One of the successful managers were asked   or     One of the successful managers was asked
One of the boys who always give/gives the correct answer is Samuel.   As per rule, one of is followed by plural noun/pronoun and singular helping verb, so we should be using gives in the sentence. But the answer is give.
I ask this Question on behalf of my neighbor.   Their 12 year old son saw his parents having sex.  As there is only one room in their home we can't say its the parents' mistake... but now the question is how do they handle the situation? How can I use ranges in a switch case statement using JavaScript? Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$ I'm working on my Discrete Mathematics homework and they are asking me this:  Prove or show a counterexample for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$  I'm not completely sure how to prove it. I was thinking to find a counterexample like zero but I'm not sure if that it's going to work. Or maybe try to approach it backwards?   I'm a little bit lost Simple Power Series Expansion for Problems similar to $f = (1 + \epsilon \,x)^{1/\epsilon}$ I was flicking through a book on perturbation methods and saw a simple question asking the reader to expand the following expression for $f$ in a power series (up to the first 2 terms):  $f = (1 + \epsilon \,x)^{1/\epsilon}$, where $\epsilon$ is a small parameter. I'm sure this is very simple, but I wasn't certain about the best way to approach this. A quick look at mathematica tells me the solution is $e^x - \frac{1}{2} (e^x x^2) \,\epsilon + ...$. How would I go about getting this answer - and more importantly, how would I systematically find series expansions for problems similar to this one? Can I create a TIN from contours lines (shp) in QGIS? I need to do a slope analysis, and would like to make a TIN from 2m contours lines.  Or do a slope analysis directly from contours? The only DEM available is not precise enough.  I do not have any elevation raster files.  And how do I then make slope classes?  The TIN properties does not seem to be able to classify anything other than elevation. \@seccntformat only for section Fast Pixel Search in Java Has the Magical Community breached the Final Frontier? (aka Wizards in Space?) Have they? Given that Muggles put the first man in space in 1961, even by 1991 a lot of Muggleborns perfectly aware of the space-travel would have passed through Hogwarts and into the Ministry, even the Department of Mysteries (which seems to be a bit like their research division/Area 51 combo) And even leaving Muggle technology (which Wizards don't care for or about) aside, Humans have wondered about air travel to &quot;other worlds&quot; and meeting aliens from the time of the Ancient Greeks, surely some Witch or Wizard somewhere might have wondered if it really was possible to fly to the moon? So, is there any canon (aka Books + Pottermore + Rowling interviews) evidence of the Wizarding community having ever travelled or trying to travel to space / other planets or satellites? ETA: Note, I am also totally okay (and in fact would be eager for) historical &quot;Famous Wizard&quot; card-like tidbits from canon-sources.  AWESOME example (that I'm frankly not expecting): When the Muggles managed to land on the Moon, the Department of Mysteries had to scramble to hide the Silver-backed Moon Dragon conservatory they had been maintaining near the landing site. ALSO AWESOME example (that I am hoping for): Warlock Flibberti and Witch Tigget misused this earth-based spell and amusingly found themselves on the moon with their pet monkey instead! Replace background while using HDRI for lighting? How can I replace the background of my scene, but keep the reflections and lighting generated from my HDRI? Maybe the underlying question is what the Voltage-Current curve looks like. Can I drive it from a voltage source (like you drive a heater) or from a current source (like you drive an LED)? Or even different than those two options?  ADDITIONAL1: Say (hypothetically) I have two commercially available identical Peltier's, they are spec'd 6V/3A. Can I connect these in series to a 12Vdc power supply without any worries?  CONCLUSION1: Current/Voltage load curve is reasonably linear, both driving from current or voltage source will do fine as long as the device is operated within its spec. (Olin Lathrop, Russell McMahon)  CONCLUSION2: Don't drive a Peltier from PWM, power loss due to current increase, grows more rapidly than cooling power. (Olin Lathrop)  CONCLUSION3: Beware the mechanical wear of the device with continues cycling. Eg. don't use a thermostat on/off controller. (Russell McMahon) Do indexes work with "IN" clause If I have a query like:  Select EmployeeId  From Employee  Where EmployeeTypeId IN (1,2,3)   and I have an index on the EmployeeTypeId field, does SQL server still use that index? Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric How can I set the box plot (i.e. axis) ratio of a usual 2D plot to a given value, say 4:3.  I don't want to use unit vector ratio since the quantities of the independent and dependent variables are of completely different orders of magnitude. Obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ where $\theta_{1}$ and $\theta_{2}$ are i.i.d $\text{Uniform}[0, 2\pi)$ I have 2 i.i.d Uniform random variables $\theta_{1}$ and $\theta_{2}$ on $[0, 2\pi)$. Here the problem pushes us to consider that all operations are made modulo $2\pi$. My question is how to obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ and then obtain the conditional PDF of $\theta_{1}$ given $\theta_{1} - \theta_{2}$??. For the second part It can be deduced from the first by writing it as the joint PDF divided by the PDF of $\theta_{1}$. But for the first part, A common idea that I saw is to derive the $\text{CDF}(x, y) = P(\theta_{1} - \theta_{2} \le x$, $\theta_{1} \le y$) and then perform derivations respect to $x$ and $y$. Is this a right approach? If yes, how to proceed with CDF especially with our uniform distribution restrictions? Creating controls within a Loop I have have some code which adds new cells to a table and fills them with text boxes.   