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likoan [24]
3 years ago
11

Find the indicated probability.

Mathematics
1 answer:
emmainna [20.7K]3 years ago
5 0

Answer:

P(A or B) = 0.9.

Step-by-step explanation:

This is a question of Venn probabilities.

We use the following relation to solve this question.

P(A \cup B) = P(A) + P(B) - P(A \cap B)

The exercise states that:

P(A) = 0.7, P(B) = 0.6, P(A \cap B) = 0.4

Then

P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.7 + 0.6 - 0.4 = 0.9

The answer is:

P(A or B) = 0.9.

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A Norman window is a window with a semi-circle on top of regular rectangular window. What should be the dimensions of the window
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Answer:

Side lengths = 1.68 ft and width = 3.36 ft.

Step-by-step explanation:

Let the side lengths of the window be L and the width = 2r ( r is also the radius of the semi-circle).

So we have

Perimeter = 2L + 2r + πr = 12

Area = 2rL + 0.5πr^2

From the first equation

2L = 12 - 2r - πr

Substitute for 2L in the equation for the area:

A = r(12 - 2r -  πr) + 0.5πr^2

A = 12r - 2r^2 -  πr^2 + 0.5πr^2

A =  12r - 2r^2 - 0.5πr^2

We need to find  r for the maximum area:

Finding the derivative and equating to zero:

A' = 12 - 4r -  πr = 0=

4r + πr = 12

r = 12 / ( 4 +  π)

r = 1.68 ft.

So the  width of the window = 2 * 1.68 = 3.36 ft.

Now  2L = 12 - 2r - πr

=  12 - 2*1.68 - 1.68π

= 3.36

L = 1.68.

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3 years ago
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3 years ago
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