Math / Science

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The Hydrogen-based MEAD Engine is my proposal for a cheap, clean source of electricity for the future of humanity to run on. It incorporates Hydrogen Fuel Cell Batteries and two of my own inventions; an Orbital Universal Gear Mechanism and Multi-Directional Universal Gyroscopes.

Say you're shopping for some ingredients which come in standard pack sizes of either 100g, 250g or 500g, having prices $0.40, $0.75 and $1.00 respectively.

Depending on the exact quantity you need, you can choose to optimise your choice of pack purchases according to price or minimum wastage, or perhaps some combination of the two.

For example if you need 350g, you could buy 1 x 500g pack for $1.00, and waste 150g, or buy 1 x 250g + 1x100g at a cost of $1.15 and have no wastage.

Given the quantity you need, how could you optimise your pack selection mathematically? (a) for minimum cost, and (b) for minimum wastage?

ie some function(quantity needed) gives the pack sizes and quantities to buy, eg:
f_mincost(350) outputs 1 x 500g
f_minwaste(350) outputs 1 x 250g, 1 x 100g

Here is a spreadsheet with some more examples:

Many thanks
A fair coin is tossed 200 times. Find the probability of getting a head an odd number of times
Sol: the number of cases favourable to E is 200C1 + 200C3 +200C5 +200C7 +200C9…. +200C199  = (2200/2)

Dear experts,

Can someone throw more light on the above binomial equation for counting odd number of items which results 2n-1.
Similar will the result change if were to add the even number of times.
What about for adding for all cases where r=prime number and less than ≤n

Kindly help.
Write a function called my_gcd() that takes parameters a and b and returns their greatest common divisor. Create your own implementation of the algorithm and test your code by comparing the output of your function to Python's gcd() function from math package.Test the code with the following inputs: (39, 91), (20, 30) and (40,40). Explain the logic of your function.
I have here what I think is a classical O.R. (operations research) problem. I'm looking to formulate it mathematically and look at the options available to solve it.

We have a list of say 100 recipes.

These recipes combined use 400 ingredients.

The quantity of ingredients required for all the recipes could be defined by a matrix dimension 100 x 400.

We can combine recipes into meal plans, so that the ingredients required for a meal plan is the total of the ingredients required for each recipe in the meal plan.

Each ingredient has an associated cost, that varies depending on the quantity bought.

Say the cost variations can be expressed with no more than 5 cost buckets per ingredient. Eg.

Bucket, Cost / kg
< 1kg, £4.00
1-5kg, £3.50
5-20kg, £3.00
20-100kg, £2.80
> 100kg, £2.50

The ingredient costs can be expressed in two matrices each of dimension 400 x 5:
a) One matrix 400 x 5 giving the buckets for each ingredient
b) Another matrix 400 x 5 giving the unit costs per ingredient and bucket number (1 to 5)

A given meal plan will have a given ingredient requirement, with associated total cost determined via the above matrices.

Suppose we constrain the number of meals in the meal plan to say 4 meals, and these 4 meals must be different recipes. For simplicity (!) we have no other constraints for now.

Our objective is to choose our meal plan (4 meals) such that the total cost is minimised.

1. How do we formulate this problem?
There are huge amount of different slot machines available online, like in the given list here All of them powered by own random generated algorithm. So I would like to know if there some strategies to play slots? I mean when you are playing for money and you want to make even a little profit and it would be great it the strategy does not include loosing money. Researches and publications are appreciated too.
The market research department at a manufacturing plant determines that 20% of the
people who purchase the plant’s product during any month will not purchase it in the
next month. On the other hand, 30% of the people who do not purchase the product
during any month will purchase it the next month. In a population of 1000 people, 100
people purchased the product this month. How many will purchase the product in 2 months?
Hi Experts,

I have tried to round off a value x = 455.77 using math .round() function but not rounded the value 466.

Code I have given to round off:

var rounded = Math.Round(x, 2, MidpointRounding.AwayFromZero);

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Could you guys please explain whats wrong here?

