lokiisnotdead

if negatives are fine, then its -2500

if it's only positive answers, then I'm pretty sure its 101

i think what hugo meant was \(\dfrac{7-2}{7}=\dfrac{5}{7}\text{ probability}\)

hi! i answered it in your private message! :)

ok so we can start off by noticing that the small triangle is similar to the larger triangle, and if triangle's are similar, the angle measures are the same.

so, a = 40 degrees

since the two sides are congruent, that means that angle c is equal to angle a, so angle c = 40 degrees

for angle b, we already know that the other 2 angles of the smaller triangle are both 40, so using the triangle theorem, we get 180-40-40= 100 degrees. so, b = 100 degrees.

lastly, angle e is part of a straight line with the other angle being 40 degrees. so angle e = 180-40=140 degrees

adding them all up becomes 40+40+100+140= 320 degrees

cause there's 6 candidates for president so that 6! 

there's 4 candidates for vp so that's 4!

there's 5 candidates for secretary so that's 5!

and there's 3 candidates for treasurer so that's 3!

so that's just 6!*4!*3!*5! = 12441600

isn't it just \(6! \cdot 4! \cdot 5! \cdot 3! = 12441600‬ \text{ ways }\)?

no problem! :)

hmm i think guest wanted it to be simplified exactly (like in simpler terms of radicals)...

here's my try at this problem:

\(\sqrt{5+\sqrt{24}}=\sqrt{5+2\sqrt{6}}\)

so we can express \(\sqrt{5+2\sqrt{6}}\)  in the form of \((a+b)^2\)

so we know that \(a^2+b^2=5 \text{ and } 2ab=\sqrt{6}\), so it's really easy to figure out that \(a=\sqrt{2} \text{ and } b=\sqrt{3}\)

so this would become \(\sqrt{(\sqrt{2}+\sqrt{3})^2}\)

which means the equation is really just equal to \(\boxed{\sqrt{2}+\sqrt{3}}\)

i hope this helped you! :)

i'm pretty sure there's a much better way to do this but here's my solution:

\(3^x=5 \text{ is equal to } \dfrac{\text{ln}(5)}{\text{ln}(3)}\)

\(5^y=9 \text{ is equal to } \dfrac{\text{ln}(9)}{\text{ln}(5)}\)

so, \(xy\) is equal to \(\dfrac{\text{ln}(5)}{\text{ln}(3)} \cdot \dfrac{\text{ln}(9)}{\text{ln}(5)}=\boxed{2}\)

ok so

if we simplify the numerator of the fraction, we get \(((3!)!)!=(6!)!=720!\)

so our new fraction is \(\dfrac{720!}{3!}\) which is equal to \(\dfrac{720 \cdot 719!}{6}\)

we can then cancel out the 720 and 6, and we get \(120\cdot719!\)

so, \(719+120=\boxed{839}\)