So once Star Wars episode IV: A New Hope starts, the Clone Wars are over, but what is the fate of the clones? Are the stormtroopers in episodes IV, V and VI leftover clone troopers? Did the Kamino cloners keep making clones for the republic/empire after the clone wars ended? When did the empire start hiring actual real people (and not just using clones) for their armies?
I understand why the Empire would want to start using more than one genetic template to create clone troopers, but why did it start using non-clone troopers instead of just continuing the cloning program?  It seems that with cloning they were able to use a training program (and genetic manipulation) that gave them completely loyalty (other than when the Kaminoan rebellion, where the Kaminoans had sabotaged the training programs).  Why stop using such troops and start using people that might question orders or aren't as easily controlled as clones were?
Take the manifold: The graph of $|x|$ on $(-1,1)$, with the induced topology from $\mathbb{R}^2$. This is a topological manifold, which is homeomorphic to $(-1,1)$ by projection. Is it a differentiable manifold? I believe it is, because we can take an atlas with only the projection, and then we will have only one transition map which is the identity, and therefore differentiable. But I'm not sure I get the definition of a differentiable manifold right...  Thanks! Number of total possibilities for an equation I need to find the number of possibilities for which the following equation exists:  $$x_1 + x_2 + x_3 + \cdots + x_{10} \leq 70$$  Each variable is a non-negative integer.  I tried simplifying the question to the point of finding the number of possible solutions to each equation seperatly:  $$x_1 + x_2 + x_3 + \cdots + x_{10} = 70,$$ which is ${79}\choose{10}$.  $$x_1 + x_2 + x_3 \cdots + x_{10} = 69,$$ which is ${78}\choose{10}$.  $$x_1 + x_2 + x_3 + \cdots + x_{10} = 68,$$ which is ${77}\choose{10}$, and so forth.  Then I thought about adding all of these together. This seems a bit too much work considering that the textbook solution is: ${80}\choose{10}$, and I can't seem to figure out the idiomatic way of approaching these kind of questions.   Any help is greatly appreciated. Elementary OS PPA gives “The repository does not have a Release file.” error I am running Ubuntu Bionic Beaver. I was trying to download the pantheon desktop environment on Ubuntu and it didn't work so I gave up. Now when I try to download themes or other things from the terminal I get an error code mentioning Elementary OS even though what I am downloading doesn't have to do with Elementary or pantheon. Here is what the terminal says:   jacob@jacob-MacBookPro:~$ sudo apt-add-repository ppa:tista/adapta -y …                                           E: The repository 'http://ppa.launchpad.net/elementary-os/testing/ubuntu bionic Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://ppa.launchpad.net/mpstark/elementary-tweaks-daily/ubuntu bionic Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. Recovering added/staged file after doing git reset --hard HEAD^? Possible Duplicate:          I've added myself back into the admin's group I think, by following   But I still can't do commands like:  sudo aptitude update   I get the message  oshirowanen is not in the sudoers file.  This incident will be reported.   How do I add myself into the sudoers group now that I am in the admin group? Rewrite rules goes away Equation of a rectangle I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere. Maximum Likelihood Estimator for $\theta$ when $X_1,\dots, X_n \sim U(-\theta,\theta)$ Exercise :     Calculate a Maximum Likelihood Estimator for the model $X_1,\dots, X_n \; \sim U(-\theta,\theta)$.   Solution :  The distribution function $f(x)$ for the given Uniform model is :  $$f(x) = \begin{cases} 1/2\theta, \; \; -\theta \leq x \leq \theta \\ 0 \quad \; \; , \quad\text{elsewhere} \end{cases}$$  Thus, we can calculate the likelihood function as :  $$L(\theta)=\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n\mathbb I_{[-\theta,\theta]}(x_i)= \bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[0,\theta]}(|x_i|) $$  $$=$$  $$\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(|x_i|)\prod_{i=1}^n \mathbb I_{[0, +\infty]}(|x_i|)$$  $$=$$  $$\boxed{\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(\max|x_i|)}$$  Question : How does one derive the final expression in the box from the previous one ? I can't seem to comprehend how this is equal to the step before.  Other than that, to find the maximum likelihood estimator you need a $\theta$ sufficiently small but also $\max |x_i| \leq \theta$ which means that the MLE is : $\hat{\theta} = \max |x_i|$. Rufus nor any other software can fix my 16GB usb drive after using RUFUS I wanted to make a bootable USB drive using Rufus. I opened the program went with all the default options and I clicked start BUT what I forgot to do is to select an iso because I thought it would just make the disk bootable without selecting anything. Unfortunately it did not. It gave me an error. I do not remember it because this was about 6 months ago after I gave up in fixing it. Anyway I tried to reformat it again using diskpart and it fails. With Rufus it says "ERROR while partitioning drive" and I think that was the initial error as well. Also during the struggle I got messages from windows saying that the disk is write protected and NO, there is no switch for that on the USB pendrive.   