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3 years ago

8

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.

0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.

1 answer:

olchik [2.2K]3 years ago

7 0

I think you have to decide each one idk

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luda_lava [24]

divide top and bottom by 3 to make 1/16

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Write the next three terms of the arithmetic sequence.

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12,6,0

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18-6=12, so on so forth.

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Nora must create a 4-character password to login to a website. The password must have three letters followed by a single digit,

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Answer:

The outcomes are {1nor} , {2nor}, {3nor}, {4nor}, {5nor}, {6nor}, {7nor}, {8nor}, {9nor}

Step-by-step explanation:

The outcomes are {1nor} , {2nor}, {3nor}, {4nor}, {5nor}, {6nor}, {7nor}, {8nor}, {9nor}

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2 years ago

Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

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