The mode of nine numbers between 0 and 100 inclusive is 12. Their median is 41, and the range is 75. Find the largest possible value of the mean.

To the nearest integer, find the harmonic mean of the numbers 20, 30, 40 and 50.

A college reports:

-75% of incoming freshmen attended a public high school.

-60% of public schoolstudents who enroll as freshmen eventually graduate.

-70% of other freshmen graduate.

What percentage of students who graduate from this college attended a public high school? Assume all students enroll as freshmen).

`y_1=|4-x|` and `y_2=4-|x-2|`. Find the area of the parallelogram formed in the first quadrant between both functions.

A number has `3` digits if expressed in base `7`, and the same `3` digits in reverse order if expressed in base `9`. Find the base `10` representation of the number.

If a positive factor of 2025 is selected at random, what is the probability that it is less than 30?

Every day, Py Thag drives to the Parthenon and aims to meet his friend, Pla To, at 6 AM. If he averages 40mph, he arrives at 6:03AM. If he averages 60mph, he arrives at 5:57AM. Find the speed (in mph) in which he should drive to arrive exactly at 6AM.

Solve for `x: 4^(32^x)=16^(8^x)`.

No motorized vehicles are allowed on Mackinac Island in Michigan, so I decided to rent a horse and buggy. The circular road around its perimeter took 2 hours and 40 minutes at 3mph. Find, in terms of `pi`, the area of the island in square miles.

A new operation `*` has the following properties:

a * b = b * a

a * 0 = a

(a * b) + b – 3 = (a + 1) * b

Find 17 * 2.