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#1 2016-05-29 13:43:39

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Help with HW concerning Algebraic Manipulation and probability

Hi people
So I have some math HW problems that I have not been able to solve...
1)Labor Day is the first monday in September. In a year where July 4th falls on a Sunday, what day is Labor Day?
Me: I have no idea what do to do here except that I think moduluses might help( mod 365??)
2) A book's pages are numbered with integers 1 through n. When the book is open to the exact middle, the sum of the two page numbers showing is 297. If every page is numbered and no pages are missing, what is n?
Me:
So I decided to do this
x = middle page #1
x + 1 = middle page #2
x + x + 1 =297
2x =296
x = 148
middle page #2 = 149
so
I just got a not-so-brilliant observation that for a 4 paged book, the middle pages are 2 and 3, and twice 2 = 4(number of pages in the book), so I did 149*2 = 298 which I am very suspicious of. Can someone verify my answer?
3) if gif.latex?%5Cfrac%7B%5Cfrac%7B1%7D%7Bx%7D+%5Cfrac%7B1%7D%7By%7D%7D%7B%5Cfrac%7B1%7D%7Bx%7D-%5Cfrac%7B1%7D%7By%7D%7D = 2009, what is the value of gif.latex?%5Cfrac%7Bx+y%7D%7Bx-y%7D
The closest I got to solving this was gif.latex?%5Cfrac%7B2009xy%7D%7By-x%7D%20%3D%20%5Cfrac%7By+x%7D%7Bxy%7D
. Can someone give me a pointer?
4)In Smalltown, with the exception of two people, each citizen's two letter combination is different from any other citizen's combination(i.e, MK would be different from KM) What is the greatest number of people Smalltown could have.
Me: I pretended that the two exception citizens had XZ and XZ as codes, so I used a permutation 2 from 24(as I already used the 2), was 552. 552 + 2(exceptions) + 1 peson who had ZX is 555 citizens. Am I right?

Thank you,

Last edited by Mathegocart (2016-05-29 13:48:50)


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#2 2016-05-29 16:13:13

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

Re: Help with HW concerning Algebraic Manipulation and probability





{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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#3 2016-05-29 17:22:08

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

Re: Help with HW concerning Algebraic Manipulation and probability

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 2016-05-29 19:02:42

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

Re: Help with HW concerning Algebraic Manipulation and probability

Till now I had thought May 1 is international labors day.


{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 2016-05-29 20:33:50

zetafunc
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Re: Help with HW concerning Algebraic Manipulation and probability

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#6 2016-05-30 01:00:28

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

thickhead wrote:

Till now I had thought May 1 is international labors day.

Apparently in the US we say that Labor Day is the first Mon in September. Alas, our great systems.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#7 2016-05-30 01:03:15

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

EDIT: I have a new problem on my 80 prob homework
If two numbers are chosen from the set (1,2,3,4,5), what is the probability that the sum is greater than the product?(1,2) is different from (2,1)


The pairs that satisfy the condition are
(1,2) (2,1) (1,3) (3,1) (1,4) (4,1) (5,1) (1,5) aka 8 combinations.
There are 20 combos possible, since repetition is not allowed.

so 8/20 = 4/10 = 2/5.
Yes?
2) Three people, each working at the same rate, finish 1 job in 20 hours. At this rate how long will it take 5 people to finish 3 JOBS?
I said 60 hrs.

Last edited by Mathegocart (2016-05-30 01:11:34)


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#8 2016-05-30 01:15:51

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

3)What is the smallest number that has 10 factors - this would be 10! right?


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#9 2016-05-30 01:31:40

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: Help with HW concerning Algebraic Manipulation and probability

mathgogocart wrote:

3)What is the smallest number that has 10 factors - this would be 10! right?

Not quite. In fact, 10! has many more factors than that. Here's a relevant exercise (which you need not attempt, but the result is important) from my Analytic Number Theory problems thread:

zetafunc wrote:

#6

(Here, d(n) denotes the number of divisors of n.)

So if
is some factorisation of n into its prime factors, then you want to solve
or equivalently,
. But
, and thus

ignoring the cases where either of them are 0. Now we simply choose the smallest distinct primes available, namely
, so that

Note that we chose
to minimise the value of n. We could just have easily taken
, but then we'd have to adjust
accordingly. (It just made more sense to have the primes
listed in ascending order.)

