I'm currently running a mega dungeon in 5e D&amp;D, and my players have recruited some monsters into their service. I have been building encounters using the dungeon masters guide rules (pg. 81-84), but these only account for groups of player characters. How should I recalculate the encounter difficulties that I have planned when they also have some recruited monsters with them?   Options I have considered are shifting the encounter multiplier  (pg. 82) according to the party size paragraph (pg. 83), but this fails to account for the inherent weakness of the recruited MOBs,   Alternatively, I could maybe add the modified experience total of the group of MOBs to the parties XP thresholds, as modified XP is probably a fairly accurate guage of additional party ability (probably without including them in the party size)  If anyone has done this before, knowing what worked would be nice, otherwise I'll use my best judgement and comment later on how well it worked out
Hypothetical party:  1st level human wizard (PC) 3x guard NPC 1x acolyte NPC    This is the player's first time, and it's a solo campaign. The first mini-adventure involves recovering the cargo of a supply caravan that didn't make it to her magic academy due to bandit hijacking (as a sort of graduate-test). The guards and healer are on contract from the school to assist her. The acolyte is essentially just to hang back and tend to wounds and probably won't engage in combat unless someone goes down or the PC is seriously wounded.  So, with that "party" makeup, how do I determine the XP budget for a "medium" or "hard" encounter since there's no clear CR->level mapping in 5e for those NPCs (who will certainly factor into any combat as meatshields and melee damage)? I was thinking about reverse-engineering them as crumby lvl2 fighters (given the 2 HD worth of HP they have), but they certainly aren't on par with a lvl2 fighter, given the lack of action surge, second wind, etc., so the encounters would end up being too hard compared to PCs or DMPCs.   Could they be lvl1-equivalents, essentially trading any abilities a PC would have for extra HP? How would this work at later levels with higher CR NPCs (veteran, priest, mage, etc.)? I'd rather not have to build a bunch of DMPCs as hirelings, because I want the NPCs to be a bit vanilla compared to the versatility of my player. I'm already introducing 1-2 DMPCs to the game for her to take control over as she gets a feel for the flow of the game (for now, she'll handle them out of combat, and I'll effectively show her how to utilize them until she's ready).     Just to be clear, I'm comfortable with the monster-generation rules for crafting NPCs as enemies to determine their CR, but I'm confused on how to use them in the adventuring party when budgeting encounter difficulty XP.
Reflection of a line in a plane The line $l_1$ has the equation $r=(6i+2-2k)+\lambda(4i+5j-k)$ and the plane $\pi_1$: $2x-y+4z=4$, the line $l_2$ is the reflection of $l_1$ in the plane $\pi_1$. Find the exact vector equation of line $l_2$   So the line intersects the plane when $\lambda=-2$, giving the point $(-2,-8,0)$ which will be common on $l_1$ and $l_2$. But I am unsure on how to find the direction vector for $l_2$. Any help would be appreciated. What causes a "Java Hotspot 64-Bit Server VM Warning"? I get this warning:     Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release   What does it mean? Do you have to take the second leg of a domestic flight? How to Select Columns in Editors (Atom,Notepad++, Kate, VIM, Sublime, Textpad,etc) and IDEs (NetBeans, IntelliJ IDEA, Eclipse, Visual Studio, etc) What's the proper way to typeset a differential operator? I can't seem to find any consensus on the right way to typeset a differential operator, whether it is:   in a standalone context:  as part of a derivative:  as part of an integral:    In all of these cases, I have seen them sometimes italicized like variables (as in the second and third examples above) and sometimes not italicized like operator names (as in the first example above). There is also additional variation in how much spacing goes between the "d" and whatever it is acting on.  Seeing as this is an incredibly common symbol in many branches of mathematics, I am curious about the lack of standardization -- I've seen all possible combinations used in all possible contexts by many respected authors and publishers.  Are there any rules of thumb that I can follow? I personally tend to prefer the non-italicized version with very little space next to it, so I add:  \renewcommand{\d}[1]{\ensuremath{\operatorname{d}\!{#1}}}   to my default preamble, and use that everywhere, but I'd like to know if I'm breaking any hard-and-fast rules here. I do love to listen to music while watching text YouTube videos, but I can't because YouTube can't be muted.  I use the respect audio focus in  Music Player.  I have tried App Volume Control but it did nothing! I have a question regarding classification in general. Let $f$ be a classifier, which outputs a set of probabilities given some data D. Normally, one would say: well, if $P(c|D) &gt; 0.5$, we will assign a class 1, otherwise 0 (let this be a binary classification).   My question is, what if I find out, that if I classify the class as 1 also when the probabilities are larger than, for instance 0.2, and the classifier performs better. Is it legitimate to then use this new threshold when doing classification?  I would interpret the necessity for lower classification bound in the context of the data emitting a smaller signal; yet still significant for the classification problem.  