Anjala Baby
Dear Experts,

Actually learning the basic of Machine Learning through the following link:

That contains an url url = "" which have the data of 150 records from the iris dataset, but I would like to test the results on more records.

Could you please advise is there on the internet availabe more iris data for free to download?

Thanks in advance,
What does it mean to be "Always On"?
What does it mean to be "Always On"?

Is your cloud always on? With an Always On cloud you won't have to worry about downtime for maintenance or software application code updates, ensuring that your bottom line isn't affected.

317.2 feets , 297feets , 338feets , 325feets .... Find the total area in acres
Hey, All,

Can you give me some good web links to where it has some very good Data Scientist Resume samples? Also, those samples are one-pagers (everyone desire one page resumes)

What are some emerging trends in Data Science for Financial Institutions?

How is Business Intelligence being applied to the Financial Management Industry? (Please provide any resources, articles, studies, etc)
Subject of the week | Tell us about a technology you'd like to learn.
I'm fascinated by developments in Machine Learning and want to, heh, learn more about it. Not so much because I want to create Machine Learning systems myself—I have very little interest in the math involved—but so I can know how to leverage the sort of things that are being built. I easily envision the future of most work being about managing various bots and knowing how to apply them to higher level problem solving.

To get started on that path, I'm currently teaching myself Python (via several books on the subject) and would then transition into the use of it to dig deeper into the Machine Learning libraries. (And if I have to, even some refresher on the math... I did pass the AP calculus test, but that was 20 years ago!)

Any of you out there with more knowledge in these areas have some advice on this?
The user is asked to input the distance, yards they want to converted to miles. The distance must be input and stored (as a variable) as an integer, not as a double. The output is the distance in miles (also as an integer) together with an explanatory message. There are 1760 yards in one miles
Watching this 6 minute video, I leaned HAARP shoots 72,000 times the maximum amount of energy for an AM station in the United States.

My question is what's a better analogy?

For example, how much energy is that compared to the output of a small nuclear plant?

I am just having a hard time sensing the scope of the comparison they created and hope someone can come up with a better description.


I'm not a student. I am revisiting some basic maths so this is not homework.

I am looking at a question which says

(2x-3)(x^2 + ax -2) = 2x^3 - 13x^2 + 11x + 6. Find the value of a.

I did this by multiplying out the brackets to get 2x^3 + 2ax^2 - 3x^2 - 4x - 3ax +6

From this i can see that 2ax^2 + 3x^2 = -13x2. From this I can see that a = -5.

But this does not match a description in the book. The books says according to factor theorem, if 2x-3 is a factor then when we substitute for x when the value when (2x-3) is 0 (e.g. 3/2) in the original equation the answer is 0. If i substitute x for 3/2 in this equation 2x^3 - 13x^2 + 11x + 6 I do not get 0. Please can you advise my mistake

I also tried the other way where if (x-a) is a factor then substituting for a will give 0 so I tried substituting for 3 but that did not work. I have also noticed in the book that substituting for a only seems to  work with a coefficient of x is 1 in the factor (e.g. x-3) but the difference between when you substitute for x rather than a is not explained. As I just said, if the factor is (2x-1) for example you substitute x for the value when (2x-1) is 0 (e.g 1/2) and not for the value of a (1) in the equation and you get 0. As i said the difference between when you substitute for a and for x is not explained. I have just noticed the book substitutes for x when the coefficient is of x in the factor is not 1 in the equation and you get an answer of 0,  and if the …
I believe electrical cable length can be measured by sending a signal down it and timing the reflections from the unterminated end..  


