Melody

Hi Guest,

You have assumed that the two must choose different digits.  I do not think that is the case.

To answer I drew a 10 by 10 grid. Like a times table grid.

There are 100 pairs of numbers in the grid. That is the sample space.

Then I ticked of the pairs that met the condition. I found 73 of them

So the answer I go was   73/100

All answers hon this site shold be verified by the asker.

A bag contains five white balls and five black balls. Your goal is to draw two black balls.
You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.)

5 white, 5 black

\(P(BB)=\frac{5*4}{10*9}=\frac{20}{90}=\frac{2}{9}\\ P(BWB)=\frac{5*5*4}{10*9*9}=\frac{100}{810}=\frac{10}{81}\\ P(WBB)=\frac{10}{81}\\ P(WWBB)=\frac{5*4*5*5}{10*9*10*9}=\frac{500}{8100}=\frac{5}{81}\)

2/9+20/81+5/81 = 0.5308641975308642 

You need to check my working.

You have used the wrong sample space.

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.

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 !