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2 years ago

6 problems, most of them I know but I need help on these by tomorrow so high point amount

Mathematics

2 answers:

Vlada [557]2 years ago

6 0

Answer:

y = -4x - 40

Perimeter = 5x^2 + 6x + 1

Area = 20x^3 + 23x^2 - 2x - 6

Step-by-step explanation:

That's how mafia works

Wittaler [7]2 years ago

4 0

Answer:

m = -4 is the slope

(x1, y1) = (12, 8) is a point on the line

The point-slope form is:

y - y1 = m(x - x1)

y - 8 = (-4)(x - 12)

The slope-intercept form is:

y = 8 + (-4)x + 16

y = (-4)x + 24

The standard form is:

y + (-4)x = 18 multiply both sides by 4

-4x = 18*4

-4x = 72

Step-by-step explanation:

2) Perimeter = 5x^2 + 2x -2

=7x^2 -2

L =49x -2

W=4x+3

49 -2 =47 x 16+3 = 19

A = 47x19

A = 893

P= 47+47+19+19= 132

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2 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

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

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

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

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

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

Then

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

$\approx\boxed{0.12886}$

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

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

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