I have no edges, no corners, and my value is the same whether you look at me right-side up or upside down, yet I represent absolute nothingness in modern mathematics. What am I?

Two cyclists start 60 miles apart and cycle straight toward one another, both maintaining a constant speed of 15 miles per hour. A fly starts on the handlebars of one bicycle and flies back and forth between them at 20 miles per hour until the bicycles meet. How many total miles does the fly travel?

Three friends pay $10 each ($30 total) for a room. The manager realizes the rate is $25 and gives $5 to the bellhop to refund. The bellhop keeps $2 and returns $1 to each friend. Now each friend paid $9 (total $27), and the bellhop kept $2, making $29. Where is the missing dollar?

You own a standard two-pan balance scale and exactly four solid weights: 1 kg, 3 kg, 9 kg, and 27 kg. By placing weights either on the object's pan or the opposite pan, how many distinct whole-number kilogram weights from 1 kg up to 40 kg can you measure?

If you take my age, multiply it by 4, subtract 10, divide by 2, and add 6, you get back to my exact age. How old am I?

I am thinking of a positive integer. If you cube me, subtract 19, and then divide by 4, the result is 11. What number am I?

I start as a prime number. If you reverse my digits, I become a different prime number. The sum of my digits is 8. What number am I?