Software Updater shows "Failed to download repository information. Check your internet connection" [18.04 LTS]
What can I do if a repository/PPA does not have a Release file?
In An Introduction to Statistical Learning (James et al.), in section 3.7 exercise 5, it states that the formula for $\hat{\beta}_1$ assuming linear regression without an intercept is  $$\hat{\beta}_1 = \dfrac{\displaystyle\sum\limits_{i=1}^{n}x_iy_i}{\displaystyle \sum\limits_{i=1}^{n}x_i^2}\text{,}$$ where $\hat{\beta}_0 = \bar{y}-\hat{\beta}_1\bar{x}$ and $\hat{\beta}_1 = \dfrac{\displaystyle S_{xy}}{S_{xx}}$ are the usual estimates under OLS for simple linear regression ($S_{xy} = \displaystyle\sum\limits_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})$).  This is not the actual exercise; I am merely wondering how to derive the equation. Without using matrix algebra, how do I derive it?   My attempt: with $\hat{\beta}_0 = 0$, we have $\hat{\beta}_1 = \dfrac{\bar{y}}{\bar{x}} = \dfrac{S_{xy}}{S_{xx}}$.  After some algebra, it can be shown that $\displaystyle S_{xy} = \sum\limits_{i=1}^{n}x_i^2 - n\bar{x}\bar{y}$ and $\displaystyle S_{xx} = \sum\limits_{i=1}^{n}x_i^2 - n\bar{x}^2$. From here, I'm stuck. How to reverse the pagination numbers of an archive? I have archive pages that each contain titles and excerpts from 10 blog entries. Both entries and archive pages are in reverse chronological order:   when a new blog entry is written its title and excerpt go to the top of the front page; when you are on one page and you click through to "Next page", you get the titles and excerpts for the 10 previous blog entries.   This is pretty standard for blogs.  But the archive pages are numbered by default in the same order. Thus Page 1 contains excerpts from the most recent 10 entries, Page 2 contains excerpts from the next 10 most recent, etc.  To be clear: at the moment, "Next page" refers to the page with the next higher number. Thus the front page, which contains excerpts from the most recent entry and the nine next most recent entries, is labelled Page 1, and the 10 entries posted before those 10 entries are on Page 2.  I need the page-numbering the other way round, namely in direct chronological order, so that for example if there are 97 entries then   entries 28-37 would be excerpted on Page 4, and the PREVIOUS page from there, containing excerpts from entries 18-27, would be called page 3.   How can I achieve this, whether by amending functions.php in the child theme (preferably), by writing a "Snippet" (next most preferred), or by amending archive.php in the Astra parent theme directly (least preferred, because of possible update problems)?  Edit  The following isn't a solution but it may be part of one. This re-numbers pages into direct chronological order, but unfortunately it also reverses the order in which they are shown (from reverse chronological to direct chronological). So it causes the front archive paget to contain excerpts from the earliest posts rather than the latest ones!  &lt;?php  add_filter('pre_get_posts', 'posts_by_forward_date');  function posts_by_forward_date($query) {   if(is_archive() || is_home()) {     $query-&gt;set('order', 'ASC');   } } ?&gt; In Python, how do I determine if an object is iterable? How to find the most common name in passwd file Springer llncs TOC not working How do I simulate in Photoshop what a piece will look like when printed on non-white paper? I'm designing a box in Photoshop that will be offset printed on unbleached paper. I haven't picked out a printer yet, so I don't know the exact kind of paper I'll be using and don't have access to it for proofs. For now I'm using a lightly-textured layer of tan color as a placeholder to mock it up.  What I'm trying to figure out is, how do I figure out how my design will look printed on natural paper rather than bleached white paper? I know that the brightness will be diminished and the hue will be altered, but I need to know how much so I can compensate for it as much as possible.  Is there a way to get at least a rough but reliably-simulated idea of how my prints will come out? Does it have to do with blend modes, or color separations? I'm at a bit of a loss here. Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$? I wonder  whether there is a function $f\colon\Bbb R\to\Bbb R$ with the folowing characteristic?   for every two real numbers $\alpha,\beta,\alpha\lt\beta$,  $$\{f(x):x\in(\alpha,\beta)\}=\Bbb R$$   I can't  say such a function does not exist, neither can I construct a example  Thanks a lot! Travelling on Business visa to UK for tourism purposes The warlock's Thirsting Blade eldritch invocation cannot be normally used with the (non-warlock) class feature Extra Attack, since both feature explicitly say you attack twice instead of once. But it seems to me that you could use both features (if you have them) when using Two-Weapon Fighting.  Assume your character is wielding two light weapons, one of which is your pact weapon. You take the Attack action on your turn to attack twice with your non-pact weapon using your  class feature.  Then, given the Two-Weapon Fighting rules, you use your bonus action to attack once using your pact weapon this time.  The  rules (PHB p. 195) state:     When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.   But since your have the Thirsting Blade invocation, and you used the Attack action, you get to attack twice with your pact weapon.  The Thirsting Blade  (PHB p. 111) says:     You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.   Does this combo work within the rules, or is there any interaction I'm not aware of? What pins on a nRF51822 do I connect to a STM32 programmer? I want to be able to program a  with  but I'm not sure what pins on the actual chip I should use, and all the guides seemed to be using a different chip Add an "I don't understand" option for review audits Under the  tag I have seen many questions on earth-616. Are there any other versions of earth as well? How do they differ from each other? Prove the statement 'World is not flat' In my graph theory book exercise, I found a problem that:     Prove that the World is not flat using Mathematics     This picture is used in the exercise, but no idea of applying it.  I would have used the angles don't add to $180^\circ$, but the author is using a fourth city. I'm trying to prove that for $p,q&gt;0$, we have $$\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}.$$    The hint given suggests that we express $\Gamma(p)\Gamma(q)$ as a double integral, then do a change of variables, but I've been unable thus far to express it as a double integral.  Can anyone get me started or suggest an alternate approach?  Note: This wasn't actually given to me as the $\Gamma$ function, just as a function $f$ satisfying $$f(p)=\int_0^\infty e^{-t}t^{p-1}\,dt$$ for all $p&gt;0$, but I recognized that. This is in the context of an advanced calculus practice exam. I just bought a new house and I'm looking to run some cables. One of the areas I would like to run it to would require drilling through a 2x10 sistered joist. Realizing that going through the joist should be a last resort, if the hole is 1/4" and in the middle of one of the joists will this weaken the integrity?  I have seen lots of articles about drilling through the depth of a joist, but very few regarding drilling vertically. When do I use "can" or "could"? When should I use can? When should I use could? What is right under what context? Geometric interpretation of the multiplication of complex numbers? I've always been taught that one way to look at complex numbers is as a Cartesian space, where the real part is the $x$ component and the imaginary part is the $y$ component.  In this sense, these complex numbers are like vectors, and they can be added geometrically like normal vectors can.  However, is there a geometric interpretation for the multiplication of two complex numbers?  I tried out two test ones, $3+i$ and $-2+3i$, which multiply to $-9+7i$.  But no geometrical significance seems to be found.  Is there a geometric significance for the multiplication of complex numbers? Integral Inequality $|f''(x)/f(x)|$ Let $f$ be a $C^2$ function in $[0,1]$ such that $f(0)=f(1)=0$ and $f(x)\neq 0\,\forall x\in(0,1).$ Prove that  $$\int_0^1 \left|\frac{f{''}(x)}{f(x)}\right|dx\ge4$$ The Stack Imgur service is no longer resizing images correctly Are counters (noun) physical things?