The probability of the union of two events is the sum of their probability, minus the probability of their interserction:
![P(A \cup B) = P(A) + P(B) - P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28A%20%5Ccap%20B%29%20)
If we plug the known values into this formula, we have
![\dfrac{3}{5} = \dfrac{1}{3} + \dfrac{2}{5} - P(A\cap B)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B3%7D%7B5%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B2%7D%7B5%7D%20-%20P%28A%5Ccap%20B%29%20)
From which we can deduce
![P(A\cap B) = \dfrac{1}{3} + \dfrac{2}{5} - \dfrac{3}{5} = \dfrac{2}{15}](https://tex.z-dn.net/?f=%20P%28A%5Ccap%20B%29%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%2B%20%5Cdfrac%7B2%7D%7B5%7D%20-%20%5Cdfrac%7B3%7D%7B5%7D%20%3D%20%5Cdfrac%7B2%7D%7B15%7D%20)
So, the probability of
is a bit less than
, we have to take away all events that belong to B as well:
![P(A \setminus B) = P(A) - P(A\cap B) = \dfrac{1}{3} - \dfrac{2}{15} = \dfrac{1}{5}](https://tex.z-dn.net/?f=%20P%28A%20%5Csetminus%20B%29%20%3D%20P%28A%29%20-%20P%28A%5Ccap%20B%29%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20-%20%5Cdfrac%7B2%7D%7B15%7D%20%3D%20%5Cdfrac%7B1%7D%7B5%7D)
Answer:
huh?
Step-by-step explanation:
whats the questionnnnnnn
ITS TOO SMALL TO SEE THAT PRINT, BUT CAN SOMEONE PLEASE HELP ME ANSWER THIS PROBLEM ON MY PROFILE I JUST POSTED IT AND NO ONE WILL HELP ME!!1
To calculate the volume of the rectangular prism and the triangular prism you will multiply the area of the base by the height of the prism.
1. V = BH
V = lwH
12 x 8 x 4
V = 384 cubic inches
2. V = BH
V = 1/2bhH
1/2 x 12 x 2 x 18
V = 216 cubic feet
Answer:
A) (1 s, 2.3 s)
B) (-4 m/s², 3.8 m/s²)
Step-by-step explanation:
The car's position which is the distance is given by the equation;
s(t) = t³ - 5t² + 7t
A) Velocity is the first derivative of the distance. Thus;
v(t) = ds/dt = 3t² - 10t + 7
At v = 0, we have;
3t² - 10t + 7 = 0
Using quadratic formula, we have;
t = 1 and t = 2.3
Thus, time at velocity of 0 is t = (1 s, 2.3 s)
B) acceleration is the derivative of the velocity. Thus;
a(t) = dV/dt = 6t - 10
At velocity of 0, we got t = 1 and t = 2.3
Thus;
a(1) = 6(1) - 10 = -4 m/s²
a(2.3) = 6(2.3) - 10 = 3.8 m/s
Thus, a(t) at v = 0 gives; (-4 m/s², 3.8 m/s²)