The way I've coded it so far works fine:          TableCell tCell1 = new TableCell();         TableCell tCell2 = new TableCell();         TableCell tCell3 = new TableCell();         TableCell tCell4 = new TableCell();         TableCell tCell5 = new TableCell();         TableCell tCell6 = new TableCell();         TableCell tCell7 = new TableCell();          TextBox txt1 = new TextBox();         TextBox txt2 = new TextBox();         TextBox txt3 = new TextBox();         TextBox txt4 = new TextBox();         TextBox txt5 = new TextBox();         TextBox txt6 = new TextBox();         TextBox txt7 = new TextBox();          tCell1.Controls.Add(txt1);         tCell2.Controls.Add(txt2);         tCell3.Controls.Add(txt3);         tCell4.Controls.Add(txt4);         tCell5.Controls.Add(txt5);         tCell6.Controls.Add(txt6);         tCell7.Controls.Add(txt7);          tRow.Cells.Add(tCell1);         tRow.Cells.Add(tCell2);         tRow.Cells.Add(tCell3);         tRow.Cells.Add(tCell4);         tRow.Cells.Add(tCell5);         tRow.Cells.Add(tCell6);         tRow.Cells.Add(tCell7);   As you can see there's basically 4 instructions getting repeated 7 times. I'm sure there has to be a way to accomplish this with just 4 lines of code within a FOR loop and having all the names dynamically assigned but I just can't seem to find anything that would point me in the direction of how to do it.  Something like the following is what I'm after:      for (int i = 0; i &lt; 6; i++)     {          TableCell tCell[i] = new TableCell();         TextBox txt[i] = new TextBox();         tCell[i].Controls.Add(txt[i]);         tRow.Cells.Add(tCell[i]);      }    Any help would be much appreciated. Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective. Suppose $X$ is a set and $f : X \to X$ is a function.  If $X$ is a finite set, prove that $f$ is injective if and only if $f$ is surjective. Show that when $X$ is an infinite set, the statement is not true in general.   For that, let $X = \mathbb{R}$ and find a function $f: \mathbb{R} \to \mathbb{R}$ which is injective but not surjective, and a function $g: \mathbb{R} \to \mathbb{R}$ which is surjective but not injective  My attempt at the first part   Suppose that the function is surjective but not injective. Let $a,b \in X$ such that $f(a)=f(b)$ but $a \not =b$. Now since this is a finite set mapping to itself then there are not enough elements in $X$ to map to $X$ since two elements were used to map to one element, thus the function can't be surjective. Therefore if the function is surjective it is also injective.   Now suppose that the function is injective but not surjective. Let $a \in X$ such that $f(b)\not =a$ for all $b \in X$. Since the function was assusmed to be injective each $a \in X$ must map to an element of $X$, thus must have two elemetns in $X$ mapping to the same element in $X$. Hence the function can't be injective, therefore if the function is injective it must be surjective.   Would an exponetial function work for injective but not surjective since can't map to negative numbers. And an example of a function that is surjective but not injective could be a log function since none of the negative numbers get mapped to anything?   Also I'm having trouble seeing why it has to be finite for the first part to work. I understand it has something to do with the pigeonhole principle but its not that clear to me. Move EFI System Partition to another drive In a ring, I was trying to prove that for all $a$, $a0 = 0$.  But I found that this depended on a lemma, that is, for all $a$ and $b$, $a(-b) = -ab = (-a)b$.  I am wondering how to prove these directly from the definition of a ring.  Many thanks! Show that some monomial ideal is primary Show that $I=(X_{k_1}^{a_1},...,X_{k_s}^{a_s})$ is $(X_{k_1},...,X_{k_s})$-primary.   I noticed  that $$\sqrt{({X_{i_1}}^{a_1},...,{X_{i_k}}^{a_k})}=\sqrt{({X_{i_1}}^{a_1})+\cdots+({X_{i_k}}^{a_k})}=\sqrt{\sqrt{(X_{i_1})^{a_1}}+\cdots+\sqrt{(X_{i_k})^{a_k}}}=\sqrt{(X_{i_1})+\cdots+(X_{i_k})}=\sqrt{(X_{i_1},...,X_{i_k})}=(X_{i_1},...,X_{i_k}).$$ I have to show that $I$ is $P$-primary (where $P=(X_{k_1},...,X_{k_s})$), i.e., if $u v\in I$ then $u\in I$ or $v\in P$. I tried to prove that if $u\notin I$ and $v\notin P$ then $uv\notin I$. (There is a similar question, but the answer is too hard for me.) I have a table like this:   Column  | Type | Modifiers  ---------+------+-----------  country | text |   food_id | int  |   eaten   | date |    And for each country, I want to get the food that is eaten most often.  The best I can think of (I'm using postgres) is:  CREATE TEMP TABLE counts AS     SELECT country, food_id, count(*) as count FROM munch GROUP BY country, food_id;  CREATE TEMP TABLE max_counts AS     SELECT country, max(count) as max_count FROM counts GROUP BY country;  SELECT country, max(food_id) FROM counts     WHERE (country, count) IN (SELECT * from max_counts) GROUP BY country;   In that last statement, the GROUP BY and max() are needed to break ties, where two different foods have the same count.  This seems like a lot of work for something conceptually simple.  Is there a more straight forward way to do it?