GingerAle

Maybe you were out in the sun too long ....

Why, when I visit this forum, does it often seem like I’m back in junior high school? 

It’s not the junior high students causing this.  

GA

Solution:

The Traveling Salesman Problem (TSP) is not NP-complete. It is not solvable, nor is its solution verifiable in polynomial time. The time complexity for brute force analysis is O(n!).

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For this question, a close approximation for brute force analysis time is \( \dfrac {(11-1)!} { (7-1)!}* (8.5E-3) = 42.85 \text { seconds.} \)

For comparison, if there were (21) cities then the computation time would exceed (910,761) years.  

Here is an animated graphic giving a visual representation for the analysis of a seven-city TSP.

You may be right. I may reconsider my answer.  This question seems to lack clarity and precision.

Suppose you were to pick up the cube, turn it around, then return it to its original position with the same colors permuted. Of the ways to reposition the cube, in how many cases does no color occupy its original position?

I interpret: “return it to its original position with the same colors permuted” to mean any color may be swapped with any other color. If so, then the derangement formula is correct.

However, if it means the colors may only be swapped by rotating the cube then the full set of permutations are not attainable, only the permutations relative to it orientation in space.  The portion of derangements will be reduced but they probably will not be a(n) (integer) factor of (e).

GA

Solution for #2:

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Solve this using the derangement formula:

\(!n = \left [\dfrac{n!}{e} \right] \qquad | \qquad \text { where [ ] is the nearest integer, and (e) is Euler’s Number ~(2.71828...).} \\\)

Solution:

This is an elementary physics question. Use the formula below, relating the physical constants of the material property to the variable properties of a circuit conductor (wire).

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\( \Large G=\sigma \frac {A}{l} \qquad|\qquad \small \text{Where G = conductance, σ =conductivity, A = cross-sectional area, and l = length of the conductor. }\\ \)

\(\text {Rearrange to solve for (l).} \\ \)

Note: In your post, you list the conductivity of the copper (wire) as 5.80E8. This value is more than nine (9) times higher than pure silver (wire) and almost 10 times higher than pure copper (wire).  

GA

Solution:

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Select the five (5) cordless phones, then select five (5) of the ten (10) non-cordless phones.

\(\text {There are $\binom{5}{5}$ ways to choose 5 phones from a set of 5 (cordless phones). }\)

\(\text {There are $\binom{10}{5}$ ways to choose 5 phones from a set of 10 (non-cordless phones). }\)

\(\text {There are $\binom{15}{10}$ ways to choose 10 phones from a set of 15.} \)

\( \dfrac {\binom{5}{5} * \binom{10}{5}}  {\binom{15}{10}} =  \dfrac {12}{143} \approx 8.392\% \leftarrow \text{Probability that all the cordless phones are among the first ten to be serviced. }\)

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I sent my Smartphone to an authorized service center. It worked after they returned it, but it looked like it had traveled through the digestive tracks of several large animals. The phone wasn’t as smart as it was before I sent it. I figured it was because it was now full of Sh....

GA

edit: display correction. 

You are right Dragan! Good work!

I corrected my ^_fuckup. 

GA

The two solutions presented above are wrong.

Apologies:  I’m so use to seeing wrong answers, and the large drop in the x value (weight) are common for these types of questions;

I failed to check and verify my own work. 

These types of questions require careful reading to understand what it is asking for. 

 Such questions are common in science and statistics, both in academics and in the real-world.  

Has anyone else here found that the calculator is ironically limited, counting the fact that it is supposed to handle up to 60 digits?

Why ...Yes I have noticed that the calculator is ironically limited!

Just last week, I attempted to calculate the subtended angle of the diameter of a proton at a distance of 13.87786452158657931656064895234587541208515998456324875125489781395482315786541289653245874512458966521447802501478488219650257012045 light-years,

...and this bloody calculator just couldn’t do it with any precise accuracy! What a POS! I may as well use a slide rule. I’m ironically limited in slide rule usage –this amazingly accurate tool is decades before my time, but I have a 350 page book that explains how to use it. So, I best get to reading if I want an accurate answer.

GA