I realize this is one way to do it. However, if this is not correct thinking of reducing the threshold, what would be some data transformations, which emphasize individual features in a similar manner, so that the threshold can remain at 0.5? Why is negative times negative = positive? Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc.  I went ahead and gave them a proof by contradiction like so:  Assume $(-x) \cdot (-y) = -xy$  Then divide both sides by $(-x)$ and you get $(-y) = y$  Since we have a contradiction, then our first assumption must be incorrect.  I'm guessing I did something wrong here. Since the conclusion of $(-x) \cdot (-y) = (xy)$ is hard to derive from what I wrote.  Is there a better way to explain this?  Is my proof incorrect?  Also, what would be an intuitive way to explain the negation concept, if there is one? Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$ I am really struggling with my proofs class, I don't really understand how to prove a statement like this, or what the epsilon is standing for..  Suppose that $(s_n)$ converges to s.  Prove that $(s_n^2)$ converges to $s^2$ directly without using the fact that $lim(s_nt_n)=st$  Suppose that $(s_n)$ converges to s. Then, since $(s_n)$ is convergent, there exists an $M_1$ such that $|S_n|&lt;M_1$, for all $n\in \!\,\mathbb{N} \!\,$. Let $M=M_1+|S|$ (I don't completely understand this step...). Then given $ε&gt;0$, there exists N such that n>N implies that $|s_n-s|&lt;ε/M$. Thus for n>N, we have $|s_n^2-s^2|=|s_n-s|*|s_n+s|&lt;(ε/M)(M)=ε$. Hence, $s_n^2$ converges to $s^2$. Network simplex method, leaving and entering variables How do you compare two folders and copy the difference to a third folder? You've got three folders:   folder current, which contains your current files folder old, which contains an older version of the same files folder difference, which is just an empty folder   How do you compare old with current and copy the files which are different (or entirely new) in current to difference?    I have searched all around and it seems like a simple thing to tackle, but I can't get it to work in my particular example. Most sources suggested the use of rsync so I ended up with the following command:  rsync -ac --compare-dest=../old/ new/ difference/   What this does however, is copies all the files from new to difference, even those which are the same as in old.  In case it helps (maybe the command is fine and the fault lies elsewhere), this is how I tested this:   I made the three folders. I made several text files with different contents in old. I copied the files from old to new. I changed the contents of some of the files in new and added a few additional files. I ran the above command and checked the results in difference.   I have been looking for a solution for the past couple of days and I'd really appreciate some help. It doesn't necessarily have to be using rsync, but I'd like to know what I'm doing wrong if possible. What's the easiest way to set up a LAMP stack? Short story about a robot who wants to become a writer Prove that $1 + \cos\alpha + \cos\beta + \cos\gamma = 0$ If $\alpha + \beta + \gamma = \pi $ and $\tan(\frac{-\alpha + \beta + \gamma}4)\tan(\frac{\alpha - \beta + \gamma}4)\tan(\frac{\alpha + \beta - \gamma}4) = 1$  Then prove that:     $1 + \cos\alpha + \cos\beta + \cos\gamma = 0$.   I have no idea how to go about this.   Please help. How do I put an image texture on a material in Cycles? I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :) What is the best collation to use for MySQL with PHP? I'm wondering if there is a "best" choice for collation in MySQL for a general website where you aren't 100% sure of what will be entered? I understand that all the encodings should be the same, such as MySQL, Apache, the HTML and anything inside PHP.  In the past I have set PHP to output in "UTF-8", but which collation does this match in MySQL? I'm thinking it's one of the UTF-8 ones, but I have used utf8_unicode_ci, utf8_general_ci, and utf8_bin before. Kernel requires an x86-64 CPU, but only detected an i686 CPU. How can I install Lubuntu/Ubuntu? I'm trying to install Lubuntu on my laptop (sorta old 2005). [Laptop stats: Intel® Celeron® CPU 410 @ 1.46 GHz 1.47GHz, 448 MB of RAM]  I press Install and this message appears:   This kernel requires an x86-64 CPU, but only detected an i686 CPU.  Unable to boot - please use a kernel appropriate for your CPU.   What can I do to install Lubuntu on my computer? How can I configure the Ubuntu Dock to show windows only from the current workspace? I would like my Dock to show only the windows of the current workspace. Especially in the little preview window. I find it very confusing to jump around workspaces when trying to find the right window. The phrase for when: working in a group to divide responsibility and reduce malicious intent Is it appropriate to ask what a public beta sites needs to graduate? I came across  today in a separate question:     The only thing holding [Code Review] back from graduating is the lack of high rep users - there just aren't enough 1k+, 3k+ users on the site, and it can't quite yet sustain an election. Every single thing about CR is ready but that - it's really just a matter of time at this point (and, well, voting).   Almost all the posts about what the criteria for graduation are vague and don't mention specific examples:       The first question specifically asks about 2 beta (now graduated) sites, but the answer is more general, "Look at this blog" with general guidance.  How often are site stats reviewed by the team in charge of betas? And is it appropriate to create meta questions asking where a site stands to get feedback to the community on how to improve?