding the use of seat-belts by drivers in a certain area after the passage of a compulsory seat-belt law are shown in the accompanying table. (Round your answers to three decimal places.) Drivers Percentage of Drivers in Group Percent of Group Stopped for Moving Violation Group I(using seat-belts) 56 0.4 Group II(not using seat-belts) 44 0.4 (a) If a driver in that area is stopped for a moving violation, what is the probability that he or she will have a seat-belt on?(b) If a driver in that area is stopped for a moving violation, what is the probability that he or she will not have a seat-belt on?
Redo exercises 17 and 18 in section 8.1 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data: If the animal is in the woods on one observation, then it is twice as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is three times as likely to be in the meadows as the woods on the next observation. Assume that state 1 is being in the meadows and that state 2 is being in the woods. (1) Find the transition matrix for this Markov process. (2) If the animal is initially in the woods, what is the probability that it is in the woods on the next three observations? (3) If the animal is initially in the woods, what is the probability that it is in the meadow on the next three observations?
NEW STUDY: Dr. Apnea conducted a study investigating the effects of sleep deprivation on complex problem solving. He gave 25 college students a problem-solving test at noon on one day and a second problem-solving test at noon the following day. He found that there was a statistically significant mean decrease of 4.7 between the two tests from the first day to the second day. The test yielded a Cohen’s d = .82. Which of the following statements is an accurate interpretation of Dr. Apnea’s research? Group of answer choices It doesn’t matter how much sleep you get, some people just aren’t good at problem solving. If you don’t get enough sleep your problem solving abilities suffer, but only with a small absolute magnitude. If you don’t get enough sleep your problem solving abilities suffer with a medium absolute magnitude. If you don’t get enough sleep your problem solving abilities suffer with a large absolute magnitude.
(PLEASE HELP WITH 1, 2, AND 3) 1. A sample point refers to the Group of answer choices set of all possible experimental outcomes numerical measure of the likelihood of the occurrence of an event individual outcome of an experiment sample space 2. One of the basic requirements of probability is Group of answer choices for each experimental outcome Ei, we must have P(Ei) 1 ∑P(Ei) ≥1 P(A) = P(Ac) - 1 if there are k experimental outcomes, then∑ P(Ei) = 1 3. An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist? Group of answer choices 16 4 32 8
CARD SIMULATIONS OF HARDY-WEINBERG PRINCIPLES INTRODUCTION: You are already familiar with alleles of genes and how different alleles affect the phenotypes of diploid individuals. Today's exercise will give you the opportunity to look at alleles in a population, and how various evolutionary agents alter the proportions, or frequencies, of each allele over time. Specifically, the class will use cards bearing either a printed "A" or "a" to simulate two alleles of a single gene. You and your classmates will be the population in which these two alleles are found. The sum total of A and a alleles in the class will represent the gene pool. Before you begin the exercise, review the Hardy-Weinberg law and equations in a general biology textbook. Briefly, the Hardy-Weinberg law describes the conditions that must be met for a population of organisms to be at equilibrium, that is, to be non-evolving. These conditions are: (1) large population size, (2) random mating, (3) no migration, (4) no…
Smoking 2009, women and men In Exercise 2, we ex-amined the percentage of men aged 18–24 who smoked from 1965 to 2009 according to the Centers for DiseaseControl and Prevention. How about women? Here’s ascatterplot showing the corresponding percentages forboth men and women:a) In what ways are the trends in smoking behaviorsimilar for men and women?b) How do the smoking rates for women differ fromthose for men?c) Viewed alone, the trend for men may have seemed toviolate the Linearity Condition. How about the trendfor women? Does the consistency of the two patternsencourage you to think that a linear model for thetrend in men might be appropriate? (Note: there is nocorrect answer to this question; it is raised for you tothink about.)
Doctor Specialties Below are listed the numbers of doctors in various specialties by gender. Psychiatry Pathology Gynecology Male 27,319 12,551 23,813 Female 14,066 6620 18,520 Send data to Excel Choose 1 doctor at random. Part: 0 / 4 Part 1 of 4 (a) Find P (female psychiatry). Round your answer to three decimal places. P (female|psychiatry) = |

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a) {x | x is a real number such that x² = 1} b) {x | x is a positive integer less than 12} c) {x | x is the square of an integer and x < 100} d) {x | x is an integer such that x² = e) {x | x is a multiple of 3 ^ 0 sxs 12} 2}