Windows 8 and file association
Change all file type associations from one program to another
How to calculate the prediction interval for an OLS multiple regression? What is the algebraic notation to calculate the prediction interval for multiple regression?  It sounds silly, but I am having trouble finding a clear algebraic notation of this. I've read through the elementary proof of why there exists a solution $x$ to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$ for $p$ an odd prime. Is there a group theory generalization for this fact as well? OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an amateur with an interest in physics, so I don't know the details of the physics. However, I have read enough about the cosmological principle and cosmic time to develop this "confusion" .  Based on evidence gathered to-date, it appears that the universe is both , as evidenced by observations and the . This principle, when combined with the FLRW metric, allows space-time to be divided into non-intersecting slices and therefore establish a "cosmic time."   Now, the existance of such a time in no way suggests that it is the "right" time or a true "now", hence violating relativity -- although some presentist philosophers (e.g., W.L. Craig) have tried to make this argument, but it is not generally accepted in philosophical circles.  However, this leaves me confused about an apparent disconnect between relativity and the cosmological principle:  Isotropy only holds if we are at rest relative to the cosmic microwave background radiation (universal rest frame), o/w anisotropy is present - yet each reference frame is supposed to allow equally valid observations. How can these two be reconciled when most reference frames would lead us to conclude that the universe is NOT isotropic?  It seems that only by appealing to the idea of being at rest relative to "universal rest frame" can we explain away any discrepancies from isotropy as due to "peculiar motion". However, doesn't this give this "universal rest frame" and its associated time an empirically privileged status, even though physical laws work just fine in every reference frame?   For example (pardon any abuse of astronomy): if look off in some part of space and see only quasars, and then in another part of space and see only brown dwarfs, but I measure both as apparently the same distance from me, then can I conclude that we are in motion, since otherwise we would have an empirical contradiction (kind of like finding dinosaur and human remains in the same strata)?  Any help on where I am going wrong would be helpful. Intuitively, I don't think there should be a way to establish absolute ordering between space-like separated events, but the above reasoning suggests otherwise. What's the derivative of: $ \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$? let $ y=\displaystyle \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$, i'm really interesting to know how do I find :  $\displaystyle \frac{dy}{dx}$ ?.  Note: I have used the definition of derivative of the square root function but i don't succed .  Thank you for any help If you visit a chat room attached to a beta site while logged out, the log in message is all but unreadable, being dark grey on a dark blue background. For example, visit  while logged out or in private browsing mode. Is it possible to turn off the Two-Factor Authentication for an Apple ID? Is it possible to turn off the Two-Factor Authentication for an Apple ID?  I have more than one device linked to this Apple ID and I know the password and security questions. Wireframe iOS design apps for iPad? Is there an app for iPad to assist in wireframe design for iPad and iPhone apps?  I don't mean actual development, just placing standard widgets and the things you usually do with photoshop and associated kits. Difference between ref and out parameters in .NET Everyone I speak to says that a 50mm lens is the best and beats them all as an all-rounder. I was wondering whether to get myself a decent, fast 50mm as well. However I'm still not 100% sure whether I really need such a lens.  I use a Pentax K10D and mainly shoot people (kids, portraits, some street shots). The lens I love and use most is the DA 70mm f/2.4 Limited. I often also use a DA 40mm f/2.8 Limited. They are great little lenses that produce very high quality images but they could be a bit faster.  Is is worth spending 400 quid on a Sigma 50mm f/1.4 in my situation? It seems like a good compromise between the 40mm and 70mm and much faster (in fact, 2 f-stops faster than the DA 70mm f/2.8!). On the other hand would the lens be sufficiently different from my current lenses? set fontsize for TikZ figure Under what condition we can interchange order of a limit and a summation? Preview on mobile page I suggest a preview on the mobile page. For questions, answers and edits to both, like on the desktop page.  I messed up formatting often enough to be annoyed that there is no preview on the mobile page and I'm surprised that noone suggested it before (at least I didn't find anything).  If it's too performance heavy to have a live preview update after every change in the text box, there could be a preview button next to the save button which leads to a page with only the preview, a back button and a save button (and the title bar and so on). I need to print an image at a certain size. What dimensions and resolution should I use? When IE10 is set as my default browser, double-clicking an internet shortcut (*.url file) opens it in a new tab of the existing IE window. However, when it is not the default, every way of opening a *.url that I've tried brings up a new IE window per file. Is it possible to keep opening files in new tabs of the same IE window when it's not set as the default browser, and how?  What I've tried and it didn't work:   "C:\Program Files (x86)\Internet Explorer\iexplore.exe" "C:\Dir1\file.url" (opens a new window every time) C:\Windows\System32\rundll32.exe "C:\Windows\System32\ieframe.dll",OpenURL C:\Dir1\file.url (opens the default browser) classexec "C:\Dir1\file.url" --class htmlFile (using  utility, opens a new window every time)   I use Windows 7 x64. How do I change my Minecraft username? Use Yaml for MongoMapper Config Best methods to fix broken tracks I've made a couple of PCBs which need the odd few 10 mil tracks, but are mostly 20/30 mil. Unfortunately the etching process isn't fantastic and there are numerous breaks in the traces, most of them small.  I've managed to convince solder lumps to go over the top of the smaller gaps, and have used components legs to bridge some of the larger ones. The solder lumps don't feel particularly reliable though, and there are some gaps which are too small and awkward to get a piece of wire across but too big to be bridged with just the iron.  Are there any standard ways to reliably fix up broken traces?  Update: Thanks for the suggestions everyone!  I found and tried out a silver conductive pen. As a first time user I found it difficult to dispense, and obviously I didn't use enough of it or mix it properly because it didn't even end up being conductive.  It seems like the main problem was that I was trying to use pieces of wire which are too short. I found some small gauge tinned wire and used longer lengths, running it over significant lengths of good track on either side of the fault. That makes it much easier to position, and you can tack them down one end at a time. WinForms Global Exception Handling? Code is supposed to be exact and "as-is". Sometimes, showing two spaces is important. In a comment, it is not possible to show code with  multiple   spaces. This became apparent in  (see comments).  EDIT: apparently this bug is larger then I thought: multiple    spaces   here are neither preserved in normal question text. Pity (though I couldn't find this reported before, I'd assume it is).  Workaround: use Alt+0160 (windows), or U+00A0 (Unicode NBSP), as I did in the example above. I'm confused about why we should change door in the Monty Hall Problem, when thinking from a different perspective  gives me equal probability.   Think about this first: if we have two doors, and one car behind one of them, then we have a 50/50 chance of choosing the right door.   Back to Monty Hall: after we pick a door, one door is opened and shows a goat, and the other door remains closed. Let's call the door we picked A and the  other closed door B. Now since 1 door has already been opened, our knowledge has changed such that the car can only be behind A or B. Therefore, the problem is equivalent to: given two closed doors (A and B) and one car, which door should be chosen (we know it's a 50/50 thing)? Then, not switching door = choosing A, and switching door = choosing B. Therefore, it seems that switching should be equally likely, instead of more likely.   Another way to think: no matter which door we choose from the three, we know BEFOREHAND that we can definitely open a door with a goat in the remaining two. Therefore, showing an open door with a goat reveals nothing new about which door has the car.   What's wrong with this thinking process? (Note that I know the argument why switching gives advantage, and I know experiments have been done to prove that. My question is why the above thinking, which seems legit, is actually wrong.) Thanks.