CPhill

x is supplemental to the 56 degree angle = 124 degrees

And y is the same measure as the angle between the 41 and 56 degree angles at the top left. And these three angles sum to 180 degrees. So, y  = 180 - 56 - 41 = 83 degrees.

In the little triangle on the right containing x, the angle at the top right = 40 degrees because it is equal to the opposite angle in the parallelogram formed by the intersection of the parallel transversals with the double and triple arrows. And the other angle in this triangle = 67 degrees. It's the corresponding angle to the other 67 degree angle formed by the intersection of  parallel transversals with the single and triple arrows. Thus. x = 180 - 67 - 40 = 73 degrees.

And in the lttle triangle at the top....the angle at the bottom right is the vertical angle to the 67 degree angle in the triangle containing x. And the angle at the bottom left of this small triangle is the corresponding angle to the 40 degree angle formed by the intersection of the parallel transversals with the double and triple arrows. So y = 180 - 67 - 40 = 73 degrees, as well.

Well...10% of 30 is 3

So.....5% is 1/2 of that.....

We have a paralleogram

The slope of the line segment from (1,1) to (3,5)  =  the slope of the line segment from (-3,2) to (-1,6) = 2

Thus, these segments are parallel

And the slope of the line segment from (-1,6) to (3,5) = the slope of the line segment from (-3,2) to (1,1) = -1/4

So these segments are also parallel.

And when two parallel transversals intersect another pair of parallel transversals, the quadrilateral formed has opposite sides of equal length. 

Therefore, we have a parallelogram.....a four-sided figure whose oppsite sides are parallel and equal.

Here's a picture......

 P.S.  - if AB = AD, we would have a rhombus but  AD > AB.....

AD = √20     AB = √17

Melody, if we have a plane of equal thickness,  the centroid can be thought of as the "balance point" of the plane. 

We have two tasks here....choose the boxes....choose the b***s to go into those boxes...

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4 2 0

We have 3  ways to choose the first box......and we want to put 4 of the 6 b***s into it

3C(6,4)  = 45

Then, out of the remaning 2 boxes, we want to choose one of the two to put the remaining two b***s into

So 45 x 2 = 90

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4 1 1

Agian we have 3 boxes to choose which 4 b***s out of 6 we put into it

So 3C(6,4)= 45 ways

And we have two ways to select the next box and two ways to select which ball goes into that box...

The last box and ball are defaulted

So we have

2C(2.,1) = 4 ways

So 45 x 4 = 180

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3 3 0

3 ways to choose the first box......and we want to choose 3 of 6 b***s to put into it

3C(6,3) = 60 ways

Then, we have 2 ways to choose the next box to place the remaining three b***s into

So 2 x 60  = 120 ways

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3 2 1

3 ways to choose the first box....choose 3 of 6 b***s to put into it   = 60 ways  

2 ways to select the next box and we want to choose 2 of the 3 remaining b***s to put into it

2C(3.2) = 6

Again, the last box and ball are defaulted

So   60 x 6 = 360 ways

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2 2 2

3 ways to select the first box .... choose 2 of 6 b***s to go into it  = 3C(6,2) = 45

2 ways to pick the next box and choose 2 of the remaining 4 b***s to put into it

2C(4,2)  = 12

The last box and remaig two b***s are defaulted

So 45 x 12 = 540 ways

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Anyway, that's what I get......!!!

I might have done it slightly differently, but I believe your answers are correct, Melody....

Here, the boxes don't matter...one is as good as the other...!!!   The only thing  that matters is choosing which b***s to group together in one (or more) boxes. 

Another 3 points from me....!!!

Yep....that answer seems reasonable, Melody......

3 points from me......

Yeah...check my math, Melody....you're not the ONLY one wearing glasses...!!! LOL!!!

What the H**L???

How was I supposed to know WHAT you wanted???

I certainly didn't see the word "centroid" anywhere in your question...!!!

I thought you were wanting the area between the curves {silly assumption on my part...}

If you want a specific thing......maybe you should INCLUDE that specific thing when you post.....!!!!