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just olya [345]
3 years ago
12

Prove step by step that 5^20-5^19 is an even number with out using a calculator Please can you tell me the steps and why?

Mathematics
1 answer:
hammer [34]3 years ago
8 0

9514 1404 393

Answer:

  factor out 5^19

Step-by-step explanation:

a) Reason from parity:

  both 5^20 and 5^19 are products with only odd numbers (5) as factors. Hence each is an odd number. The difference of odd numbers is always even.

__

b) Factor:

  5^20 -5^19 = 5^19(5 -1) = 5^19×4

This product has an even factor (4), so is even.

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3 years ago
Let f(x)=2x2−8 .
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Over the course of a month, a person’s weight decreases. What type of relationship is this?
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Sophie [7]

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7 0
3 years ago
What is the value of the correlation coefficient r of the data set?
enyata [817]

The correct option will be:  C) 0.84

<u><em>Explanation</em></u>

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

<em>(Please refer to the attached image for the table )</em>

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

So, the value of the correlation coefficient is 0.84

4 0
3 years ago
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