Show that there are infinitely many powers of two starting with the digit 7
Starting digits of $2^n$.
Batch Requests/sec reported by DMV millions of times larger than Activity Monitor I have verified through SQL Server Profiler that my request per-second are around 30 request/s as is corroborated by SSMS Activity Monitor but sys.dm_os_performance_counters is reporting hundreds of millions/s.  Any idea what might be causing this gross discrepancy?  Query:  SELECT     RTrim(LTrim(object_name)) as object_name,     RTrim(LTrim(counter_name)) as counter_name,     cntr_value FROM     sys.dm_os_performance_counters  WHERE      instance_name IN ('', '_Total')     and counter_name IN (         N'Batch Requests/sec'         , N'SQL Compilations/sec'         , N'SQL Re-Compilations/sec'         , N'Transactions/sec')   Results:  object_name counter_name    cntr_value SQLServer:Databases Transactions/sec    191721399 SQLServer:SQL Statistics    Batch Requests/sec  242955426 SQLServer:SQL Statistics    SQL Compilations/sec    42048371 SQLServer:SQL Statistics    SQL Re-Compilations/sec 1200947 I've been reading up on STL containers in my book on C++, specifically the section on the STL and its containers. Now I do understand each and every one of them have their own specific properties, and I'm close to memorizing all of them... But what I do not yet grasp is in which scenario each of them is used.  What is the explanation? Example code is much prefered. A word that means stage-fright, but for a person? Suppose you met a famous person, and you were shy and anxious and almost overwhelmed by them.   Is there a word for describing that? Similar to getting stage fright, or "choking", except in this case for a person?     When he said hello to me, I couldn't respond. I (was) __________. Why can't two series-connected diodes act as a BJT? I have to find an easy ring which this ring is isomorphic with.  I can prove that $5 = (2+i)(2-i) \in (2+i)$ but this doesn't help me further.  My book says the answer is $\mathbb {Z_5} $ CSS bug with printing site pages (now with 100% more suggested fix included!) Total number paths between two nodes in a complete graph Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$ Show that for $n \geq 5$, the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$.     I'm not sure on how to handle this problem. I know that the commutator subgroup $G'$ will consist of products of commutators $[\sigma_{i}, \tau_{i}]$ for permutations $\sigma_{i}, \tau_{i} \in S_{n}$. However, I don't know where to start. What would be the best way to approach this? Find the sum : $\frac{1}{\cos0^\circ\cos1^\circ}+\frac{1}{\cos1^\circ \cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+$ Find the sum of the following :   (i) $$\frac{1}{\cos0^\circ \cos1^\circ}+\frac{1}{\cos1^\circ\cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+\frac{1}{\cos88^\circ \cos89^\circ}$$  I tried :  $$\frac{1}{\cos1^\circ}\left[\frac{\cos(1^\circ-0^\circ)}{\cos0^\circ\cos1^\circ} + \frac{\cos(2^\circ-1^\circ)}{\cos1^\circ\cos2^\circ}+...\right]$$  = $$\frac{1}{\cos1^\circ}\left[\frac{\cos1^\circ\cos0^\circ}{\cos0^\circ\cos1^\circ} - \frac{\sin1^\circ \sin0^\circ}{\sin0^\circ\cos1^\circ} + \frac{\cos2^\circ \cos1^\circ}{\cos1^\circ\cos2^\circ} -\frac{\sin2^\circ \sin1^\circ}{\cos1^\circ\cos2^\circ}...\right]$$  For this, as well, I am not getting any pattern to solve further. Please suggest, thanks. Making a private method public to unit test it...good idea? We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? Adding a class to “body” I'm trying to add a custom CSS class to the &lt;body&gt; tag, How can I modify or pre-process the &lt;body&gt; tag to add the class body, Is it right to style the &lt;body&gt; tag with css file? I'd like to delete a file from my Time Machine backups, but there seems to be no option to do so in the Big Sur version of Time Machine. I go to the Time Machine menu and select &quot;Enter Time Machine&quot;. Then I see the view with the stack of windows. I browse to a file and select it. Now I want to delete it so it doesn't exist and take up space in backups. There is no option to delete it - either the action menu in the toolbar, or the control-click context menu. How do I delete a file from Time Machine backups? There used to be a way to do this. (I'd take a screenshot, but the key shortcuts for screenshots don't work in Time Machine. Not sure if this is just a Big Sur thing or if that's always the case.) Update: I should mention I'm using APFS for my Time Machine volume. That seems to be relevant. Also, I contacted Apple support about deleting entire snapshots (slightly different goal than the one here in this question). They said you can't do it anymore. It seems like there's some bugs here, because I have a &quot;Move to Trash&quot; option if I control-click one of my backups. It seems to work initially but then the backup comes back.  I don't like losing this much control over my files. I may look for another backup solution. How much money do you need to have on hand when entering USA? My friend, a Chilean citizen, is entering the US via waiver program to spend 3 weeks in USA in a couple of weeks. She already got her ESTA approval, the plane ticket, all hotels are already booked (but paid by me, not her).  How much money would she need to bring with her when entering US? Do they still check this? She would of course have credit cards with her. My question is simple, why do we believe  to be absurd? Is the Ultra-violet catastrophe incorrect or is it only because we can not create or know of a perfect emitter? I am a bit confused as to why Quanta was necessary. Anyone ever seen a "wok adapter" for induction cooktops? In theory a cheap pressed steel wok would work on an , but the "contact patch" for a traditional round bottomed wok would be so small it would be ineffective.  Has anyone seen a steel or cast-iron "wok adapter" with a flat bottom and a concave "bowl" on top to sit the wok in, serving dual purposes of supporting the wok on the stovetop and transferring the induction heat to the wok?  Could anyone speculate if this would this even work? Or wouldn't you be able to get the wok hot enough? When studying weak border conditions (in Sobolev Spaces), the usual motivation for the weak meaning of inequalities is that the boundary of most open sets in $\mathbb{R}^n$ has zero Lebesgue measure. But is there any open set $U\subseteq\mathbb{R}^n$ such that it's boundary has positive Lebesgue measure? I really can't think of anything like that. The order of words in a clause: "tell me who is the real man" vs. "tell me who the real man is" Flag abusive users I think the community does a great job policing questions/answers, etc. and the community has some good tools available to do this.  Between flagging questions with some reasons behind it and editing posts, closing them, and deleting them, the only thing that seems to be missing to me is the ability to flag a user.  Reasons to flag a user as abusive:   Duplicate User Abusive Behavior Offensive user name or profile User profile consists of spam Others? Why "?v=hash" is added to my URLs? I'm new to wordpress, I set up everything, but there's something that bothers me: on every single URL or link, there's a "?v=hash" appended everywhere (example.com/?v=d21feabed96b).  I tried to see inspect every plugin, I don't understand how this parameter is added.  It looks like it's added in js, because if I see the source, there's no trace of this hash, but I can see in firebug live source.  Plugins installed:   jetpack sumome wp-piwik wp super cache woocommerce   Theme: Storefront  I tried to disable everything, but still I get this hash, does anyone knows how and why it's added?  I'm also using cloudflare