AoPS Academy
where 
is prime?
has Area of 
. If point 
is the midpoint of 
, then line 
is 
, which cuts the equilateral triangle in half. What is the sum of the perimeters of 
and 
?
. How many positive 3-digit quadnumbers are there? (ex. 
is a quadnumber because it is positive, 3-digit, and the digits sum to )
equal sections with the numbers from 
to written on them. If you spin the wheel 
times, what is the probability that you will land on a prime number on any of the spins? (Clarification: Probability of Landing on a prime AT LEAST ONCE in the N spins)
mph. Car B is a probabilistic car, and at the start of every hour, it gets the option for a 
chance of traveling at 
mph, an 
chance of traveling at mph, and a chance of traveling at 
mph. Once Car B decides on a speed, it acts like a normal car for the rest of the hour with a constant speed at which it picked at the start of the hour, and then the same options happen at the start of the next hour, and so on. Car A and Car B leave at the same time, and they both go in the same direction. What is the probability that Car B is right next to Car A (same speed, same position) for only 
hours in the next 6 hours?
, and 
, and 
, what is the least positive value of 
.
and 
is 
, what is 
?
?
, and ball B costs 
, what is the average cost per ball if you buy of ball A and of ball B? Please write as an improper fraction
have?
, then what is 
?
, sum to 50, what is the greatest possible value of 
such that 
? satisfies: 
? is inscribed in a square, which is inscribed in another circle, what is the area of the outer circle minus the area of the inner circle?
and 
such that the roots of 
sum to 
and multiply to 
?
, what is the largest possible value of 
given that is a positive integer?
I fixed it
be the rate at which one person mows the lawn (in lawns per minute). We have
Now, let 
be the number of minutes it will take for 
people to mow 
Therefore, the answer is it will take 
hours.
