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#1 2016-08-28 09:33:06

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

Quickies #10, Mathematics.

1.How many unique sets of 4 prime numbers exist for which the sum of the members of the set is 45 ?

2. Bobbym wrote on a gigantic piece  of paper all the numbers from 1 to 9999 . How many zero digits did he have to write down?

3. Find
696bdade5a2938d77cd9350d7d440deee46e8388.png.

4. Find x.
637e19dfc34ac7f15b7c45111fbf58d9981b242b.png

5. Which is greater?

[edited by admin](he latexed my post, gratitude to BOBBYM.

6. Find the sum of all perfect squares that divide 2016.

7. Find the greatest possible value of pq + r, where p, q, and r are (not necessarily distinct) prime numbers
satisfying pq + qr + rp = 2016.

8. Positive integers m and n are both greater than 50, have a least common multiple equal to 480, and have a
greatest common divisor equal to 12. Find m + n.

9. Bobbym is stuck fighting his nefarious lizard neighbors yet again though he has another weapon in his math... A LASER! He has 15 health, and the lizard has 20 health. He can deal any integer amount of damage from 1 to 4 and he has a 1/5 chance of dealing 3 damage, a 1/2 chance of dealing 1 damage, and a 1/5 chance of dealing  2 damage, and a 1/10 chance of deleaing 4 damage. Calculate the probability that bobbym will make it out alive, given that bobbym strikes first. The lizards have a 50% chance of dealing 1 damage, and a 50% chance of dealing 2 damage.
10. Find all continuous functions such that 904cf01fc90d3288a1d01c897e21ca7ff5f4a9ab.png
and 4f26f243ab1456c1cf741e39b0487dde5e46d60b.png

Last edited by Mathegocart (2016-08-30 04:45:39)


The integral of hope is reality.

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#2 2016-08-28 09:36:57

zetafunc
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Registered: 2014-05-21
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Re: Quickies #10, Mathematics.

I think you're missing some information in #5.

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#3 2016-08-28 10:22:10

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

Re: Quickies #10, Mathematics.

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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#4 2016-08-28 11:13:42

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

Re: Quickies #10, Mathematics.

Fixed.(5)


The integral of hope is reality.

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#5 2016-08-28 11:14:58

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

Re: Quickies #10, Mathematics.

Are you sure?


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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#6 2016-08-28 11:18:34

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

Re: Quickies #10, Mathematics.

bobbym wrote:

Hi;

Everything is correct, and I have fixed problem number 5.(VERIFIED.)

Last edited by Mathegocart (2016-08-28 11:18:46)


The integral of hope is reality.

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#7 2016-08-28 11:19:29

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

Re: Quickies #10, Mathematics.

Number 5 is rather easy, are you sure that is what you want? I need more for 9.


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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#8 2016-08-28 11:21:25

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

Re: Quickies #10, Mathematics.

I meant gif.latex?10%5E%7B30%7D.


The integral of hope is reality.

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#9 2016-08-28 11:22:44

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

Re: Quickies #10, Mathematics.

Number 9 requires more information. What happens at the endpoints and what kind of damage does the large lizard do?


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 2016-08-28 11:37:00

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

Re: Quickies #10, Mathematics.

bobbym wrote:

Number 9 requires more information. What happens at the endpoints and what kind of damage does the large lizard do?

Didn
't I already specify what kind of damage he does? And how much damage you deal?


The integral of hope is reality.

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#11 2016-08-28 11:41:35

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

Re: Quickies #10, Mathematics.

Sorry, yes you did.


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 2016-08-28 12:36:15

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

Re: Quickies #10, Mathematics.

bobbym wrote:

Sorry, yes you did.

I just wanted to verify.


The integral of hope is reality.

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#13 2016-08-28 16:54:42

thickhead
Member
Registered: 2016-04-16
Posts: 1,085

Re: Quickies #10, Mathematics.


Last edited by thickhead (2016-08-28 19:54:32)


{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 2016-08-28 18:51:20

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

Re: Quickies #10, Mathematics.

Hi Mathegocart;


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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#15 2016-08-28 19:56:49

thickhead
Member
Registered: 2016-04-16
Posts: 1,085

Re: Quickies #10, Mathematics.


{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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#16 2016-08-28 23:58:34

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

Re: Quickies #10, Mathematics.

bobbym wrote:

Hi Mathegocart;

The battle is, indeed, described in this manner.


The integral of hope is reality.

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#17 2016-08-29 04:25:48

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

Re: Quickies #10, Mathematics.

thickhead wrote:

Wait, what? One of his acquaintances is named Liz?


The integral of hope is reality.

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#18 2016-08-29 06:33:22

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

Re: Quickies #10, Mathematics.

Not that I know of.


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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#19 2016-08-29 16:47:47

thickhead
Member
Registered: 2016-04-16
Posts: 1,085

Re: Quickies #10, Mathematics.

(2)
No.of 0's in unit place=9999 div 10=999
No. of 0's in tens place=10*(9999 div 100)=990
No. of 0s in hundred place=100*(9999 div 1000)=900    Total=2889
No of any other digit=( 9999 div 10+1)+10*(9999 div 100+1)+100*(9999 div 1000+1)+1000*(9999 div 10000+1)=4000


{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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#20 2016-08-29 23:42:18

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

Re: Quickies #10, Mathematics.

thickhead wrote:

(2)
No.of 0's in unit place=9999 div 10=999
No. of 0's in tens place=10*(9999 div 100)=990
No. of 0s in hundred place=100*(9999 div 1000)=900    Total=2889
No of any other digit=( 9999 div 10+1)+10*(9999 div 100+1)+100*(9999 div 1000+1)+1000*(9999 div 10000+1)=4000

Strange, because with casework, I have gotten the same solution as bobbym has. I will check if I made a naive mistake, but..


The integral of hope is reality.

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#21 2016-08-30 00:26:19

thickhead
Member
Registered: 2016-04-16
Posts: 1,085

Re: Quickies #10, Mathematics.

My solution is same as bobbym's. Only i have added result for any  digit other than 0.


{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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