Using Only Five 5's and any mathematical operator make sum as 37

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

You need to arrange three 7 and mathematical symbols to form number 1?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?