Answer:
7 7/20
Step-by-step explanation:
4 3/5 - -3 3/4
4 3/5 + 3 3/4
4 12/20 + 3 15/20
7 7/20
Let's define variables:
x: number of times the ticket price increases ($ 1).
The income is given by:
I(x) = (15 + x)(500-20x)
We can rewrite this function in the following way:
I (x) = - 20x ^ 2 + 200x + 7500
We use the following equation to find the maximum:
max = (-b)/(2a)
where:
then, we have:
max = (-200)/(2(-20))
max = (200)/(40)
max=5
Thus, the ticket price that maximizes the benefit is:
15 + x = 15 + 5 = 20 $
Answer:
A ticket price that will maximize the charity's profit, if there are total 500 seats in the concert hall is:
$ 20
Answer:
x = 11, y = 17
Step-by-step explanation:
Set the equations equal to each other. Since the vertical angles are congruent, 8x + 7 = 9x - 4 and 5y = 7y - 34. Now, solve your equations for the x and y values.
8x + 7 = 9x - 4
x = 11
5y = 7y - 34
2y = 34
y = 17
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%.