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3 years ago

In figure find the area of the red part.

Mathematics

2 answers:

Liula [17]3 years ago

8 0

The first one is correct

larisa [96]3 years ago

5 0

Step-by-step explanation:

Given : A rectangle 4 x 8 , a semicircle

Diagonal intersecting semicircle

To Find :Area of red part

<h3>Solution:</h3>

Angle AC make AB α = ∠BAC

tan α = BC/AB = 4/8 = 1/2

=> α = 26.565°

∠ECA = ∠BAC = α

EC = EF = 4

=> ∠CEF = 180° - 2α

∠AED = 45° as AE is diagonal of Square of side 4

=> ∠AEF + 180° - 2α + 45° = 180°

=> ∠AEF = 2α - 45° = 8.13°

in Left side area between square and circle is split in 2 Equal parts

(1/2) area - area AFG = area of Red part

in Left side area between square and circle = 4² - (1/4)π4²

= 3.4336 sq unit

half = 1.7168 sq unit

Now find area AFG = area ΔAEF - sector EGF

area ΔAEF

AE = 4√2 , EF = 4 angle = 8.13°

area ΔAEF = (1/2) 4√2 * 4 sin 8.13° = 1.6 sq unit

area sector EGF = (8.13/360)π4² = 1.135 sq unit

area AFG = 1.6 - 1.135 = 0.465 sq unit

Area of Red part = 1.7168 - 0.465 sq unit

= 1.2518 sq unit

= 1.252 sq unit

= 1.25 sq unit.

Hope this helps!!

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Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter

sweet [91]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

What is P(A and B)?

What is P(A | B)?

Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Solution:

The probability of the two events <em>A</em> and <em>B</em> are:

P(A) = 0.30 and P(B) =0.40

(a)

Compute the value of P (A ∩ B) as follows:

$P(A\cap B)=0$

This is because mutually exclusive events are those events that cannot occur together.

(b)

Compute the value of P (A | B) as follows:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0$

Thus, the value of P (A | B) is 0.

(c)

No, P (A | B) is not equal to the P (A).

(d)

As mentioned in part (a), mutually exclusive events are those events which cannot occur together.

That is, $P(A\cap B)=0$ .

Events A and B are independent if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is, $P(A\cap B)=P(A)\times P(B)$ .

The concepts of mutually exclusive events and independent events are not the same.

(e)

As the it is provided that A and B are mutually exclusive events, we know that $P(A\cap B)=0$ .

Now compute the value of $P(A)\times P(B)$ as follows:

$P(A)\times P(B)=0.30\times 0.40=0.12\neq 0$

Thus, the events A and B are not independent.

Thus, if two events are mutually exclusive events they cannot be independent.

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3 years ago

Find the inverse function for

kifflom [539]

$\bf \stackrel{f(x)}{y}=\sqrt{2x-6}\qquad \qquad \stackrel{f^{-1}(x)}{y}=\cfrac{x^2+6}{2}$

that is correct hmmmm, yes, I think the restriction is also correct, it has to be x > 0, because, the domain on the original, has a restriction of x⩾3, otherwise the radicand turns negative.

now, the graph of that original function is a parabola sideways opening to the right, if you include both sides of the vertex of the parabola, it will not pass the vertical-line-test and not be a function, but if you restrict it to only positive roots, so it'll only be on the 1st quadrant, then it functions ok.

that means, the range of the original function, has to stick to only 0 or positive root values, now, recall that the range of the original is the domain of the inverse. Therefore, the domain of the inverse, will have to stick to only 0 or positive values, since it's bound to the same restriction as the original's range.

notice the picture below of both, the dashed section is the positive range for each, if you include it, the original will fail the vertical-line-test, and the inverse will fail the horizontal-line-test.

recall that for a function to have an inverse, they both must pass the vertical and horizontal line test, or be a one-to-one functions.

6 0

4 years ago

a package of 8 rechargeable batteries cost 12. at the rate how much would 20 rechargeable batteries would cost

Anettt [7]

Step-by-step explanation:

8 battery =12

20 battery =?(x)

8x=240

x=240÷8

x=30

for 20 battery..it would cost 30

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3 years ago

1. Calculate the volume of a cube with the following measurements. Length = 5 cm Height = 10 cm Width = 16 cm 800 cubic cm 400 c

Finger [1]

Answer:

800

Step-by-step explanation:

lol ain't even a cube das a rectangle

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3 years ago

It takes 213 yards of denim to make one pair of jeans. How many yards would it take to make 5 pairs of jeans?

SVETLANKA909090 [29]

Answer:

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Step-by-step explanation:

Multiply 213 by 5 to get your final answer.

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3 years ago

In figure find the area of the red part.​

In figure find the area of the red part.