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3 years ago

Describe the steps in solving the linear equation 3(3x − 8) = 4x + 6.

Mathematics

2 answers:

Fittoniya [83]3 years ago

5 0

Answer:

x=6

Step-by-step explanation:

3(3x-8)=4x+6

First you would distribute the 3 on the L side to the parenthasies

9x-24=4x+6

Then, you would subtract 4x from both sides because it is the smallest X value

5x-24=6

Add 24 to both sides (inverse operations)

5x=30

divide both sides by 5

x=6

aniked [119]3 years ago

3 0

the answer is x=6

3(3x − 8) = 4x + 6.

9x-24 =4x+6

9x-4x=6+24

5x=30

5 5

x=6

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a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have

$\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}$

so both conditions are met and f(y) is indeed a PDF.

b) The probability P(Y > 4) is given by the integral,

$\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}$

c) The mean is given by the integral,

$\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy$

Integrate by parts, with

$u = y \implies du = dy$

$dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}$

Then

$\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)$