You deal a pile of cards, face down, from a standard 52-card deck. What is the least number of cards the pile must have before you can be assured that it contains at least five cards of the same suit

we need at least 17 - card deck

Step-by-step explanation:

From the information given :

We can attempt to solve the question by using pigeonhole principle;

"The pigeonhole principle posits that if more than n pigeons are placed into n pigeonholes some pigeonhole must contain more than one pigeon"

Thus; the minimum number of pigeon; let say at least n pigeons sit on at least one same hole among m hole can be represented by the formula:

m(  n - 1 ) + 1

where ;

pigeons are synonymous to card

pigeonholes  are synonymous to suits

So; m = 4 ; n = 5

∴  4 (5 -1 ) + 1 ⇒ 4 (4) + 1

= 16 + 1

= 17

Hence; we need at least 17 - card deck

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation:

the area of the rectangle is 35units^2.

step-by-step explanation:

graph it and find the distance.

it is a 5*7 rectangle.

therefore the area is 35units^2.