tertre

(x+y)^2=x^2+y^2+2xy.

x^2+y^2+2(13)=78, x^2+y^2=52.

(x-y)^2=x^2+y^2-2ab, so 52-2(13)=52-26=26-answer.

1. How many positive solutions are there to w+x+y+z=60?

2. 6 students are running for class president out of 20 members. How many vote counts are possible, if some people decide not to vote?

After you finish these problems, I will give you new ones.

Enjoy!

No problem...this is a very hard concept to grasp. I could give you a few more practice problems if you would like.

We can split this up into multiple cases to consider.

One-dollar bills: Set up the dividers to get  (7-1)C(2)=6C2=15 ways.

Five-dollar bills Again...use the same method to get (6-1)C2=5C2=10 ways.

Twenty-dollar bills: (5-1)C2=6 ways.

Hundred-dollar bills: Any three nephews can get it, so there are three ways or (4-1)C2=3C2=3 ways.

Thus, the answer is 2700 ways.

1. 3!=6 ways to arrange the three-digit number...and 132, 312 are multiples of 4. Thus, 2/6=1/3?

Hint for number 2: Count the number of possible arrangements...and subtract by the number of arrangements that the letters are next to each other. For this, try to use a superblock for (A), (L), (S)...because they all repeat twice

We need to find this...: (Just watch American Idol)+(Just watch Lost)+(Watch both television series). Thus...we have (21-8)+(39-8)+8=13+31+8=52 people.

We have to place an isosceles triangle, 45-45-90 triangle such that the center of the isosceles triangle is the center of the square. The only way to do this is by rotating the isosceles triangles, such that the side is opposite the 90-degree angle. This is 1/4 of the total square or 1/4*100-25 square units.

Welcome back, hectictar!

No problem...and the answer to the second question should be \(\frac{8!}{3!*5!}=\boxed{56}\) different sequences.

Yes, congrats to both of you!