Melody

1*2*3*4*5*6*7   *8*10*12*17   * 15*18*  etc

Guests answer sounds better than Ginger's

Subtract 5 yards, 2 feet, 8 inches from 7 yards 2 feet.

after the subtraction we have  2 yards minus 8 inch

which is  1 yard + 3feet - 8 inches

whcih is  1 yard + 2feet +12 inches - 8 inches

which is  1 yard  2feet  4 inches

$a^3-b^3=(a-b)(a^2+ab+b^2)\\ sub \;\; a-b=4\qquad and \qquad a^3-b^3=52\\ 52=4(a^2+ab+b^2)\\ 13=(a^2+ab+b^2)\\ 13-3ab=a^2+ab+b^2-3ab\\ 13-3ab=a^2-2ab+b^2\\ 13-3ab=(a-b)^2\\ 13-3ab=4^2\\ -3ab=3\\ ab=-1\\~\\ 13=(a^2+ab+b^2)\\ 13+ab=(a^2+ab+b^2+ab)\\ 13+ab=(a^2+2ab+b^2)\\ 13+ab=(a+b)^2\\ 13-1=(a+b)^2\\ 12=(a+b)^2\\ a+b=\pm\sqrt{12}$

So now check that i have not made any careless errors and solve simultaneously to get all possible values of a and b

Latex:

a^3-b^3=(a-b)(a^2+ab+b^2)\\
sub \;\; a-b=4\qquad and \qquad a^3-b^3=52\\
52=4(a^2+ab+b^2)\\
13=(a^2+ab+b^2)\\
13-3ab=a^2+ab+b^2-3ab\\
13-3ab=a^2-2ab+b^2\\
13-3ab=(a-b)^2\\
13-3ab=4^2\\
-3ab=3\\
ab=-1\\~\\
13=(a^2+ab+b^2)\\
13+ab=(a^2+ab+b^2+ab)\\
13+ab=(a^2+2ab+b^2)\\
13+ab=(a+b)^2\\
13-1=(a+b)^2\\
12=(a+b)^2\\
a+b=\pm\sqrt{12}

there are 38 woman and 17 like to dance so    so the prob is   17/38

All the other information is irrelevant.

Hi TastyB, It is nice to see you active here. Welcome to this site  

But..

What makes you think that this is a spam question TastyB ?

It may be repeated because a whole class of  students probably got the same question but that doen't make it a spam question.

Note:  As for it being unsolvable I have not looked at the question at all so I would not know.

None of your LaTex is displaying properly for me.

You need to find out how long one side is.

The the ends of the side are the intersection of  y=7  and  y = 2x^2 + 8x + 4

Solve simultaneously

$7=2x^2+8x+4\\ 2x^2+8x-3=0\\ x=\frac{-8\pm\sqrt{64+24}}{4}\\ x=\frac{-8\pm\sqrt{88}}{4}\\ x=\frac{-8\pm2\sqrt{22}}{4}\\ x=\frac{-8\pm2\sqrt{22}}{4}\\ x=-2\pm\frac{\sqrt{22}}{2}\\ \text{Subtract the little from the big and you get the side length of }\;\;\\\ \frac{2\sqrt{22}}{2}=\sqrt{22}\\ \text{So area is 22 }units^2$

Here are the stickers    XXXXXXXXXX  ten of them.

now separate these into 8 groups by puting up dividers.  You only need 7 dividers because each person gets the stickers in front of their divider but the last person just gets the ones at the end. Draw it on a peice of paper to see what I mean.

So there are now 10+7 = 17 objects

you need to see how many ways the dividers can be placed in the queue.

17C7   ways      ofcourse  17C10  would give the same result. 

I expect you are meant to find the rate of change for each unit interval of x and then average those.

The rate of change between x=4 and x=5    is    $\frac{-2-\;-4}{5-4}=\frac{2}{1}=2$

Now you can do the others and average the answers.