Okay let’s take  for example they have an alternate racial trait called cats claws which give a 1d4 claw attack. Then take a look at  and I just realized how awkward that is to say. Anyways the bloodrager gives a a claw attack that deals 1d6 for medium creatures from the get go. So that begs the question which source of claws wins? Granted these are just examples that I noticed first there’s probably other ones out there that I’m not aware of.
My character has a bite attack from his race.  What happens if he gains another bite attack from class abilities or spells?  Does the damage increase?  Can he make more than one attack?  Or is it simply that only the better version applies?  I would prefer answers from a Pathfinder context but 3.5e is also acceptable.
Choosing numbers without consecutive numbers. In how many ways can we choose $r$ numbers from $\{1,2,3,...,n\}$,   In a way where we have no consecutive numbers in the set? (like $1,2$) Reference - What does this error mean in PHP? What solutions does the equation 4x≡2mod10 have? (Hint, it will have more that one.) What about solutions to an equation ax≡dmodn, where d=gcd(a,n)? What solutions does the equation $4x\equiv2\mod10$ have? (Hint, it will have more that one.) What about solutions to an equation $ax\equiv d\mod n$, where $d=\gcd(a,n)$?  This is the question that appeared in our universities last year paper. But it seems very difficult for me like for first part I am able to solve by simplifications I got $x=5\cdot Z +3$ as solution which makes sense and seems fair but for the second one, I have no idea how can I approach that. Can you please help me out with that one. I tried to simplify that by using Euclidean algorithm but still, I didn't get any idea that what actually the solution will be. My final exam is on 2nd of next month and because of covid I am unable to contact in person for any help. So any help from this site will be appreciated. Thank you for looking at this question! What does the register keyword do in C language?  I have read that it is used for optimizing but is not clearly defined in any standard.  Is it still relevant and if so, when would you use it? Can this identity be derived from the binomial theorem?  $$n(n+1)2^{n-2} = \sum_{i=1}^{n}  i^2 \binom{n}{i}$$    I tried starting from $2^n = \displaystyle\sum_{i=0}^{n} \binom{n}{i}$ and dividing it by $4$ in order to get $2^{n-2}$. Background: I'm making a retro style game for both fun, and an unofficial contest.   I have bought a song, song X. However, I then found notation for song X, and all the instruments. So basically, it's a program recreating song X in a sense.  I took the notation, and used another program to make it sound like a chiptune does (just for the fun of it, and it sounds good :P). However, I would like to use this in my game. It's non-commercial, but is this allowed? I would've said yes, because I'm not actually using the original, copyrighted song.  I think the main point is can I:   Use the music with no reference to the author Use the music with a reference, since it's non-profit. Not use the music at all since the melody and rhythm is copyright. Let's say I have code like this:  $dbh = new PDO("blahblah");  $stmt = $dbh-&gt;prepare('SELECT * FROM users where username = :username'); $stmt-&gt;execute( array(':username' =&gt; $_REQUEST['username']) );   The PDO documentation says:     The parameters to prepared statements don't need to be quoted; the driver handles it for you.   Is that truly all I need to do to avoid SQL injections?  Is it really that easy?  You can assume MySQL if it makes a difference.  Also, I'm really only curious about the use of prepared statements against SQL injection.  In this context, I don't care about XSS or other possible vulnerabilities. This is not for homework. (I am a grader for a class.)  The case in which $G$ is finite is trivial. (That is, use a corollary to Lagrange's Theorem, and set $[G:H] = \dfrac{|G|}{|H|}$, and similarly for $[H:K]$.) How do you prove this for when $G$ is infinite?   The proof of this statement that I know well tries to show that $[G:K]$ is finite iff $[G:H]$ and $[H:K]$ are finite, but I am not a fan of that proof. For pedagogical purposes, I'm looking for a better proof. (The course uses right cosets by convention.)  The course has just started covering normal subgroups, so things like the Isomorphism Theorems are not known yet. Mechanics of Horizontal Stretching and Shrinking I know $y=2f(x)$ doubles the $y$ value in vertical shifting, and I know that $y=(1/2)f(x)$ halves the $y$ value. But, why does $y=f(2x)$ halve the $x$ value, and why does $y=f((1/2)x)$ double the $x$ value in horizontal shifting? I looked at the graphs, and I see the difference, but I want to know the math behind why it halves instead of doubling the $x$ value for $y=f(2x)$. Maybe this is a stupid question, but could someone help me out?  