Answer:
![P(A\ and\ B) = \frac{3}{7}](https://tex.z-dn.net/?f=P%28A%5C%20and%5C%20B%29%20%3D%20%5Cfrac%7B3%7D%7B7%7D)
Step-by-step explanation:
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Required
Find P(A n B)
where
A = Event that the place is a city
B = Event that the place is in North
The first step is to get the sample space;
Let S represent the sample space;
![S = \{India,\ Tokyo,\ Houston,\ Peru,\ New York,\ Tijuana,\ Canada \}](https://tex.z-dn.net/?f=S%20%3D%20%5C%7BIndia%2C%5C%20Tokyo%2C%5C%20Houston%2C%5C%20Peru%2C%5C%20New%20York%2C%5C%20Tijuana%2C%5C%20Canada%20%5C%7D)
![n(S) = 7](https://tex.z-dn.net/?f=n%28S%29%20%3D%207)
The next is to list events A and B
A = City
![A = \{Tokyo,\ Houston,\ New York,\ Tijuana\}](https://tex.z-dn.net/?f=A%20%3D%20%5C%7BTokyo%2C%5C%20Houston%2C%5C%20New%20York%2C%5C%20Tijuana%5C%7D)
B = North America
![B = \{Houston,\ New York,\ Tijuana,\ Canada\}](https://tex.z-dn.net/?f=B%20%3D%20%5C%7BHouston%2C%5C%20New%20York%2C%5C%20Tijuana%2C%5C%20Canada%5C%7D)
The next is to list common elements in A and B
![A\ n\ B = \{Houston,\ New York,\ Tijuana\}](https://tex.z-dn.net/?f=A%5C%20n%5C%20B%20%3D%20%5C%7BHouston%2C%5C%20New%20York%2C%5C%20Tijuana%5C%7D)
![n(A\ and\ B) = 3](https://tex.z-dn.net/?f=n%28A%5C%20and%5C%20B%29%20%3D%203)
The probability of A and B is calculated as follows;
![P(A\ and\ B) = \frac{n(A\ and\ B)}{n(S)}](https://tex.z-dn.net/?f=P%28A%5C%20and%5C%20B%29%20%3D%20%5Cfrac%7Bn%28A%5C%20and%5C%20B%29%7D%7Bn%28S%29%7D)
Substitute
and
in the expression above
![P(A\ and\ B) = \frac{3}{7}](https://tex.z-dn.net/?f=P%28A%5C%20and%5C%20B%29%20%3D%20%5Cfrac%7B3%7D%7B7%7D)
Answer:
I'm not sure if i'm correct but i'm guessing no
Step-by-step explanation:
Answer:
x = 3 ± ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)
or
x = 3 +
, x = 3 - ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)
Step-by-step explanation:
given f(x) = 2(x - 3)^2 - 8, find when f(x) = 40
So, we plug in 40 for f(x) in the 1st equation and solve for x. (Aim to got x on its own)
40 = 2 (x - 3)^2 - 8
+ 8 + 8
-----------------------------
48 = 2 (x - 3)^2
/2 /2
-----------------------------
24 = (x - 3)^2
square root both sides
--------------------
= x - 3
x = 3 ± ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)
(slope) The higher the gradient<span> of a graph at a point, the steeper the </span>line<span> is at that point.</span>