7people enter a race. there are 4 types of medals given as prizes for completing the race. the winner gets a platinum medal, the runner-up gets a gold medal, the next two racers each get a silver medal, and the last 3 racers all get bronze medals.
what is the number of different ways the medals can be awarded?

a) 7! /3! b) 7! /2! 3! c) 1*1*2! *3! d) 7*6*2! *3! e) 7*6*5*4

b)

Step-by-step explanation:

The number of ways of awarding the medals is equal to the number of ways of choosing a winner, a runner up, the next two racers and the last 3 racers from our group of 7 people (the different positions of the racers).

To count this, we use the multiplication principle from combinatorics. It says that if there are A ways of doing something and B ways of doing another thing, there are A×B ways of doing both things.

First, there are 7 people and we have to choose 1 winner. This can be done in 7 ways. This person earns the platinum medal

After choosing the winner, 6 people remain. We have to choose 1 runner-up from this group, which can be done in 6 ways.

Now, 5 people remain. We have to choose 2 of them for the silver medal. Since the order between them doesn't matter (they get a silver medal regardless who was 3rd or 4th) the number of ways of doing this is equal to the binomial coefficient .

3 people remain. They will be the last racers, so there is only 1 way of choosing them.

Using the multiplication principle, the number of ways of awarding the medals is

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

#15. square

step-by-step explanation:

because quadrilatural (idk how to spell it) means somthing that is not 3d or like, equal sides (or somthing like that   you know what i meanz)

hope this halps!

bai!