Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y = 3, x = 4
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Answer:
(a1) The probability that temperature increase will be less than 20°C is 0.667.
(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.
(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.
(c) The expected value of the temperature increase is 17.5°C.
Step-by-step explanation:
Let <em>X</em> = temperature increase.
The random variable <em>X</em> follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].
The probability density function of <em>X</em> is:
(a1)
Compute the probability that temperature increase will be less than 20°C as follows:
Thus, the probability that temperature increase will be less than 20°C is 0.667.
(a2)
Compute the probability that temperature increase will be between 20°C and 22°C as follows:
Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.
(b)
Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:
Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.
(c)
Compute the expected value of the uniform random variable <em>X</em> as follows:
Thus, the expected value of the temperature increase is 17.5°C.
Let the distance be d
Using pythagorean theorem,
d ≈ 119
The player ran for 119 meters
Using pythagorean theorem,
d ≈ 119
The player ran for 119 meters
The probability of picking one girl would be . That is because there are 5 girls out of the 12 students, and the probability of an event occuring is:
.
Using that same logic, the next student should be easier. We reduced the student population by 1, so we have 11 possible ways it can happen now instead of 12, so that gives us:, for the probability of picking a boy as the second pick.
And lastly, using the same logic shown above, the probability of picking a girl on the third pick would be:.
We are not done, though. We have the separate probabilities, but now we have to multiply then together to figure out the probability of this exact event happening:
Which when reduced is: