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julia-pushkina [17]
3 years ago
8

Please explain how to do this!!

Mathematics
1 answer:
Tatiana [17]3 years ago
6 0

9514 1404 393

Answer:

  y = 55°

Step-by-step explanation:

You know the sum of angles in a triangle is 180°. So, ...

  25° +30° +x = 180°

And, you know a linear pair of angles totals 180°:

  x + y = 180°

Substituting for 180°, we have ...

  25° +30° +x = x + y

Subtracting x from both sides, we get a relation that is useful to remember:

  25° +30° = y

  y = 55°

_____

This relation is usually described as ...

  An exterior angle is equal to the sum of the remote interior angles.

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3 years ago
A box of cereal is 13 ounces. About how many grams is it?
DaniilM [7]

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kotegsom [21]
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3 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]

a.

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}

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

\approx\boxed{0.012262}

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3 years ago
If there are 26 states east of the Mississippi River and 24 states west of the Mississippi River, what is the probability that t
Aneli [31]
I’m not sure what ur asking
6 0
3 years ago
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