2011 District 1 Questions

[Jeremy2012x]

21) Simplify:[unparseable or potentially dangerous latex formula]

22) Roland Bones tosses a pair of standard dice. What is the probability that the sum of the top faces of the dice is a prime number?

31) A secant, AP, and a tangent, CP intersect in the exterior of a circle. Point B lies on AP and on the circle such that CP = 16 and BP = 8. Find AB.

39) Find the sum of the series 1 + 2 + 2 + 1[unparseable or potentially dangerous latex formula] + [unparseable or potentially dangerous latex formula] + [unparseable or potentially dangerous latex formula] + ....

41) Hope I. Whenn throws 3 darts at the square target containing 9 congruent smaller squares. Each dart lands in a different small square. What are the odds that the 3 squares the darts land in are the shaded squares?

42) A tub of apples contains red apples and green apples. The probability of selecting a green apple is 25%. If 10 green apples are added to the tub, the probability of selecting a green apple becomes 40%. How many red apples are in the tub?

49) How many elements are in { [unparseable or potentially dangerous latex formula] } ?

[Salvadoramerican]

Double check my answer cause I'm sick and not in the right mind with all the medicine i've been prescribed
21. since we are looking at two series the first series in the numerator is the sum of suare numbers the formula is [unparseable or potentially dangerous latex formula] so the last number is 17 which we plug in for n which leads to the number 1785. Now the denominator are triangular numbers which formula is pretty similer [unparseable or potentially dangerous latex formula] since the last number is the 17th triangular number you plug that in divide this number from the number in the numerator

22. the possible prime numbers are (1,1),(2,1),(1,2),(3,2),(2.3),(4,1),(1,4),(6,1),(1,6),(5,2),(2,5),(4,3),(3,4),(6,5),(5,6) or [unparseable or potentially dangerous latex formula]which reduces to [unparseable or potentially dangerous latex formula]

49. I would graph it

31. [unparseable or potentially dangerous latex formula]

What are the shaded squares?

39. Its a power series for [unparseable or potentially dangerous latex formula] thus plug in 2

42. I have an idea but its too much work and their might be a faster way than mine

[Jeremy2012x]

could someone possibly draw 31) for me?

[nsguy1350]

Get a piece of paper, and I'll try to tell you how to get to the figure, in a weird way, through words.

Draw a square, then draw a circle within that square.
The top side is the tangent line.
Now, draw that tangent line outside of the square so that it extends past the top right corner square.
Next, connect the bottom left corner to the extended part of the tangent line.
Now, erase the 3 sides of the square that are not part of the tangent line.
That should yield a square. You definitely do not have to follow those steps, but that was the first idea that came to my head when I wondered how I could explain it.
Hopefully that works! All you have to do now is label the correct points.