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We can use complementary counting.  There are 12/(5!*7!) = 792 paths to (5,7).  You must subtract 7!/(4!*3!) = 35 paths, so there are 792 - 35 = 757 good paths.

Is this an AoPS question?

Thank you for atempting the problem, but I am trying to learn, just an answer is not enough.

Also I double checked and 13/3 is not the correct answer to this problem.

Can someone else please atempt this problem?

Using the distance formula, the radius is √(2-(-1))^2 + (3-6)^2 = √3^2 + 3^2 = √18. The equation is shown as (x -2)^2 + (y-3)^2 = 18. If we expand this, we get x^2 - 4x + y^2 - 6y + 9 - 18 + 4 = 0 which is is x^2 + y^2 - 4x - 6y - 5 = 0. So j*k*l = -4* -6* -5= -120.

The area of the polygon is 13/3.

a = 5/4.

12 + 43 = 55, so I guess A.

Wrong :/ it was 3

What's aops?? 
 

Edit: uhhh is it? Abstract of Operations System (US Coast Guard)?

Here, unlike Heureka's question where there were four equations, there are only three equations in the four unknowns, so it's unlikely that there is a unique solution.

1.04 x = 598

x = 598/1.04 = 575

Let me try to load the picture again...sorry

Sooooo... we'll have to guess !    Sorry, we don't have the image 

I guess  B               Anyone else?

sec = 1/cos      csc = 1/sin   so we need sin and cos for all of the objects

5pi/6    sin = 1/2        cos =   - sqrt3/2

5pi/4    sin = - sqrt2/2    cos = -srt2/2

11pi/6   sin = -1/2      cos  = sgrt3/2

so ....adding all of these inverses

2 - 2 /sqrt3    - 2/sqrt2   -  2/sqrt2   - 2 + 2/sqrt3   =  -   4 / sqrt 2   = - 4 sqrt 2/2   = - 2 sqrt 2

Nvm i have answer XD

The expansion of $(mx+n)^2$ is $m^2x^2+2mnx+n^2$. If $$16x^2+36x+56 = m^2x^2+2mnx+n^2,$$ we can equate the coefficients of $x^2$ to get $16=m^2$, and thus $m=4$ (we ignore the solution $-4$ because we are given that $m$ is positive). We can also equate the coefficients of $x$ above to get $36=2mn=2(4)n=8n$, and thus $n=\frac{36}{8}=\frac{9}{2}$. So, $mn=4\cdot\frac92 = \boxed{18}$. Solution 2: The expansion of $(mx+n)^2$ is $m^2x^2+2mnx+n^2$. If $$16x^2+36x+56 = m^2x^2+2mnx+n^2,$$ we can equate the coefficients of $x$ to get $36=2mn$, and so $mn=\frac{36}{2}=\boxed{18}$.

I checked

is that on AoPS?

I dont really know sorry

what is that

We know that there are 13 heartsuit cards in a deck of 52 cards. Therefore, the chance of one being the top card (there's nothing very special about being the top card, it's just like picking one out of the 52 cards) is13/52.

Hope this helped!

Caffeine :)

Looking at the multiple choices, you can immediately rule out the first two, because the exponent is only applied to the fraction in the parentheses. Then, looking at the remaining options, it is the third one because when you raise a fraction to a certain power you raise both the numerator and the denominator to that power. So, $(\frac{1}{4})^2 = (\frac{1^2}{4^2}) = \frac{1}{16}$ so the answer is the third option.

No problem :)

Thanks!

Thanks!