The 64 students in a classical music lecture class were polled, with the results that 37 like Wolfgang Amadeus Mozart, 35 like Ludwig von Beethoven, 29 like Franz Joseph Haydn, 13 like Mozartand Beethoven, 20 like Mozart and Haydn, 13 like Beethoven and Haydn, and 7 like all three composers. Use a Venn diagram to complete parts (a) through (1) belowComplete the Venn diagram. Let M be the set of students that like Mozart, B be the set of students that like Beethoven, and H be the set of students that like Haydn.MtoUwVEwwya2NH(a) How many of these students like exactly two of these composers?student(s)(Simplify your answer)(b) How many of these students like exactly one of these composers?

Given:Total number of studentsFrom the given information, we have:

Answered: The 64 students in a classical music…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A large bakery has many different products for sale. Suppose that 200 come in between 6am and 10am. Of the 200 customers 140 order donuts, 100 order cinnamon rolls, and 80 order both. Make a Venn Diagram to model the situation.
How many of these students like Haydn and exactly one of the other two?
Ten kids line up for recess. The names of the kids are: {Alex, Bobby, Cathy, Dave, Emy, Frank, George, Homa, Ian, Jim}. Let S be the set of all possible ways to line up the kids. For example, one order might be: (Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby) The names are listed in order from left to right, so Frank is at the front of the line and Bobby is at the end of the line. Let T be the set of all possible ways to line up the kids in which George is ahead of Dave in the line. Note that George does not have to be immediately ahead of Dave. For example, the ordering shown above is an element in T. Now define a function f whose domain is S and whose target is T. Let a be an element of S, so a is one possible way to order the kids. If George is ahead of Dave in the ordering r, then f(x) = a. If Dave is ahead of George in z, then f(x) is the ordering that is the same as z, except that Dave and George have swapped places. (a) What is the output of f on the following…
Let U= {1,2,3,4,5,6,7,8,9} A= {2,4,6,8} B= {1,2,3,4} and C= {5,7,9} Give a set, D, that is equivalent to C, but not equal to C. I am confused on the difference and how to proceed with this.
Construct a Venn diagram to answer the question. Doctor X and Doctor Y have 24 patients. 12 patients have fever, 6 patients have colds, 15 patients have headache. 1 patient has all three sicknesses. 2 patients have fever and colds, but no headache. 2 patients have colds and headache, but no fever. If all the patients of Doctor X and Doctor Y have at least one of the mentioned sickness, how many patients have fever and headache, but no colds?
5) A survey was conducted to see what genre of movies students enjoy watching. 56% watched comedies 55% watched action movies 38% watched dramas 30% watched comedies & action movies 19% watched comedies & dramas 18% watched action movies & dramas 16% watched all three movie genres a) Create a Venn Diagram to represent the genres students enjoy watching. b) What percentage of students only enjoyed watching action movies? b) If 1500 students were surveyed, how many said that they did not enjoy watching any of the three genres?
A survey of 300 adults found that during the last year, 82 purchased apples but not strawberries, 91 purchased oranges but not apples, 50 purchased strawberries but not apples or oranges, 32 purchased strawberries and oranges, 22 purchased all three, and 178 purchased strawberries or apples. Fill out a Venn diagram and determine how many of the adults surveyed did not purchase any of the three fruits.

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