Receiving $30k from mother for house down payment
How to avoid having my father's down payment assistance get taxed as a gift
What's the maximum hand luggage volume you can take with you to match all (or important) airline regulations considering only international connections?  In case my question is not clear, I'm looking for the one biggest carry-on bag that is accepted by all (or important) airlines on international connections. Accepted dimensions tend to be somewhat different on different airlines, meaning that a specific bag might be allowed on one airline, but not on another.  So, my question is what is the biggest bag that meets all (or important) airline requirements? Double Whatsapp Backup in iCloud I am not sure if this is the case, but when you do iCloud Backup of your phone, it will backup Whatsapp. ( I am unsure if this include the Photos and Video )   Then Whatsapp itself has backup option to backup itself in iCloud Drive Backup.   Is that a double Backup? Because i see 2.1GB inside the iCloud Backup, and then 1.7Gb inside document and settings. Anonymous questions and Avatars Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$ Let ${\rm f}:\left[a, b\right]\to\mathbb{R}$ be twice differentiable, and suppose   $$\lim_{x\to a^{+}} \frac{{\rm f}\left(x\right) - {\rm f}\left(a\right)}{x - a} = \lim_{x\to b^{-}}\frac{{\rm f}\left(x\right) - {\rm f}\left(b\right)}{x - b} =0 $$  Show that there exists $\xi \in \left(a, b\right)$ such that $\displaystyle{% \left\vert\vphantom{\Large A}\,{\rm f}''\left(\xi\right)\right\vert \geq \frac{4\left\vert\vphantom{\Large A}% \,{\rm f}\left(a\right) - {\rm f}\left(b\right)\right\vert} {\left(b - a\right)^{2}}}$.  I don't know how to start. Any hints ?. What is Chromatic Aberration? Is it a physical part of the lens, or just an optical illusion? Calculating MEAN and STANDARD DEVIATION confussed [] ** calculate the mean and standard deviation of each investment, assume that both returns come from independent samples, are both normally distributed and that the (true but unknown) variances are the same,, Can someone could check my  calculations for  mean and standard deviation? I did calculations but not sure what to do with negative values of distances(If if am correct Investment A MEAN= 78.6875 when it comes to calculating standard deviation i have to power difference by 2 ?  ** Beginner Physics Resources? I'm interested in learning physics. I do realize that the subject is large and that it would be easier if I had a specific area of interest. However, I do not. I suppose I want to learn about the fundamentals of it all; the axioms that combine all physics fields. Or, in other words, a high school physics class.   Specifically, a book or series of videos would be helpful. I looked over MIT and unfortunately the material wasn't for me. I don't mean to be "picky" so I am not completely ruling out any resource just yet.   Thanks in advance. I have a dual boot laptop (Windows 10). I ran general updates and now my Ubuntu won't boot.   I ran in recovery mode and still it freezes in the same place.      Kernel panic – not syncing: Attempted to kill init! exit code=0x00007f00 Who decides which half of the universe should be destroyed? I know what you're thinking: "of course it has, for example, it can be used to tell you how many times you can go around a circle". But that isn't really true, now is it? You'd be dead or the world would go under long before an infinite amount of loops had been reached.  Are there any practical applications for the concept of infinity? Is it a useful concept in maths at all?  I know that Donald E. Knuth has argued that for all practical purposes, a very, very large number has the same effect as infinity, in his book "Things a Computer Scientist Rarely Talks About" (can't remember the exact quote, nor find it online, unfortunately).  Examples are appreciated. How to extend the text under summation symbol without making extra space has now probably made around 15 accounts. He consistently uses the , , ,  and  tags, and does not ever do anything constructive.  was his latest.  Unfortunately I haven't been bookmarking his other questions, but here are some of his previous accounts:          He has also gone by many other names (Iraq War Veteran is the one that comes to mind), but those accounts have been deleted.    Is there nothing we can do about this? Deleting and suspending his accounts just seems to give him more reason to create other accounts. Is there a way to block him entirely?    Edit:  seems to have been deleted by Community ♦ Why is Excel truncating my 16-digit numbers? If I type in a 16 digit number (format: number, no decimals) it changes the number on me. Example: 1234567812345678 changes the view to 1234567812345670.    If I type it in as a general format it changes the numbers above so it displays 1.23457E+15 but if you click on the cell, the display shows the last digit as a 0 instead of an 8 once again.   I opened the file on a different computer and same issue now with it.  I have changed the auto correction and auto formatting all to no avail.  Help! Real Analysis, Folland Problem 1.3.15 Measures Given a measure $\mu$ on $(X,M)$, define $\mu_0$ on $M$ by $$\mu_0(E) = \sup\{\mu(F): F\subset E \ \text{and} \ \mu(F) &lt; \infty\}$$ a.) $\mu_0$ is a semifinite measure. It is called the semifinite part of $\mu$. b.) If $\mu$ is semifinite, then $\mu = \mu_0$ (Use Exercise 14) c.) There is a measure $\nu$ on $M$ (in general, not unique) which assumes only the values of $0$ and $\infty$ such that $\mu = \mu_0 + \nu$.  The proof of Exercise 14 can be found  For a.) I believe we need to show that $\mu_0(E) = \infty$. Perhaps we can do this by proof of contradiction, similarly to what the proof in the link above does (actually it seems identical). For b.) I am not sure how we can show $\mu = \mu_0$ I think maybe we have to show by construction that $\mu \leq \mu_0$ and $\mu \geq \mu_0$ For c.) I haven't any idea for. Any suggestions is greatly appreciated. Is the cube root of a prime number rational? The question is: if $P$ is prime, is $P^{1/3}$ rational?   I have been able to prove that if $P$ is prime then the square root of $P$ isn't rational (by contradiction) how would I go about the cube root? I have an older Nvidia video card and my PC crashes when installing the driver for the video card in Ubuntu 16.04. When I get to the login screen but no further: after entering my password, the system went into a loop and returned always back to the login screen [with funny stripes present].   How do I fix this problem? Blown out blue/red light making photos look out of focus How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound. Correct way to use include and includeonly when writing a large document like a thesis Pull-up and Pull-down Resistor Usage on Input or Output MCU Pins Are pull-up/down resistors (whether internal or external) only needed for MCU INPUT pins? In contrast, an MCU pin configured as an OUTPUT "knows what level it's at" because it does the driving - a "floating" MCU OUTPUT pin tied to some input of another circuit doesn't make sense, because the state of the MCU pin can only be high or low... do I have this right? Now, upon MCU bootup or failure, it may be beneficial to have a pull-up/down tied to this "MCU output to IC input" line to ensure that the input to some IC is never floating.  Maybe I just answered my own question here... pull-up/down resistors can be used on both input and output pins, depending on application?