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## #1 2016-07-15 13:42:57

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Mathematics Challenges, #1

1. We have a unit square [0,1],[0,1]. I pick 2 random numbers from this unit square with uniform distribution. What is the average length  between these two numbers? What is the median length?  What is the modus??
2. Find the sum of the reciprocals of the triangular numbers.

3. I choose 2 integers from the set [1,100]. What is the probability that $\sqrt{xy} > x - y$

4.Does there exist a function f:R→R such that $f(f(x)) = x^2-2x$ for every real number x? Prove whether or not this exists.

5. Find all numbers x for which the equation where 3^x + 3^-x = 3.

Last edited by Mathegocart (2016-07-16 03:24:28)

The integral of hope is reality.

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## #2 2016-07-15 14:23:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Mathematics Challenges, #1

Hi;

For 3) with replacement or without? Also, you mean

We are going to have to teach you some latex. It is pronounced lah - tek?! Now ain't that just as weird as a two headed squirrel? Us bumpkins say lay-tex like the sap they make rubber from.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2016-07-16 01:41:38

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Mathematics Challenges, #1

bobbym wrote:

Hi;

For 3) with replacement or without? Also, you mean

We are going to have to teach you some latex. It is pronounced lah - tek?! Now ain't that just as weird as a two headed squirrel? Us bumpkins say lay-tex like the sap they make rubber from.

Bobbym, modus means method, and I already know LATEX.

The integral of hope is reality.

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## #4 2016-07-16 03:14:55

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Mathematics Challenges, #1

I think √  and x²  are  copied from top of this page and not LaTex.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #5 2016-07-16 03:18:44

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Mathematics Challenges, #1

I think √  and x²  are  copied from top of this page and not LaTex.

True but I was too lazy to put LATEX on the top. I will now.

The integral of hope is reality.

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## #6 2016-07-16 03:38:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Mathematics Challenges, #1

I think √  and x²  are  copied from top of this page and not LaTex.

That is precisely the point.

True but I was too lazy to put LATEX on the top. I will now.

Penguins are hard workers so they can not claim they are lazy. So what is it for 3? With replacement or not?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2016-07-16 22:03:20

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Mathematics Challenges, #1

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #8 2016-07-17 00:36:39

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

### Re: Mathematics Challenges, #1

So what is it for 3? With replacement or not?

When you're in doubt do both.

bobbym, what do you think of the second answer?

Last edited by ElainaVW (2016-07-17 00:37:03)

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## #9 2016-07-17 00:41:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Mathematics Challenges, #1

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #10 2016-07-17 00:43:40

ElainaVW
Member
Registered: 2013-04-29
Posts: 580

### Re: Mathematics Challenges, #1

How about how I used the probability command with a conditional in the latter?

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## #11 2016-07-17 00:46:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Mathematics Challenges, #1

I already knew about that, figured it out about an hour ago. It neatly handles the permutation aspect.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #12 2016-07-17 02:38:37

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Mathematics Challenges, #1

bobbym wrote:

I think √  and x²  are  copied from top of this page and not LaTex.

That is precisely the point.

True but I was too lazy to put LATEX on the top. I will now.

Penguins are hard workers so they can not claim they are lazy. So what is it for 3? With replacement or not?

I meant to say without. Penguins are busy animals, surely.

The integral of hope is reality.

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## #13 2016-07-17 03:15:36

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Mathematics Challenges, #1

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #14 2016-07-17 03:49:44

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Mathematics Challenges, #1

The integral of hope is reality.

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## #15 2016-07-17 03:50:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Mathematics Challenges, #1

Hi;

I do not agree.

Why assume x > y? The problem does not state that. And why combinations? x and y are two different variables, so order should count. I think that EVW has the correct two answers for the problem as stated.

Please Mathegocart be more specific which answer, he has 3 different answers, is the one you think is correct.

Where did that little guy go?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #16 2016-07-17 04:38:41

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Mathematics Challenges, #1

Mathegocart wrote:

I am at a loss to know which of my answers is correct.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #17 2016-07-17 12:36:19

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

### Re: Mathematics Challenges, #1

bobbym wrote:

Hi;

I do not agree.

Why assume x > y? The problem does not state that. And why combinations? x and y are two different variables, so order should count. I think that EVW has the correct two answers for the problem as stated.

Please Mathegocart be more specific which answer, he has 3 different answers, is the one you think is correct.

Where did that little guy go?

That was quite late at night for me, I believe now that EVW's answers are right.

The integral of hope is reality.

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## #18 2016-07-17 13:09:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Mathematics Challenges, #1

My young friend please listen to me. When you pose a mathematics question you must be very careful and very thorough. As a matter of fact, the question needs to be just as precise as the answer. I know you are still in the early stages of your training and that you will get better as you go along.

EVW's answers are also not adequate. This is not her fault. The question as written is very ambiguous. One thing you must always state in the problem whenever you are drawing from a list of numbers, a bunch of urns with balls in them, a deck of cards... is whether or not it is with replacement or not. Please see EVW's post for an explanation of those terms. If you need more please ask.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline