Melody

sum of 6 numbers is   6*14 =  84

Sum of 5 numbes is   5* 10  = 50

so ahat is the 6th number?

I will start you off.

\(\dfrac{7x^{2014}}{4x^{2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}\)

\(=\dfrac{7x^{2014-2013}}{4^{2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}.\\ ~\\=\dfrac{7x^{1}}{2^{2*2013}}\cdot{\dfrac{2x^{2012}}{2x^{2007}}}\cdot\dfrac{27x^{2006}}{x^{2002}}\cdot\dfrac{6x^{2008}}{8x^{2010}}\)

Now it is your turn.

x(x+5) = -n

\(x(x+5) = -n\\ x^2-5x+n=0\\ x=\frac{5\pm\sqrt{25-4n}}{2}\\ \)

this will NO real solutions if the number under the square root is negative.

\(25-4n<0\\ 25<4n\\ 4n>25\\ n>6.25\)

So there will be no real solution if n = 7,8,9 or 10

that is  4/10 = 2/5 probability

There is no second one.

ok I answered it.

There were some avocados in 3 boxes, E, F and G. 30% of the number of avocados in Box E was equal to 60% of the number of avocados in Box F. The number of avocados in Box G was 60% of the total number of avocados in Box E and F. After Oscar removed 20% of the avocados in Box G, there were 88 more avocados in Box F than in Box G. In the end, how many avocados should be transferred from Box F to Box G so that the avocados in Box G would be the same as Box E?

I do not think that this scenario is possible.

30% of the number of avocados in Box E was equal to 60% of the number of avocados in Box F

so

0.3E=0.6F

E=2F

So in the beginning there are 2 times more in box E than in box F     (And  each one has a muliple of 10)

G=0.6(E+F)

G=0.6(3F)

G=1.8F

Now 20% are removed from box G

so box G will then have    0.8*1.8F = 1.44F

So now

It is clear that there are now mow avocados in the last box than in the middle one.

So there cannot be 88 more in the middle one, that is a contradiction.

these are just numbers in binary. (base 2)

\(7=4+3+1 = 1*2^2+1*2^1+1 = 211\\ 17=16+1 = 1*2^4+0*2^3+0*2^2+1 = 1001\)

Now I have given you 2 examples you and work out what 12 is in base 2

You have not asked a question.  

This function BELONGS to some question, which you have not asked,

Oh course it is is schoolwork.  Almost every question here is schoolwork.

Great work Catmg and Max :)