how to create a term-life annuity timeline like this
I was wondering, how can I create a timeline exactly like this one:    on LaTeX?  I am a Finance student, and write all of my notes using LaTeX. These timelines, are giving me a headache. Since we use a lot of different timelines because of annuities. I want to learn how to create one basic timeline, so that I can then change anything I want. But basically, I want something like this, with the arrows and everything.  Thank you so much guys!
The definite article implying the generic idea of something I know that the definite article "the" can be used to mean a generic idea of something as in "the lion is the king of the animals." In this sentence, the in "the lion" is used to imply the general image of lions, so not specifying a particular lion.   However, I am confused in identifying where a "the" in a sentence is used for a general idea or a specific reference. For example, in the sentence "the price of gas is soaring", I heard that "the" in the sentence is an example of the generic use of the. Although I can easily understand the generic use of "the" in the lion example, but I do not understand how there is an general idea about gas price. Soaring gas price is something real,and gas prices in different regions( in a hypothetical situation) can be different. So, if I say "the price of gas is soaring", do I mean the price of gas that is determined by the world's oil system or can I say "the gas price" even when I am indicating the state of gas price in "a particular region"?    I know it is even difficult to understand my question, but I hope someone could find what I am confused about and give an answer. Do I need to explicitly call the base virtual destructor? I accidentally unset all the directories of $PATH while trying to add a new one in ~/.bashrc. I opened a new terminal window as I was editing and now $PATH is empty. I'm worried if I boot from another drive to find the $PATH I won't be able to boot into this drive again.  Basically, what is the default result of echo $PATH? How can I load a Python module given its full path? Note that the file can be anywhere in the filesystem, as it is a configuration option. Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$ Is there a closed-form expression for the sum $\sum_{k=0}^n\binom{n}kk^p$ given positive integers $n,\,p$? Earlier I thought of this series but failed to figure out a closed-form expression in $n,\,p$ (other than the trivial case $p=0$).  $$p=0\colon\,\sum_{k=0}^n\binom{n}kk^0=2^n$$  I know that $\sum_{k=0}^n\binom{n}k=2^n$ and $\sum_{k=0}^nk^n=\frac{k^{n+1}-1}{k-1}$ but I am unsure of whether these would be of much use now.    Additionally, what about the similar series $\sum_{k=0}^n\binom{n}kk^n$ where $p=n$? Get the generated SQL statement from a SqlCommand object? I have the following code:  Using cmd As SqlCommand = Connection.CreateCommand     cmd.CommandText = "UPDATE someTable SET Value = @Value"     cmd.CommandText &amp;= " WHERE Id = @Id"     cmd.Parameters.AddWithValue("@Id", 1234)     cmd.Parameters.AddWithValue("@Value", "myValue")     cmd.ExecuteNonQuery End Using   I wonder if there is any way to get the final SQL statment as a String, which should look like this:  UPDATE someTable SET Value = "myValue" WHERE Id = 1234   If anyone wonders why I would do this:   for logging (failed) statements for having the possibility to copy &amp; paste it to the Enterprise Manager for testing purposes As a bulk sender, is there a way to make Gmail show my avatar?    I would like to obtain this without creating a Google Account.  Maybe embedding my vCard? Or maybe ? "the Red Cross" but no article in Greenpeace, UNICEF, or Amnesty International In an English language textbook for Italian middle school students, there is a reading exercise where students have to fill in the gaps. Here is a completed excerpt     The International Red Cross/Red Crescent is a global charity and humanitarian organisation. It believes that people everywhere have a right to life and health. …blah, blah, blah… The Red Cross / Red Crescent began its work in 1863. Today, it operates in 186 countries and every year it gives help to about 250 million people.    My two private students had to write a paragraph about a charitable institution of their own choice. We came up with 1. Médecins Sans Frontières (in Italian Medici Senza Frontiere) which is also known as Doctors Without Borders 2.  and 3. Amnesty International. They each chose an institution and they all started their paragraphs with the definite article "the" just like in the textbook.         The Doctors Without Borders is a global charity and humanitarian…   The Greenpeace is a global charity and pacific organisation…      I crossed out the articles and said they weren't needed. Samuele asked me why–good for him–but I didn't know what to say, so I promised I would look into it.  While I can explain that the definite article is needed when we mention the  because it is a collection of states/nations, and it is omitted when it is shortened to UNICEF. I don't know why the article is needed for the  but not for  or .   I'm also aware that if the name of a company or band starts with "The" e.g. The Beatles,  The Leathersellers’ Company, and The Body Shop  the article is always obligatory and always capitalised. However, the charity's name used in the book name is , and yet the article is needed.    