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website: not really. You need msoffice to run the sheet, so unless you manually execute the sheet previously so that the data is available for read (not execute) you can’t do it with ms excel. You can do it with a programming language, depending on what you need and what you are familiar with you have many options VB(script) should be the simplest and PHP the most powerful of the most known. After just learn about the math specific issues and functions!
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server: sure you can use that laptop, but it not only stores but also processes the page requests. Remember it should be set up properly with web serving software. Connecting by cable would be safe but the question is how reliable do you want it to be? A home connection and weak server might not be so reliable but it works fine for testing and small scenarios otherwise it’s simpler to just hire a hosting solution. May cost from 15$ to 60$ for a basic site depending on what you need.
P.S.: there is an easy to use server software called xampp that runs smoothly on windows. It supports many languages and databases.
A1. Yes, a scripting language it’s much slower and overall less capable, it depends on what you want to achieve if VB is enough.
A2. It is most powerful when it comes to calculations because it runs on the server and is versatile. for data storage i recommend databases but that can be complicated for you.
A3. No, you can’t abandon HTML it is essential to web pages like a core structure.
new A1. Java is also powerful and more portable than php but with more issues since it runs client side. Jsp runs server side and is like php. Potatoes potAtoes. Start by choosing a language maybe but remember scripting languages are usually client side which means it depends on the users pc and the code is available to them.
new A2. Maybe not the best choice, but workable.
new A3. Excel speed is closer to php/server side languages i would recommend php for many reasons. Secure fast precise (no rounding) powerful many math functions might also have a few financial, not sure.
new A4. Yes, PHP and HTML work fine together but remember one runs on the server and HTML on the client.
new A5. Many on the web, also “php for dummies” as a book is a starting point.
new A6. You got me there, I’m not familiar with R.
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solved MS EXCEL and a CUSTOM WEBSITE