How can I create a circuit with a total resistance of 144.7 ohm which is composed of 10-ohm resistors? How many parallel and/or series resistors should it contain?  I've tried solving this but the nearest total resistance to 144.7 ohm that I get is 144 ohm exactly. Actually, this isn't for real-life usage rather just a circuit analysis problem. Please help.
In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem?
Number of bins when computing mutual information I want to quantify the relationship between two variables, A and B, using mutual information. The way to compute it is by binning the observations (see example Python code below). However, what factors determines what number of bins is reasonable? I need the computation to be fast so I cannot simply use a lot of bins to be on the safe side.  from sklearn.metrics import mutual_info_score  def calc_MI(x, y, bins):     c_xy = np.histogram2d(x, y, bins)[0]     mi = mutual_info_score(None, None, contingency=c_xy)     return mi Order of a group and subsequent subgroups I want to prove that if the order of a group G is greater than 1 and non-prime, then G has a subgroup other than the trivial subgroups {e} and G itself.   I am confused because I am only being able to prove the case for prime order by using Lagrange’s theorem i.e. if I have a group of order p, where p is a prime number, then the order of subgroups must divide p, hence the order can be either 1 or p.   How do I go about proving the case for non prime order let’s say x > 1? Show that $F\subset Y$ is closed in $Y$ iff $F=Y\;\cap\;H$ where $H\subset X$ is closed in $X$. I have the following problem:      Let $(X,\tau)$ be a topological space and $(Y,\tau_y)$ be its    subspace, that is $Y\subset X$ and $\tau_y=\{\;A\;\cap\;Y\mid  A\in\tau\;\}$. Let also $F\subset Y$ and $H\subset X$, where $H$ is    closed in $X$. Show that $F=Y\;\cap\;H$ if and only if $F$ is closed   in $Y$.   I solved this problem by assuming that if $F$ is closed then $F=Y\;\cap\;H$, where $H$ is closed in $X$, but I got stuck proving this in the other direction, that is showing that if $F=Y\;\cap\;H$ then $F$ is closed in $Y$.  I tried to do something like this:   Assumption: $F=Y\;\cap\;H$, where $H$ is closed in $X$. If $H$ is closed in $X$ then $X\;\setminus\;H$ is open in $X$ and then $X\;\setminus\;H \in \tau$ which means that $B = (X\;\setminus\;H)\;\cap\;Y\in \tau_y$.  How should I proceed now? Should I investigate the set $B$ now more or what? Setuid bit seems to have no effect on bash Most common C# bitwise operations on enums For the life of me, I can't remember how to set, delete, toggle or test a bit in a bitfield. Either I'm unsure or I mix them up because I rarely need these. So a "bit-cheat-sheet" would be nice to have.  For example:   flags = flags | FlagsEnum.Bit4;  // Set bit 4.   or  if ((flags &amp; FlagsEnum.Bit4)) == FlagsEnum.Bit4) // Is there a less verbose way?   Can you give examples of all the other common operations, preferably in C# syntax using a [Flags] enum? Community FAQ For sites in the Stack Exchange 2.0 network To see a list of commonly used words and phrases, see the . 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First look at questions tagged  to see if there is a question not in this index that might have the answer you seek. If you still can't find an answer, then see the following instructions for proposing an FAQ question. How can a question be added to this FAQ?  Ask only the question, stated plainly and simply, in the question body. The answer goes in an answer.  Link back to this index. Paste this at the end of the question:  [Return to FAQ index](/q/7931)   Tag as  and .  When a post seems to have hit a mature state, it will have  added by a moderator.  Flag for a moderator to mark community wiki.  Any FAQ post not yet community wiki should be made into a community wiki.  After the post has the  tag added to it, add a link in the above . What can I use instead of the arrow operator, `->`? Add an unnmbered section to the table of Contents in Lyx I need to find out the modular inverse of 5(mod 11), I know the answer is 9 and got the following so far and don't understand how to than get the answer. I know how to get the answer for a larger one such as 27(mod 392) but am stuck because they are both low numbers.  11=5 (2)+1  5=1 (5) + or @ mark after running 'ls -al' In Mac OS X, run 'ls -al' gives me something like this.   drwxrwxrwx+  4 smcho  staff     136 May  5 09:18 Public drwxr-xr-x+  6 smcho  staff     204 Feb  1  2010 Sites drwxrwxrwx   9 smcho  staff     306 Feb  2  2010 backup drwxr-xr-x@ 36 smcho  staff    1224 Sep  4 22:51 bin    What's the + or @ at the end of the first column means? Is this unique to Mac, or common in UNIX?   ADDED  After Michael Mrozek's answer, I ran 'ls -ale' to get the following.   