Suppose I have both  and  under my control. They have two similar abilities:     Kor Spiritdancer: Whenever you cast an Aura spell, you may draw a card.      Mesa Enchantress: Whenever you cast an enchantment spell, you may draw a card.   If I now cast an Enchantment &mdash; Aura card, do I draw two cards or one?
Lets say I have a  creature that says "Whenever another creature enters the battlefield under your control, you may gain 1 life." and I currently have all 4 of them in the battlefield. Then I cast another creature and : Do I get 1 or 4 life? Does that effect trigger for every priest or just once? thanks for help
Showing order of $Z (G) =1$ or $pq$ "To work for" vs. "to work in" vs. "to work at" Use of a semicolon before and comma after "however" Several years ago, a previous boss told me to use a semicolon and comma with the word "however".  I've always questioned this and would like to know if the following random sentences are using the correct method.        Our plane was delayed overnight; however, the airlines reimbursed us for lodging.   It looks as though he's upset; however, she told me he always has that look on his face.   I want to find him a nice gift; however, I am a broke until payday.      Normally I would use a less "wordy" sentence in casual writing, but hopefully the example will suffice.  For example, on number 3 I would usually type:      I want to get him a nice gift, but I'm broke until payday. Give the "some of your recent flags have been declined" banner some room The "some of your recent flags have been declined" message recently got a banner, which makes it stand out  more (which is nice) but it touches the 'Flag' button, which is less nice. Can it have some margin at the bottom (and perhaps less padding?)    Tested in the latest Safari and Firefox on macOS Catalina. Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$ Let $S\subset\mathbb{R}$ be a non-empty bounded above set. Then there exists a monotone increasing sequence $\{x_n\}\subset S$ such that    $$\lim_{n\to\infty}x_n=\sup S.$$   I'm struggling with creating a formal proof for this problem. I understand that this has to be true, but I'm unsure of how to go about proving it.  I said that $\sup S = C$ and $x_n= C - y/n$ where $y$ is dependent on the size of $S$, but this is just a bunch of jumbled ideas and I can't really think of a way to formalize a proof. Any idea, even totally different from mine would be appreciated. If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$ If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$   I was practicing quadratic equation questions online but I am stuck on this question.  I found the values of roots $a= 1$, $b= 1/2$ How to install Ubuntu on VirtualBox? How to stop the Facebook app from updating itself automatically? I have the Facebook app installed on my Android 7 phone.   Auto-update is disabled for all applications on my Play Store account I have disabled installation from unknown sources   For some reason, whenever there is an update of the Facebook app, it automatically updates itself even though I disabled auto-updates for all applications.  How to stop the Facebook app from updating itself automatically? Submodule of free module over a p.i.d. is free even when the module is not finitely generated? Can magnets rotate infinitely? There are many videos on youtube in which people arranged magnets in circle and rotated one placing in middle of that circle on a shaft, and the magnet (magnet motor) starts madly and continues its movement. Do they really rotate infinitely? If so, do they from where they get that extra energy to move so fast and infinitely?    EDIT: This question is about real world scenario  UPDATE: I am unable to find that particular video about which i talked about -- I added them to my favourites, but they are all now deleted :( -- there are hundreds of that that kind of videos. Some example videos links How many ways can N elements be partitioned into subsets of size K? I do as follows  $(1+x)^n= \binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+...+\binom{n}{n}x^n$   differentiating in both sides  $n(1+x)^{n-1}= \binom{n}{1}+2\binom{n}{2}x+3\binom{n}{3}x^2...