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2 years ago

What is the equation of the line that passes through (5, -2) and (-3, 4)?

2 answers:

7 0

First figure out the slope, the equation is Y2-Y1/ X2-X1.. m=-3/4 So far your equation is y=-3/4x + b. b is the y intercept. Plug in either points in the equation to have so far.. you will receive 7/4. The equation is y=-3/4 + 7/4

MatroZZZ [7]2 years ago

4 0

Answer: $4y=-3x-7$

Step-by-step explanation:

The equation of a line passing through (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

The equation of a line passing through (5, -2) and (-3, 4) is given by :-

$(y-(-2))=\dfrac{4-(-2)}{-3-5}(x-5)\\\\\Rightarrow\ y+2=\dfrac{6}{-8}(x-5)\\\\\Rightarrow\ y+2=\dfrac{-3}{4}(x-5)\\\\\Rightarrow\ 4(y+2)=-3(x-5)\\\\\Rightarrow\ 4y+8=-3x+15\\\\\Rightarrow\ 4y=-3x-7$

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Step-by-step explanation:

Data

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2 years ago

Suppose a certain type of fertilizer has an expected yield per acre of mu 1 with variance sigma 2, whereas the expected yield fo

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Answer:

See the proof below.

Step-by-step explanation:

For this case we just need to apply properties of expected value. We know that the estimator is given by:

$S^2_p= \frac{(n_1 -1) S^2_1 +(n_2 -1) S^2_2}{n_1 +n_2 -2}$

And we want to proof that $E(S^2_p)= \sigma^2$

So we can begin with this:

$E(S^2_p)= E(\frac{(n_1 -1) S^2_1 +(n_2 -1) S^2_2}{n_1 +n_2 -2})$

And we can distribute the expected value into the temrs like this:

$E(S^2_p)= \frac{(n_1 -1) E(S^2_1) +(n_2 -1) E(S^2_2)}{n_1 +n_2 -2}$

And we know that the expected value for the estimator of the variance s is $\sigma$ , or in other way $E(s) = \sigma$ so if we apply this property here we have:

$E(S^2_p)= \frac{(n_1 -1 )\sigma^2_1 +(n_2 -1) \sigma^2_2}{n_1 +n_2 -2}$

And we know that $\sigma^2_1 = \sigma^2_2 = \sigma^2$ so using this we can take common factor like this:

$E(S^2_p)= \frac{(n_1 -1) +(n_2 -1)}{n_1 +n_2 -2} \sigma^2 =\sigma^2$

And then we see that the pooled variance is an unbiased estimator for the population variance when we have two population with the same variance.

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2 years ago