Melody

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 :)

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.

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

Find the number of five-digit positive integers such that the digits are alternately odd and even (either odd-even-odd-even-odd or even-odd-even-odd-even)

o e,o,e,o      5*5*5*5*5

e,o,e,o,e       4*5*5*5*5

now add them

Good question guest and thanks for your answer Nivana,

I'm going to answer the same, just with slightly different words.

A fraction line, which is shown as / here, is exactly the same thing as a divide by sign.

For instance.

\(\frac{9}{2}=4\frac{1}{2}\\ 9\div 2 = 4\frac{1}{2}\\\)

See how the divide by sign looks like a fraction, only it has dots top and bottom instead of numbers?

Well, that is no coincidence.  

Asker guest,

My answer is different from guests. I have not checked mine super well, there could be an error. 

It is up to you to work out which, if either, of us is correct

Feel free to ask questions if you want to.

Thanks guest,

I think I have a different approach.

An ellipse has foci at (0,2) and (3,0). The ellipse has two x-intercepts, one of which is the origin. What is the other x-intercept? (Remember to enter your answer as an ordered pair.)

The locus of an ellipse is the set of all points such that the sum of the distances to the foci are equal to some constant.

The two loci are     (0,2) and (3,0)       and one point on the ellipse is (0,0)

I have always enjoyed solving question using the locus of points that fit a given condition. It is easier becasue you do not need to remember a whole heap of formulas. You only need to know definitions which are usually really simple.

The distance from (0,0) to (0,2) is 2

The distance from (0,0) to (3,0) is 3

2+3=5

So the constant is 5.

Let (x,y) be a point on the ellipse.

\(\text{The distance from (x,y) to (0,2) }=\sqrt{ x^2+(y-2)^2} \\ \text{The distance from (x,y) to (3,0) }= \sqrt{(x-3)^2+y^2} \\so\\ \sqrt{ x^2+(y-2)^2}+ \sqrt{(x-3)^2+y^2}=5\\ \)

Now I need the other x intercept which is where y=0

so sub in y=0

\(\sqrt{ x^2+(y-2)^2}+ \sqrt{(x-3)^2+y^2}=5\\ \sqrt{ x^2+(-2)^2}+ \sqrt{(x-3)^2+0^2}=5\\ \sqrt{ x^2+4}+ \sqrt{(x-3)^2}=5\\ \sqrt{ x^2+4}+ |x-3|=5\\ \sqrt{ x^2+4}=5-|x-3|\\ \sqrt{ x^2+4}=5-(x-3)\quad if \;\;x\ge3\quad and \quad \sqrt{ x^2+4}=5+(x-3)\quad if \;\;x<3\\ \sqrt{ x^2+4}=8-x \qquad if \;\;x\ge3\qquad and \qquad \sqrt{ x^2+4}=2+x\quad if \;\;x<3\\ x^2+4=x^2-16x+64 \quad if \;\;x\ge3\quad and \qquad x^2+4=x^2+4x+4\quad if \;\;x<3\\ -60=-16x \quad if \;\;x\ge3\qquad and \qquad 0=4x\quad if \;\;x<3\\ x=\frac{60}{16}=\frac{15}{4}=3.75 \quad if \;\;x\ge3\qquad and \qquad x=0\quad if \;\;x<3\\ so\\ \text{The two x intercepts are 0 and 3.74} \)

**   There is a typo in the coding.  The second x intercept it    3.75

If you multiply by 2 five times then you get 0 

So the biggest interger on the too little side  that you cannot get it -1.    The smallest is    - infinity.   (but that is not an integer)

Of course numbers do not have to be integers, they do not even have to be real, so the question should have been better stated.

What is the smallest distance between the origin and a point on the graph of y=(1/sqrt(2))(x^2-3) ?

\(y=\frac{1}{\sqrt2}(x^2-3) \\ \sqrt2\;y+3=x^2\\ x^2=\sqrt2\;y+3\)

this is a concave up parabola with the vertex at (0,3)

So what do you think the smallest distance to the origin is?