The warehouse already has 27 pallets of stock waiting to be unloaded, and the delivery van arrives with another 8. The warehouse
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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.
Answer:
In Right Δ ABC with right angle B,
∠A=(3 x -8)°, ∠B=90°, ∠C=(x-2)°
∠A+∠B+∠C=180°[∠ sum property of triangle]
3 x-8+90 + x-2=180
Adding and subtracting like terms
4 x-10+90=180
4 x+80=180
4 x=180-80
4 x=100
x=100/4
x=25°
∠A=3×25-8=75-8=67°
