... of stamp is used? This is just a plain letter with a check inside.

The post office will be better able to answer your question. :)

Have to add, much cheaper, quicker, and safer to send it via paypal or an email money transfer.

... of stamp is used? This is just a plain letter with a check inside.

Seriously? Is this is a real question? Have you not EVER used the mail before? If you are worried about a few days more or less then pay extra to send it overnight.

Generally speaking regular first class mail will take anywhere from 3-6 days normally.

Did you drop the letter in a mailbox or a slot in a PO? At what time of day? You have to allow time for the letter to be processed in Atlanta which means going from where you deposited it to a central station from which it is routed to Vegas. In Vegas it has to be sorted to the recipient's local PO, where a carrier delivers it to the recipient.

Generally speaking regular first class mail will take anywhere from 3-6 days normally.

Did you drop the letter in a mailbox or a slot in a PO? At what time of day? You have to allow time for the letter to be processed in Atlanta which means going from where you deposited it to a central station from which it is routed to Vegas. In Vegas it has to be sorted to the recipient's local PO, where a carrier delivers it to the recipient.

What about the stamp needed? The OP asked that as well.

What about the stamp needed? The OP asked that as well.
49 cents for a first-class stamp

This is likely a generational thing. Ask anyone under the age of 35 when the last time was that they mailed anything - chances are it's been a long time, and they probably don't have any stamps at home. I did an informal poll at work and several people under 35 said they can't remember the last time they used a stamp - they do everything on line (even Christmas cards). These are not just college kids but adults with families and homes. Ask a Millennial and you'll find they probably have no idea how much a stamp costs.

Wow, postage is 49 cents for one letter? I have been out of the US too long.
But yes less than a week to reach, normally a few days. I can get one from Atlanta to China in 2 to 3 weeks.