The conditional probability that the carbon emission is beyond the permissible emission level and the test predicts this is given by:
a. 0.2975.
<h3>What is Conditional Probability?</h3>
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which:
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem, we have that the events are as follows:
- Event A: Carbon emission beyond the permissible emission level.
- Event B: Test predicts this.
We have that 35% of the units have carbon emission beyond the permissible emission level, and the test is 85% accurate, hence:
![P(A) = 0.35, P(B|A) = 0.85](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.35%2C%20P%28B%7CA%29%20%3D%200.85)
Then:
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
![0.85 = \frac{P(A \cap B)}{0.35}](https://tex.z-dn.net/?f=0.85%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7B0.35%7D)
![P(A \cap B) = 0.85(0.35) = 0.2975](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.85%280.35%29%20%3D%200.2975)
Which means that option a is correct.
More can be learned about conditional probability at brainly.com/question/14398287
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Answer:
![{2}^{7}](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7B7%7D%20)
Step-by-step explanation:
![{2}^{7} = 128](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7B7%7D%20%20%3D%20128)
![{7}^{2} = 49](https://tex.z-dn.net/?f=%20%7B7%7D%5E%7B2%7D%20%20%3D%2049)
So,
![128 > 49 \\ {2}^{7} \: \: \: \: > {7}^{2}](https://tex.z-dn.net/?f=128%20%3E%2049%20%5C%5C%20%20%7B2%7D%5E%7B7%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%20%20%3E%20%20%7B7%7D%5E%7B2%7D%20)
Therefore 2^7 is greater
Answer:
Length of the side be=11.9cm
Be=14sin58
Nvm=14 times 0.8480
Bc=11.9 cm
Step-by-step explanation:
Answer:
Option A.
Step-by-step explanation:
Note: Let as consider, we have to find the total amount after 9 years.
It is given that,
Principal amount = $1000
Rate of compound (yearly) interest = 15% = 0.15
Time = 9 year
The formula for total amount is
where, P is principal, i is rate of interest and n is number of years.
Substituting P=1000, i=0.15 and n=9, we get
So, the total amount after 9 years is $3517.88.
Therefore, the correct option is A.
Answer:
B=95°
E=95°
D=20°
C=65°
BC=7cm
Step-by-step explanation:
the triangles look like they are identical, just different in size only. Since DE= 15 and AB=10 that may mean that they have a 5cm difference making side BC= 7cm since EF= 12 minus 5 equals 7cm. Now for the other angles, a triangle no matter what,if we put all their angles together equal 180°. We already know angle A= 20 so the same applies to angle D. We also know that angle F=65 degrees, that makes angle C the same. The only thing that's left are angles B and E that can be found by adding our other angles. So if A+C(20+65)=85 then 180-85=95 degrees is angle B and since the triangles are identical the same goes to E.