Can anyone please help me? I dont understand this!

Mathematics

2 answers:

mel-nik [20]2 years ago

4 0

$\bf \stackrel{\textit{force of gravity}}{F}~~,~~\stackrel{\textit{gravitational constant}}{G}~~,~~\stackrel{\textit{first mass}}{m_1}~~,~~\stackrel{\textit{second mass}}{m_2}
\\\\\\
\stackrel{\textit{distance of masses centers}}{d}\implies \stackrel{\textit{squared that}}{d^2}\\\\
-------------------------------\\\\
\stackrel{\textit{F equals product of }G\cdot m_1\cdot m_2\textit{ divided by square of }d}{F=\cfrac{G\cdot m_1\cdot m_2}{d^2}}$

xeze [42]2 years ago

3 0

"The force of gravity, F..."
So we start with just
F

"... is equal to..."
F=

"... the product of..." means we're going to multiply some things. What will we be multiplying together? Answer: "the gravitational constant (G), the mass of the first object (m1), and the mass of the second object (m2)..."
F = G × m1 × m2 ...

"... divided by..."
F = (G × m1 × m2) ÷ (...)

"... the square of..."
F=(G × m1 × m2) ÷ (...)^2

"...the distance between their centers (d)."
F=(G × m1 × m2) ÷ (d^2)

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What is the value of the correlation coefficient r of the data set?

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The correct option will be: C) 0.84

Explanation

Formula for Correlation coefficient :

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}$

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

(Please refer to the attached image for the table )

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}\\ \\ r=\frac{7(1480)-(44)(183)}{\sqrt{[7(362)-(44)^2][7(6575)-(183)^2]}}\\ \\ r=\frac{10360-8052}{\sqrt{(598)(12536)}}\\ \\ r=\frac{2308}{\sqrt{7496528}}\\ \\ r=0.84$