If 20 students can clean 5 classrooms in 4 hours, so in how many hours can 40 students clean 40 classrooms?
I came across the following question:     If 3 boys can paint a fence in 2 days what part of the job can     be completed by two boys in 1 day?   The answer to this problem is $\frac13$.  I can't manage to tackle this problem. Could anyone tell me what would be the quickest way to solve this problem (This question is a standardized test based question). Any help would be appreciated.
I'm trying Google's PageSpeed online service  Ironically, it's primarily highlighting Google's own services as something that needs improvement on my site  1) jQuery from Google: blocking. So I moved all javascript from &lt;head&gt; to the end of the document before &lt;/body&gt;. That helped  2) Linking to external Google Font CSS (in &lt;head&gt;): blocking. But the font is critical to the design of the page and should load before much else  3) Google Analytics: Caching is not good. (Google has set it internally to 2 hours expiration). Don't know how to change this (this is also placed at the bottom of page)  The Google Font is highlighted as a big priority to change.  How can I fix this? Where/how should I call the the font? What free/open source image design programs can you recommend? Are there any free/ open source image designing programs that you can recommend? How can I install software or packages without Internet (offline)? I'm trying to make a basic Windows application that builds a string out of user input and then adds it to the clipboard. How do I copy a string to the clipboard using Python? What is the effect where some objects are a single bright color but the rest is black and white? There is an option to filter only one color (R,G,B,Y) in my camera. What I want to know is can this effect be achieved in photoshop? And what is this called? I tried googling monochrome and came up with nothing. My camera calls it part color. How to evaluate a math expression given in string form? Per-chapter bibliographies in biblatex I'm really new in using biblatex, compile the sample placed in , but what I get is    1.1 Foo    Some text [B02x ].    1.2 Bar    Some text [B02y ].   Do not get the bibliography by chapters, or the global references.  Really not remains to be done   \documentclass{report}  \usepackage[style=alphabetic]{biblatex}  \addbibresource{references.bib}  \begin{document}  \chapter{First chapter}  \section{Foo}  Some text \cite{childs_temperature}.  \printbibliography  \chapter{Second chapter}  \section{Bar}  Some text \cite{hashemian}.  \printbibliography  \newpage  \printbibliography  \end{document}   And the references.bib    @BOOK{childs_temperature,   title = {Practical Temperature Measurement},   publisher = {Butterworth - Heinemann},   year = {2001},   author = {Childs, Peter R N},   address = {Great Britain},   edition = {1},   isbn = {0 7506 5080 X}   }    @PHDTHESIS{hashemian,   author = {Hashemian, Hashem Mehrdad},   title = {Measurements of dynamic temperatures and pressures in nuclear power plants},   school = {{The University of Western Ontario}},   year = {2011},   type = {PhD {T}hesis}   }   I need to obtain references by chapter and global cited references, but i don't know how compile. Counterexamples to the avoidance lemma for arbitrary ideals Let $A$ be a commutative ring with $1$. Let $I$ and $J_k$, $k=1,\dots,n$ be ideals of $A$ with $I\subseteq \cup _{k=1}^n J_k$. Then I have obtained the following:  (1) If $J_k$, $k=1,\dots,n$, are prime ideals, then there exists some $j$ such that $I\subseteq J_j$.   (2) If $A$ is a principal ideal ring, then there exists some $j$ such that $I\subseteq J_j$.   I want some counterexamples that for all $k=1,\dots,n$, $I$ is not contained in $J_k$. How to get the counterexamples? Sharing Jupyter notebooks within a team I would like to set up a server which could support a data science team in the following way: be a central point for storing, versioning, sharing and possible also executing Jupyter notebooks.  