Discrete Math 8. Consider the function f : {1,2,3,4} → {1,2,3,4} given by the graphbelow.f(x) ₁4321123 4 x(a) Is f injective? Explain.(b) Is f surjective? Explain.(c) Write the function using two-line notation.

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Answered: 8. Consider the function f : {1,2,3,4}…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Number Gender Exam 1 Exam 2 Exam 3 Homework Lab Number grade Letter grade Z-score Absolute z-score 1 0 61 94 76 94 87 82.4 B 0.18 0.18 2 0 99 97 90 100 89 95 A 1.38 1.38 3 0 64 76 69 88 87 76.8 C -0.36 0.36 4 0 77 82 86 98 94 87.4 B 0.66 0.66 5 0 70 89 81 93 97 86 B 0.52 0.52 6 0 67 62 65 60 90 68.8 D -1.13 1.13 7 0 87 83 81 85 68 80.8 B 0.02 0.02 8 0 74 88 65 49 90 73.2 C -0.71 0.71 9 0 91 97 87 81 94 90 A 0.90 0.90 10 0 94 87 77 90 67 83 B 0.23 0.23 11 0 47 72 54 59 63 59 F -2.07 2.07 12 0 81 64 78 84 73 76 C -0.44 0.44 13 0 87 90 81 93 80 86.2 B 0.54 0.54 14 0 96 100 84 97 84 92.2 A 1.12 1.12 15 0 80 76 90 85 85 83.2 B 0.25 0.25 16 0 64 51 69 74 78 67.2 D -1.28 1.28 17 0 70 86 84 77 75 78.4 C -0.21 0.21 18 0 80 93 98 95 98 92.8 A 1.17 1.17 19 0 88 83 83 90 84 85.6 B 0.48 0.48 20 0 52 46 62 70 59 57.8 F -2.19 2.19 21 0 97 83 83 85 98 89.2 B 0.83 0.83 22 1 80 74 90 83 65 78.4 C -0.21 0.21 23 1 86 81 72 85 97 84.2 B 0.35 0.35 24 1 88 99…
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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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An instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second time, the students took the instructor's course to try to improve their critical reading test scores. At a = 0.01, is there enough evidence to support the instructor's claim? Complete parts (a) through (f). Student Score on first test Score on second test 450 698 674 448 489 630 496 543 636 558 643 407 374 493 10 11 12 13 14 D 444 635 616 409 545 605 516 395 561 471 632 387 337 461 1 2 3 4 7 8 9. (b) Find the critical value(s) and identify the rejection region(s). (Use a comma to separate answers as needed. Type an integer or a decimal, Round to three decimal places as needed.) Identify the rejection region(s). Choose the correct answer below. O A. t>3.012 O B. t 2.650 O C. t 3.012 Click to select your answer(s). 225 PM 12/17/2020

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8. Consider the function f : {1,2,3,4} → {1,2,3,4} given by the graph below. f(x) ₁ 4 3 2 1 1 2 3 4 x (a) Is f injective? Explain. (b) Is f surjective? Explain. (c) Write the function using two-line notation.