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3 years ago

I need help with this question

Mathematics

1 answer:

VikaD [51]3 years ago

7 0

Using the given information, the value of x is -66

<h3>Linear equation </h3>

From the question, we are to determine the value of x

In the given diagram,

∠UYV and ∠WYX are vertically opposite angles

By vertical opposite angles theorem,

∠UYV = ∠WYX

∴ 56° = (-x - 10)°

56° = -x° - 10°

56° + 10° = -x°

66° = -x°

∴ x = -66

Hence, the value of x is -66.

Learn more on Linear equations here: brainly.com/question/23087234

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kompoz [17]

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

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$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

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$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

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