Answer:
5
Explanation:
1/4 of 12 = 3
2 + 3 = 5
Answer:
The percentage of admitted applicants who had a Math SAT of 700 or more is 48.48%.
Step-by-step explanation:
The Bayes' theorem is used to determine the conditional probability of an event <em>E</em>
, belonging to the sample space S = (E₁, E₂, E₃,...Eₙ) given that another event <em>A</em> has already occurred by the formula:
![P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\limits^{n}_{i=1}{P(A|E_{i})P(E_{i})}}](https://tex.z-dn.net/?f=P%28E_%7Bi%7D%7CA%29%3D%5Cfrac%7BP%28A%7CE_%7Bi%7D%29P%28E_%7Bi%7D%29%7D%7B%5Csum%5Climits%5E%7Bn%7D_%7Bi%3D1%7D%7BP%28A%7CE_%7Bi%7D%29P%28E_%7Bi%7D%29%7D%7D)
Denote the events as follows:
<em>X</em> = an student with a Math SAT of 700 or more applied for the college
<em>Y</em> = an applicant with a Math SAT of 700 or more was admitted
<em>Z</em> = an applicant with a Math SAT of less than 700 was admitted
The information provided is:
![P(Y)=0.36\\P(Z)=0.18\\P(X|Y)=0.32](https://tex.z-dn.net/?f=P%28Y%29%3D0.36%5C%5CP%28Z%29%3D0.18%5C%5CP%28X%7CY%29%3D0.32)
Compute the value of
as follows:
![P(X|Z)=1-P(X|Y)\\=1-0.32\\=0.68](https://tex.z-dn.net/?f=P%28X%7CZ%29%3D1-P%28X%7CY%29%5C%5C%3D1-0.32%5C%5C%3D0.68)
Compute the value of P (Y|X) as follows:
![P(Y|X)=\frac{P(X|Y)P(Y)}{P(X|Y)P(Y)+P(X|Z)P(Z)}](https://tex.z-dn.net/?f=P%28Y%7CX%29%3D%5Cfrac%7BP%28X%7CY%29P%28Y%29%7D%7BP%28X%7CY%29P%28Y%29%2BP%28X%7CZ%29P%28Z%29%7D)
![=\frac{(0.32\times 0.36)}{(0.32\times 0.36)+(0.68\times 0.18)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%280.32%5Ctimes%200.36%29%7D%7B%280.32%5Ctimes%200.36%29%2B%280.68%5Ctimes%200.18%29%7D)
![=0.4848](https://tex.z-dn.net/?f=%3D0.4848)
Thus, the percentage of admitted applicants who had a Math SAT of 700 or more is 48.48%.
Hello, 2^36 3^48 is the correct answer.
Please mark brainliest.
Answer:
Area of circle is ![\dfrac{225n^{2}}{4\pi} cm^{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B225n%5E%7B2%7D%7D%7B4%5Cpi%7D%20cm%5E%7B2%7D)
Step-by-step explanation:
Formula for circumference of circle is given as,
![C=2\pi r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r)
Given that C = 15 n cm,
Substituting the value,
![15n=2\pi r](https://tex.z-dn.net/?f=15n%3D2%5Cpi%20r%20)
Solving above equation for r, divide both side by ![2\pi](https://tex.z-dn.net/?f=%202%5Cpi%20)
![\dfrac{15n}{2\pi}=\dfrac{2\pi r}{2\pi}](https://tex.z-dn.net/?f=%5Cdfrac%7B15n%7D%7B2%5Cpi%7D%3D%5Cdfrac%7B2%5Cpi%20r%7D%7B2%5Cpi%7D)
Simplifying,
![\dfrac{15n}{2\pi}=r](https://tex.z-dn.net/?f=%5Cdfrac%7B15n%7D%7B2%5Cpi%7D%3Dr)
Formula for area of circle is given as,
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
Substituting the value of r,
![A=\pi \left(\dfrac{15n}{2\pi}\right)^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%5Cleft%28%5Cdfrac%7B15n%7D%7B2%5Cpi%7D%5Cright%29%5E%7B2%7D)
Squaring the parenthesis,
![A=\pi \left(\dfrac{225n^{2}}{4\pi^{2}}\right)](https://tex.z-dn.net/?f=A%3D%5Cpi%20%5Cleft%28%5Cdfrac%7B225n%5E%7B2%7D%7D%7B4%5Cpi%5E%7B2%7D%7D%5Cright%29)
Cancelling out the common term,
![A=\dfrac{225n^{2}}{4\pi}](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B225n%5E%7B2%7D%7D%7B4%5Cpi%7D)
Therefore, area of circle in terms of n is ![A=\dfrac{225n^{2}}{4\pi} cm^{2}](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B225n%5E%7B2%7D%7D%7B4%5Cpi%7D%20cm%5E%7B2%7D)