drwx------+ 66 smcho  staff    2244 Aug 30 13:40 Library  0: group:com.apple.sharepoint.group.3 allow search  1: group:everyone deny delete drwxr-xr-x   3 smcho  staff     102 Sep  4 15:01 Mail drwx------+ 13 smcho  staff     442 Aug 28 17:55 Movies  0: group:everyone deny delete drwx------+  6 smcho  staff     204 Jul  9 09:37 Music  0: group:everyone deny delete drwx------+ 11 smcho  staff     374 Aug 28 16:55 Pictures  0: group:everyone deny delete drwxr-xr-x   3 smcho  staff     102 Mar 18 15:43 Projects drwxrwxrwx+  4 smcho  staff     136 May  5 09:18 Public  0: group:everyone deny delete drwxr-xr-x+  6 smcho  staff     204 Feb  1  2010 Sites  0: group:everyone deny delete   What those appended messages mean? Why do I have them for some of the files? I don't remember doing anything particular for them. Why didn't the Emperor realize that torturing Luke to death in front of Vader might be a bad idea? I had an application for returning closest matches to certain values in a large  cluster of values( as in my earlier )   and I chose a VBA solution. While in the course of using the said application, I observed that the results for the value of 0.5 were not correct. I had been using the VBA Round function which I found to be returning 0 for 0.5 rounded to integer whereas the worksheet round function returns 1. Strangely, the VBA round function returns 2 for 1.5. I had to substitute the worksheet function in place of the VBA one.  Am I missing something? Lookup list dependant on the contents of another cell hope someone can help to crack this one?  I've got a table on my data entry tab (sheet 1) where each row includes two data validation drop down lists (source is on sheet2). I want the options in the second drop down list (k13) to be dependant on what is selected in the first drop down list (g13)...  ie. if you select 'Diary' in the first drop down box then the second drop down only has 'Cheese', 'Milk' and 'Yogurt' - likewise, if you select 'Fruit' in the first box - I want the only options to be available specific to that categories column in the lookup table on sheet 2 (which are 'apple', 'pear' and 'banana' in this case)?  Please help - i think this is a vlookup indirect formula?? Is zero odd or even? I just started playing Dark Souls 2 without playing the first one.  Since I don't see any sell option in any merchant: Can I sell my old-unused-equipment for souls? If I cannot sell it, does it have any value to be keep until later? I can't seem to log in with my Stack Exchange OpenID. When I try, I get the error message:     Unable to log in with your OpenID provider:      The openid.return_to parameter (.) does not match the actual URL (.) the request was made with.   It works if I disable the HTTPS-Everywhere plugin in Firefox, but if I then re-enable the plugin and go to a site on which I am not logged in (in which case login is normally nearly seamless), it fails again with the same error message, or at least something very similar.  I'm not aware of having done anything that might have caused this, although I will admit I don't recall seeing https:// in the address bar on Stack Exchange before (I do now, and that's a good thing IMO!). I was using the site  and it worked fine then, but not now... Why does println(array) have strange output? ("[Ljava.lang.String;@3e25a5") At a movie theater, the whimsical manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket.  You have the option of choosing any position in the line. Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout the year (365 days year), what position in line gives you the best chance of getting free ticket? Google Chrome is not starting I've just installed Ubuntu 16.04 LTS on dual boot. I've looked for many solutions and tried them all but Chrome never starts; the logo appears on the left but no window opens.  I downloaded the deb file on google chrome website and installed it through Ubuntu Software, but it doesn't start.   I have tried installing it through the command line with   sudo dpkg -i --force-depends google-chrome-stable_current_amd64.deb sudo apt-get install -f   I have checked with uname -a and my system is 64 bit. I have also tried gdebi with the same result.   My repository universe is up to date.  I only have one display in settings>displays> so I can't turn off built-in display nor check the mirror display (I read it could be the problem as I also have a graphic card but it seems it is not in my case).  Here is what I get in the command line when I try to run Chrome from it ( the message is the same, whatever the method I used to install Chrome):  ~$ google-chrome [11831:11831:1122/114854.195473:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195493:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195508:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195515:ERROR:process_singleton_posix.cc(280)] Failed to create /home/basil/.config/google-chrome/SingletonLock: Permission denied (13) [11831:11831:1122/114854.195538:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195564:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195622:ERROR:chrome_browser_main.cc(1498)] Failed to create a ProcessSingleton for your profile directory. This means that running multiple instances would start multiple browser processes rather than opening a new window in the existing process. Aborting now to avoid profile corruption. [11831:11868:1122/114854.209297:ERROR:browser_gpu_channel_host_factory.cc(108)] Failed to launch GPU process.   Any new approach will be much appreciated I've been having trouble defeating this monster. Even with lots of buff potions, health potions, high tier armor (Molten), and ranged weapons with plenty of ammo (Minishark), I can't seem to kill this boss.  Worse, when I get it down to about 2000 hp, even if I'm fairly far away, it'll suck me in and continually rise towards the skybox, which doesn't allow me to do anything for some reason.  How do I defeat the Wall of Flesh? What gear should I be using and what kind of potions do I need?