More info:     Transcend 16 GB     Rufus 1.4.9,     Frustrated student :/ Touchpad stopped working 20.04 Can there be only one extension to the factorial? Usually, when someone says something like $\left(\frac12\right)!$, they are probably referring to the Gamma function, which extends the factorial to any value of $x$.  The usual definition of the factorial is $x!=1\times2\times3\times\dots x$, but for $x\notin\mathbb{N}$, the Gamma function results in $x!=\int_0^\infty t^xe^{-t}dt$.  However, back a while ago, someone mentioned that there may be more than one way to define the factorial for non-integer arguments, and so, I wished to disprove that statement with some assumptions about the factorial function.    the factorial   is a  for $x\in\mathbb{C}$ except at $\mathbb{Z}_{&lt;0}$ because of singularities, which we will see later. is a monotone increasing function that is concave up for $x&gt;1$. satisfies the relation $x!=x(x-1)!$ and lastly $1!=1$     From $3$ and $4$, one can define $x!$ for $x\in\mathbb{N}$, and we can see that for negative integer arguments, the factorial is undefined.  We can also see that $0!=1$.  Since we assumed $2$, we should be able to sketch the factorial for $x&gt;1$, using our points found from $3,4$ as guidelines.  At the same time, when sketching the graph, we remember $1$, so there can be no jumps or gaps from one value of $x$ to the next.  Then we reapply $3$, correcting values for $x\in\mathbb{R}$, since all values of $x$ must satisfy this relationship.  Again, because of $1$, we must re-correct our graph, since having $3$ makes the derivative of $x!$ for $x\in\mathbb N$ undefined.  So, because of $1$ and $3$, I realized that there can only be one way to define the factorial for $x\in\mathbb R$.  Is my reasoning correct?  And can there be only one extension to the factorial?    Oh, and here is a  to how I almost differentiated the factorial only with a few assumptions, like that it is even possible to differentiate.  Putting that in mind, it could be possible to define the factorial with Taylor's theorem? Since I installed EasyTag on my Arch Linux several other programs use EasyTag instead of Nautilus as filebrowser.  For example, Firefox starts EasyTag if I click on "open containing folder".  Where can I set Nautilus as my "standard file browser"? Why do you cast downvotes on answers? How can I improve Light Armor as an Archer? I play as an archer, which means sneaking and killing foes off at long range. Problem is, once a creature gets too close to me, I am in a world of troubles. (A random dragon encounter is fair game if I can snipe it off, but a random bear encounter is the thing I fear mostly. Three strikes of such a vicious beast and I drop dead.)  At short range, I use a one-hand sword with shield, but I do not want to put much perks into those skills, as I want to be a sneaky archer first.  Which leaves Light Armor. But to get certain perks I need some skill points, e.g., 30 points are required for the "Custom Fit"- and 40 for "Agile Defender 2/5"-perk. Yet I have no clue how to accumulate those points.  Many enemies won't even see me, so I seldom will be hit. Getting hits means getting skills point. Letting some enemies come close to me and let me hit me on purpose sometimes helps, but since I cannot stand much damage I mostly die erasing any hard earned process.  So is there a teacher for Light Armor like there is for other skills? And if not, how should I go on to improve the Light Armor skill? How to find a global minimum for $\frac{1}{2}x^tQx-b^tx$ Is "laic" an alternative word to the word "layperson"? Finding CPU usage of a service Because my laptop fan was spinning up for no reason, I had a look at the CPU usage and I see  svchost with 12.5% CPU, which is basically a full core.  Now, I'm aware that  svchost runs services and I know how to display the services it runs in Task Manager or Process Explorer ().  Now I know which services are run, but I don't know which service eats the CPU time. I could disable one service after another, but I don't really like doing this (it could break things that are currently in use and I could forget turning the service back on later).  Therefore I'd like to know whether it's possible to instruct Windows to run only one service per svchost the next time I boot my PC. While I might have the slight disadvantage of several processes, I could immediately find out which one it is and it would be a much easier decision of whether or not to stop or restart the service. Where to get 2010 Census Block data? I would like to download 2010 Census Block Data for several towns and I can't seem to find it on American Factfinder.   Is it there? And if not, does anyone know where I could find it? Detecting device for debugging (ADB) does not work Building a graph from OSM? I spent days looking in all questions here and trying tutorials. I need to build a graph for a region (It will be my input in simulation) I downloaded Postgresql and Postgis and osm2pgsql. Now i can load .osm files into a database. I want to have a complete database with roads ids so i can generate a table of edges and nodes then build my graph  nodes = intersections and edges = roads for a city using python.  Please any detailed help with steps.I saw a lot of keywords (Postgresql/postgis, Networkx, QGIS ..) but i couldn't manage to assemble a good tutorial  I am a very beginner.