$Center\ of\ the\ circle\ is\ the\ midpoint\ AB\ where\ A(-2;\ 4)\ \&\ B(4;\ 2)\\\\center:O\left(\frac{-2+4}{2};\ \frac{4+2}{2}\right)\to O(1;\ 3)\\\\Radius\ of\ the\ circle\ is\ distance\ O\ to\ A:\\\\r=|OA|=\sqrt{(-2-1)^2+(4-3)^2}=\sqrt{9+1}=\sqrt{10}\\\\Equation\ of\ a\ circle:\\\\(x-a)^2+(y-b)^2=r^2\ whete\ center\ is\ (a;\ b)\ and\ radius\ is\ r.\\\\Equation\ of\ this\ circle:\\\\(x-1)^2+(y-3)^2=(\sqrt{10})^2\\\\(x-1)^2+(y-3)^2=10$

3 0

4 years ago

find the ratio which are the points p(X,2) divides the line segment joining the point a(12,5) and b(4,-3) also find X plz give a

chubhunter [2.5K]

Answer: ratio a:b = 3:5 p(X, 2) = p(9, 2)

Step-by-step explanation:

Plot points a = (12, 5) and b = (4, -3) and draw a line segment from a to b.

Notice that when y = 2, X = 9 so point p = (9, 2) see graph

The distance from a to p = 3√2

The distance from b to p = 5√2

So the ratio of a:b = 3√2:5√2 = 3:5 when simplified

To find the distance, use the distance formula OR pythagorean theorem.

7 0

3 years ago

Relationships between means, standard deviations, X values,and z-scores

Vlada [557]

Answer:

a) The average salary of firefighters in Portugal is $583.

b) The standard deviation of the salary of firefighters in Portugal is $319.8

Step-by-step explanation:

We are given the following in the question:

a) Standard Deviation, σ = $145.80

We are given that the distribution of salary of professor is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

A salary of $510.10 has a z-score of -0.50.

Putting values, we get,

$-0.50 = \displaystyle\frac{510.10-\mu}{145.80}\\\\\mu = 0.50(145.80) + 510.10\\\Rightarrow \mu = 583$

Thus, the average salary of firefighters in Portugal is $583.

b) Mean, μ = $2,132

We are given that the distribution of salary of computer programmers is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

The salary of $2,291.90 has a z-score of +0.50

Putting values, we get,

$0.50 = \displaystyle\frac{2291.90-2132}{\sigma}\\\\\sigma= \frac{2291.90-2132}{0.50}\\\\\sigma = 319.8$

Thus, the standard deviation of the salary of firefighters in Portugal is $319.8

6 0

4 years ago