I'm doing some simple wiring in a shed I built and will have an actual electrician connect it to the panel.   I ran 12-2 for all my outlets so they can be on a 20 amp circuit and 14-2 for all my lights on a single switch and they will be on a 15 amp circuit.  The thing I was noticing yesterday though is I ran 12-2 from the future panel to the switch, and then 14-2 from the switch to all the light fixtures.  I texted my electrician buddy and asked if that was ok and he said yes as long as it's on a 15 amp circuit only.  Then I got to thinking about a time when I was tearing apart an old house and there was some wire running that was either 12-2 to an outlet and then 14-2 from there, or possibly vice versa and the guy I was working with said "whoa that's definitely a fire hazard".  Can someone explain to me what is safe, what is not safe, etc when mixing wire size on a single circuit (I know it's not a great idea to mix, but if you were to). Is it solely related to breaker size?
My father-in-law is a builder. He has put in 20 amp and 15 amp breakers, and ran 12-2 as the home runs to the switch's and the first plug to make them hot. He then ran 14-2 to feed the rest of the plugs, lights, and ceiling fans.   Is it okay that he used different gauge wires on the same circuit?
Edit source differs from question view? Or are we each other's friends now? How to make many copies of similar graphs systematically? I want to make various copies of a graph in tikz. The graph I want has 10 vertices. But only has the edges between the vertices a_i,a_(i+1),t,b.  I would like to automatically create 8 copies of this graph. and draw them. I just don't know how to code it. Here is my current code, but it adds all of the edges to the same copy of the graph:  \begin{tikzpicture} [main_node/.style={circle,fill=blue!20,draw,minimum size=2em,inner sep=3pt]}] \node[main_node] (8) at (0:0.5) {b}; \node[main_node] (9) at (180:0.5) {t}; \foreach \x in {0,1,...,7}     \node[main_node] (\x) at (360/8*\x:2) {$a_{\x}$}; \foreach \x in {0,1,...,7}{     \pgfmathsetmacro{\y}{int(mod(\x+1,8))}     \path[draw,thick] (\x) edge node {} (8);     \path[draw,thick] (\x) edge node {} (9);     \path[draw,thick] (\x) edge node {} (\y);     \path[draw,thick] (8) edge node {} (9);     \path[draw,thick] (8) edge node {} (\y);     \path[draw,thick] (9) edge node {} (\y);    }   I want each of the edge sets to be drawn seperately. I have an equation like this:     \begin{align}       P(A \cup B) = \sum_{\omega \in A \cup B} P(\omega) = \sum_{\omega \in A} P(\omega) + \sum_{\omega \in B} P(\omega)       = P(A) + P(B)     \end{align}   For some reason, LaTeX is automatically labeling the equation. How do I turn that off? Secondly how do I write something in LaTeX on this site. I tried enclosing in '$' but it doesn't work. If light rays obey to the wave equation, why can they be thought as straight lines? I'm a newbie with physics but I'm wondering how a ray of light can essentially be represented. I have always known that a ray of light proceeds in a straight line until it encounters another object (or material) that refracts/reflects it. But a light ray should be part of an electro-magnetic wave, is this correct? If it is so, it should obey to the  and this doesn't seem to me to describe a straight line ray.  I'm having problems visualizing how light is emitted and how it relates with the wave equation. Can someone with a clear understanding of the problem explain it to me in simple terms? How to replace the_post_thumbnail template tag and show the first inside the post image instead If I change the ISO settings on my camera, obviously the gain of the system is increased, amplifying the signal from the sensor. What's not clear to me is where the amplification takes place. I see several possibilities:   In the sensor, by increasing voltage or some other mechanism Via an analog amplifier outside of the sensor Digitally, after the signal has been digitized, but before storing data in the RAW file As a parameter applied solely in creating an image from RAW   If #4 is true, then you could take a 4-stop overexposed RAW picture at ISO 1600, and then in post processing produce a JPEG at ISO 100 that would be the same as if the original photo had been shot at ISO 100.  If #1 or #2 is true, then a RAW file shot at ISO 1600 would actually contain more information about shadows, and an ISO 100 RAW would contain more information about highlights. It started happening today... all of a sudden, no apparent reason!  Here's the output from df:   assp:~# df -k Filesystem           1K-blocks      Used Available Use% Mounted on /dev/simfs             6291456   1378384   4913072  22% / tmpfs                  8202680         0   8202680   0% /lib/init/rw tmpfs                  8202680         0   8202680   0% /dev/shm  assp:~# df -i Filesystem            Inodes   IUsed   IFree IUse% Mounted on /dev/simfs           55781934   83005 55698929    1% / tmpfs                2050670       2 2050668    1% /lib/init/rw tmpfs                2050670       1 2050669    1% /dev/shm  assp:~# df -h Filesystem            Size  Used Avail Use% Mounted on /dev/simfs            6.0G  1.4G  4.7G  22% / tmpfs                 7.9G     0  7.9G   0% /lib/init/rw tmpfs                 7.9G     0  7.9G   0% /dev/shm   Here's an actual entry from /var/log/mail.warn:   Dec 11 17:55:37 assp postfix/smtpd[30614]: warning: not enough free space in mail queue: 0 bytes &lt; 1.5*message size limit Dec 11 17:55:37 assp postfix/cleanup[30617]: warning: 4361D850D54: write queue file: No space left on device   . MySQL Error 1093 - Can't specify target table for update in FROM clause I have a table story_category in my database with corrupt entries. The next query returns the corrupt entries:  SELECT *  FROM  story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category INNER JOIN         story_category ON category_id=category.id);   I tried to delete them executing:  DELETE FROM story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category        INNER JOIN story_category ON category_id=category.id);   But I get the next error:      #1093 - You can't specify target table 'story_category' for update in FROM clause    How can I overcome this? Is "life" a countable noun in English? I am a learner of English. Sometimes I see an article (a and the) before the noun (life) but sometimes I also see the noun without any article. So I am confused when should I use an article before the noun and when I should not. Please check the examples and let me know are they correct?     