I was reading an  over on Law.SE, and it made me wonder about how the IRS calculates tax on barter transactions.  Lets say that I do a job in January, and get paid for my work with 20 goats and when I received the payment, goats were worth about $100 each.  Later that year, in October, I do another job of about the same value, but this time I get paid with 5 goats.  The goat market has gone absolutely crazy and they are now worth about $400 a head.  In December, the goat bubble officially popped, and they're down to $20 each.  I didn't earn any goats in December, but this market downturn might be important.  So, for the year, my taxable income was 25 goats.  How would I, or more importantly, how would the IRS allow me to calculate taxes on my earnings?  Would I have to prove the market value of the goat when I received payment?  Can I claim that I only earned 25 * $20 since that's what the goats are worth now?  Note:  Assume that this small income is taxable as if I just made $50k/year.  I realize that with such a small earning taxes wouldn't normally be due and I'd be living in poverty with my goats, but that's not a part of my question.
Can someone help me elucidate the definition of "income" from a tax perspective? More specifically, if Joe is paid for his work in avocados instead of dollars, then would Joe be exempt from paying any income tax for the year? Or would the value of avocados earned for the year be translated into dollars which would then be considered Joe's annual income? If so, what guidelines would one use to make this translation? (Make the assumption that Joe does not sell the avocados (for dollars) at a later date and either eats them or trades them for other real property)  What if he was paid in gold instead of avocados?
If no exact time (such as 15:00 or 21:00) is specified about the deadline and only the date itself is given, does that mean that the Deadline date is inclusive or exclusive?  For example, if the deadline for my Research Project is 10th October (no other exact times are specified) does that mean that I can turn it in on 10th October before it turns into 11th October? Or should I submit it on 9th October before it turns into 10th? Completing a 3x3 correlation matrix: two coefficients of the three given I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same? Show that $S + T$ and $aT$ are linear Let  $S:  V \to W$ and $T: V \to W$ be linear transformations. Given $a$ in $\mathbb{R}$, define functions $(S+T): V \to W$ and $(aT): V \to W$ by $(S+T)(v)=S(v) + T(v)$ and $(aT)(v)= aT(v)$ for all $v$ in $V$. Show that $S+T$ and $aT$ are linear transformations. Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? Is it possible to change the Environment of a parent process in Python? In Linux When I invoke python from the shell it replicates its environment, and starts the python process. Therefore if I do something like the following:  import os os.environ["FOO"] = "A_Value"   When the python process returns, FOO, assuming it was undefined originally, will still be undefined. Is there a way for the python process (or any child process) to modify the environment of its parent process?  I know you typically solve this problem using something like  source script_name.sh   But this conflicts with other requirements I have. I'm trying to use the ant migration tool to retrieve all the Custom Metadata records for a single Custom Metadata Type.  However, I can't figure out the syntax.  I would think that something like this would work:    &lt;Package xmlns="http://soap.sforce.com/2006/04/metadata"&gt;     &lt;types&gt;         &lt;members&gt;State_Sales_Tax.*&lt;/members&gt;         &lt;name&gt;CustomMetadata&lt;/name&gt;     &lt;/types&gt;     &lt;types&gt;         &lt;members&gt;State_Sales_Tax__mdt&lt;/members&gt;         &lt;name&gt;CustomObject&lt;/name&gt;     &lt;/types&gt;     &lt;version&gt;36.0&lt;/version&gt; &lt;/Package&gt;   but no dice. I was having trouble playing the game on my android so I downloaded it to my wife's phone (Galaxy S6). I read some posts on how to get it running on my android and it worked but, my level 7 account is on my wife's phone.  How do I get it back to my android? When I sign out and back in it doesn't ask for any sign in info. I've tried deleting the app's data and even uninstalling and re-installing, but it still doesn't ask for sign-in info. Can I get a certificate from a root CA that I can then use to sign my own web server certificates? I would, if possible, use a signed certificate as an intermediate to sign other certs.  I know that I would have to configure my systems in a certain way with "my" intermediate certificate in order to supply information about the chain of trust to my clients.   Is this possible? Are root CAs willing to sign a certificate like this? Is it expensive?  BACKGROUND  I'm familiar with the basics of SSL as it pertains to securing web traffic over HTTP. I also have a basic understanding of the way the chain of trust works, in that web traffic is secured "by default" if you encrypt with a certificate that has a valid chain all the way back to a root CA, as determined by the browser/OS vendor.  I am also aware that many of the root CAs have begun signing certificates for end users (like me) with intermediate certificates. That may require a bit more setup on my end, but otherwise, those certificates will work fine. I guess this has to do with protecting their all-valuable private key for the CA and the disaster that it would be if i were ever compromised.  