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3 years ago

1. y=3x² table of values

Mathematics

1 answer:

Leviafan [203]3 years ago

4 0

Answer:

0 - 0

1 - 3

2 - 12

3 - 27

4 - 48

5 - 75

6 - 108

7 - 147

8 - 192

9 - 243

10 - 300

Step-by-step explanation:

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chegg Y=4X−2 XX has a PDF of f_X(x)=\begin{cases} 3e^{-3x} & 0 \leq x \\ 0 & \text{otherwise}\end{cases}f X (x)={ 3e −

Licemer1 [7]

$\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]$

so by definition of expectation,

$\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx$

Integrate by parts (twice).

$\displaystyle \int_a^b u\,dv = uv\bigg|_a^b - \int_a^b v\,du$

First, let

$u = (4x-2)^2 \implies du = 8(4x-2)\,dx \\\\ dv = 3e^{-3x} \, dx \implies v = -e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx$

Next,

$u = 4x-2 \implies du = 4\,dx \\\\ dv = e^{-3x} \, dx \implies v = -\dfrac13 e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}$

7 0

2 years ago

A company that makes hair-care products had 8,000 people try a new shampoo. Of the 8,000 people, 64 had a mild allergic reacti

disa [49]

Answer:

Every one out of 125 people got a mild allergic reaction or 0.8%

Step-by-step explanation:

64/8000 simplified by 8 is 8/1000 simplified by 4 is 2/250 simplified by 2 is 1/125

7 0

4 years ago

-3a - 3 = -2 + 3p ˢᴼᴸᵛᴱ ᶠᴼᴿ ᴬ

skad [1K]

Hi!

$-3a - 3 = -2 + 3p$

$-3a=3p+1$

$\frac{-3a}{3}=\frac{3p+1}{-3}$

$Answer------>a=-p+\frac{-1}{3}$

Explanation: <u><em>First you had to add by 3 from both sides. It gave us -3a=3p+1. Then divide into -3 from both sides. It gave us -3a/-3=3p+1/-3, or a=-p+-1/3 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie</em></u>

8 0

3 years ago

Make v the subject of the formula T = v/6 -5

OverLord2011 [107]

Answer:

Step-by-step explanation:

T=V/6-5

T+5=V/6

6(T+5)=V

V=6T+30

8 0

3 years ago

The new number, 550, is 200 more than the original number. What is the approximate percent change?

Volgvan

Answer:150

Step-by-step explanation: you see what makes 550 200 plus what 350 then it equal 550 then you see 200 plus what equals 350 150 so that is a 150%

3 0

3 years ago

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1. y=3x² table of values ​

1. y=3x² table of values