Some desired properties:   Different users can access the server and open and execute notebooks that were stored by them or by other team members. The interesting question here is what would be the behavior if user X executes cells in a notebook authored by user Y. I guess the notebook should NOT be changed: Solution should be self-hosted. Notebooks should be stored either on the server or on Google drive or on self-hosted instance of owncloud. (Bonus) Notebooks will be under git versioning control (git may be self-hosted. Cannot be bounded to GitHub or something of that sort).   I looked into  and . With the former, I didn't understand how to allow cross users access. The latter seems to only support GitHub as the storage of the notebooks.  Do you have experience with either of the solutions? Custom Tools not Saving in Toolbar on Startup/ Normal.mxt? Is there any way to erase personal information from my phone that has already been stolen? My phone has been stolen. I do not want the thief to have access to any of my personal information such as calls, texts, and information saved in the phones contents. Is there any possible way I can get this information erased from my phone? Function pointers/delegates in Java? For my Java game server I send the Action ID of the packet which basically tells the server what the packet is for. I want to map each Action ID (an integer) to a function. Is there a way of doing this without using a switch? Can I travel to Dublin, Republic of Ireland with UK Tier 2/Schengen visas with Indian Passport Graph theory: Tree holds two sub-tree with an amount of vertices line of mathematicians guess their own hat color out of c colors There is a common problem in which a long line of N mathematicians are each given a hat that is either red or blue.  They cannot see their own hat but can see all in front of time and can hear any response. They must state their own hat color from the back of the line forwards and no information may be passed besides their guess.  They may have a planning session in advance.  What is the maximum number of correct guesses can they guarantee?  The answer is (look away if you don't know) $N-1$.  If, instead of 2 colored hats, we use $c$ different colored hats, how many can we guarantee?  Assuming $N&gt;&gt;c$  I believe the answer to be $N-c+1$ and have confirmed this for $c=2, 3$, and $4$.  I believe this should be simple to prove by using the concept of "$x$ formulas allow you to solve for $x$ variables" but I am not well versed enough in pure mathematics to answer this. I just installed Ubuntu and it is great.  However, I installed in beside the Windows Vista OS.  I now want to remove Windows in an effort to improve performance.  What is the easiest way to do this? Nonlinear function continuous but not bounded I would like an example of a map $f:H\rightarrow R$, where $H$ is a (infinite dimensional) Hilbert space, and $R$ is the real numbers, such that $f$ is continuous, but $f$ is not bounded on the close unit ball $\{ x\in H : \|x\| \leq 1\}$.  Actually, $H$ could be replaced by any Banach space (but not just a normed space-- that's too easy).  My motivation is that if $f$ is linear, this is impossible; but I have next to no intuition about non-linear functions.  Edit: Here's an example for $c_0$ which is even differentiable (disclaimer: I found it here: ).  Define $f:c_0\rightarrow F$ (where F is your field, real or complex) by $$ f(x) = \sum_{n=1}^\infty x_n^n \qquad (x=(x_n)). $$  You can estimate the sum by a geometric progression, so it does converge.  A bit of checking shows that f is Frechet differentible (so certainly continuous).  But $f(1,1,\cdots,1,0,\cdots)=n$ (if there are $n$ ones) so $f$ is not bounded on the closed unit ball.  