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I believe hectictar is right!. I think he/she means that when you are summing up  a sequence of numbers, say from 1 to 10, why do you do this: [10 x (10+1)] / 2 = 55.

If you mean that 3541 has a multiple which consists of all ones, then by trial and error do this on a calculator with a large display: 11111 / 3541 , 111111 / 3541,  1111111 /3541.......and so on until you get an even division with no remainder.

I automated the process, through a short code, and it turns out that 3541 has multiple of all ones, which is 20 digits long!! In other words:11,111,111,111,111,111,111 / 3541 =3,137,845,555,241,771.

The sample space is 6^2 =36

The probability of rolling a prime number is 15 / 6^2 =5 / 12

The probability of a rolling a sum of 7 is 6 / 36 = 1 / 6

mmm maybe.

Hi Hectictar!     

Yes you are right :)

find the average value of the function g(x)=2sin(x)+e^(x/pi) on the interval 0, (2pi)

The average is the infinite sum of the g(x) values divided  by the number of x values.

The integral sign is an stylized S because it stand for Sum. 

I know this is not explained well. There would be a number of youtube clips on it if you look.

anyway....

Average g(x) value =

 \(=\frac{1}{2\pi-0}*\displaystyle\int_0^{2\pi}\;2sin(x)+e^{x/\pi}\;dx \\ =\frac{1}{2\pi}*\left[-2cos(x)+ \pi e^{x/\pi}\right]_0^{2\pi}\\ =\frac{1}{2\pi}*\left [(-2cos(2\pi)+ \pi e^{2\pi/\pi})-(-2cos(0)+ \pi e^{0/\pi}) \right]\\ =\frac{1}{2\pi}*\left [(-2+ \pi e^2)-(-2+ \pi ) \right]\\ =\frac{1}{2\pi}*\left [(-2+ \pi e^2+2- \pi ) \right]\\ =\frac{1}{2}*\left [( e^2- 1) \right]\\ =\frac{e^2-1}{2} \)

Here is a visual representation of the average value of the function. 

The average value is the height of the horizonal orange line.

Maybe Guest is referring to this:

\(\sum\limits_{k=1}^{n}k\ =\ \frac{n(n+1)}{2}\)

in which case, the following might help:

hi melody

i think the answer is 2/5 (simplify from 6/15)

because 1,1 is a combination too, 2 is a prime

I think that is very good advise Nivana.    

The point (0,-2) is on the graph.

That is   F(0)=-2

Substitute x=0 into each of the equations above and see which ones give an answer of -2

Now (3,0) is another point on the graph.

substitute x=3 into the graphs that have not yet be ruled out and see which one gives an answer of 0

You can ask questions if you want to.

Please no one answer this question in full.

What does this mean

"Manu finds no sign changes in and 3 sign changes in."

Full question.

1. Manu determines the roots of a polynomial equation by applying the theorems he knows. He organizes the results of these theorems. From the fundamental theorem of algebra, Manu knows there are 3 roots to the equation. From Descartes’ rule of sign, Manu finds no sign changes in and 3 sign changes in. The rational root theorem yields as the list of possible rational roots. The lower bound of the polynomial is. -6. The upper bound of the polynomial is 1. What values in Manu’s list of rational roots should he try in synthetic division in light of these findings?

I have only just now noticed your question.

It is excellent that you have worked it out by yourself !    

Mahowny rolls two fair, six-sided dice. You don't know what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the two rolls is 7?

prime number rolls

1,1   added after guest pointed out my error of omision    1

1,2    2,1                                              2

1,4    4,1    23,  32,                              4

1,6     2,5    3,4   doubled                     6

5,6   6,5                                               2

Total                                                   15     edited

probability is     6/15    

Thanks for picking up my error guest :)

Actually,

I'm gonna answer my own question...

I figured it out!

:)

Yayyyy!

How do you post a picture?

Thank you!

Hi Tom,

I really don't know. I don't remember seeing that symbol before.

I think it has been labelled as a high priority question. Maybe it is advertised in FaceBook or somewhere else.

It is bordered top an bottom by a heavy line in the question list.

GingerAle  is the one most likely to be able to answer your question.

I've noticed in this problem there is a person icon in the corner...

What's that about?

Half of 125 is 62.5

So if the biggest number was 62 then 2 of them  could not add to 125.

So I expect the answer is 62.

Here is your ellipse