We have that
<span>points A (-5, 6) and B (7, -1)
Part A)
find the distance
d=</span>√[(y2-y1)²+(x2-x1)²]-------> d=√[(-1-6)²+(7+5)²]----> d=√(49+144)
d=√193 units
Part B)
find the midpoint
ABx=(x1+x2)/2-----> (-5+7)/2-----> ABx=1
ABy=(y1+y2)/2-----> (-1+6)/2-----> ABy=2.5
the midpoint is (1,2.5)
Part C)
find the slope
m=(y2-y1)/(x2-x1)-----> m=(-1-6)/(7+5)--------> m=-7/12
the slope m=-7/12
The correct answer is 5460 cubic feet or 5460 ![ft^{3}](https://tex.z-dn.net/?f=ft%5E%7B3%7D)
Explanation:
The silo has a cylindrical shape, in this context, the volume of the silo or any other cylinder can be calculated by using the formula
. In this formula the symbol
refers to the number 3.1415..., the letter
refers to the radius of the base and the letter
refers to the height.
Moreover, in this case, it is known the heigh (21 feet) and the area of the base (260 square feet). Additionally, this area of the base is the result of the formula
, which is exactly the first section of the formula to find the volume. This implies that by multiplying the area of the base by the height the volume is known. Here is the process:
or
(Area of the base × height)
× ![21 feet](https://tex.z-dn.net/?f=21%20feet)
![V = 5460 cubic feet](https://tex.z-dn.net/?f=V%20%3D%205460%20cubic%20feet)
Answer and Step-by-step explanation:
The computation is shown below:
Let us assume that
Spam Email be S
And, test spam positive be T
Given that
P(S) = 0.3
![P(\frac{T}{S}) = 0.95](https://tex.z-dn.net/?f=P%28%5Cfrac%7BT%7D%7BS%7D%29%20%3D%200.95)
![P(\frac{T}{S^c}) = 0.05](https://tex.z-dn.net/?f=P%28%5Cfrac%7BT%7D%7BS%5Ec%7D%29%20%3D%200.05)
Now based on the above information, the probabilities are as follows
i. P(Spam Email) is
= P(S)
= 0.3
![P(S^c) = 1 - P(S)](https://tex.z-dn.net/?f=P%28S%5Ec%29%20%3D%20%201%20-%20P%28S%29)
= 1 - 0.3
= 0.7
ii. ![P(\frac{S}{T}) = \frac{P(S\cap\ T}{P(T)}](https://tex.z-dn.net/?f=P%28%5Cfrac%7BS%7D%7BT%7D%29%20%3D%20%5Cfrac%7BP%28S%5Ccap%5C%20T%7D%7BP%28T%29%7D)
![= \frac{P(\frac{T}{S}) . P(S) }{P(\frac{T}{S}) . P(S) + P(\frac{T}{S^c}) . P(S^c) }](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BP%28%5Cfrac%7BT%7D%7BS%7D%29%20.%20P%28S%29%20%7D%7BP%28%5Cfrac%7BT%7D%7BS%7D%29%20.%20P%28S%29%20%2B%20P%28%5Cfrac%7BT%7D%7BS%5Ec%7D%29%20.%20P%28S%5Ec%29%20%7D)
![= \frac{0.95 \times 0.3}{0.95 \times 0.3 + 0.05 \times 0.7}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B0.95%20%5Ctimes%200.3%7D%7B0.95%20%5Ctimes%200.3%20%2B%200.05%20%5Ctimes%200.7%7D)
= 0.8906
iii. ![P(\frac{S}{T^c}) = \frac{P(S\cap\ T^c}{P(T^c)}](https://tex.z-dn.net/?f=P%28%5Cfrac%7BS%7D%7BT%5Ec%7D%29%20%3D%20%5Cfrac%7BP%28S%5Ccap%5C%20T%5Ec%7D%7BP%28T%5Ec%29%7D)
![= \frac{P(\frac{T^c}{S}) . P(S) }{P(\frac{T^c}{S}) . P(S) + P(\frac{T^c}{S^c}) . P(S^c) }](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BP%28%5Cfrac%7BT%5Ec%7D%7BS%7D%29%20.%20P%28S%29%20%7D%7BP%28%5Cfrac%7BT%5Ec%7D%7BS%7D%29%20.%20P%28S%29%20%2B%20P%28%5Cfrac%7BT%5Ec%7D%7BS%5Ec%7D%29%20.%20P%28S%5Ec%29%20%7D)
![= \frac{(1 - 0.95)\times 0.3}{ (1 -0.95)0.95 \times 0.3 + (1 - 0.05) \times 0.7}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%281%20-%200.95%29%5Ctimes%200.3%7D%7B%20%281%20-0.95%290.95%20%5Ctimes%200.3%20%2B%20%281%20-%200.05%29%20%5Ctimes%200.7%7D)
= 0.0221
We simply applied the above formulas so that the each part could come