10.Suppose that we have 50 balls labeled 0 through 49 in a bucket. What is the minimum number of balls that we need to draw to ensure that we get at least 3 balls which end with the same digit

Following are the response to the given question:

Pigeon Hole's Principle can also be used to tackle this problem. Assuming that we already have labels ranging from

Each digit ending is represented by five balls.

In the pigeonhole principle, it objects are distributed among n boxes, one of the boxes will contain at least objects. Assume that you draw a ball and place it in a box labeled with its last digit. So there will be n = 10 boxes.

According to the pigeon hole concept, you need to draw balls to assure that at least one of the boxes includes objects. Because we require three objects in at least one box (we need three balls ending with the same digit).

Therefore, we have to draw balls, , at least must be drawn to ensure that at least three of them have the same 1 digit.

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21 drawings

Step-by-step explanation:

The number labelings are 0 - 49

The minimum set that could be the same number is the labeling 0, 10 , 20

It could also be 1, 11, 21 or even 2,12,22

In all the cases, we can be sure that we might have three labelings ending with the same number when we pull our ball labeled 20

That makes a total of 21 drawings

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)

x+14

step-by-step explanation: