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3 years ago

Prove that for any natural n the value of the expression (n+7)^2–n^2 is divisible by 7.

Mathematics

1 answer:

Afina-wow [57]3 years ago

3 0

Step-by-step explanation:

(n + 7)² – n²

n² + 14n + 49 – n²

14n + 49

7 (2n + 7)

7 is a factor, so for any natural n, (n + 7)² – n² is a multiple of 7.

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Use a table to identify three equivalent ratios of 2/5.

zlopas [31]

Answer: The simplest form of ratio 6:15=2×3:5×3=2:5

Step-by-step explanation: So, 2:5 is equivalent to 6:15.

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1 year ago

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A new washing machine uses 45% less water than an older

enot [183]

Answer:The family will use 792 gallons of water in the new washing machine

Step-by-step explanation:

1440 X 0.55=792

100-45=55

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2 years ago

Here are two rectangular prisms:

Leno4ka [110]

Answer:

hey there buddy

Step-by-step explanation:

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3 years ago

WILL GIVE BRAINLIEST IF CORRECT!!

vfiekz [6]

Answer:

$\displaystyle y=-0.927x+13.63$

Step-by-step explanation:

<u>Simple Linear Regression </u>

It a function that represents the relationship between two or more variables in a given data set. It uses the method of the least-squares regression line which minimizes the error between the estimate function and the real data.

Let's compute the best-fit line for the data

$x=\{1,5,6,12,15\}$

$y=\{14,11,4,2,1\}$

First, we find the sums

$\displaystyle \sum x=1+5+6+12+15=39$

$\displaystyle \sum y=14+11+4+2+1=32$

Then, we compute the averages values

$\displaystyle \bar{x}=\frac{39}{5}=7.8$

$\displaystyle \bar{y}=\frac{32}{5}=6.4$

We will also compute the sums of the cross-products and the sum of the squares

$\displaystyle \sum xy=(1)(14)+(5)(11)+(6)(4)+(12)(2)+(15)(1)=137$

$\displaystyle \sum x^2=1^2+5^2+6^2+12^2+15^2=1+25+36+144+225$

$\displaystyle \sum x^2=431$

We will compute Sxy and Sxx

$\displaystyle S_{xy}=\sum xy-\frac{\sum x\ \sum y}{n}$

$\displaystyle S_{xy}=137-\frac{(39)(32)}{5}$

$\displaystyle S_{xy}=-117.6$

$\displaystyle S_{xx}=\sum x^2-\frac{(\sum x)^2}{n}$

$\displaystyle S_{xx}=431-\frac{39}{5}^2=126.8$

The slope of the linear regression function is given by

$\displaystyle m=\frac{S_{xy}}{S_{xx}}=\frac{-117.6}{126.8}=-0.927$

The y-intercept ot the linear function is

$\displaystyle b=\bar{y}-b\bar{x}=6.4-(-0.927)(7.8)$

$\displaystyle b=13.63$

Thus the best-fit line is

$\displaystyle y=-0.927x+13.63$

The correct option is the last one

5 0

2 years ago

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x

kumpel [21]

Answer:

12m

Step-by-step explanation

If the height of the ball after x seconds be modelled by the equation

h(x)=−(x−2)² +16

The height of the ball at the time it is thrown will be the height at the initial time. At that point that it is initially thrown the time is 0seconds i.e x = 0

To get the height at t x = 0seconds, we will substitute x = 0 into the modeled function to have;

h(0) = -(-0-2)²+16.

h(0) = -(-2)²+16

h(0) = -4+16

h(0) = 12

The height of the ball at the time the ball is thrown is 12m

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3 years ago

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