Answer:
![P(S/I)=0.375](https://tex.z-dn.net/?f=P%28S%2FI%29%3D0.375)
Step-by-step explanation:
Let's start defining the conditional probability of an event :
Given two events A and B :
![P(A/B)=\frac{P(A,B)}{P(B)}](https://tex.z-dn.net/?f=P%28A%2FB%29%3D%5Cfrac%7BP%28A%2CB%29%7D%7BP%28B%29%7D)
with P(B) > 0
Where P(A/B) is the probability of event A given that event B occur
P(A,B) is the probability of the event in which A and B occur both at the same time.
Let's write the events for our exercise
S : ''A random student speaks Spanish''
I : ''A random student speaks Italian''
![P(S)=0.23\\P(I)=0.08\\P(S,I)=0.03](https://tex.z-dn.net/?f=P%28S%29%3D0.23%5C%5CP%28I%29%3D0.08%5C%5CP%28S%2CI%29%3D0.03)
Applying the conditional equation we obtain :
![P(S/I)=\frac{P(S,I)}{P(I)}=\frac{0.03}{0.08}=0.375](https://tex.z-dn.net/?f=P%28S%2FI%29%3D%5Cfrac%7BP%28S%2CI%29%7D%7BP%28I%29%7D%3D%5Cfrac%7B0.03%7D%7B0.08%7D%3D0.375)
Then, 0.375 is the probability that we are looking for
( don't report ill help not lieing ) so whats the equasions?
Answer:
Relation between V and c is represented as:
![V = \pi c^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20c%5E%7B3%7D)
When c is halved, V becomes
of its initial value.
Step-by-step explanation:
Height of cylinder = Radius of cylinder = c
Volume of cylinder = V
As per formula:
![V = \pi r^{2} h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E%7B2%7D%20h)
Where
is the radius of cylinder and
is the height of cylinder
Putting ![r = h =c](https://tex.z-dn.net/?f=r%20%3D%20h%20%3Dc)
![V = \pi c^{2} \times c\\\Rightarrow V = \pi c^{3} ......(1)](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20c%5E%7B2%7D%20%5Ctimes%20c%5C%5C%5CRightarrow%20V%20%3D%20%5Cpi%20c%5E%7B3%7D%20......%281%29)
The values of c is halved:
Using equation (1), New volume:
![V' = \pi (\dfrac{c}{2})^3\\\Rightarrow \dfrac{1}{8} \pi c^{3}](https://tex.z-dn.net/?f=V%27%20%3D%20%5Cpi%20%28%5Cdfrac%7Bc%7D%7B2%7D%29%5E3%5C%5C%5CRightarrow%20%5Cdfrac%7B1%7D%7B8%7D%20%5Cpi%20c%5E%7B3%7D)
By equation (1), putting ![\pi \times c^{3} = V](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%20c%5E%7B3%7D%20%20%3D%20V)
![V' = \dfrac{1}{8} \times V](https://tex.z-dn.net/?f=V%27%20%3D%20%5Cdfrac%7B1%7D%7B8%7D%20%5Ctimes%20V)
So, when c is halved, V becomes
of its initial value.
Answer:
m^2+4m-21
Step-by-step explanation:
(m-3)(m+7)
m^2-3m+7m-21
m^2+4m-21
Answer:
answer
Step-by-step explanation:
positive
negative