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sp2606 [1]
3 years ago
11

Which benchmark angles (multiples of 30 degrees or 40 degrees) are closest to the rotation angles below?

Mathematics
1 answer:
Setler [38]3 years ago
4 0

The benchmark angles are angles that are used as references like- 30 degrees, 45 degrees, 60 degrees, etc.

The closest angles to given rotation angles are:

A- 40- closest to the multiple of 45 degrees.

B- 140- closest to the multiple of 45 degrees (135 degree).

C- 170- closest to the multiple of 30 degrees (closest to 180 degrees which is multiple of both 30 and 45 degrees).

D- 220 -closest to the multiple of 30 degrees (210 degree).

E- 250- closest to the multiple of 30 degrees (240 degree).

F- 310- closest to the multiple of 45 degrees (315 degree).

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astraxan [27]

Answer:

Y will arrive earlier than X one fourth of times.

Step-by-step explanation:

To solve this, we might notice that given that both events are independent of each other, the joint probability density function is the product of X and Y's probability density functions. For an uniformly distributed density function, we have that:

f_X(x) = \frac{1}{L}

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Now, as  X is distributed over a 1 hour interval, and Y is distributed over a 0.5 hour interval, we have:

f_X(x) = 1\\\\f_Y(y)=2.

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\iint_A f_{X,Y} (x,y) dx\, dy

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It's useful to draw a diagram here, I have attached one in which you can see the integration region.

You can see there a box, that represents all possible outcomes for Y and X. There's a diagonal coming from the box's upper right corner, that diagonal represents the cases in which both X and Y arrive at the same time, under that line we have that Y arrives before X, that is our integration region.

Let's set up the integration:

\iint_A f_{X,Y} (x,y) dx\, dy\\\\\iint_A f_{X} (x) \, f_{Y} (y) dx\, dy\\\\2 \iint_A  dx\, dy

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2 \iint_A  dx\, dy= 2 \times \frac{0.5 \times 0.5 }{2} \\\\2 \iint_A  dx\, dy= \frac{1}{4}

That means that one in four times Y will arrive earlier than X. This result can also be seen clearly on the diagram, where we can see that the triangle is a fourth of the rectangle.

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CaHeK987 [17]

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x - 4 = (1/2)y
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Plug f^-1(x) in for y.
f^-1(x) = 2x - 8

f^-1(4) = 2(4) - 8
f^-1(4) = 0
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