Write only the answers to the questions given.
to be more exact:
in years 2002-08 time was 90' for part A and 120' for part B
red balls and 
white balls. Audi took two balls at once from inside the bag. The chance of taking two balls of the same color is ...
unit. The area of the hexagon is ...
and 
.
is ...
so that 
and 
is ...
,
,
,
has an average of 
and a median of 
.
are integers greater than 
which are four consecutive quarters of an arithmetic row with 
.
and 
are squares of two consecutive natural numbers, then the smallest value of 
is ...
,
and 
.
and 
lies on the line segment 
and 
.
is ...
meet 
for each natural number 
.
is ....
provided that the difference of any two numbers at least 
is ...
which satisfies 
are as many as ...
and 
.
.
is a point on the side extension 
is perpendicular to 
and 
.
is ...
consists of 
with 
positive reals is ....
with 
is ....
square units. Two plots are said to be neighbors if they both have one side in common. Initially, there are a total of 
coins on the chessboard where each coin is only loaded exactly on one square and each square can contain coins or blanks. At each turn. You must select exactly one plot that holds the minimum number of coins in the number of neighbors of the plot and then you must give exactly one coin to each neighbor of the selected plot. The game ends if you are no longer able to select squares with the intended conditions. The smallest number of 
and 
.
be a positive root of the equation 
.
Y by Adventure10
The triangle 
is right in 
and 
is the midpoint of the hypotenuse 
. On the major leg 
the point 
is marked such that 
and on the segment 
the point 
is marked such that the triangle 
is equilateral. If the area of triangle is 
, calculate the area of triangle .
is right in 
and 
is the midpoint of the hypotenuse 
. On the major leg 
the point 
is marked such that 
and on the segment 
the point 
is marked such that the triangle 
is equilateral. If the area of triangle is 
, calculate the area of triangle .
![[asy]
pair A = (0,0), B = (sqrt(3),0), C = (0,1);
draw(A--B--C--A);
pair R = (B+C)/2, P = (2A+B)/3, Q = (A+2B)/3;
draw(P--R--Q);
draw(C--P,dashed);
dot(P^^Q^^R^^A^^B^^C);
label("$A$", A, dir(-135));
label("$B$", B, dir(-30));
label("$C$", C, dir(120));
label("$P$", P, dir(-90));
label("$Q$", Q, dir(-90));
label("$R$", R, dir(60));
[/asy]](http://latex.artofproblemsolving.com/a/6/b/a6b73469f604e8ed71de1de6beea7711c77d8057.png)
is isosceles by definition. Now, since 
,
is a median, and since 
,
and 
.
.
-
-
and 
.
and thus 
and 
.
,
.
is 
.
is simple 
,![$\tfrac{[\triangle{PRQ}]}{[\triangle{ABC}]}=\tfrac{1}{6}$](http://latex.artofproblemsolving.com/4/3/3/433b17a0ff2db19b94a227a96ff2d2d37bab5036.png)
.![$[\triangle{ABC}]=27$](http://latex.artofproblemsolving.com/2/f/3/2f396705747bc28b529a0aad7baf0d07cd31ea3e.png)
,![$[PQR]=\boxed{\tfrac{9}{2}}$](http://latex.artofproblemsolving.com/8/2/2/822c4e4d1551623ccd762aee48c1975944ae86ab.png)
.
Your one is right
