When mixing 16 ounces of chocolate and 4 ounces of oil together and melting it how long will it last ? How should I store it ? Can it cause botulism ?
When I melt 16 oz of chocolate I add 4 oz of oil how long can I keep this and how should it be stored. Someone said something about botulism ??
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$ I got a function:       $f(x,y) = \frac {\sin (xy)}  {\sqrt {x^2 + y^2}}$ if $(x,y) \not =  (0,0)$, otherwise $f(x,y) = 0$,   and I should look at its continuity in $(0,0)$   I tried the sandwich theorem but got slightly stuck unfortunately  $ 0 \le \left|\frac {\sin (xy)}  {\sqrt {x^2 + y^2}}\right| \le 1$   I was thinking that $\sin (xy)$ is a restricted function, but not sure what to with $\sqrt {x^2 + y^2}$ if $x,y$ are too small so I think my idea doesn't work. Then it would look like:  $ 0 \le \left| {\sin (xy)} \right| \le \sqrt {x^2 + y^2} = 0$  Any other idea please? How to use more than 10 tab stops in bmatrix or other amsmath matrix environments? Is the power set of the natural numbers countable? What's the difference between Normalization and Standardization? At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean then dividing by its SD. But they seem interchangeable with other possibilities as well.   When creating some kind of universal score, that makes up $2$ different metrics, which have different means and different SD's, would you Normalize, Standardize, or something else? One person told me it's just a matter of taking each metric and dividing them by their SD, individually. Then summing the two. And that will result in a universal score that can be used to judge both metrics.  For instance, say you had the number of people who take the subway to work (in NYC) and the number of people who drove to work (in NYC).   $$\text{Train} \longrightarrow x$$ $$\text{Car} \longrightarrow y$$  If you wanted to create a universal score to quickly report traffic fluctuations, you can't just add $\text{mean}(x)$ and $\text{mean}(y)$ because there will be a LOT more people who ride the train. There's 8 million people living in NYC, plus tourists. That's millions of people taking the train everyday verse hundreds of thousands of people in cars. So they need to be transformed to a similar scale in order to be compared.  If $\text{mean}(x) = 8,000,000$  and $\text{mean}(y) = 800,000$  Would you normalize $x$ &amp; $y$ then sum? Would you standardize $x$ &amp; $y$ then sum? Or would you divide each by their respective SD then sum?  In order to get to a number that when fluctuates, represents total traffic fluctuations.  Any article or chapters of books for reference would be much appreciated. THANKS!  Also here's another example of what I'm trying to do.   Imagine you're a college dean, and you're discussing admission requirements. You may want students with at least a certain GPA and a certain test score. It'd be nice if they were both on the same scale because then you could just add the two together and say, "anyone with at least a 7.0 can get admitted." That way, if a prospective student has a 4.0 GPA, they could get as low as a 3.0 test score and still get admitted.  Inversely, if someone had a 3.0 GPA, they could still get admitted with a 4.0 test score.  But it's not like that. The ACT is on a 36 point scale and most GPA's are on 4.0 (some are 4.3, yes annoying). Since I can't just add an ACT and GPA to get some kind of universal score, how can I transform them so they can be added, thus creating a universal admission score.  And then as a Dean, I could just automatically accept anyone with a score above a certain threshold.  Or even automatically accept everyone whose score is within the top 95%.... those sorts of things.  Would that be normalization? standardization? or just dividing each by their SD then summing? How to graphically represent a language How to load a taxonomy term with case-sensitive? I used this      $this-&gt;termStorage-&gt;loadByProperties(['name' =&gt; 'test']);   I got two terms: Test, test. I want to get only one: test  This is working without case-sensitive:       $this-&gt;termStorage-&gt;getQuery()-&gt;condition('name', 'test', '=')-&gt;execute();       \Drupal::database()-&gt;select('taxonomy_term_field_data', 't')       -&gt;condition('t.name', 'test')       -&gt;fields('t', ['name'])       -&gt;execute()       -&gt;fetchAll();       \Drupal::database()-&gt;query("SELECT name FROM taxonomy_term_field_data WHERE name='test'")-&gt;fetchAll(); Word for a task which is flawed or doomed to failure but which you have to do anyway? When should I use "when" and "while"? But you can't find anything while you're crying.   But you can't find anything when you're crying.   I'll tell you about it while Frank saddles the horse.   I'll tell you about it when Frank saddles the horse.     When should I use when, and when while? Are these sentences correct? Complex differential equation How do I solve $$x'=e^{it}\overline{x}?