A painting measures 2.4 feet from left to right. It's hung in the center of a rectangular wall measuring 20 feet from left to ri
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You're going to need to use Pythagoras' theorem to work this one out!
As you know, the perimeter of a triangle is just all the lengths of the sides added up.
We'll start with side AC first. We can see that A is (-8, -4) and C is (-6, -2). That means to get from A to C, we need to go 2 units to the right, and 2 units up. Which means we have our two sides to work out the length from Pythagoras' theorem. 2² + 2² = c², c = √8.
Now we'll move onto side AB. We already know A is (-8, -4) from above, and B is (-7, -8). That means to get from A to B, we have to go 4 units down, and 1 unit to the right. So once again: 4² + 1² = c², c = √17.
Lastly, we'll work out side BC. We know that B is (-7, -8) and C is (-6, -2). That means to get to C from B, we have to go 1 unit to the right and 6 units up. So, again: 1² + 6² = c², c = √37.
Now that we have all of our lengths, we simply just add them up!
√8 + √17 + √37 ≈ 13.03 units.
(I've also attached something to help you visualise how I worked it out.)
Let 
denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by 
, each independently and identically distributed with distribution 
.
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
, then the sampling distribution 
with 
being the size of the sample.
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to