Discrete Mathematics 5 of 8A group of four friends goes to a restaurant for dinner. The restaurant offers 12different main dishes.(i) Suppose that the group collectively orders four different dishes to share.The waiter just needs to place all four dishes in the center of the table.How many different possible orders are there for the group?(ii) Suppose that each individual orders a main course. The waiter must re-member who ordered which dish as part of the order. It's possible for morethan one person to order the same dish. How many different possible ordersare there for the group?How many different passwords are there that contain only digits and lower-caseletters and satisfy the given restrictions?(iii) Length is 7 and the password must contain at least one digit.(iv) Length is 7 and the password must contain at least one digit and at leastone letter.Pages 5 to 6 of 8108%. OLTReady Automaticen US.UTF-8

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Chi - square According to genetics theory (e.g. Mancuso, et al. 2009; doi:10.1038/nature08401), red-green colour blindness in humans is a recessive gender-linked characteristic. Theory shows that 50% of children have normal vision and are not carriers of the colour blindness gene, whilst 25% of children have normal vision and are carriers of the colour blindness gene, and 25% of children are red-green colourblind and are carriers of the colour blindness gene. A random sample of 200 children was taken with the following results: *view table down below* a) use descriptive statistics to represent the data b) test at the 1% level of significance, if the sample follows genetics theory
Researchers are wondering whether they can predict college GPA with the number of hours studying per week. To test this, they randomly select 8 college students, record their GPA and the number of hours spent studying per week. ID GPA 1 2.5 2 2.7 3 3.4 4 3.7 5 2.7 6 1.9 7 2.0 8 4.0 Hours studying per week 25.0 Based on the information in the table above, the researchers compute the regression equation: Y = -0.970+ 0.125 X. Do the researchers have enough evidence to claim that the number of hours studying predicts students' GPA? Select the null hypothesis for the statistical test: b=0 OB=0 B = -0.970 Ob = 0.125 27.6 30.2 35.0 31.6 25.6 30.0 40.0
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Modules Section 4.1 Introduction to Probability Grades Score: 8.67/15 8/15 answered Progress saved Done Syllabus Question 6 E 0/1 pt People A group of people were asked if Marilyn Monroe had an affair with JFK. 114 responded "yes", and 340 responded "no". Student Evaluations Find the probability that if a person is chosen at random, he believes Marilyn Monroe had an affair with JFK. Probability = (Please enter a reduced fraction.) Submit Question 1094746..jpg A pic_16131095275.jpg pic 16131095275..jpg Zoomday17bsp21.docx pic_1615670389...jpg wx P N MacBool 411 20 13 FS F4 23 24 % 3 4. 5 6. 8 2 T. K D F
Researchers are wondering whether they can predict college GPA with the number of hours studying per week. To test this, they randomly select 8 college students, record their GPA and the number of hours spent studying per week. ID 1 2 3 4 5 6 7 8 GPA 2.5 2.7 3.4 3.7 2.7 1.9 2.0 4.0 O Reject Hours studying per week 25.0 Based on the information in the table above, the researchers compute the regression equation: Y = -0.970 + 0.125 X. Do the researchers have enough evidence to claim that the number of hours studying predicts students' GPA? Should you reject or fail to reject the null hypothesis? Fail to reject 27.6 30.2 35.0 31.6 25.6 30.0 40.0
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Subject: Discrete StructuresQuestion: You have a fever, you take the COVID-19 PCR test. For people who have COVID, the test goes positive 80% of the time. 10% the time are false positives. If 1% of the population have COVID-19, and your PCR test is positive, what are your chances that you really have COVID-19?
Understanding hypothesis tests in general: One use of a Chi-square test is to determine whether factors are independent from each other or dependent on each other. For example, consider the following: A marketer, who works for a brewery, has to promote a new beer. She samples 150 people and wants to determine whether there is an association between gender and beer preference. If there is an association, then it means that a persons beer preference can be predicted by knowing the persons gender. The results are: Beer preference Gender Light ale Lager Best bitter Total Male 20 40 20 80 Female 30 30 10 70 Total 50 70 30 150 The null hypothesis always says that the factors are independent, i.e. H0: Beer preference and Gender are independent The alternative hypothesis always says the opposite, i.e. H1: Beer preference and Gender are dependent The hypothesis test was performed at the 2.5% level of significance and the p-value was found to be 0.0149. From this you…

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