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Viefleur [7K]
2 years ago
9

The length of time Y necessary to complete a key operation in the construction of houses has an exponential distribution with me

an 13 hours. The formula C = 100 + 80Y + 3Y2 relates the cost C of completing this operation to the square of the time to completion. The mean of C was found to be found to be 2,154 hours and the variance of C was found to be 10,440,820.
Mathematics
1 answer:
Angelina_Jolie [31]2 years ago
5 0

Answer:

Reference The length of time Y necessary to. ... construction of houses has an exponential distribution with mean 10 hours. The formula C = 100 + 40Y + 3Y 2 relates the cost C of completing this operation to ... Find the mean and variance of C. ... The length of time necessary to complete a key operation in the construction of ...

Step-by-step explanation:

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Answer:

sin\theta_1 = \dfrac{\sqrt{217}}{19}

Step-by-step explanation:

It is given that:

cos\theta_1 = -\dfrac{12}{19}

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As per trigonometric identities, the relation between sin\theta\ and \ cos\theta can represented as:

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Putting \theta_1 in place of \theta Because we are given

sin^2\theta_1 + cos^2\theta_1 = 1

Putting value of cosine:

cos\theta_1 = -\dfrac{12}{19}

sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}

It is given that \theta_1 is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}

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