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aksik [14]
3 years ago
11

What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)? 3 4 5 9

Mathematics
2 answers:
ICE Princess25 [194]3 years ago
7 0

1.5(x+4)-3=4.5(x-2)

First, distribute 1.5 into x and 4, and 4.5 into x and -2, to get rid of the parentheses. Everything that we do to solve this equation is to isolate x to solve for its value.

1.5x+6-3=4.5x-9

Combine like terms on both sides (6-3).

1.5x+3=4.5x-9

Subtract 1.5x from both sides.

3=3x-9

Add 9 to both sides.

12=3x

Divide both sides by 3.

4=x

The answer is 4.

I hope this helps :)

Rashid [163]3 years ago
6 0

Answer:

4

Step-by-step explanation:

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5 0
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}

7 0
3 years ago
Please explain how u got the answer!!!!!
alex41 [277]

Answer:

D. 7 units.

Step-by-step explanation:

The length is not altered by the 2 translations.

It is   √[ (-1-6)^2 + (2-2)^2]

= 7 units.

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