DISCRETE MATH problem 12. A lazy math teacher is writing an exam.a.The lazy math teacher has a class of 31 students and wants to assignsome of them A's, some B's, some C's, some D's, and some F's. If it is notimportant to the teacher how many of each grade is assigned, how manyways can they choose how many of each to give?b. The lazy math teacher has a class of 31 students and wants to assign 3 A's,6 B's, 10 C's, 6 D's, and the rest F's. It is not important to the teacher whichstudent gets which grade. How many ways can this assignment be done?

Answered: a. The lazy math teacher has a class of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3. Piece of cake A cake is sliced roughly in half, the largest piece being chosen each time, the other pieces discarded. We will assume that a random cut creates pieces of proportions: P = 3 w.p. w.p. 4 Thus, for example, the first cut (and choice of largest piece) may result in a piece of size 3. Cutting and choosing from this piece might reduce it to size (3/3) (3/3) at time 2, and so on. How large, to first order in the exponent, is the piece of cake after n cuts?
Question 23 When does Type II error occur? O Ho is the same as Ha. O Ho is assumed right when it is actually wrong O Ho is neither right nor wrong. O Ho is assumed wrong when it is actually correct.
Question 1133503: A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.**The column titles are (left to right above each of the number columns) are as follows: better, same, worseRepublican 38 104 44Democrat 12 87 137none 21 90 118Express each of your first five answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).(a) What fraction of survey respondents identified themselves as Republicans?(b) What fraction of survey respondents thought the economy was getting worse?
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In a hospital, there are N = 5000 patient records and a simple random sample of n= 15 will be drawn. Using Table A.2 given in the Appendix, list the steps to generate random numbers to satisfy the conditions in simple random sampling (a) (b) determine which records to be included in the sample of size n= 15.
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QUESTION 8 Inside a black bag there are 10 balls numbered 0 - 9. The experiment is to pull out a ball at random, record the number, place the ball back in the bag, and repeat this until you have a 6-digit number. (Ex: 111111, 123456, 526587, etc). HINT: 123456 is a different number from 654321 How many 6-digit numbers are possible? (DO NOT USE COMMAS IN YOUR ANSWER) ONLY DO THE PART BELOW: Repeat the experiment from number 8 involving pulling balls from a black bag, except a ball once drawn from the baf is NOT placed back in the bag. How many 6-digit numbers are possible? (DO NOT USE COMMAS IN YOUR ANSWER)
Question 2 (Hand Calculations) Researchers studied the association between birth mother's smoking habits and the birth weights of their babies. A sample of size n = 11 subjects was selected from each of the four groups. Group 1-nonsmokers Group 2 - smokers who smoked less that 1 pack per day Group 3-smokers who smoke more than 1 Pack but less than 2 packs per day Group 4-smokers who smoke more than 2 packs per day. Table: Birth weights (in grams) of infants of mothers (n = 11) in four smoking groups nonsmokers 3510 3174 3580 3232 3884 3982 4055 3459 3998 3852 3421 2 packs 2232 2331 2200 2121 2001 1566 1676 1783 2002 2118 1882 Use the above data to construct an ANOVA table to determine if there is a significant difference in the average birth weight amongst the four groups. Illustrate your findings graphically

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a. The lazy math teacher has a class of 31 students and wants to assign some of them A's, some B's, some C's, some D's, and some F's. If it is not important to the teacher how many of each grade is assigned, how many ways can they choose how many of each to give?