What I don't immediately see is how to adapt this to $\ell^2$, say. Types of photon qubit encoding How many types of qubit encoding on photons exist nowadays? I know only two:   Encoding on polarization: $$ \lvert \Psi \rangle = \alpha \lvert H \rangle + \beta \lvert V \rangle $$ $$ \lvert H \rangle = \int_{-\infty}^{\infty} d\mathbf{k}\ f(\mathbf{k}) e^{-iw_k t} \hat{a}^\dagger_{H}(\mathbf{k}) \lvert 0 \rangle_\text{Vacuum} $$ $$ \lvert V \rangle = \int_{-\infty}^{\infty} d\mathbf{k}\ f(\mathbf{k}) e^{-iw_k t} \hat{a}^\dagger_{V}(\mathbf{k}) \lvert 0 \rangle_\text{Vacuum} $$ Time-bin: $$ \lvert \Psi \rangle = \alpha \lvert 0 \rangle + \beta \lvert 1 \rangle $$ $$ \lvert 0 \rangle = \int_{-\infty}^{\infty} dz\ f\left(\frac{t -z/c}{\delta t_{ph}}\right) e^{-i w_0 (t-z/c)} \hat{a}^\dagger(z) \lvert 0 \rangle_\text{Vacuum} $$ $$ \lvert 1 \rangle = \int_{-\infty}^{\infty} dz\ f\left(\frac{t -z/c+\tau}{\delta t_{ph}}\right) e^{-i w_0 (t-z/c+\tau)} \hat{a}^\dagger(z) \lvert 0 \rangle_\text{Vacuum} $$   Is there anything else? I want to know how to format a storage drive from the terminal. Helpful things to provide in the answer would be often used options for commands and base knowledge that one can use to extrapolate future uses. Specifically I would like to know how to format in the different file systems such as NTFS, FAT32, EXT4, etc. Information on how to partition the drive via terminal is also wanted.  I am trying to format a high capacity external hard drive (EHDD) into NTFS - from the terminal.   I know I can use gparted for this as well as other GUI programs, but I still want to now how to do it from the terminal. simple process builder failing with error "failed to access the value for variable because it hasn't been set or assigned" Note: This error might look like a familiar error but the   resolution mentioned in the  is not working in the below case and I am not sure why, hence posting this question.   Problem description:   I have a process builder on case object set to fire for every time new record is created. Criteria is set to 'Formula evaluates to True' with below formula: AND(NOT(ISBLANK([Case].AccountId)),ISPICKVAL([Case].Account.Active__c,'Yes')) With immediate action set to update custom field on the Case object. Custom field Active__c on the Account object is type picklist with two possible values 'yes' and 'no'.   Screenshots of the process builder:        Creating a case as shown in the below screenshot with very minimal details and especially not populating account details:    Throws below error:     The flow failed to access the value for   myVariable_current.Account.Active__c because it hasn't been set or   assigned.   Relevant data from log file:     22:14:31.0 (12479016)|WF_FLOW_ACTION_BEGIN|09L370000000FEJ 22:14:31.13   (13607478)|FLOW_CREATE_INTERVIEW_BEGIN|00D37000000H8hr|300370000008ZTl|301370000004weE   22:14:31.13   (15394571)|FLOW_CREATE_INTERVIEW_END|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test   22:14:31.15 (15820974)|FLOW_START_INTERVIEWS_BEGIN|1 22:14:31.15   (16674702)|FLOW_START_INTERVIEW_BEGIN|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test   22:14:31.15 (35470120)|FLOW_ELEMENT_ERROR|The flow failed to access   the value for myVariable_current.Account.Active__c because it hasn't   been set or assigned.|| 22:14:31.15   (35479812)|FLOW_START_INTERVIEW_END|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test 22:14:31.15 (35517783)|FLOW_START_INTERVIEWS_END|Interview error.   Aborting all.|5525dfa7819c33f438ce3cef9b6c15c668d8ff2-3d11|Test   22:14:31.15 (35528335)|FLOW_START_INTERVIEWS_END|1 22:14:31.0   (35588898)|WF_FLOW_ACTION_ERROR|09L370000000FEJ|300370000008ZTl|Error   executing flow: test, FlowDefId: 300370000008ZTl, FlowVersionId:   301370000004weE 22:14:31.0   (35612585)|WF_FLOW_ACTION_ERROR_DETAIL|An unhandled fault has   occurred in this flowAn unhandled fault has occurred while   processing the flow.  Please contact your system administrator for   more information. 22:14:31.0   (35683203)|WF_FLOW_ACTION_END|09L370000000FEJ   URL to the complete debug log :  (Note: You can see from the log that there are no other workflow rules or triggers on the case object).  My analysis: When the first condition inside the AND expression is evaluating as false, why is it trying to evaluating the second condition to check the custom field on the Account object? It shouldn't right?  Any help?  EDIT: I am looking to solve this using option 'Formula Evaluates to True' only because I have other complex criteria like checking the day(Mon vs Tue and etc) of the case creation.