I have an array of data.for example {25,26,11}.I want to rescale them to an array in which the summation of the 3 data is a definite value (for example 10).how can i do that?!
At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean then dividing by its SD. But they seem interchangeable with other possibilities as well.   When creating some kind of universal score, that makes up $2$ different metrics, which have different means and different SD's, would you Normalize, Standardize, or something else? One person told me it's just a matter of taking each metric and dividing them by their SD, individually. Then summing the two. And that will result in a universal score that can be used to judge both metrics.  For instance, say you had the number of people who take the subway to work (in NYC) and the number of people who drove to work (in NYC).   $$\text{Train} \longrightarrow x$$ $$\text{Car} \longrightarrow y$$  If you wanted to create a universal score to quickly report traffic fluctuations, you can't just add $\text{mean}(x)$ and $\text{mean}(y)$ because there will be a LOT more people who ride the train. There's 8 million people living in NYC, plus tourists. That's millions of people taking the train everyday verse hundreds of thousands of people in cars. So they need to be transformed to a similar scale in order to be compared.  If $\text{mean}(x) = 8,000,000$  and $\text{mean}(y) = 800,000$  Would you normalize $x$ &amp; $y$ then sum? Would you standardize $x$ &amp; $y$ then sum? Or would you divide each by their respective SD then sum?  In order to get to a number that when fluctuates, represents total traffic fluctuations.  Any article or chapters of books for reference would be much appreciated. THANKS!  Also here's another example of what I'm trying to do.   Imagine you're a college dean, and you're discussing admission requirements. You may want students with at least a certain GPA and a certain test score. It'd be nice if they were both on the same scale because then you could just add the two together and say, "anyone with at least a 7.0 can get admitted." That way, if a prospective student has a 4.0 GPA, they could get as low as a 3.0 test score and still get admitted.  Inversely, if someone had a 3.0 GPA, they could still get admitted with a 4.0 test score.  But it's not like that. The ACT is on a 36 point scale and most GPA's are on 4.0 (some are 4.3, yes annoying). Since I can't just add an ACT and GPA to get some kind of universal score, how can I transform them so they can be added, thus creating a universal admission score.  And then as a Dean, I could just automatically accept anyone with a score above a certain threshold.  Or even automatically accept everyone whose score is within the top 95%.... those sorts of things.  Would that be normalization? standardization? or just dividing each by their SD then summing?
So here is the problem      Solve $$4^x + 6^x = 9^x$$ for $x$.   I am trying to find its real solution.  I was trying in this way!! $$6^x\left( \frac {4^x}{6^x} + 1\right) = 9^x$$ $$\left({\frac 23}\right)^x +1=\left({\frac 32}\right)^x$$ but I'm stuck . . . Will anyone help ? What does it mean to say "a divides b" I am not a number theorist and I am learning about relations.  I encountered a relation that says      $a \leq b$ if $a$ divides $b$   Can someone clarify what it means to a number to divide another number?  Does it mean what I think? $a$ divides $b$ if $a | b \in \mathbb{Z}$?     So given a set $S = \{a, a^2, a^3, \ldots\}$, with relation $a | b \leftrightarrow a \leq b$, does the relation hold   going from left to right or right to left? i.e. $a|a^2, a^2|a^3, \ldots$ Is there any research or data on horizontal vs. vertical navigational menus? I've seen many sites using both horizontal (top) navigation, vertical (left) navigation, and both across web sites for a long time. My understanding is that they're both conventions, but I would assume there must be some data out there supporting one route over the other.   My question is: are any studies or data for or against horizontal or vertical navigation (as suggested above) with regards to primary navigation (specifically on a smaller site or web app).  I've read some interesting things that are flipping me back and forth between liking horizontal more than vertical and vice versa. For example if you look at Jacob Nielsen's post on  you get the feeling that more important content should be on the left -- but you could take that as it being more important for the navigation (the user's escape routes) to be in that valuable space. I am pretty sure that this is such a stupid, stupid question, but how do you prove that $d_2(x,y)={|x-y|\over {1+|x-y|}}$ satisfying the third condition to be a metric, which is the triangle inequality.   I know that I should really be able to do this, but I just can't, I keep seeing a contradiction. Please help me. I took some shots recently and I noticed that I'm getting a lot of little black dots in my images.  I cleaned my lens thoroughly with the Nikon camelhair brush and retook the pictures but once again, the dots appear.  I'm shooting with a Nikon D7000 and using a starter lens. I've attached an example (notice the black spots on the chairs, on the ceiling, etc). I have a Redstone Power loop that connects to a Command Block that is set to kill all entities except for myself (/kill @e[type=!Player]), because I'm building a creative map, but don't want slimes all over the place. Problem is if I want to place an Item Frame than the Command Block kills it.  So, is there anyway to exclude items from getting deleted, or make it so it will only target mobs? Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed? Is Ubuntu compatible with my hardware? I am a bit financially strapped and received a Gateway GT5056 tower. The tower has an AMD dual core 64-bit processor in it. Will Ubuntu 12.04 run on this machine? I will not have any other application other than LibreOffice installed. Is there a standard delay for consumer ratings of apps on the App Store? I have an app that's been out for a couple of weeks. Its not exactly selling like hot cakes yet, but I'm pretty sure I've gotten a rating or a review by now. But nothing shows when viewing either in iTunes or directly on the AppStore on the iPhone.  Is there a standard delay as to when ratings/reviews show up, that Apple imposes, especially for new apps? Or do you think there is some problem with Apple's system? Is there a word or phrase for something that one might wish exists, but most certainly doesn't? How to import a module given the full 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. Can we omit parentheses when creating an object using the "new" operator? $\lim\limits_{n \to \infty} \frac{a_n}{b_n}=l$ ; Prove $\sum\limits_{k=1}^\infty a_k$ converges iff $\sum\limits_{k=1}^\infty b_k$ converges. Written, in Ex.8 Ch.9.1 of the book Advanced Calculus by P. M. Fitzpatrick :     Suppose that $\sum\limits_{k=1}^\infty a_k$ and $\sum\limits_{k=1}^\infty b_k$ are series of positive numbers such that $$\lim_{n \to \infty} \frac{a_n}{b_n}=l \ \ \ \text{and} \ l&gt;0.$$ Prove that the series $\sum\limits_{k=1}^\infty a_k$ converges iff the series $\sum\limits_{k=1}^\infty b_k$ converges.   Am I correct by the following (sketch of) proof? :  1- For a given $\epsilon_1$ there is $N_1$ such that $\left|\frac{a_n}{b_n} - l\right| &lt; \epsilon_1$ for all $n \ge N_1$.  2- Since the series $\sum\limits_{k=1}^\infty a_k$ converges, for a given $\epsilon_2$ there is $N_2$ such that $\left|b_{n+1}+\dots+b_{n+k}\right|&lt; \epsilon_1$ for all $n \ge N_2$ any for all natural numbers $k$.  3- Define $N = \max {\{N_1,N_2}\}$.   4- From Step (1), $a_{n+k} &lt; (\epsilon_1+l) b_{n+k}$ for all $n \ge N$ any for all natural numbers $k$. [Also, $a_i$'s and $b_i$'s are all positive]. Thus $a_{n+1}+\dots+a_{n+k} &lt; (\epsilon_1+l) (b_{n+1}+\dots+b_{n+k})&lt; \epsilon_3$. Then the convergence of the series $\sum\limits_{k=1}^\infty b_k$ implies the convergence of the series $\sum\limits_{k=1}^\infty a_k$.  5- For the reverse implication, we use the fact that $\lim\limits_{n \to \infty}\frac{a_n}{b_n}=l \iff \lim\limits_{n \to \infty}\frac{b_n}{a_n}= \frac{1}{l}= l' &gt;0$ and repeat the process this time for a and b exchanged.   6- The Quotient Property For Sequences hold for a nonzero limit in the denominator, but since the limit in the numerator also is zero so we may use the The Quotient Property For Sequences.    Thanks. A children's book series about a farm that grows massive food There was a series of illustrated children's books that I was introduced to as a child in the late 1980's early 1990's.  The main character was a farmer - I can't remember the name, but I think it was Mc or Mac something. He bought his farm from a sleazy character who was trying to cheat him. The farmland was originally some kind of swampy land, but this industrious character (and his family) discovered that the land would grow plants to a massive size - radishes the size of basketballs, etc.  There were some pretty fantastic stories and adventure that the character would get into, such as one winter the weather got so cold that the wind (not the air) outside froze. They went out and cut it up and stored it in the icebox and would thaw out some of the cold breeze later in the hot summer.  The sleazy character made a constant appearance, trying to swindle this family out of the farm.  My Google-Fu seems to fail me at every turn. Do you know what this series is? Unicode Regex; Invalid XML characters The list of valid XML characters is well known, as defined by the spec it's:  #x9 | #xA | #xD | [#x20-#xD7FF] | [#xE000-#xFFFD] | [#x10000-#x10FFFF]   My question is whether or not it's possible to make a PCRE regular expression for this (or its inverse) without actually hard-coding the codepoints, by using Unicode general categories. An inverse might be something like [\p{Cc}\p{Cs}\p{Cn}], except that improperly covers linefeeds and tabs and misses some other invalid characters. Variable parameters in C# Lambda I want my Qt application to be able to save simple vector graphics to clipboard in a compatible way. On windows I want to be able to paste the graphics into Microsoft Word or Powerpoint. On Linux I want to be compatible with the Open Office.   Which format would you recommend? Can Qt generate EMF in an easy way? Is SVG an option?  Update:  My current plan is to add a piece of native win32 code to render the graphics to emf on windows. This code will not be available on linux. As a physics student, I have occasionally run across the gamma function  $$\Gamma(n) \equiv \int_0^{\infty}t^{n-1}e^{-t} \textrm{d}t = (n-1)!$$  when we want to generalize the concept of a factorial.  Why not define the gamma function so that   $$\Gamma(n) = n!$$  instead?  I realize either definition is equally good, but if someone were going to ask me to choose one, I would choose the second option.  Are there some areas of mathematics where the accepted definition looks more natural?  Are there some formulas that work out more cleanly with the accepted definition? Topological proof on discrete topology where $X$ is infinite How must I prove this problem? Let $X$ be an infinite set and let $T$ a topology in $X$ in which all infinite subsets of $X$ are open.   Prove: $T$ is a discrete topology in $X$. How to Measure Luck vs Skill in Games?