Math / Science

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

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Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of a car A exceeds the velocity of car B. Does that mean that the acceleration of A is greater than that of B at that instant? Explain.
Dear experts,
I am preparing for GRE /GMAT
I have come across a few standard results in Inequalities.

Can anyone share problems related to these standard results.

I am not with a Math background and I could not find anything relevant from google search.

Kindly help.

Thank you
It is for a science project we just don't have any weighing scales to test it ourselves
How to find molecular weight of bilirubin by knowing the concentration in miligrams per deciliter and micromoles per litre
Dear experts,

I am aware that the following are different types of triangles
Based on angles
1 Right angle triangle
2 Obtuse
3 Acute

Side length
4 Equilateral
5 Isosceles
6 Scalene

I am aware that a secondary figure can be formed by joining the mid points of the sides of each of the above triangle.

Can someone please point to an article/book which discuss the figures/properties of the above features in the triangle.

Kindly help.

Thank you
Btw petrol = gasoline (UK / US terms).

Occasionally I drive past petrol kiosks (that have offer) for
Octane 100 & I thought of topping them to the max (as my
wife doesn't want me to keep petrol at home & there's a
legal requirement to register for using container to buy
them as petrol could be used for malicious purpose).

So if my petrol is half tank & I fill up a nearby kiosks with
Octane 92 petrol (the kiosks also have Octane 95 & 98),  

Does the 2 grades of petrol mix well or they form 2 separate
layers in my car's petrol tank?  If they don't mix, which one
will float to the top

if they mix well, do we then get an average of Octane 96?

Any degradation / adverse effects of mixing the 2 petrols?
Suppose I have a sequence of N numbers a1,a2,
a1 is repeated b1 times
a2 is repeated b2 times.

I want to split the total sequence of N numbers into 2 separate sequences of N/2 numbers where the order does not matter.
The user does not care if they an a1 or an a2 ...or an an.

For example suppose the sequence is   111122223333 which has 12 characters.
I can split it into several sequences of 6 characters  for example


What is the formula for determining how many combinations there are of 6 characters?
i need an answer to this equation z^3+4|z|=0
up vote
down vote
We are trying to calculate a mathematical formula can someone help me out please. Scenario we have 10 wholesale dealers in a state. we sell products to dealers and they sell it to customers we are trying to get (%a particular product bought by dealer + % a particular product sold to customer) * 1.1 but we are not getting the current sales

eg sold to dealer 1000 boxes are sold for a particular product one dealer bought 200 so percentage of that dealer for that product is 200/1000 eg: sold to customer by dealer total boxes sold to customer by all 10 dealers is 800 a particular dealer sold is 150 so total percent sold by that dealer is 150/800.

now we have a product our total allocation is 200 for all 10 dealers. how can we distribute 200 boxes between all 10 dealers.

can someone help me how to do it please.
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How much more will the cost be for a wager on V5 compared to V4 when adjusting for difference in probability, price per unit and track's deduction?:

For V5 (a type of wagering on harness racing where you should pick the winner in 5 races), the probability to pick the winners in the five races is 12 times more difficult compared to for V4 (1/248832 divided with 1/20736; (12x12x12x12x12)/(12x12x12x12)), which means you need to spend 12 times more units on V5 to achieve the same probability. However, this should be adjusted first for price per unit, which for V4 is 2 SEK and for V5 is 1 SEK, so the adjustment becomes 12 x 0.5 = 6.

The final adjustment is for the racing track's deduction, which for V4 is 25 % and for V5 is 35 %.

Is this correct?:

6 + (0.1/0.25) = 6.4

Which means in order to compensate for lower probability in V5 compared to V4, and for difference in price per unit (V4: 2 SEK; V5 1 SEK) and difference in track's deduction (V4: 25 %; V5 35 %), I need to spend 6.4 times more units/money on V5 compared to V4 so that I in the end have the same probability to win on my wager on both V4 and V5, provided that the payouts on both the wagers are the same.

Or do I get it wrong? Is it that the payout on V5 needs to be 6.4 times higher than on V4 in order to compensate for the difference in probability, price per unit and track's deduction?
We have 12 players, and we would like to set up a 6 team round-robin tournament for a few different backyard games. We'd like to play as many different backyard games as possible with these 12 players (6 teams of 2 players), while ensuring that no two players get matched up more than once across the different games.

Looking for a grid of as many of these unique matchups (round robins) as mathematically possible.


Players: 1 - 12
Teams of 2
As many combination of 6 teams as mathematically possible while ensuring no two people end up together on a team more than once
I received a solution here at EE for this question:

Which would the probability formulas be for calculating the difficulty in percentage for 6 different types of wagering?

And this was the answer:

Place:      1/4=25 %      
Winner:      1/12=8,3 %      
Twins:      1/66=1,5 %      
DD:            1/144=0,7 %      
Trio:      1/1320      
Top 7:      1/3991680

Among these combinations, there are many that are logically and statistically not possible at all, such as that for the wagering type Tvilling in a race with 12 horses, the horse with the 11th lowest odds and the 12th lowest odds would end as the first two horses in the race. So I wonder if, with help from Excel's matrix layout, it would be possible to create formulas in a matrix for each wagering type, and then mark combinations in this matrix as impossible, and Excel then would calculate a new total probability factor.