Is there a reason? Why is the definite article necessary in the International Red Cross, but not for Greenpeace or Amnesty International? How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$? Problem:   Find the value of $$\sum_{r=0}^{44} \tan^2(2r+1)$$  Note: The angles here are in degrees.    I don't know how to solve this question because trigonometric simplifications didn't get me anywhere. I think there was a method to solve this question using complex numbers which I no longer remember. Any hint/help will be appreciated. In the book , at page 27 we find the exercise asserting that       Exercise I.XXXVI.   The underlying space of a zero-dimensional scheme is discrete; if the scheme is Noetherian, it is finite.     Thoughts I thought that a zero-dimensional scheme is one such that, in every local ring $\mathscr O_{X,p}$, the only prime ideal is its unique maximal ideal $\mathfrak m_{X,p}.$ Hence, supposing that $X=\operatorname{Spec} R$ is affine, we deduce that every prime ideal is maximal, so each ponit in $X$ is closed. But how does this imply the discreteness? It only implies the Hausdorff-ness of $X$, right? Furthermore, I cannot perceive what the "Noetherianity" has to do with the finiteness claimed here. In the affine case, it seems to be claiming that there are only a finite number of prime ideals in a Noetherian ring, if its scheme is zero-dimensional? For example, $\mathbb Z$ is a Dedekind domain, hence its scheme is zero-dimensional, but it has infinitely many primes: does this contradict the statement?    Thanks in advance for any reference or hint, and point out any inappropriate point if any is presented. Edit I see why my example cannot work now: it is one-dimensinoal: don't forget the pirme $(0)$. But I am still wondering why the statement is true... "Its" as a Possessive Pronoun How to calculate $\lim_{n\to\infty}(1+1/n^2)(1+2/n^2)\cdots(1+n/n^2)$? How can we compute the following limit:     $$\lim_{n\to\infty}(1+1/n^2)(1+2/n^2)\cdots(1+n/n^2)$$   Mathematica gives the answer $\sqrt{e}$. However, I do not know to do it. How do Belgian fries differ from the French fries we are accustomed to eat in the US and Canada in such places as McDonald's, Wendy's, Burger King and so on? Is it the variety of potato, the preparation involved or something totally different? What oil do they use in Belgium?   I remember having them while I was visiting family in Belgium. The fries were somewhat crispy and thicker than over here. Can I keep the Rueful Axe and get Clavicus Vile's Mask? Is there a way to keep the Rueful axe and get Clavicus's Mask?  I thought you could kill Barbas after receiving the mask, but he is a statue now.  Did I miss my chance? What does (obj.length === +obj.length) compare? In terminal emulation applications, pressing CTRL + Left / Right arrows jumps from one word to the previous or next one. Is it possible to have the same functionality in a Linux console, whether it is in text or in framebuffer modes?  In my configuration, the CTRL + arrow keys are transformed into escaped character sequences and not interpreted. From what I've seen it looks to me like Libav's avconv is thought to become a successor of ffmpeg — is that correct?   If that's true, why is that so? What exactly is libav doing better and why would I want to choose it over ffmpeg?   I came to this "issue" while installing Ubuntu 12.04.1 LTS in a VM and when I've installed ffmpeg it came up with a message telling mit ffmpeg is deprecated and I first thought "wtf?".  If I use avconvWill I be able to migrate my scripts depending on ffmpeg more or less easy to libav? I'm mostly using it for writing meta data and doing audio conversion (wav, flac, vorbis, mp3, aac). Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$. I'm using Microsoft Word 2010 and I worked in a word-2003 compatible document (.doc). After hours of working, I selected a half of text and did Ctrl+X to copy it into another document. Surprising, after closing the current document and opening a new one and pressing Ctrl+V, nothing happened. After closing original document, ms word asked me if I want to save the clipboard buffer and I pressed No, as I didn't knew that MS Word has it's own clipboard.  Is there a way to recover that text that was "cutten" from original document and never "pasted" to the new one? The PC was not rebooted so i guess all my temp files are here. System settings won't open on Ubuntu 20.04 LTS after adding System76/pop PPA I'm trying to open System Settings but it won't open in any way. Using GUI, Settings are trying to load for a moment and then they are gone. Using Terminal (gnome-control-center), I get: (gnome-control-center:8823): GLib-ERROR **: 14:44:15.433: ../../../glib/gmem.c:138: failed to allocate 13477064712 bytes Trap Trace/breakpoint (core dumped)  I tried: sudo apt-get remove gnome-control-center sudo apt autoremove sudo apt-get install gnome-control-center  With multiple reboots, but I had no result. UPDATE!: Same errors persist BUT, when I type: sudo gnome-control-center  (instead of just &quot;gnome-control-center&quot;) suddenly System Settings appear! Is it a user permissions issue? Any suggestions? UPDATE#2: After some system updates, sudo gnome-control-center now spawns &quot;Segmentation fault&quot;.