Answer:
The overall change in field position is 7yds, 0 - 5 + 12 = 7, if that isn't a "sum of integers" I apologize.
Step-by-step explanation:
Answer:
![P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89](https://tex.z-dn.net/?f=%20P%28A%29%3D%200.48%2C%20P%28B%29%3D%20%3F%2C%20P%28A%20%5Ccap%20B%29%3D%200.21%2C%20P%28A%20%5Ccup%20B%29%20%3D0.89)
And for this case we can use the total rule of probability given by:
![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%2BP%28B%29%20-P%28A%5Ccap%20B%29)
And if we solve for
we got:
![P(B)= P(A \cup B) -P(A) +P(A \cap B)](https://tex.z-dn.net/?f=%20P%28B%29%3D%20P%28A%20%5Ccup%20B%29%20-P%28A%29%20%2BP%28A%20%5Ccap%20B%29)
And replacing we got:
![P(B) = 0.89 -0.48 +0.21= 0.62](https://tex.z-dn.net/?f=%20P%28B%29%20%3D%200.89%20-0.48%20%2B0.21%3D%200.62)
Step-by-step explanation:
We have the following probabilities given:
![P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89](https://tex.z-dn.net/?f=%20P%28A%29%3D%200.48%2C%20P%28B%29%3D%20%3F%2C%20P%28A%20%5Ccap%20B%29%3D%200.21%2C%20P%28A%20%5Ccup%20B%29%20%3D0.89)
And for this case we can use the total rule of probability given by:
![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%2BP%28B%29%20-P%28A%5Ccap%20B%29)
And if we solve for
we got:
![P(B)= P(A \cup B) -P(A) +P(A \cap B)](https://tex.z-dn.net/?f=%20P%28B%29%3D%20P%28A%20%5Ccup%20B%29%20-P%28A%29%20%2BP%28A%20%5Ccap%20B%29)
And replacing we got:
![P(B) = 0.89 -0.48 +0.21= 0.62](https://tex.z-dn.net/?f=%20P%28B%29%20%3D%200.89%20-0.48%20%2B0.21%3D%200.62)
Hello!
We know that the sum of all angles in a triangle is 180 degrees. This can be represented by the following formula:
(angle 1) + (angle 2) + (angle 3) = 180
Insert all known values and variables of triangle ABC into the formula above:
30 + (80 + y) + y = 180
Simplify and combine like terms:
30 + 80 + y + y = 180
110 + 2y = 180
Now subtract 110 from both sides of the equation:
2y = 70
Divide both sides by 2:
y = 35
We have now proven that Y is equal to 35 degrees. Using the known value of Y, we can find the value of X using the same formula as above. Begin by inserting all known values and variables of triangle BCD:
y + y + x = 180
(35) + (35) + x = 180
Combine like terms:
70 + x = 180
Subtract 70 from both sides of the equation:
x = 110
We have now proven that X is equal to 110 degrees. Therefore, considering the known values of X and Y, the answer to this problem is C.
I hope this helps!
What took place in the Roman amphitheater’s
Answer:
Water level in the reservoir is falling at the rate of 0.398 ft per minute.
Step-by-step explanation:
From the figure attached,
Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.
Let the level of water in the reservoir after time t is h where radius of the water level becomes r.
ΔABE and ΔCDE are similar.
Therefore, their corresponding sides will be in the same ratio.
![\frac{r}{h}=\frac{4}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%3D%5Cfrac%7B4%7D%7B10%7D)
--------(1)
Now volume of the water V = ![\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
From equation (1),
V = ![\frac{1}{3}\pi (\frac{2}{5}h)^{2} h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7B2%7D%7B5%7Dh%29%5E%7B2%7D%20h)
V = ![\frac{4\pi h^{2}\times h}{75}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20h%5E%7B2%7D%5Ctimes%20h%7D%7B75%7D)
![\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bd%7D%7Bdt%7D%28h%5E%7B3%7D%29)
![\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%283h%5E%7B2%7D%29%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B12%5Cpi%20h%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Since
feet³ per minute and h = 5 feet
![5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B12%5Cpi%20%285%29%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![5=4\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D4%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{5}{4\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B5%7D%7B4%5Cpi%7D)
feet per minute
Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.