Last edited by zetafunc (2016-05-30 01:40:09)

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#10 2016-05-30 02:02:00

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

zetafunc wrote:
mathgogocart wrote:

3)What is the smallest number that has 10 factors - this would be 10! right?

Not quite. In fact, 10! has many more factors than that. Here's a relevant exercise (which you need not attempt, but the result is important) from my Analytic Number Theory problems thread:

zetafunc wrote:

#6

(Here, d(n) denotes the number of divisors of n.)

So if
is some factorisation of n into its prime factors, then you want to solve
or equivalently,
. But
, and thus

ignoring the cases where either of them are 0. Now we simply choose the smallest distinct primes available, namely
, so that

Note that we chose
to minimise the value of n. We could just have easily taken
, but then we'd have to adjust
accordingly. (It just made more sense to have the primes
listed in ascending order.)

Indeed, you are right. I had not noticed(idiot me!) that there would be LOTS more factors. Kinda surprising considering this problem looked so easy.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#11 2016-05-30 06:13:25

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

Re: Help with HW concerning Algebraic Manipulation and probability

If two numbers are chosen from the set (1,2,3,4,5), what is the probability that the sum is greater than the product?(1,2) is different from (2,1)

2 / 5 is what I am getting also.


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 2016-05-31 04:17:45

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

Re: Help with HW concerning Algebraic Manipulation and probability

2) Three people, each working at the same rate, finish 1 job in 20 hours. At this rate how long will it take 5 people to finish 3 JOBS?
I said 60 hrs.

Please check your work, that answer is not correct.


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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#13 2016-06-01 09:34:19

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

3 people 1 job 20 hrs,
so 1 person can do 1/3 of a job in 20/3 hours,
or 5 people can do 5/3 jobs in 100/3 hours,
so 1 person can do 5 jobs in 200/3 hours.
so 5 people can do 5 jobs in 40/3 hours,
so 5 people can do 3 jobs in 8 hours.
Yes?


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#14 2016-06-01 09:42:21

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

Re: Help with HW concerning Algebraic Manipulation and probability

Hi;

This is how I do it, hope this is okay...

2) Three people, each working at the same rate, finish 1 job in 20 hours. At this rate how long will it take 5 people to finish 3 JOBS?

So 3 people can do 1/20 of the job per hour.

Therefore 1 person can do (1/20)/3 = 1/60 of the job per hour.

The work rate of 5 people is 5(1/60) = (1/12) of a job per hour.

It takes 36 hours.


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 2016-06-01 12:36:33

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

bobbym wrote:

Hi;

This is how I do it, hope this is okay...

2) Three people, each working at the same rate, finish 1 job in 20 hours. At this rate how long will it take 5 people to finish 3 JOBS?

So 3 people can do 1/20 of the job per hour.

Therefore 1 person can do (1/20)/3 = 1/60 of the job per hour.

The work rate of 5 people is 5(1/60) = (1/12) of a job per hour.

It takes 36 hours.

bobbym I feel like a idiot now! Thanks.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#16 2016-06-01 12:45:29

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

Re: Help with HW concerning Algebraic Manipulation and probability

Was the answer right?


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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#17 2016-06-02 15:33:28

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Help with HW concerning Algebraic Manipulation and probability

EDIT:
My teacher has also told me to find the date
for number 1),



I also have a new problem my teacher says is going to be on the test
6)What percent of the palindromes between 100 and 500 contain at least one 5.
I said 11%, but I have doubts as I did this when I was sleepy. Can someone verify?


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#18 2016-06-02 16:39:21

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

Re: Help with HW concerning Algebraic Manipulation and probability

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.

Offline

#19 2016-06-02 18:19:22

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

Re: Help with HW concerning Algebraic Manipulation and probability

mathgogocart wrote:

EDIT:
My teacher has also told me to find the date
for number 1),



I also have a new problem my teacher says is going to be on the test
6)What percent of the palindromes between 100 and 500 contain at least one 5.
I said 11%, but I have doubts as I did this when I was sleepy. Can someone verify?

This is too simple .There would be some need to think if it included the domain 500 to 600 also.


{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 2016-06-02 21:05:40

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

Re: Help with HW concerning Algebraic Manipulation and probability

Last edited by thickhead (2016-06-02 21:06:32)


{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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