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4 years ago

Sheldon says that the expression 8(4x - 2)=32x-16

Mathematics

1 answer:

Arte-miy333 [17]4 years ago

8 0

Answer:

That is correct

Step-by-step explanation:

distribute the 8

8*4x = 32x

8*2 = 16

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What’s the value of x? y= 5x + 9 y= -x + 3

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Answer:

x=-1 y=4 (-1,4)

Step-by-step explanation:

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3 years ago

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The equation y=1/3xis the boundary line for the inequality y>1/3x. Which sentence describes the graph of the inequality

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If the equation y=1/3x is the boundary line for the inequality y>1/3 x, then the solution set is illustrated by shading the area ABOVE the line y=(1/3)x.

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3 years ago

Find each missing angle Please

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Answer:

m<1=61

m<2=40

m<3=60

m<4=80

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Step-by-step explanation:

180/3=60

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3 years ago

What is the equation for the line described in #9And #10?

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2 years ago

Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard devia

Anna35 [415]

With 10 integers available, $X$ has PMF

$\mathbb P(X=x)=\begin{cases}\dfrac1{10}&\text{for }0\le x\le9,x\in\mathbb Z\\\\0&\text{otherwise}\end{cases}$

We're interested in the statistics of the new random variable $Y=5X$ . To do this, we need to know the PMF for $Y$ . This isn't too hard to find.

$\mathbb P(Y=y)=\mathbb P(5X=y)=\mathbb P\left(X=\dfrac y5\right)$

Since the PMF for $X$ gives a value of $\dfrac1{10}$ whenever $x$ is an integer between 0 and 9, it follows that $\dfrac y5$ must also be an integer for the PMF to give the identical value of $\dfrac1{10}$ . This means

$\mathbb P(Y=y)=\begin{cases}\dfrac1{10}&\text{for }y\in\{0,5,\ldots,45\}\\\\0&\text{otherwise}\end{cases}$

Now the mean (expectation) is

$\mathbb E(Y)=\displaystyle\sum_yy\mathbb P(Y=y)=\frac1{10}\sum_{y\in\{0,\ldots,45\}}y$
$\mathbb E(Y)=\dfrac{225}{10}=22.5$

The variance would be

$\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb V(X)=\displaystyle\sum_yy^2\mathbb P(Y=y)-\mathbb E(Y)^2$
$\mathbb V(X)=\displaystyle\frac1{10}\sum_{y\in\{0,\ldots,45\}}y^2-\left(\frac{225}{10}\right)^2$
$\mathbb V(X)=\dfrac{7125}{10}-\dfrac{50625}{100}=206.25$

The standard deviation is the square root of the variance, so you have

$\sqrt{\mathbb V(X)}=\sqrt{206.25}\approx14.3614$

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3 years ago