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4 years ago

VENN DIAGRAMS HELP?

Mathematics

1 answer:

user100 [1]4 years ago

7 0

Answer:

a. Probability of student having both cat and dog = 9/25

b. Probability of student not in drama club or sports team = 105/330

c. Probability of student who play both cricket and football = 10/32

Step-by-step explanation:

a. Given,

Total Students = 25

A = Students with cat = 15

B = Students with dog = 16

Students with both dog and cat = A∩B

A∪B = Total students - Students with neither dor or cat = 25-3 =22

A∪B = A + B - A∩B

A∩B = A + B - A∪B

A∩B = 15 + 16 - 22 = 9

Hence probability (A∩B) = A∩B÷Total Students = 9/25

b. Given,

Total Students = 330

A = Students with in drama club = 85

B = Students with in sports team = 200

Students in both drama and sports team = A∩B = 60

A∪B = Total students - Students in neither in drama or sports

A∪B = A + B - A∩B

A∪B = 85 + 200 - 60 = 225

A∪B =300 - Students in neither in drama or sports

Students in neither in drama or sports = 300 - 225 = 105

Hence probability (Students in neither in drama or sports) = Students in neither in drama or sports/Total Students = 105/330

c. Given,

Total Students =

A = Students playing football = 14

B = Students playing cricket = 21

Students playing both football and cricket = A∩B = 10

A∪B = Total students - Students playing neither football or cricket

A∪B = A + B - A∩B

A∪B = 14 + 21 - 10 = 25

A∪B = Total students - Students playing neither football or cricket

A∪B = Total students - 7

Total students = 25 + 7 = 32

Hence probability (A∩B) = A∩B÷Total Students = 10/32

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2 years ago

What is the maximum value of the objective function, P, with the given constraints? P=25x+45y 4x+y≤16 x+y≤10 x≥0 y≥0

Usimov [2.4K]

Answer:

the maximum is 450 and the minimum is 0.

Step-by-step explanation:

We know that:

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First, is easy to see that as x and y increase, also does the value of P(x, y)

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We know that:

4x+y ≤ 16

x + y ≤10

x≥0

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Let's start with the second inequality, let's solve this for y:

y ≤ 10 - x

and from the first one we get:

y ≤ 16 - 4*x

Just to show that maximizing x does not work, let's do it:

from the second one, knowing that the minimum value of y is y = 0

we have that:

0 ≤ 16 - 4*x

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P(1, 0) = 25*1 + 47*0 = 25

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y ≤ 10 - x

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If now we take the minimum value of x, x = 0, we get:

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Because the first one is more restrictive, we know that the maximum value that y can take (when x = 0) is y = 10

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P(0, 10) = 25*0 + 45*10 = 450

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For the minimum, we just need to take the two lowest possible values of x and y, which are the two given by the equalities on:

x≥0

y≥0

The smallest values are:

x = 0

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Replacing that in the equation we get:

P(0, 0) = 25*0 + 47*0 = 0

So the maximum is 450 and the minimum is 0. (with the given restrictions)

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Soloha48 [4]

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In Point Slope formula:

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