EXAMPLES        Now, we are definitely not the size of any of those organizations, but they seem to be doing something like this. It would definitely make the management of these certificates a lot more palatable, especially considering one way we are expanding the reach of our e-commerce platform. Rank correlation statistics comparison I am trying to understand the relative behavior of the following rank correlation statistics:   Spearman coefficient Kendall Tau / Concordance percentage Normalized Gini coefficient (area under curve of percentage captured versus percentage observations) Normalized Area under ROC curve (for binary classifiers)   I don't believe any of these are functionally related to the others.  The accepted answer  references  and Spearman and Kendall are highly correlated (as one would expect).  Are there good intuitions behind/discussions of relative (across datasets) or absolute (for a given dataset) differences for (any pair of) these measures? Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$ How can I implement "cut outs" for lighting in OpenGL? Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$ Problem  Suppose $f$ is a non-negative integrable function on a measure space $(X,\mathcal{A},\mu).$ Prove that $$\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$$  Attempt  Let $E_t=\{x:f(x)\geq t\}$ Note that $f\chi_{E_t}\leq f$. Since $f$ is integrable, the Lebesgue dominated convergence theorem tells us that $$\lim_{t\to\infty} \int f\chi_{E_t}\rightarrow \int \lim_{t\to\infty} f\chi_{E_t}=0,$$ since $\lim_{t\to\infty} f\chi_{E_t}=0$ a.e. $\ ^{(1)}$ The result follows from the fact that $$t\mu(E_t)\leq\int f\chi_{E_t}.$$  Question  I am having trouble proving $(1)$. That is, how can I show that $f\chi_{E_t}\rightarrow 0$ a.e? How does the color of a car influence its inner temperature change over time when parked outside in windless, hot and sunny regions?  I know what's the common idea about that: black cars are supposed to build up high temperatures faster because black objects absorb radiations instead of reflecting them off. Is it true? And then, what happens during the steady state? Some claim the black car will stay hotter, some others claim it will be the same whatever the color. Do all cars have the same temperature inside in the long run, or are some of them hotter?  I've Googled it but the best I could find was . It claims to be based upon ~20 articles. But there's not even a mention of absorption or emission spectrums. A priori, a black car could absorb all visible radiations and emit it as infrared while reflecting all of the Sun's infrared. And it's still only qualitative. I've found nothing on Physics stackexchange, the closest being . Delete files older than X days + I have found the command to delete files older than 5 days in a folder  find /path/to/files* -mtime +5 -exec rm {} \;   But how do I also do this for subdirectories in that folder? Why can't I install Ubuntu or Wubi on a Windows Dynamic Disk? I've been trying to install 12.04 for a while now, I'm running on Windows 7 and I already made the partition (it's dynamic). I've tried booting from a disc and also the Windows installer. I haven't tried used any repair-boot programs or anything. Every time I tried to load from either, I get an error:  command=C:\windows\sysnative\bcdedit.exe /set {03f9077f-661f-11e1-845a-d08b36406c3d} device partition=U;  retval=1  stderr=An error has occured setting the element data. The request isn't supported  stdout=   Then after that, it makes a log file with information that I don't understand.  If it is simply due to the fact of it being a dynamic partition, someone please help. If it is more extensive, anyone with details on possible solutions or definite ones please express them. How can I get my external IP address in a shell script? So I am using cryptopp to encrypt a file in a project and I am using AES-GCM. I have a 256bit key and a 128bit ivec and a 128bit tag that I use to encrypt files.  However, I want to know where the authentication tag is stored? I notice if I specify a tag size of 0 then the encrypted file size is the same number of bytes as the original file.  Is the authentication tag simply appended to the end of the file? A characterisation of quadratic extensions contained in cyclic extensions of degree 4 Let $D$ be a squarefree integer. I am trying to prove that $\mathbb Q[\sqrt D]$ is contained in a Galois extension of $\mathbb Q$ with Galois group $\mathbb Z/4$ if and only if $D$ is the sum of two squares, $D = a^2 + b^2$ with $a,b\in \mathbb Q$.   The hint in the exercise in Dummit and Foote suggests considering the extension $\mathbb Q[\sqrt{s + s\sqrt D}]$ for the forward direction. However, I am unsure how to show that this extension is Galois, much less that its Galois group is cyclic of order 4.   For the reverse direction, I expressed the given Galois extension as $\mathbb Q[\sqrt{a+b\sqrt D}]$ for some $a,b\in \mathbb Q$. I showed that this extension has $\mathbb Q[\sqrt{c^2 - d^2 D}]$ as a subfield for some $c,d \in \mathbb Q$. From this, I deduced that the $\sqrt D$ and $\sqrt{c^2 - d^2 D}$ generate the same extension, so $\sqrt D = x \sqrt{c^2 - d^2 D}$ for some $x$, and hence that $D = \frac{x^2 c^2}{1 + x^2 d^2} $. It seems that there should be a way to decompose this as a sum of two squares, but I did not see how.   I did not tag this as homework as I am studying it independently. How can I reliably and accurately identify the passive voice in writing or speech? How can I reliably and accurately identify the passive voice in writing or speech? I'm not interested in advice about whether or not to use it yet... I just want to know for sure what it is, so that I don't look as stupid as . Installing PHP 5.3 in Ubuntu 14.04