Answer:
(E) 0.71
Step-by-step explanation:
Let's call A the event that a student has GPA of 3.5 or better, A' the event that a student has GPA lower than 3.5, B the event that a student is enrolled in at least one AP class and B' the event that a student is not taking any AP class.
So, the probability that the student has a GPA lower than 3.5 and is not taking any AP classes is calculated as:
P(A'∩B') = 1 - P(A∪B)
it means that the students that have a GPA lower than 3.5 and are not taking any AP classes are the complement of the students that have a GPA of 3.5 of better or are enrolled in at least one AP class.
Therefore, P(A∪B) is equal to:
P(A∪B) = P(A) + P(B) - P(A∩B)
Where the probability P(A) that a student has GPA of 3.5 or better is 0.25, the probability P(B) that a student is enrolled in at least one AP class is 0.16 and the probability P(A∩B) that a student has a GPA of 3.5 or better and is enrolled in at least one AP class is 0.12
So, P(A∪B) is equal to:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 0.25 + 0.16 - 0.12
P(A∪B) = 0.29
Finally, P(A'∩B') is equal to:
P(A'∩B') = 1 - P(A∪B)
P(A'∩B') = 1 - 0.29
P(A'∩B') = 0.71
Step-by-step explanation:
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Answer:
a = 1
b = -1
c = -2
Step-by-step explanation:
We reorder the equation in such way that let us see the usual
ax² + bx + c = 0
Then the original quation is:
-2 = - x + x² - 4 ⇒ 0 = 2 - x + x² - 4 ⇒ x² - x - 2 = 0
Now we are able by simply inspection to identify a, b . c comparing our equation with the general equation so :
a = 1
b = -1
c = -2