+n\binom{n}{n}x^{n-1}$  then, for $x=1$  $n \cdot2^{n-1} = \sum_{k=1}^{n}k\binom{n}{k}$  From here, I don't know how to proceed, I have tried to multiply both sides for $(1+x)$ to make $n \cdot2^{n}$ but then the summatory changes, I don't know how to prove the equality. Is the current obtained using Ohm's law that which passes through the resistor or that which passes through the circuit? Shouldn't the current passing through a resistor be lesser than that which passes through a circuit? My understanding is that since Current = Charges/Time. If there exists a resistance to the flow of charges, then that must mean the charges slow down, meaning that more time is required to pass through a point. So, the current should then decrease. But, since this opposition to the flow of charges doesn't exist in the ENTIRE circuit, it should really only decrease the current in the resistor, right? Am I confusing the resistance of the resistor with the resistance of the wire? Any help will be appreciated! Thanks a bunch for lending me some of your time :D Why are Python's 'private' methods not actually private? The output from the following script \documentclass{article} \usepackage{tikz} \usepackage{graphicx} \begin{document} \begin{tikzpicture}   \node(title)[text width = 0.25\textwidth, text height = 3 cm, draw]{title};   \end{tikzpicture} \end{document}  is  How can I vertically align the text in the node? Specifying the text depth as in \node(title)[text width = 0.25\textwidth, text height = 1cm, text depth = 1 cm, draw]{     title line 1\\     title line 2\\     title line 3};  Does not result in the text being vertically centred. Probability Interval for Gamma Distribution There is something that I am doing wrong in the exercise below and I would appreciate some help figuring it out.  Let $X_1, X_2, \ldots, X_5$ be a random sample from a $\Gamma \left(3,3 \right)$ distribution . Define $W=\sum_{i=1}^5 X_i $.    Obtain the distribution of $W$ and of $2W/3$ Find $c_1$ and $c_2$ such that $P \left( c_1 &lt; W &lt;c_2 \right)=0.95 $     Since $W$ is the sum of iid gamma variables, $W \sim \Gamma \left(15,3 \right)$ and now a straightforward transformation argument shows that $Y=\frac{2}{3} W \sim \chi^2 \left(30 \right) $. This completes question 1.  Now for question 2, my thoughts were to transform these probabilities using the result from question 1, namely that $\frac{2}{3} W \sim \chi^2 \left(30 \right) $. Hence, unless I have made a horrible mistake here:  $$P \left( \frac{2}{3} c_1 &lt; Y &lt; \frac{2}{3} c_2 \right)=0.95 $$  We can find the constants from a chisquare table for $30$ degrees of freedom. In my case, they are $16.791$ for the lower bound and $46.979$ for the upper one.   Then if we equate $\frac{2}{3}c_1=16.791$ and solve for $c_1$ we should be able to find the constant for the above gamma confidence interval, right?   The problem is that according to $R$, $P \left( W&lt;c_1 \right) =1 $, instead of  the desired $0.025$ which means I have gone wrong somewhere. I do not think it is in question though $1$ as I have verified the result many times.   Thank you. Converting FLV to MP4 Using FFMPEG and Preserving the Quality Im trying to use ffmpeg to convert my flv files to mp4 to play them on iOS devices but the converted video has a much worse quality than the original one.  Here is the command i use:  ffmpeg -i input.flv -ar 22050 output.mp4   I would really appreciate if someone could provide me with the best settings for flv to mp4 conversion. Is there a closed form expression for $\text{n}^{\text{th}}$ coefficient of Maclaurin series of  $$\ln(1-x+x^2)$$ Why does getopts only work the first time? Let $X_1$ and $X_2$ be two independent exponential random variables with the PDFs $f_{X_1}(x_1)=\lambda_1 \exp(-\lambda_1 x_1)$ and $f_{X_2}(x_2)=\lambda_2 \exp(-\lambda_2 x_2)$.   Let $X= \frac{X_1X_2}{X_1+X_2+a}$ be a r.v. for which I want to derive the CDF, where $a$ is a positive constant.  In other words, I need to calculate $\mathbb{P}\{X &lt;x \}$.  Any ideas or hints?  Edit (attempt):  Using a similar approach to that used , we have $X_1 \in [0, \infty)$ and  $X_2 \in [0, \frac{x(x_1+a)}{x_1-x})$. The latter interval results from: $\frac{x_1x_2}{x_1+x_2+a} &lt; x$, thus $x_2(x_1-x)&lt;x(x_1+a)$ which implies $x_2 &lt; \frac{x(x_1+a)}{x_1-x}$; but I am not sure if this is correct since $x_1-x$ can sometimes be negative (?). Based on the above, we can write: \begin{align}  \mathbb{P} \{ \frac{X_1X_2}{X_1+X_2+a} &lt; x \}  &amp; = \int_{x_1=0}^\infty \int_{x_2=0}^{ \frac{x(x_1+a)}{x_1-x}} \lambda_1 \exp(-\lambda_1 x_1) \lambda_2 \exp(-\lambda_2 x_2)  dx_2 dx_1  \\ &amp;= \int_{x_1=0}^\infty \left(1-\exp(-\lambda_2\frac{x(x_1+a)}{x_1-x}) \right) \lambda_1 \exp(-\lambda_1 x_1) dx_1  \\ &amp; = 1-\lambda_1 \int_{x_1=x}^\infty \exp(-\lambda_2\frac{x(x_1+a)}{x_1-x} ) \exp(-\lambda_1 x_1)   dx_1 \end{align} In the last equality: for the integral of $\lambda_1 \exp(-\lambda_1 x_1) dx_1$, I suppose that $x_1 \in [0,\infty)$, whereas for the second term I suppose that $x_1 \ge x$ (since $x_2$ should be positive) (?).  Is my approach correct ?