PROBLEM 1 Peter has many socks, all the same except that they are in three different colours. He is leaving to catch an early train to go on a business trip, and he does not want to wake his wife, so he packs in the
dark. He needs eleven pairs of socks, each sock in each pair the same colour. How many socks must he take from his drawer to be sure of achieving this?

24 socks

Step-by-step explanation:

The given parameters are;

The number of different colors of socks = 3

Therefore, we have the worst case, the first three socks are different colors, since there are three different colors, the fourth socks is first pair in the worst case scenario

After which, every other two socks makes a pair in the worst case process, the number of socks he must take to make sure he has eleven pairs are given by the pairing table

Number of socks123456789101112131415161718192021222324

Number of pairs000112233445566778899101011

Therefore, he must take 24 socks to make sue he has 11 pairs of the same color.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

7

step-by-step explanation: