Y varies jointly with x. Y=16 when x=4 and z=1/2. Find y when x=2 and z=1/4. Enter the value of y in the box. Picture attached,
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1 answer:
Answer:
y = 4
Step-by-step explanation:
Given that y varies jointly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 16 when x = 4 and z = , that is
16 = k × 4 × = 2k ( divide both sides by 2 )
8 = k
y = 8xz ← equation of variation
When x = 2 and z = , then
y = 8 × 2 × = 16 ×
= 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.