For example, the total probability factor now for Twins is 1/66 (1.5 %) to pick which two horses will end on the first two places in the race. Let's say I decide, on the basis of statistics and logics, that it's impossible that the horses with 11th and 12th highest odds can win, so I want to mark this combination as impossible in the matrix, and then Excel should re-calculate a new total probability factor. If this is possible to do for each of the different wagering types, I could easily increase the probability factor for picking a winning combination, for example for Twins I might be able to increase the probability factor from 1/66 (1.5 …
Here is the code

Function EIGEN_JK(ByRef M As Variant) As Variant

'**  Function computes the eigenvalues and eigenvectors for a real        **
'**  symmetric positive definite matrix using the "JK Method".  The       **
'**  first column of the return matrix contains the eigenvalues and       **
'**  the rest of the p+1 columns contain the eigenvectors.                **
'**  See:                                                                 **
'**  EIGENVALUES OF A REAL SYMMETRIC MATRIX", The Computer Journal,       **
'**  VOL.15, 271-273.                                                     **

Dim A() As Variant, Ematrix() As Double
Dim i As Long, j As Long, k As Long, iter As Long, p As Long
Dim den As Double, hold As Double, Sin_ As Double, num As Double
Dim Sin2 As Double, Cos2 As Double, Cos_ As Double, Test As Double
Dim Tan2 As Double, Cot2 As Double, tmp As Double
Const eps As Double = 1E-16
    On Error GoTo EndProc
    A = M
    p = UBound(A, 1)
    ReDim Ematrix(1 To p, 1 To p + 1)
    For iter = 1 To 15
        'Orthogonalize pairs of columns in upper off diag
        For j = 1 To p - 1
            For k = j + 1 To p
                den = 0#
The probability formulas are to be used for wagering on harness racing. There are 6 types of wagerings:

1. Win: You wager on that a certain horse will win the race, and there might be 12 horses in the field.
2. Place. You wager on that a certain horse will end 1st, 2nd or 3rd in the race.
3. Twins: You wager on that two horses in the field will end 1st and 2nd irrespective of the order in the race.
4. Trio: You wager on that three horses will end 1st, 2nd and 3rd in exactly that order in the race.
5, Top 7 Pro: You wager on that 7 horses end 1st, 2nd, 3rd, 4th, 5th, 6th and 7th in exactly that order in the race.
6. DD: You wager on that a certain horse will win race 1 and a certain horse will win race 2.

So type 1-5 are for only one race, whereas type 6 is for 2 races.

Type 1 is not difficult: If there are 12 horses in the race, then each horse has a 1/12th chance to win (8.3 %) if they would have exactly the same capability.

What would the function be for the other five types, assuming there are always 12 horses in the field?

Logically the order of most easy to most difficult would be this:

2. Place
1. Win (difficulty/probability 8.3 %)
3. Twins
6. DD
4. Trio
5. Top 7 Pro

Which formulas could I enter in this online probability calculator for example?:
Can you please explain this question?

1. What value or values of ml are allowable for an orbital with l = 2?
a. 0
b. 2
c. -1
d. none of the above
e. all of the above
Does any one knows a web site where can I practice the nomenclatures?
Imagine you have a dataset of rowers. You have X variables such as weight, benchpress, deadlift, squat, nutrition, etc. You also have each rower's lap time.

Now, let's say for a given rower, you want to optimize her lap time, but you can only train along ONE DIMENSION. How would you identify the best attribute to optimize?

I thought about a grid search, but that seems awful. Which family of machine learning algorithms would be best for this type of problem, and how would you attack it?

Thanks a million!
Can someone help with this?

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Let p = 4x - 7

Is the below equation equivalent to (4x−7)^2 + 16 = 40x - 70 in terms of p ?

p^2​​ −10p+16=0
Hello Experts!

Please bear with me, as I start from the beginning...

The Setup:

(Real details have been removed)

Our customers have the ability to print their artwork/logo on 10x10 sheets of paper. Through the years, we have converted many printed jobs.  So I have a dataset that includes:

  • Product Dimensions
  • Artwork Dimensions

With knowing that information, I can calculate the '% of Ink Coverage' for each printed job.

So for example,... "Our customer printed a 5x5 logo, on a 10x10 sheet of paper. Thier % of Ink Coverage is 50%".

The Problem

The overwhelming majority of our customers, do not know artwork dimensions at the time of quoting. As you can imagine, determining a price can be very difficult.

As of today, in order to still offer a quote to our customer - we quote them: 10x10 sheet of paper with a 2x2 artwork dimension.

The major flaw with this approach,... is the 2x2 artwork dimension we are quoting - really is just a guess. (Maybe not a complete stab in the dark but I know we did not take a close look at historical data to determine this 'temporary' artwork value)

The Goal

While it's near impossible to guess the exact printed dimension our customer will ultimately use, it's our goal to suggest dimensions that will be close to or OVER what the customer will most likely choose at the time of order.

(Before final artwork was received)
10x10 …
If I raise a number to the power of five the last digit of the result is always the same as the last digit of the number with which I started.  For example  7^5 = 16807.  The last digit of both numbers is a five.
Are there any rules regarding when the last 2 digits are repeated?  For example 25 is always repeated.  I don't think 12 is ever repeated.
How can I solve these kind of problems in my brain without using pencil and calculator?

I have the Excel file below with 3 columns.
On one row I have a pair of q, k corresponding to a certain x.
In the sheet are different values for x.
I need to find what pairs of q, k are common for all values of x.
How do you do that fast and easy?
What is the best and easiest approach, method, software to solve a system like the one below?


Could you help to find a set of solutions? I guess are more than one.
This is not homework, but rather one of that engineering approximation problem that ended up in a set of unknown variables.

Basically the function is.
with p, q, k, r, s unknown.
And next known set of solutions with 1 digit approximation allowed for S5x:
x - S5x
1 - 0
2 - 1
4 - 2
8 - 3
16 - 6
32 - 13
64 - 25
128 - 50
256 - 101
512 - 201
1024 - 401
2048 - 799
4096 - 1567
8192 - 2896
16384 - 4096

Math / Science

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