A fly is flying between two trains, each travelling towards each other on the same track at 30 km/h. The fly reaches one engine, reverses itself immediately, and flies back to the other engine, repeating the process each time. The fly is flying at 60 km/h.  At the start the trains were separate for 180 km.  What is the distance that the fly travels to the moment when both of the trains hit each other?
Two trains travel on the same track towards each other, each going at a speed of 50 kph. They start out 100km apart. A fly starts at the front of one train and flies at 75 kph to the front of the other; when it gets there, it turns around and flies back towards the first. It continues flying back and forth till the two trains meet and it gets squashed. How far did the fly travel before it got squashed?  The question is relatively simple - the trains take an hour to collide, and in an hour the fly would travel 75 km. However, the question got me wondering: Lets say you are given a time $t$ in hours(where $t&lt; 1$) How many &quot;rounds&quot; would the fly make in $t$ time? A round  is defined as moving from one train to another and back. How would I model the equation?
Provide a means to reward users and their answers (decoupled from bounties) Where did the age go on the network profile? Ever since the profile redo, the age was shown in the network profile, but not in the per-site profiles. So if someone wanted to see the age, they had to go to the network profile. However.. It's vanished! The field is still there in the profile editing, however. It doesn't appear as if this was implemented:   So... Where is it? $\newcommand{\P}{\mathbb{P}}$Is it valid to interpret $\P(B|A)$ as "infinite probability" when $\P(A) = 0$? dpkg: error: dpkg status database is locked by another process I just wondered if somebody could tell me what this means:  E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem. reidsr@ubuntu:~$ sudo dpkg --configure -a dpkg: error: dpkg status database is locked by another process reidsr@ubuntu:~$    How do I run sudo dpkg --configure -a  manually? How do you handle "that that"? The double "that" problem Have you ever had a case where you felt compelled to include strange things like a double that in a sentence? If so, then what did you do to resolve this?  For me, I never knew whether it was acceptable grammar. However, what I did learn was that it was a logic distractor, could lead to confusion, and therefore should be reworded to avoid this. [Salutations]  (check one)  [ ] Well trained professional, [ ] Casual reader, [ ] Hapless wanderer,   I have a (check all that apply)  [ ] query [ ] stored procedure [ ] database thing maybe     that was running fine (if applicable)   [ ] yesterday [ ] in recent memory [ ] at some point    but is suddenly slower now.  I've already checked to make sure it's not being blocked, and that it's not the victim of some long running maintenance task, report, or other out of band process.  What is the problem, what should I do, and what information can I provide to get some help?  [*Insert appropriate closing remarks*] "1 in 10 are" or "1 in 10 is"? Take the examples:   "One in ten children are dyslexic."  "One in ten children is dyslexic." "One in ten children has dyslexia." "One in ten children have dyslexia."   The "one" is singular so 2 and 3 should be correct. But the "one in ten" is a fraction" so 1 and 4 should be correct. And yet I think I usually say 1 and 3. Which is/are correct?! How can I get the list of all fields(API name,Label,type) of any sObject? I'm trying to build a Dynamic list(table) of records by selecting the Sobject and its fields.So I need to get all the fields with its API name,label,type.But I can't get the label and type.(Tried DescribeSObjectResult Class methods to get label,but it didn't help to get the label dynamically)  I tried it with the following code.  System.debug('Selection-----'+selectedObject); Map&lt;String, Schema.SObjectType&gt; gd = Schema.getGlobalDescribe();  Schema.SObjectType ctype = gd.get(selectedObject);  Map&lt;String, Schema.SobjectField&gt; fmap = ctype.getDescribe().fields.getMap();    List&lt;FieldWrap&gt; strList = new List&lt;WrapMap&gt;(); for(String s: fmap.keySet()) {     WrapMap wmp = new WrapMap();     wmp.name = s;     wmp.label = String.valueOf(fmap.get(s));     strList.add(wmp);  }   Where FieldWrap is my wrapper class with name and field of String types. I'm getting the List of API name of fields,but not the Label and type of it.Is there a way to get the label and type of field.If so, please help me. We  that there's a difference in meaning between try used with the infinitive and  try used with the gerund:     I tried sending her flowers. (Meaning: An experiment: I sent her flowers to see what will happen).   I tried to send her flowers. (Meaning: I tried to go through the procedure necessary to send flowers to her. The procedure might have been difficult.)   (per Michael Swan's PEU, Unit 299.6)   Will the same distinction hold if we use trying:     A man is trying setting up a password on his computer. (Is he experimenting, wanting to see what will happen?)   A man is trying to set up a password on his computer. (Is he trying to go through all the necessary steps, probably difficult, of setting up a password?) Do I need a transit visa for a layover via airports in the UAE, such as Dubai International Airport or Abu Dhabi International Airport? If so, what are the requirements for such a visa? Can I get the transit visa on arrival? I was doing some re-tagging and I noticed that the automatically generated revision comment says that I edited the post body where I only edited the tags. Avoiding unused variables warnings when using assert() in a Release build I am looking for one word to describe someone who always does what he loves.   Loving means enjoying something very much, free-spirited means not restrained by convention. Is there a hybrid word?   