Suppose that 25 days are chosen at random from a calendar. explain why at least 3 of the 25 days must lie in the same month. do some research to find the name of the principle you've used, and clearly describe it in your own words.

Explanation:

There are 12 months in a year, if we chose 25 random dates we'll have two dates per month

2x12=24

and one extra day that will fit in another month.

The principle used for this kind of problem is the pigeonhole principle, supposing we have a number k of pigeonholes and n pigeons to be placed in them, If the number of pigeons is bigger than the pigeonholes, there will be at least one pigeonhole with more than one pigeon.

This happens with our problem, 25 days is a larger number than 12 months two times (24), this means we'll choose at least one month three times.

I hope you find this information useful! good luck!

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.