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
Inequalities-standard-results.pdf

How to find molecular weight of bilirubin by knowing the concentration in miligrams per deciliter and micromoles per litre

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),  

Q1:
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

Q2:
if they mix well, do we then get an average of Octane 96?

Q3:
Any degradation / adverse effects of mixing the 2 petrols?

i need an answer to this equation z^3+4|z|=0
thanks!

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.

Overview:

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

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:                                                                 **
'**  KAISER,H.F. (1972) "THE JK METHOD: A PROCEDURE FOR FINDING THE       **
'**  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#
               …

Can you please explain this question?

ANSWER=E
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

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!

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 …

How can I solve these kind of problems in my brain without using pencil and calculator?

2.3*10^7*5.2*10^-5/4.3*10^2

What is the best and easiest approach, method, software to solve a system like the one below?

1=1*(3.14*2^p-1*1*[(23.14-5)*2^q-1*1*(3.14-3)/2^k]/2^r)/2^s
3=8*(3.14*2^p-8*8*[(23.14-5)*2^q-8*8*(3.14-3)/2^k]/2^r)/2^s
50=128*(3.14*2^p-128*128*[(23.14-5)*2^q-128*128*(3.14-3)/2^k]/2^r)/2^s
2896=8192*(3.14*2^p-8192*8192*[(23.14-5)*2^q-8192*8192*(3.14-3)/2^k]/2^r)/2^s
4096=16384*(3.14*2^p-16384*16384*[(23.14-5)*2^q-16384*16384*(3.14-3)/2^k]/2^r)/2^s

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.
S5(x)=x*(PI*2^p-x*x*[(2PI-5)*2^q-x*x*(PI-3)/2^k]/2^r)/2^s
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