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There is not a good scientific study on actual test scores, but there is proof that soft instrumental music can help a person to concentrate better. Loud music, or music that has words and heavy rhythm, actually distracts a person worse than silence.
Yes, because sometimes it can be very distracting to the students. Especially if they are trying to concentrate.
There is not a formula for music.
Studying math builds your mind, prevents senility, may provide you with some useful tools, is totally harmless and can give great personal satisfaction at little cost. Do it every reasonable opportunity. I am not sure what you mean by "in tourism". If you mean while you are a tourist, there is often some dead time while traveling, so instead of reading trash fiction or mindlessly listening to pop music, you will profit more from studying math. The pleasant, but perhaps not the most efficient way to study math is by thinking about problems that you do not know how to solve.
not sure but there was a very popular song in the 1950's called music, music. music by Teresa brewer......