How many numbers must be selected from the set left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right curly bracket in order to guarantee that at least one pair adds up to 11

6 numbers

Step-by-step explanation:

Given

Required

Pairs that add up to 11

The pairs are:

In the above set, we have:

Using pigeonhole principle

This principle implies that, there is at least 1 more pair.

Hence, the numbers that must be selected to guarantee the required sum of 11 is:

--- The 1 represents (at least 1 more)

need more information

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have