Answer:
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Step-by-step explanation:
Answer:
![\displaystyle\frac{30}{73}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B30%7D%7B73%7D)
Step-by-step explanation:
The formula of conditional probability is:
![\displaystyle P(F|E)=\frac{P(E \cap F)}{P(E)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28F%7CE%29%3D%5Cfrac%7BP%28E%20%5Ccap%20F%29%7D%7BP%28E%29%7D)
And if we called N(U) the total number of possible outcomes, then remember by definition of probability:
![\displaystyle P(E \cap F)=\frac{N(E \cap F)}{N(U)}\\\displaystyle P(E)=\frac{N(E)}{N(U)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28E%20%5Ccap%20F%29%3D%5Cfrac%7BN%28E%20%5Ccap%20F%29%7D%7BN%28U%29%7D%5C%5C%5Cdisplaystyle%20P%28E%29%3D%5Cfrac%7BN%28E%29%7D%7BN%28U%29%7D)
Then plugging them into the formula of conditional probability we get:
![\displaystyle P(F|E)=\frac{\frac{N(E \cap F)}{N(U)}}{\frac{N(E)}{N(U)}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28F%7CE%29%3D%5Cfrac%7B%5Cfrac%7BN%28E%20%5Ccap%20F%29%7D%7BN%28U%29%7D%7D%7B%5Cfrac%7BN%28E%29%7D%7BN%28U%29%7D%7D)
Then we simplify and we get:
![\displaystyle P(F|E)=\frac{N(E \cap F)}{N(E)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28F%7CE%29%3D%5Cfrac%7BN%28E%20%5Ccap%20F%29%7D%7BN%28E%29%7D)
We just plug the given info and we get:
![\displaystyle P(F|E)=\frac{300}{730}=\frac{30}{70}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28F%7CE%29%3D%5Cfrac%7B300%7D%7B730%7D%3D%5Cfrac%7B30%7D%7B70%7D)
The product of two even numbers is even.
Let m and n be any integers so that 2m and 2k are two even numbers.
The product is 2m(2k) = 2(2mk), which is even.
Things to think about:
Why didn’t I just show you by using any two even numbers like the number 4 and the number 26?
Why did I change from "m" to "k" ? Are they really different numbers or could they be the same?
Why did I specifically say that m and k were integers?
The product of two odd numbers is an odd number.
Let m and k be any integers. This means that 2m+1 and 2k+1 are odd numbers.
The product is 4mk + 2m + 2k + 1 (hint: I used FOIL) which can be written as
2 ( 2mk + m + k ) + 1 which is an odd number.
Answer:
an isosceles right triangle
Step-by-step explanation:
The square of the length of a side can be found from the distance formula:
d^2 = (x2-x1)^2 +(y2-y1)^2
The square of the length of WX is ...
WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74
The square of the length of XY is ...
XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148
The square of the length of YW is ...
YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74
The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.
0.32. Because you need to find the area, as size 8*8/2 then divide by 100 to get the decimal.I hope this helps.