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Ket [755]
3 years ago
14

The 65 students in a classical music lecture class were polled, with the following results: 37 like Wolfgang Amadeus Mozart 36 l

ike Ludwig van Beethoven 31 like Franz Joseph Haydn 14 like Mozart and Beethoven 21 like Mozart and Haydn 14 like Beethoven and Haydn 8 like all three composers. How many of these students like:________.
a. exactly two of these composers?
b. exactly one of these composers?
c. like only Mozart?
d. like Beethoven and Haydn, but not Beethoven?
e. like none of these composers?
Mathematics
1 answer:
Anna35 [415]3 years ago
4 0

Answer:

a) 25

b) 30

c) 10

d) Not Mozart, 6

e) 2

Step-by-step explanation:

We use a Venn Diagram to solve this question.

I am going to say that:

A are the students who like Mozart.

B are the students who like Beethoven

C are the students who like Haydn.

We have that:

A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)

In which a are those who only like Mozart, (A \cap B) are those who like Mozart and Beethoven, (A \cap C) are those who like Mozart and Haydn and (A \cap B \cap C) are those who like all three of them.

By the same logic, we have that:

B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)

C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)

We start finding these values from the intersection:

8 like all three composers

This means that A \cap B \cap C = 8

14 like Beethoven and Haydn

This means that:

(B \cap C) + (A \cap B \cap C) = 14

So

B \cap C = 6

21 like Mozart and Haydn

This means that:

(A \cap C) + (A \cap B \cap C) = 21

Then

A \cap C = 13

14 like Mozart and Beethoven

This means that:

(A \cap B) + (A \cap B \cap C) = 14

A \cap B = 6

31 like Franz Joseph Haydn

This means that C = 31. So

C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)

31 = c + 6 + 13 + 8

c = 4

36 like Ludwig van Beethoven

This means that B = 36

So

B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)

36 = b + 6 + 6 + 8

b = 16

37 like Wolfgang Amadeus Mozart

This means that A = 37. Then

A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)

37 = a + 6 + 13 + 8

a = 10

a. exactly two of these composers?

(A \cap B) + (A \cap C) + (B \cap C) = 6 + 13 + 6 = 25

b. exactly one of these composers?

a + b + c = 10 + 16 + 4 = 30

c. like only Mozart?

a = 10

d. like Beethoven and Haydn, but not Beethoven?

I will use not Mozart.

So B \cap C = 6

Not Mozart, 6.

e. like none of these composers?

At least 1:

(A \cup B \cup C) = a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 10 + 16 + 4 + 6 + 13 + 6 + 8 = 63

The total is 65

So 65 - 63 = 2 like none of these composers

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Answer:

  1. you can scrap your knee if you don't have knee pads
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  5. keep your eyes one the ball

Step-by-step explanation:

8 0
3 years ago
The diffrence between 2 numbers is 1 and their product Is 132
il63 [147K]

Answer:

x = 12

y = 11

For any clarification, Please contact me in the comment section :)

I Hope It Helps .

Step-by-step explanation:

Let -the-unkonown- numbers-be-x-and-y \\x-y = 1       (1)\\xy = 132    (2)\\Make-x-subject-of-formula-in-equation1 \\x = 1+y\\Substitute , 1+y  for- x -in -equation ,2\\y(1+y) = 132\\y + y^{2} =132\\y^{2} +y-132=0\\Solve- the-quadratic-equation.\\y = 11\\substitute- 11 -for- y- in- equation -1- 0r- 2\\x -y = 1\\x-11 = 1\\x = 1+11\\x = 12

6 0
3 years ago
The equation y = 2x + 1 is a function rule.<br> x y<br> 0 <br> 1<br> 2<br> 3
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Answer:

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8 0
3 years ago
The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard devia
MaRussiya [10]

Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation is 9.5 for a population.

This means that \sigma = 9.5

Sample of 60:

This means that n = 60

What is the standard deviation of the distribution of sample means for samples of size 60?

s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

4 0
3 years ago
HELP URGENT!! EDGINUITY!!
Nataliya [291]

Hello from MrBillDoesMath!

Answer:

The first choice  (2x + 4y >=3,  2x +4y <=3)



Discussion:

Suppose a variable M met these conditions: M >=3 and M <=3. The only way this can happen is that M = 3. In our case letting M = 2x + 4y, we find the inequalities give


2x + 4y = 3


which is the equation of a line.  (The other choices do NOT include the boundary line because they use strict < or > signs.)


Thank you,

MrB

7 0
3 years ago
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