Math / Science

The Math / Science topic primarily includes discussions of mathematics, physics, statistics and economic analysis, but also biology, chemistry and other sciences.

I have difficulties to understand the hierarchical notation of turing machine which is shown in the attached photo. Note that this is not assignment , it is already question and solution in the book but i didn't understand the solution. Please tell me the solution step by step , i didn't understand it.(i must understand it because it can be asked in final exam.) Or if you find and understand similar questions , you can explain it too.
Similar examples and the topic exist in the below links:
downloads .word

Any help is much appreciated.
I had previously had a 50% off for and now I can't locate code.  Anyone know the code for 50% or similar offer?  Lastly, are there other similar sites for brain exercises?
I'm using a mathematical function to convert dates in the past into a number that I can use as a multiplier.  Here's is an explanation:

Date Boosting

Boosting more recent content is a common use case. One way is to use a recip function in conjunction with ms.

There are approximately 3.16e10 milliseconds in a year, so one can scale dates to fractions of a year with the inverse, or 3.16e-11. Thus the function recip(ms(NOW,mydatefield),3.16e-11,1,1) will yield values near 1 for very recent documents, 1/2 for documents a year old, 1/3 for documents two years old, etc.  

I understand the gist of what it's doing, but I'd like to modify it and don't have the math chops to figure it out.  

I'm basically asking how to soften the curve of this formula, as it seem to 1/2 itself every year away from the current date.  I would like the curve to roughly reduce from 1 to 0 over 10 years - e.g., drop 10% every year a date is away from today.  Anyone have any ideas?  Thanks!
Hey guys,

I'm helping my kid with a Science project and to be honest I need a hand here...

The experiment he chose was to test the conductivity of different types of metal wires (we have copper, steel, aluminum, and nickel)

We put an RC battery at one end (7.2 Volt NiCd, 1800 mAh) , grounded the negative of the battery and Volt meter, and then basically stuck different wires into the positive clip of the battery and tested the wire at the other end with the volt meter to measure the Volts DC output.

I had thought since different metals have different conductivity that there would be some difference among the wires, with copper showing the most conductivity.

But - in all cases except for the aluminum wire, the measurements of the output out the wires were exactly the output out the battery directly.

So the copper, steel and nickel wires all had the same conductivity.

That wasn't what I was expecting so I'm a bit stumped.  This doesn't invalidate the experiment I don't think, as long as we can come up with a good explanation for why this is.

Problem is I have no clue. Is it because at such low battery power they are all equally conductive? (except the aluminum).  I need to somehow explain why they all showed no resistance (except aluminum)

Any help/guidance/explanation would be much appreciated.

I wanted to know what the difference is between interest rate vs. APR?  More within a mortgage environment.
I can see that it is
1+q +q to degree of 2+q to degree of 3+...........................q to degree of (n-1)
q +q to degree of 2+q to degree of 3+...........................q to degree of (n-1)
q to degree of 2+q to degree of 3+...........................q to degree of (n-1)
n(q to degree of (n-1))
How to prove that for n > 2  
n to degree of n+1 is larger than (n+1) to degree of n
If you answering from the MATH forum, you can simply explain your solution rather than using code

I am writing a serial number program.

This will sound like a weird request, but I need a function that will return the following values:

values: 7 , 10, 27, 8, 19, 3 , 21, 30

I don't care what the function body does, so long as it returns those values.

The function parameter is a number from 0 to 9.

I am totally stumped. I just can't figure it out.


function Generate_Code( someInt ){

     // Do something here that will return 7 ( the first number in my list )
    .// based upon the parameter passed.


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The reason I need those specific values is because they correspond to a keyphrase.

For MATH FORUM EXPERTS, I need ONE SINGLE algorithm that will return the values I listed above. So somehow, if I pass X to your algorithm, it will return 7. Then next time, I pass A DIFFERENT X , it will return 10, etc. I am interested in X, as it will be part of my serial number.
I purchased a house that came with a pool. The drawback is that tile is covering the outside of the pool which makes it extremely slippery for my family and guests. What a good solution to this challenge? Lastly, what's going to be the best and cheapest alternative to this? Someone mentioned to me that the rubbery mats they use at restaurants works very well, but I need to know the best and cheapest alternative.
Hi Guys,
Im trying to figure out from my intranet traffic and news letter sign ups, the sign up ratio between Cellphone and Desktop in Excel.