$$  This is a complex differential equation, but I don't see how to solve it.  Edit: the original ODE is given by $$(x', y')=\begin{pmatrix}\cos t&amp; \sin t\\ \sin t&amp;-\cos t\end{pmatrix}(x,y)$$ I want to show that solutions of this ODE do not remain bounded for all $t$, and the idea was to solve the complex equation. Would a very small creature inside a sealed container carried by a character take damage from AOE spells? Assume character A is in the AOE of a damaging spell.  Character A is carrying a closed container inside his backpack, alongside several sheets of parchment.  Damaging spell description specifically states that items carried by a creature are not damaged even on a failed save. Unattended objects are damaged, though.  Inside said container there is a small creature. Creature has no problem living inside container for a long amount of time.  Does this creature take damage from the spell? If it does not, what mechanic prevents damage? Prove $g$ is a generator if $g^q=1 \pmod p$ Let $p$ be an odd prime and let $q=\frac{p-1}{2}$. If $g^q=-1\pmod p$ and $q$ is a prime, show that $g$ is a primitive root mod $p$.  I want to show $\{g,g^1,...,g^{p-1}\}=\{1,2,...p-1\}$. I argue by contradiction that if there're $x,y\in \{1,2,...p-1\},x&lt;y,g^x=g^y\pmod p$. Then $g^{y-x}=1\pmod p$. I don't know how to use the fact that $q$ is prime to lead to a contradiction. Infinite product with sign changes. For infinite products I know the following theorems:  Theorem I. If $a_n \geq 0$ for all $n$ then $\prod (1+a_n)$ converges if and only if $\sum a_n$ converges.  Theorem II. If $-1 &lt; a_n \leq 0$ for all $n$ then $\prod (1+a_n)$ converges if and only if $\sum a_n$ converges.  My question is what are necessary and sufficient conditions (possibly including more restrictions than in I and II) for $\prod (1+a_n)$ convergence/divergence as related to  $\sum a_n$ convergence/divergence  if the sequence of terms $a_n$ can switch signs repeatedly but always stay greater than $-1$.  I already know the trivial equivalence of $\prod(1+a_n)$ and $\sum\ln(1+a_n)$. I was wondering if $\mathbf{A}\times\mathbf{C}=\mathbf{B}$ and $\mathbf{A}\cdot{\mathbf{C}}= p$, is it possible to express C in terms of A, B, and p?  Note: A, B, C are vectors and p is a scalar.  Sorry if this question has been asked before. If so, can anyone give me a link to it? Increase partition size on which Ubuntu is installed? I have Ubuntu installed on a drive. The problem is it is running low on disk space. This is installed on vmware. I expanded the virtual drive and booted into ubuntu. But when I opened gparted(sudo gparted), the move/resize option is unavailable. This is the partition Ubuntu is installed on, but I need to resize it. Any ideas? I am comfortable using command line I remember being taught that the correct order of adjectives in English was something along the lines of "Opinion-Size-Age-Color-Material-Purpose."  However, it's been a long time and I'm pretty sure I've forgotten a few categories (I think there were eight or nine). Can anyone fill them in? Derivation of Maxwell's equations from field tensor lagrangian I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ (where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$ is the field tensor).  Substituting in for the definition of the field tensor yields $L = -\frac{1}{2}[(\partial_\mu A_\nu)(\partial^\mu A^\nu) - (\partial_\mu A_\nu)(\partial^\nu A^\mu)]$.  I know I should be using $A^\mu$ as the dynamical variable in the Euler-Lagrange equations, which become $\frac{\partial L}{\partial A_\mu} - \partial_\mu\frac{\partial L}{\partial(\partial_\mu A_\nu)} = - \partial_\mu\frac{\partial L}{\partial(\partial_\mu A_\nu)}$, but I'm confused about how to proceed from here.  I know I should end up with $\partial_\mu F^{\mu\nu} = 0$, but I don't quite see why.  Since $\mu$ and $\nu$ are dummy indices, I should be able to change them: how do the indices in the lagrangian relate to the indices in the derivatives in the Euler-Lagrange equations? Entering Unicode characters in LaTeX After some searching, I find very little on the incorporation of observation weights/measurement errors into principal components analysis. What I do find tends to rely on iterative approaches to include weightings (e.g., ). My question is why is this approach necessary? Why can't we use the eigenvectors of the weighted covariance matrix? By accident, I used rm on a file I didn't want to delete. Is there a way that I can get it back under Linux? How can I add a class to a block with code (development) For theming reasons I'd like to add a specific class at the "block" level to some of the blocks I'm generating with a custom module. I know there is a module , but I would rather like to do it directly in code (there is no need to change is afterwards).   I also know of , but that does not seem to allow adding or editing classes.  Is it possible to add a class with to a block from within my module code? I'm using Drupal 7.