Mathematics: Determine the distance between points (x1, y1) and point (x2, y2), and assign the result to point Distance. The calculation is:

The empirical rule states that approximately 68% of a normal distribution falls within one standard deviation of the mean, or . This means, by symmetry of the distribution, that Now, since the distribution is symmetric about the mean, you have .So,More precisely, this probability is around ....

Determine the distance between points (x1, y1) and

Ответ:

zanaplen27

22.07.2021

Mathematics

Given:

The two points are (x_1,y_1) and (x_2,y_2) .

To find:

The distance between given points.

Solution:

Plot the two points (x_1,y_1) and (x_2,y_2) randomly randomly on a coordinate plane, then form a right angle triangle as shown in the below figure.

Now, the hypotenuse is the distance between the two points.

$\text{Perpendicular}=y_2-y_1$

$\text{Base}=x_2-x_1$

Using Pythagoras theorem,

$\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2$

d^2=(x_2-x_1)^2+(y_2-y_1)^2

Taking square root on both sides, we get

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ [Distance is always positive]

Therefore, the distance between the two points is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . It is also known as distance formula.

Determine the distance between points (x1, y1) and point (x2, y2), and assign the result to point Di

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Ответ:

Ayallaric6875

10.01.2023

Mathematics

$\mathbb P(X\le104)=\mathbb P\left(\dfrac{X-98}6\le\dfrac{104-98}6\right)=\mathbb P(Z\le1)$

The empirical rule states that approximately 68% of a normal distribution falls within one standard deviation of the mean, or $\mathbb P(-1\le Z\le1)\approx0.68$ . This means, by symmetry of the distribution, that $\mathbb P(0\le Z\le1)\approx0.5\times0.68=0.34$

Now, since the distribution is symmetric about the mean, you have $\mathbb P(Z\le0)=0.5$ .

So,

$\mathbb P(Z\le1)=\mathbb P(Z\le0)+\mathbb P(0\le Z\le 1)\approx0.5+0.34=0.84$

More precisely, this probability is around 0.841345

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Determine the distance between points (x1, y1) and point (x2, y2), and assign the result to point Distance. The calculation is:

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