I need a formula that calculates for every X cellphone visits I get 1 newsletter signup and for every X desktop visits I get 1 newsletter signup.

I would have something like this "Every 10 cellphones visits = 1 newsletter signup" and "Every 5 Desktop = 1 newsletter signup"

Do I simply divide cellphones and desktop signups  by intranetvisits ?


Newsletter Signups,

                   Week1            Week2            Week3            Week4
CellPhones      110                       90                    113                     134      
Desktops              234                      300            310                     320
Total SignUp      344                      390            423                     454

IntranetVisits 2040            2400            2521            2701
I wanted to know if there's a website that will pin point my current location?  Basically, where I'm presently connecting from to get out to the internet.
given an equilateral triangle where all three sides are 100mm, how does one calculate from any point to the center of the triangle?
Question explained graphically

I have been trying to work out how to calculate the following question.

You calculate that you need to achieve a climb gradient of 440 ft/ nm in order to clear a small hill. What is this expressed as a 'rate of climb' if your groundspeed is 90 knots?

The answer is 660ft/min.

The previous question that I worked out by doing height = distance x angle / 60.
Which asked approximately what height would you be on a three degree glideslope 3nm from the aerodrome. I converted 3nm to 18228 feet x 3 / 60 to give 911 feet. Which was ok.

I am not sure if this is using the 1 in 60 logic?

I am trying to work out how to get to the 660ft/min.

Thanks for the help.



We're doing some unusual split-testing of ads in AdWords.  We manage campaigns for many different local businesses, within a specialty healthcare niche.  For a lot of keywords, we use identical ad copy across the different businesses - which isn't an issue, since the businesses are local, and the areas where their ads show don't overlap. \

Within each ad group, a small group of keywords triggers one of two competing ads.  The ads are rotated evenly, so each ad is shown 50% of the time.

Because the ads are so specific, and the local targeted areas are so small, it takes a VERY long time to accumulate enough impressions/clicks to determine which of the two ads has a statically higher click through rate in a given area.  But across, many different accounts, running essentially the same ads - we should be able to accumulate enough data to declare one of the ads more effective at generating clicks.

I admittedly forgot everything I learned in grad school about stats, but I'm thinking we have 1 variable in question (click thru rate of the individual ad) and multiple groups.  Across 20 accounts, 20 groups that saw Ad#1 and 20 groups that saw Ad#2 - and the size of the groups are dramatically different.

What type of test should I use to make this declaration, and what would it look like?  Any software I can plug this into?
hello there,
I am trying to calculate how many combinations can be made with 25 chars
using "abcdefghijklmnopqrstuvwxy0123456789"

each password is 25 characters total:

how many millions or billions unique combinations can be made?
Maltesers are small chocolate balls filled with honeycomb (Wikipedia for anyone not in the UK who may not know them by the same name)

If I was to get a bathtub full of them, about how many packets or boxes of them would I need?!

H2G2 has a count of how many Maltesers are in a bag or box, but I've no idea how many boxes would fill a bath.
I'm trying to reverse engineer the following payment options. These options come from a point of sale system and i do not have access to the calculation code.

(Principle is $1000, interest rate is 17% a year, calculated and added to the account monthly. Payments are due at the end of each period)

# Mnths	# Pmts	$ PMT	Interest
1	2	$500.00 $0.00 
2	4	$251.77 $7.03 
3	6	$169.02 $14.09 
4	8	$127.66 $21.18 
5	10	$102.84 $28.31 
6	13	$79.87  $38.25 
7	15	$69.65  $44.62 
8	17	$61.84 	$51.20 
9	19	$55.69 	$57.95 
10	21	$50.71 	$64.81 
11	23	$46.61 	$71.78 
12	26	$41.62 	$82.02 

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I think the part i am struggling with is that there is no interest charged when one month is selected (and this may carry through the other options).

