Answer:
Proofs for Pythagoras Theorem usually use visual/geometry approaches. I don't post pictures in my answers, so I will present a linear algebra approach. You can see it in the blog posted by Professor Terence Tao.
Note that there are several elegant proofs using animations and drawings, but this is just personal.
I've seen this some time ago, it is really interesting proof.
It states that 
is equivalent to the statement that the matrices
and 
have the same determinant.
The determinant of the first matrix is 
The determinant of the second matrix is 
Once the linear transformations associated with these matrices differ by rotation, we claim that
Answer:
He will have 160 because in this equation you are solving for total cookies at the end of cooking or y. And since he's making 5 batches then x=5 so....
Step-by-step explanation:
Y=90+14(x)=
Y=90+14(5)
14(5)=7
Y=90+70
Y=160 cookies
4 steps more north from where he started
I think
Answer:
The probability that in a randomly selected game, the player scored greater than 24 points is 0.0013 or 0.13%
Step-by-step explanation:
Given that
Mean = μ = 15 points
SD = σ = 3 points
For calculating probability for a data point, first of all we have to calculate the z-score of the value.
We have to find the probability of score greater than 24, then the z-score of 24 is:
z-score = (x-μ)/σ
z = (24-15)/3
z = 9/3
z = 3
Now we have to use the z-score table to find the probability of z<3 then it will be subtracted from 1 to find the probability of z>3
So,
Converting into percentage
0.0013 * 100 = 0.13%
Hence,
The probability that in a randomly selected game, the player scored greater than 24 points is 0.0013 or 0.13%
