find the coordinates of the point p that divides the direct line segment from A to B in the given ratio A ( -9,5) B (15,-11)7 to

1 answer:

3 0

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
A(-9,5)\qquad B(15,-11)\qquad
\qquad \stackrel{\textit{ratio from A to B}}{7:1}
\\\\\\
\cfrac{A\underline{p}}{\underline{p} B} = \cfrac{7}{1}\implies \cfrac{A}{B} = \cfrac{7}{1}\implies 1A=7B\implies 1(-9,5)=7(15,-11)\\\\
-------------------------------$

$\bf p=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\
-------------------------------\\\\
p=\left(\cfrac{(1\cdot -9)+(7\cdot 15)}{7+1}\quad ,\quad \cfrac{(1\cdot 5)+(7\cdot -11)}{7+1}\right)
\\\\\\
p=\left(\cfrac{-9+105}{8}~~,~~\cfrac{5-77}{8} \right)\implies p=\left( \cfrac{96}{8}~~,~~\cfrac{-72}{8} \right)
\\\\\\
p=(12~,~-9)$

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The weekly salaries of a sample of employees at the local bank are given in the table below. Employee Weekly Salary Anja $245 Ra

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The variance for the data is 17,507. 5.

Given

The weekly salaries of a sample of employees at the local bank are given in the table below.

Employee Weekly Salary Anja $245 Raz $300 Natalie $325 Mic $465 Paul $100.

<h3>Variance</h3>

Variance is the expected value of the squared variation of a random variable from its mean value, in probability and statistics.

The mean value of the salaries of employees is;

$\rm Mean= \dfrac{245+300+325+465+100}{5}\\\\Mean=287$

The variance is given by;

$\rm Variance=\sqrt{\dfrac{(245-287)^2 +(300-287)^2 +(325-287)^2 +(465-287)^2 +(100-287)^2}{5-2}} \\\\Variance = 132.316}\\\\On \ Squaring \ both \ the \ sides\\\\Variance^2=17,507. 5$