Member: I like Serena

1 Questions
63 Answers

755

+135

Someone should animate this!

I like Serena Mar 31, 2014

+135

reinout-g:
I had an exam yesterday of the class 'introduction to operations research' and one of the questions was the following;

Now I don't know whether there is anyone at this forum with knowledge of the simplex method, but I'm still wondering how this question can be done.

Hey Reinout!

First read off the optimal solution.
If you dive into your papers, you should find x1=x4=x5=0, x2=1, x3=3, Z*=c2+3c3.

Substitute back in the equations.
That should give you the value of b.

Execute the simplex method on the system with b substituted.
Use that you know that the 2nd column and the 3rd column need to be pivoted.
As a result you should get 3 equations with the unknowns c1, c2, c3, and additionally Z*=c2+3c3 that you already had.
Solving the system gives you the remaining unknowns.

Have fun!

I like SerenaApr 6, 2014

+135

reinout-g:
Almost had it

Yep. Got it!

I like SerenaApr 2, 2014

+135

kateeelllyyynn:
99% CI for the population proportion of voters opposing a new tax was calculated to be (.68,.76). What was the sample proportion of voters who oppose the new tax

The CI of a population proportion is

(p - z SE, p + z SE)

where p is the mean sample proportion, SE is its standard error, and z is the critical z-value of the confidence interval.

In other words, the requested sample proportion is the mean of the CI, which is:

p = (.68 +.76) / 2

Additionally, we can estimate the number of voters n.

From the CI we know that z SE = (.76 - .68) / 2 = 0.04.
The critical z-value of a 99% CI is z = 2.575.
So SE = 0.04 / 2.575 = 0.015534.

The SE of a proportion is:

SE = √ (p (1 - p) / n)

Therefore:

n = p (1 - p) / SE ² = .72 (1 - .72) / .015534 ² = 835

I like SerenaMar 29, 2014

+135

Princess Sophie E:
The electrostatic force between two charges Q1 and Q2 at a distance r apart is given by F=(Q1*Q2)/(4Pie*Eo*r^2). What is the unit of E?

Hey Princess Sophie!!!

From your formula we can deduce that:

ε ₀ = (Q ₁ Q ₂) / (4π F r ²)

Since 4π does not have a unit, the unit of ε ₀ must be:

(C C) / (N m ²)

If you want to convert it to SI units, you need that C=A s and N=kg m s ^-2.
Then it comes out as:

(A s A s) / (kg m s ^-2 m ²) = (A ² s ⁴) / (kg m ³)

Cheers!

I like SerenaMar 25, 2014

+135

kat:}:
:| [size=150]a wheelbarrow can carry up to 300 pounds of weight. A bag of soil weighs 20 pounds. write and solve an inequality to represent the number of bags of soil the wheelbarrow can carry.[/size]

Hi kat:}!

Suppose we give this number of bags a name, or rather a symbol.
Let's call it n. That is the first letter of "number of bags", just to make it easy to remember.

Since 1 bag weighs 20 pounds, that means that n bags must weight n x 20 pounds.
This total weight has to be less than the wheelbarrow's capacity of 300 pounds.
We can write that as:

n x 20 <= 300

Let's write a variant of that that between [ math ] tags so that this site's calculator can solve it:

n * 20 = 300

Do you see what the maximum number of bags is that the wheelbarrow can carry?

I like SerenaMar 20, 2014

+135

I agree.

I like SerenaMar 19, 2014

+135

Irreverent Statistic:
What is the probability that "I like Serena" will make a comment on a question that either states the obvious or is trivial and useless.

My preferred mode of operation is to state the obvious, which then leads to ooh and aah - now I understand!
This is usually how mathematics works: once you see it, it is obvious and in retrospect you can't understand why you didn't see it before.
Ah well, often it helps if someone points out the obvious.

I like SerenaMar 11, 2014

+135

I suspect that to the nearest hundredth was intended, which would then be 0.62.

I like SerenaMar 11, 2014

+135