Answer:
73.33% probability that they also took the SAT
Step-by-step explanation:
We have these following two events.
Event A: Taking the ACT exam. So P(A) = 0.3.
Event B: Taking the SAT exam. So P(B) = 0.37.
The conditional probability formula is:
![P(B|A) = \frac{P(A \cap B)}{P(B)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28B%29%7D)
In which P(B|A) is the probability of event B happening given that A has happened,
is the probability of both events hapenning.
22% of graduating seniors too both exams.
This means that ![P(A \cap B) = 0.22](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.22)
If the student took the ACT, what is the probability that they also took the SAT?
![P(B|A) = \frac{P(A \cap B)}{P(B)} = \frac{0.22}{0.3} = 0.7333](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28B%29%7D%20%3D%20%5Cfrac%7B0.22%7D%7B0.3%7D%20%3D%200.7333)
73.33% probability that they also took the SAT
Profit function is the difference between the revenue function, and the cost function
The polynomial that represents their share factor is given as:
![P(x) = 6x^2 + 11 x - 35](https://tex.z-dn.net/?f=P%28x%29%20%3D%206x%5E2%20%2B%2011%20x%20-%2035)
<h3>Q1. The total profit</h3>
This means that we calculate P(10).
So, we have:
![P(10) = 6(10)^2 + 11(10) - 35](https://tex.z-dn.net/?f=P%2810%29%20%3D%206%2810%29%5E2%20%2B%2011%2810%29%20-%2035)
![P(10) = 675](https://tex.z-dn.net/?f=P%2810%29%20%3D%20675)
Hence, the total profit when x = 10 is (d) 675
<h3>Q2. The possible expressions</h3>
We have:
![P(x) = 6x^2 + 11 x - 35](https://tex.z-dn.net/?f=P%28x%29%20%3D%206x%5E2%20%2B%2011%20x%20-%2035)
Factorize the above expression
![P(x) = (2x + 7)(3x - 5)](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%282x%20%2B%207%29%283x%20-%205%29)
Hence, the possible expressions for the individual shares are (b) 3x - 5 and 2x + 7
<h3>Q3. Equal shares</h3>
When their shares are equal, we have:
![2x + 7 = 3x - 5](https://tex.z-dn.net/?f=2x%20%2B%207%20%3D%203x%20-%205)
Collect like terms
![3x - 2x = 7 + 5](https://tex.z-dn.net/?f=3x%20-%202x%20%3D%207%20%2B%205)
![x =12](https://tex.z-dn.net/?f=x%20%3D12)
Hence, the value of x when their shares are equal is (a) 12
<h3>Q4. The Sum of their shares</h3>
The sum of their shares is represented as:
![Sum = 2x + 7 +3x - 5](https://tex.z-dn.net/?f=Sum%20%3D%202x%20%2B%207%20%20%2B3x%20-%205)
Collect like terms
![Sum = 2x +3x + 7 - 5](https://tex.z-dn.net/?f=Sum%20%3D%202x%20%2B3x%20%2B%207%20%20-%205)
![Sum = 5x+ 2](https://tex.z-dn.net/?f=Sum%20%3D%205x%2B%202)
Hence, the sum of their shares is (b) 5x + 2
Read more about profit functions at:
brainly.com/question/10009899
Answer:
He must mow 40 lawns next summer to reach $1000.
Step-by-step explanation:
1000/25=40
462 is how much more then 75 ?
The only way to find out is to subtract 75 from 462.
= 387