With the choices of months 2-12, the total interest charged (as shown above) is less than if you calculate it from: Total interest = #pmts * $pmt - $1000.

Essentially, I am looking for assistance in determining how these amounts are calculated.

Using the PMT function in excel, I can calculate the following:

Pmt	Int
504.91   $9.82 
254.10	$16.40 
170.50	$23.01 
128.71	$29.65 
103.63	$36.31 
80.49	$46.37 
70.21	$53.10 
62.35	$59.87 
56.14	$66.66 
51.12	$73.49 
46.97	$80.34 
41.95	$90.67 

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But these values are different from the original schedule.
I have two tables of temperature destribution;

And I want to know if these two distributions are significally different;

Therefore I want to apply the Kolmogorov-Smirnov Test for two distributions,

can anyone adapt the test for my needs?


see my attached code
Finding the x intercepts for a tan graph like 3tan(2x)  ?
I have a list of values that are grouped into 5 dollar ranges.  I was wondering if I change it to 10 dollar ranges is there a way to statistically measure which is better or shows the data better.

Suppose I have a table of soccer player salaries (in terms of high/medium/low):

High: 99
Medium: 165
Low: 157

I also have a table of soccer player goals scored (again in terms of high/medium/low):

High: 167
Medium: 112
Low: 142

And suppose I have a third table showing a breakdown of soccer player salaries and goals:

                              Low             Medium        High
          Low              70                   52               20
Goals Medium       43                   47               22
          High             44                   66               57

Now suppose I want to calculate the probability that if I pick a soccer player at random, what is the chance that I will pick one with a high salary who scores a lot of goals?

It would seem there are two ways of calculating this - one from the separate goals and salaries tables - find the chance of picking one with a high salary, and combine it what the probability of picking one who scores a lot of goals, or look at the combined table and calculate the probability from that table.

The trouble is, each method gives a different answer.

Is there a way of finding what the correct answer is?

I am confused about finding more than 1  x intercepts from a sin graph.
Take 2cos (2x-1)=0 for x intecept

cos2x=.5=60 deg
x=30deg is 1 intercept but what about 3 others ?
I came across the following:

"If the distance estimated at 150 feet is really 140 ft, the percent of error in this estimate is 7 1/7%."

Can you tell me how this answer was expressed as a fraction? I get 7.1428%. How is the .1428 converted to 1/7?

Please demonstrate how you computed it. Thanks.
I'm not sure if this is the appropriate site to pose this, and if not I'm open to suggestions of sites where I might more appropriately directed it (if that is not against the EE terms-of-use).

The problem below I thought at first this would be a fairly simple, but it turns out to be a lot more complicated than I first anticipated.  I was good at maths at school, but that was 20 years ago and after attempting this I've realized it is beyond my scope..

I have 3 known inputs, LongStdDev, ShortStdev and MarketStdev.  And I have two targeted inputs, PortfolioBeta and PortfolioStdev.

I only have two variables, LongWeight and ShortWeight.

PortfolioBeta = LongWeight - ShortWeight
PortfolioStdev = Sqrt((LongWeight*LongStdev)^2 + (ShortWeight*ShortStdev)^2 + (abs(LongWeight-ShortWeight)*MarketStdev)^2)

From these two formulas and five inputs is it possible to calculate the LongWeight (and by Inference the ShortWeight)?  Trying to use what I remember from high school maths I hit a wall when I try to substitute {PortfolioBeta-LongWeight} for {ShortWeight} and then square it.
I'm trying to understand statistics here:
I read that the difference between the Population Standard Deviation and Sample is
The StDevP function evaluates a population, and the StDev function evaluates a population sample.

If your sample size is N.

StDev will divide by N
and StDevP will divide by N-1

1.  This does not make sense.  How does subtracting one item turn a data set from a whole population into a sample?
2.  Which do I use when I'm evaluating my company's sales numbers.  the "P" or "S"?
I guess population because I'm including the entire group of sales people in my firm?