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2 years ago

A point is randomly chosen in the circle shown below.

Mathematics

1 answer:

quester [9]2 years ago

7 0

Answer:

in a region with a letter

Step-by-step explanation:

For a certainty, then probability is 1.

That means sum of probability of all events in the sample space.

This means P(A)+P(B)+P(C)+P(D)=1

This is equivalent to:

P(A or B or C or D)=1

Hence for certainty, the region must be:

A or B or C or D

So the correct answer is in a region with a letter.

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3 years ago

A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 in. Let x be the len

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Answer:

a. V = (20-x) $x^{2}$ $in^{3}$

b . 1185.185 $in^{3}$

Step-by-step explanation:

Given that:

The height: 20 - x (in )
Let x be the length of a side of the base of the box (x>0)

a. Write a polynomial function in factored form modeling the volume V of the box.

As we know that, this is a rectangular box has a square base so the Volume of it is:

V = h * $x^{2}$ $in^{3}$

<=> V = (20-x) $x^{2}$ $in^{3}$

b. What is the maximum possible volume of the box?

To maximum the volume of it, we need to use first derivative of the volume.

<=> dV / Dx = -3 $x^{2}$ + 40x

Let dV / Dx = 0, we have:

-3 $x^{2}$ + 40x = 0

<=> x = 40/3

=>the height h = 20/3

So the maximum possible volume of the box is:

V = 20/3 * 40/3 *40/3

= 1185.185 $in^{3}$

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2 years ago