I mean a word that describes someone who is independent and always does what he loves. Please also try to not make the word too esoteric. Also, the word needs to be positive.  How will it be used?  I am submitting an application for college, and they require me to supply a word to describe myself. I have always done what I love. So, I require a word to describe someone who loves what they want. There is no sentence, in particular, just a prompt asking me to describe myself in one word. systemctl --user not available for www-data user systemctl --user seems to be working fine for the desktop user:  dev@dev-VirtualBox:~$ systemctl --user &gt; /dev/null dev@dev-VirtualBox:~$ echo $? 0   But when running the same command under the www-data user I get an unexpected response  dev@dev-VirtualBox:~$ sudo su www-data -s /bin/bash www-data@dev-VirtualBox:~$ systemctl --user &gt; /dev/null  Failed to connect to bus: No such file or directory  www-data@dev-VirtualBox:~$ echo $?  1   How to enable systemctl --user here?  Running Ubuntu 16.04 I am interested in setting up a Ruby on Rails environment on my 10.10 laptop.   Is there anything special I need to keep in mind for installation (i.e. that could be new or unique to 10.10)?   Are there any suggested walkthroughs that I could follow along with?  Thanks in advance. Alternative ways to say "if and only if"? There are some scenarios about which I would like to get some confirmation:   when defining a concept A,      We call A, if ... [definition of   concept A]   Does "if" here mean equivalence instead of just sufficiency? Is it incorrect to replace "if" with "if and only if"?    For precisely what condition is    B satisfied?   Does "precisely" mean asking for necessary and sufficient condition for B? Some other ways to say "if and only if" / "necessary and sufficient"?   Some references that summarize some standard terminologies in Mathematics  such as this one?  Thanks and regards! How to apply for a UK standard visitor visa as a family? I am an Indian citizen residing in the United States. My wife and I are planning to travel to the UK for a week. We plan to apply for the UK standard visitor visa from the US. I was filling out the application and I have a few questions.   Travel History - The application asks for travel history to the United States, Canada, Australia and New Zealand. Considering that we're resident aliens in the United States, should we consider all the times we've traveled back to the US from India? Travel History - Should we also list out the times we've traveled to India from the US? Cost of the trip - Hypothetically if we plan to spend a total of ~4,000 USD on this trip, should I split up the cost and write down 2,000 USD on my application and 2,000 USD on my wife's application? Income - From what I've read on the forum, my wife must say that "someone else" i.e. me - is paying for her costs and mention my GWF number in the remarks on her application. Would that be sufficient considering that I'll be sending all income documents with my application? Savings - We have joint savings accounts. Should I mention the same amount on both our applications? Posting the documents - Is the up-to-date advice to send all documents in one packet? Or would sending them in separate packets at the same time be better? My thought was to annotate my wife's packet with my GWF number if we were to send them separately. Bank statements - We get e-statements. Would printing those out be enough? I have recently been reading a lot on this site (@Aniko, @Dikran Marsupial, @Erik) and elsewhere about the problem of overfitting occuring with cross validation - (Smialowski et al 2010 Bioinformatics, Hastie, Elements of statistical learning).  The suggestion is that any supervised feature selection (using correlation with class labels) performed outside of the model performance estimation using cross validation (or other model estimating method such as bootstrapping) may result in overfitting.   This seems unintuitive to me - surely if you select a feature set and then evaluate your model using only the selected features using cross validation, then you are getting an unbiased estimate of generalized model performance on those features (this assumes the sample under study are representive of the populatation)?  With this procedure one cannot of course claim an optimal feature set but can one report the performance of the selected feature set on unseen data as valid?  I accept that selecting features based on the entire data set may resuts in some data leakage between test and train sets. But if the feature set is static after initial selection, and no other tuning is being done, surely it is valid to report the cross-validated performance metrics?   In my case I have 56 features and 259 cases and so #cases > #features. The features are derived from sensor data.  Apologies if my question seems derivative but this seems an important point to clarify.  Edit: On implementing feature selection within cross validation on the data set detailed above (thanks to the answers below), I can confirm that selecting features prior to cross-validation in this data set introduced a significant bias. This bias/overfitting was greatest when doing so for a 3-class formulation, compared to as 2-class formulation.  I think the fact that I used stepwise regression for feature selection increased this overfitting; for comparison purposes, on a different but related data set I compared a sequential forward feature selection routine performed prior to cross-validation against results I had previously obtained with feature selection within CV. The results between both methods did not differ dramatically. This may mean that stepwise regression is more prone to overfitting than sequential FS or may be a quirk of this data set. How to open a web page from my application? There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers I need help with this question: There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also primes.  Where should I start? what proof techniques will be useful?  Any input will be very useful to me.