Is there a similar method to measure the length of metal pipes or bars of say 15 mm and up cross section.. I guess in theory it should work. But ruling again this is the lack of insulation, very large cross section. Perhaps a metal bar will not work like a wave guide.  

i am searching for method to sense the lenght of lengths of track.. Just by touching a probe electrically.
1. Write the pseudocode and draw the flowchart for a hotel program to determine the cost a customer has to pay for a stay based on the following pricing policy of the choice of room:
>>>Room for 1 to 2 people: RM85
>>>Room for 3 to 4 people: RM90
>>>Room for 5 to 6 people: RM120
>>>Room for > 6 people, RM125 plus charge for additional people at RM25 per person

If the customer has a membership card, there is a 20% discount. If the customer wants to pay using credit card, there is a 15% discount. A customer cannot receive both discounts. If the customer wants to pay using credit card and has a membership card, the highest discount rate will be given.

Answer these questions before you start solving the problem.
What is the output?
→Cost of customer has to pay for a stay
How many input(s) is/are needed?
What is/are the input(s)?
→number of people, number of days, payment type,
What is the process (equation) to find the output?                                                                                                                    
→cost = number of days * 85
→cost = number of days * 90
→cost = number of days * 120
→additional people = number of people - 6
→cost = number of days * [125 + 25 (additional people)]
→membership card =  cost * 80/100
→credit card = cost * 85/100
How many different calculation(s) is/are needed?
What structure need to be used to select which is the correct calculation to use? Repetition or decision? →decision…
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Not sure about "huge", but at least plausible. Lots of research needed for use by football players, since they won't quite match species evolved for constant usage like that. Veins/capillaries might not have quite the appropriate wall strength for regular stress, and other related issues might arise. Long term effects might approach those of high blood pressure.

It maybe could be much more interesting if we could learn effects at much younger ages. But it's not so easy studying younger than informed consent ages.
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by:Kyle Santos
This article covers the basics of data encryption, what it is, how it works, and why it's important. If you've ever wondered what goes on when you "encrypt" data, you can look here to build a good foundation for your personal learning.
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by:Thomas Zucker-Scharff
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by:Adam Brown
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I'll correct that to say "longer than the universe has existed" instead of as long as. I was working off my memory of the calculations...Not a huge issue, though, since both lengths are stupendously long.
Can anyone help with regression using Stata ?

I've recently been trying to learn more about color codes and complementary colors, particularly when using the color boxes in Microsoft Office apps. I'd appreciate answers to questions and comments regarding accuracy/inaccuracy of the following notes:

• RGB is an initialism representing Red, Green, & Blue
• RGB code uses a scale of 0-255 in order to maintain a 1:1 ratio with hexadecimal values (since 16^2 = 256).
• RGB numerical values have nothing to do with complementary colors.

• HSL is an initialism representing Hue, Saturation, & Luminosity where
• Hue is the color as measured between 0° and 360° on the color wheel (with 0° representing red).
• Saturation is the dullness vs brightness measured between 0% & 100% (with 0% = gray with no color and 100% = full saturation).
• Luminosity is the darkness vs lightness (with 0% = black and 100% = white).

• Different colors are complementary when saturation is kept constant.

Is there a linear relationship between the 0-255 scales used in the MS Office color box for Hue, Saturation, & Luminosity and the scales described above? In other words:
• is one tick on the H scale equivalent to 1.4118° (360°/255 = 1.4118)?
• is one tick on the S & L scales equivalent to 0.3922% (100/255 = 0.3922)?

What method/formula is used to convert between the two systems?

I do not have the information at my fingertips to do these calculations, and am doubtful if I have the math do support such a comparison.

Here's my new favorite site regarding Bitcoin usage and transactions, which may provide some key stats.

I am wondering what the odds are for the fastest ASIC processor of winning the prize of submitting the next blockchain update compared to the odds of some popular Lottery, so I picked Mass Powerball. From what I have learned, each GPU that is "playing the game" is merely submitting a series of picks, like Powerball.

The first GPU to submit the winning numbers, wins.

Once we have the prospects for the fastest ASIC, we can then look for the average hardware that is "playing the game" to find how low those odds become. That would be a follow-on question.

Anyone want to try and make that comparison?
I saw on History Channel that HAARP shoots up 72,000 times the energy as the most powerful AM radio station in the lower 48.

Where does this energy come from?


Math / Science

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