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3 years ago

Explain how multiplying fractions is similar to mulitiplying whole numbers and how it is different

Mathematics

2 answers:

tigry1 [53]3 years ago

3 0

You could find the difference on the internet if not found tell me and I would explain for you

Allisa [31]3 years ago

3 0

Multiplying fractions and whole are the same cause it’s both multiplying

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Vlad1618 [11]

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4 years ago

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What is the solutions for y=3x-5 and y=x-3

MArishka [77]

Answer: x=1, y=-2

Step-by-step explanation:

System

y=3x-5

y=x-3

3x-5=x-3

3x-x=-3+5

2x=2

x=2:2=1

y=x-3=1-3=-2

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klemol [59]

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3 years ago

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kkurt [141]

Answer:

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Step-by-step explanation:

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3 years ago

G with the definition of covariance, prove cov[(ay − b),(cy − d)] = accov(x, y ), where x, y are random variables and a, b, c, d

____ [38]

By definition of covariance,

$\mathrm{Cov}(X,Y)=\mathbb E[(X-\mathbb E[X])(Y-\mathbb E[Y])]$

$\mathrm{Cov}(X,Y)=\mathbb E[XY-\mathbb E[X]Y-X\mathbb E[Y]+\mathbb E[X]\mathbb E[Y]]=\mathbb E[XY]-\mathbb E[X]\mathbb E[Y]$

We have

$\mathbb E[(aX-b)(cY-d)]=\mathbb E[acXY-adX-bcY+bd]$

$=ac\mathbb E[XY]-ad\mathbb E[X]-bc\mathbb E[Y]+bd$

$\mathbb E[aX-b]=a\mathbb E[X]-b$

$\mathbb E[cY-d]=c\mathbb E[Y]-d$

$\mathbb E[aX-b]\mathbb E[cY-d]=ac\mathbb E[X]\mathbb E[Y]-ad\mathbb E[X]-bc\mathbb E[Y]+bd$

Putting everything together, we find the covariance reduces to

$\mathrm{Cov}(aX-b,cY-d)=ac(\mathbb E[XY]-\mathbb E[X]\mathbb E[Y])=ac\mathrm{Cov}(X,Y)$

as desired.

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3 years ago