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The propability to get one specifik number with a dice is   $${\mathtt{P}} = {\frac{{\mathtt{1}}}{{\mathtt{6}}}}$$   because there is one specifik number out of 6 possible. the propability for even numbers is 3/6 because there is 3 "whished" numbers outof 6 possible.

However, if you roll the dice 2400 we can expect that 1/6 of all rolls would be  a four.

So you just multiplie 2400 with 1/6.

I hope you find this helpfull! :)

Nice work Zacismyname!!!

But is it possible that  there is a couple of brackets missing?

$${\frac{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}{{\mathtt{2}}}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}$$       multiplie all terms with 2 in order to remove the denominator on the left side.

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}$$     get all x to the left side and all terms without x on the other side.

$$\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}} = \left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right){\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}$$

Good luck

It´s just to replace the a with 4 and the b with 3

$${\mathtt{c}} = {\sqrt{{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}}}}$$

$${\mathtt{c}} = {\sqrt{{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{3}}}^{{\mathtt{2}}}}}$$

$${\mathtt{9}}{\mathtt{\,\times\,}}\left({\mathtt{n}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\times\,}}\left({\mathtt{n}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}\right) = \left({\mathtt{9}}{n}{\mathtt{\,\small\textbf+\,}}{\mathtt{27}}\right){\mathtt{\,\small\textbf+\,}}\left({\mathtt{4}}{n}{\mathtt{\,\small\textbf+\,}}{\mathtt{32}}\right) = {\mathtt{9}}{n}{\mathtt{\,\small\textbf+\,}}{\mathtt{27}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{n}{\mathtt{\,\small\textbf+\,}}{\mathtt{32}} = {\mathtt{13}}{n}{\mathtt{\,\small\textbf+\,}}{\mathtt{59}}$$

$${{\mathtt{27}}}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)} = {\left({{\mathtt{27}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}^{{\mathtt{2}}} = {{\mathtt{3}}}^{{\mathtt{2}}} = {\mathtt{9}}$$

the answer is 9

s=total numbers of steps

v= velocity of the escalator  (steps/seconds)

make two different equation with the info given in the text. "Mr anonumous" climbs 20 step by his own, the escalator helps him with v*60 steps. "Mrs anonymous" climbs 16 steps by her own, the escalator helps her with
v * 72 steps.

(1)  s=20+60v

(2)  s=16+72v

(1)------> v=(s-20)/60

now use the "new"(1) and put that one into equation number 2.

s=16+72*(s-20)/60     72/60=6/5 therefore multiplie everything with 5

5s=80+6(s-20)----> 5s=80+6s-120

5s-6s=80-120

s=40

"Mr anonymous"have to climb 40 steps instead of 20 if the escalator breaks down.

A=(pi*d^2)/4

                             pi~3,14,  d=diameter  r=radius=d/2

A=(pi*r^2)  

$${\frac{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{52}}}^{{\mathtt{2}}}\right)}{{\mathtt{4}}}} = {\mathtt{2\,123.716\: \!633\: \!826\: \!700\: \!229\: \!2}}$$ 

$${\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{26}}}^{{\mathtt{2}}} = {\mathtt{2\,123.716\: \!633\: \!826\: \!700\: \!229\: \!2}}$$

Oops, thank you Alan.

I´m to slow ;)

Have a nice day and thanks for the rule!

Thanks Melody for notice my wrong.

Alan, do you know how to do it with the change?

the answer is 1/3 if that helps.

Will check out L´Hopital´s rule, thanks for your help!

oh sorry it will be 3*2^x