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shtirl [24]
4 years ago
7

3. A rectangular prism has dimensions of 1 , 2, and in. (a) What is the volume of the prism? Show your work and express your ans

wer as a decimal or mixed number. eazy e
Mathematics
1 answer:
Vedmedyk [2.9K]4 years ago
6 0
Although you only put 2 of the 3 needed dimensions into the question, what you would do is multiply the 3 dimensions together and you would get your answer. To find the volume of a rectangular prism you multiply the width, the height, and the length. 
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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}

7 0
3 years ago
Question VVVVVVVVVVVVVVVVVVVVVVVVVVVV
Keith_Richards [23]

Answer:

  {x| x≤ 1/2 or x ≥ 3/4}

Step-by-step explanation:

The values of x that make the factors zero are 3/4 and 1/2. The product of these factors will be positive when both factors are negative (for x < 1/2) or when both factors are positive (x > 3/4). The matching answer selection is the third one.

7 0
3 years ago
What is the simplest form of the ratio 18b^2 to 45b
Svetradugi [14.3K]
Treat it like a fraction
18b^2/45b
divide top and bottom by b
18b/45
divide top and bottom by 3
6b/15
divide top and bottom by 3 again
2b/5
2b:5 is the simpliest form of the ratio
7 0
4 years ago
Can you please help me with this please ty
rjkz [21]
Both of the answers are 50%. your welcome person.
4 0
4 years ago
(as a expression)
motikmotik

Answer:

4 or 5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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