Thank you. Lagrangian of Schrodinger field The usual Schrodinger Lagrangian is $$ \tag 1 i(\psi^{*}\partial_{t}\psi ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi, $$ which gives the correct equations of motion, with conjugate momentum for $\psi^{*}$ vanishing. This Lagrangian density is not real but differs from a real Lagrangian density  $$ \tag 2 \frac{i}{2}(\psi^{*}\partial_{t}\psi -\psi \partial_{t}\psi^{*} ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi $$ by a total derivative.  My trouble is that these two lagrangian densities lead to different conjugate momenta and hence when setting equal time commutation relations, I am getting different results (a factor of 2 is causing the problem). I can rescale the fields but then my Hamiltonian also changes. Then applying Heisenberg equation of motion, I don't get the operator Schrodinger equation.   Is it possible to work with the real Lagrangian density and somehow get the correct commutation relations? I would have expected two Lagrangians differing by total derivative terms to give identical commutation relations (since canonical transformations preserve them). But perhaps I am making some very simple error. Unless all conjugate momenta are equivalent for two Lagrangians differing by total derivatives, how does one choose the correct one?   I guess the same thing happens for other first order systems like Dirac Lagrangian also. The following question is on my homework assignment that I cannot figure out:     Let U and V be independent random variables, each having a normal distribution with mean zero and variance one. Find the moment generating function of the random variable W = UV .   I have looked around online, and cannot find an answer to this question. In fact, the only answers I can find that even relate to the product of standard normal random variables are using techniques that we never covered in my class. We covered in class how to find the MGF for linear combinations of random variables, by W isn't linear, its a product of two normals. So that technique won't work.   What am I supposed to do? I am completely at a loss. I have tried multiplying the MGFs of U and V together, but that leaves me with something ugly that I can't reduce. A word for someone who you share a half-sibling with This is probably best explained with an example.  Alice and Bob have a child, Erin. Bob and Carol have a child, Frank. Carol and Dan have a child, Grace. Clearly, Erin and Frank are half-siblings, because of their father, Bob. Similarly, Grace and Frank share their mother, Carol.  Erin and Grace have no parents in common, and are thus not half-siblings. However, is there a term for their relation? unable to printout arrayOfInt initialised within the class constructor What has been proved about the big bang, and what has not? Ok so the universe is in constant expansion, that has been proven, right? And that means that it was smaller in the past.. But what's the smallest size we can be sure the universe has ever had?  I just want to know what's the oldest thing we are sure about. I have a polygon shape file that has many overlapping features. Each feature represents an area used by polar bears. So some of the polygons overlap and some don't, and there are separate clusters of overlapping areas.   I would like to get a measure of how much overlap there is in a particular area. But I have no clue how to do this. I'm pretty new to GIS and am still learning the ropes, it just seems I can't find an answer. Log of products to sum of logs Today I updated to version 2.18.52 &amp; I can’t see the names of the people who send me a message. The only thing I see is the WhatsApp logo and the word “message”.    I can’t also see the status my friends posts, they all look black. I uninstalled the app, reset my phone &amp; nothing seems to work so far. It seems "See votes, expandable user card" goes on a second line on the activity page of the user profile resulting in a pretty bad look:    You can see it live on  (though of course that may change any day now depending on their rep-growth).  I'm using Chrome Version 67.0.3396.99 (Official Build) (64-bit) Why is median age a better statistic than mean age? If you look at       Or this Wikipedia page      Clearly  seems to be the statistic of choice when it comes to ages.  I am not able to explain to myself why  would be a worse statistic. Why is it so?  Originally posted  because I did not know this site existed. Does encrypting my home folder make my computer more secure? Do I have to enter my password more if my home folder is encrypted? What else should I know about encrypting my home folder?