Pls help me 20 points
1 answer:
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Answer:
a) P(X∩Y) = 0.2
b) = 0.16
c) P = 0.47
Step-by-step explanation:
Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.
So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67
Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.36 + 0.51 - 0.67
P(X∩Y) = 0.2
On the other hand, the probability that he must stop at the first signal but not at the second one can be calculated as:
= P(X) - P(X∩Y)
= 0.36 - 0.2 = 0.16
At the same way, the probability that he must stop at the second signal but not at the first one can be calculated as:
= P(Y) - P(X∩Y)
= 0.51 - 0.2 = 0.31
So, the probability that he must stop at exactly one signal is:
The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)
<h3>What is integration?</h3>It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)
x(t) = (1-t)0 + t×2 = 2t
y(t) = (1-t)0 + t×3 = 3t
z(t) = (1-t)0 + t×4 = 4t
Finding its derivative;
x'(t) = 2
y'(t) = 3
z'(t) = 4
The line integral is given by:
After solving the integration over the limit 0 to 1, we will get;
or
= 73037.99 ≈ 73038
Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)
Learn more about integration here:
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