Examples:      His life is an awesome life.      I want to get a beautiful life.      I like the life he lived. Euclidean geometry in non-inertial frame How to discard unsaved changes to a view when editing it leads to a WSOD? How can I use multiple accounts with Telegram? Is there a way to have two copies of  app in Ubuntu each with a different account?  It seems copying the app in another folder does not work. $$ 3x+6y+5z=7 $$ The general solution to this linear Diophantine equation is as described    $$ x = 5k+2l+14 $$ $$ y = -l $$ $$ z = -7-k $$ $$ k,l \in \mathbb{Z} $$  If I plug the original equation into  the solution is: $$ y = 5n+2x+2  $$ $$ z =-6n-3x-1 $$ $$ n \in \mathbb{Z} $$  I can rewrite this as:  $$ x = l $$ $$ y = 5k+2l+2 $$ $$ z = -6k-3l-1 $$ $$ k,l \in \mathbb{Z} $$  However now two equations depend on two variables ($k,l$) and one on one variable $l$. In the first solution one equation depends on two variables and two on one variable.  Questions:  How can I come from a representation like the one from wolfram alpha for the general solution to one where all equations depend on one distinct variable except one equation.  Is there always such a representation? Give a sequence such that root test works while ratio test fails Distance between points along polyline ArcGIS for Desktop? I'm using ArcGIS 10.3 (Desktop), and I'm trying to measure the distance between points following a path determined by a set of polylines.  Hand measurement is not a viable option-- there are ~7500 points, and my polyline set is the global coastline.  The ultimate goal is to get the spacing of these points along the polylines, so that I can analyze this with respect to a few other variables.   I can read python-- with a bit of effort-- but not write or edit it, so code-based solutions will not be particularly useful to me.  I have tried using the linear referencing tools-- I snapped the points to the lines, then transformed the polylines to routes and used 'locate features'-- but because my points are not (entirely) ordered along the path, using the difference between  linear reference locations of subsequent points yields some fairly unlikely answers.  In addition, spot checks of (hand-measured, using the built-in path length measuring tool) point-to-point along-polyline distance yield different answers than given by the corresponding linear references for the point pair. (Some of the answers were close enough that they could very well be measurement error on my part, but others were nearly 20%, despite my having zoomed in and snapped the measurement cursor to the polyline, proceeding vertex-to-vertex.)  Sorting first by linear distance seems to fix the first problem, but in light of the second one, I remain skeptical of this process.   I then tried simply splitting the polylines into segments ('split line at point') using the (snapped) points as the dividers, with the eventual goal of finding the segment length with the calculate geometry feature.  This produced gibberish. I'm not sure what criteria ArcGIS used to split the lines, but it wasn't the point set I provided.  Segments in the resulting shapefile ran right through tens of points, only to terminate at a place with no point. (Also, there were segments utterly empty of points...you get the gist.) I reiterate that the pointset was specifically snapped to the polylines, so this problem shouldn't be caused by excessive distance between the point and the polyline.  I'm at a bit of a loss, here: could someone point out where I might have gone astray and/or suggest a solution?  Or, failing that, a new method that I could try?  It seems like a fairly basic (not necessarily simple, but fundamental) analysis to do with geographic data, and I don't understand why it has presented so many difficulties. How can I utilize the whole terminal, like htop or emacs do? I want to write a program that can "draw" in the terminal the same way as htop or emacs. By that I mean "get rid of the prompt and make the output dependent on the current size of the terminal".   To make this a bit more clear:   I want to use the terminal this way:     in stead of this way: What websites or other resources do users of Blender have available to them to report bugs or problems with the program?  I would like to get this issue cleared in Q&amp;A format so that we can link new users with bug-report-style questions to this post. A cop vs a superhuman criminal I read the story over ten years ago while I was still trying to learn English, so I can only vaguely remember that the story is about a cop trying to track down a criminal who had superhuman abilities. Some of his abilities were pyrokinesis, using his mind to form a golem from earth and roam around while he stays in the room and stopping time. Eventually the cop was able to catch the criminal and shot him dead.   If anyone could identify the book I would be very grateful. I'd love to read it for nostalgic purposes. How does Cooper get out of the black hole? In the movie Interstellar,  Cooper (played by ) enters a black hole and sends a message to Murph (his daughter). Later, he is found by rangers, but I don't understand how he gets out of the black hole?  As far as I know, nothing can get out of a black hole, as it has extremely high gravity. If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely Assume that $X$ and $Y$ are two random variables such that $Y=E[X|Y]$ almost surely and $X= E[Y|X]$ almost surely. Prove that $X=Y$ almost surely.   The hint I was given is to evaluate: $$E[X-Y;X&gt;a,Y\leq a] + E[X-Y;X\leq a,Y\leq a]$$  which I can write as: $$\int_A(X-Y)dP +\int_B(X-Y)dP$$ where $A=\{X&gt;a, Y\leq a\}$ and $B=\{X\leq a,Y\leq a\}$.  But I need some more hints.