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2 years ago

Determine the explicit formula of the following sequence -3,-18,-108...

Mathematics

1 answer:

kvv77 [185]2 years ago

3 0

Answer:

$a_{n}$ = - 3 $(6)^{n-1}$

Step-by-step explanation:

Note the common ratio r between consecutive terms, that is

r = - 18 ÷ - 3 = - 108 ÷ - 18 = 6

This indicates the sequence is geometric with n th term ( explicit formula )

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = - 3 and r = 6, thus

$a_{n}$ = - 3 $(6)^{n-1}$

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HELP ASAP Calculate the residuals for your scatterplot in step 2d.

postnew [5]

The residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7

<h3>How to determine the residuals?</h3>

The regression equation is given as:

y = 0.141x + 0.842

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.141 * 13.8 + 0.842 = 2.78

y = 0.141 * 18 + 0.842 = 3.38

y = 0.141 * 16.7 + 0.842 = 3.20

y = 0.141 * 18 + 0.842 = 3.38

y = 0.141 * 0.7 + 0.842 = 0.94

y = 0.141 * 21.9 + 0.842 = 3.93

y = 0.141 * 15.5 + 0.842 = 3.03

y = 0.141 * 9.2 + 0.842 = 2.14

y = 0.141 * 19.5 + 0.842 = 3.59

y = 0.141 * 16.7 + 0.842 = 3.20

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

Residual = 1.42 - 2.78 = -1.36

Residual = 3.7 - 3.38 = 0.32

Residual = 3.21 - 3.20 = 0.01

Residual = 4 - 3.38 = 0.62

Residual = 1.11 - 0.94 = 0.17

Residual = 3.69 - 3.93 = -0.24

Residual = 3.92 - 3.03 = 0.89

Residual = 2.23 - 2.14 = 0.09

Residual = 3.77 - 3.59 = 0.18

Residual = 2.5 - 3.20 = -0.7

Hence, the residuals of the linear regression equation are -1.36, 0.32, 0.01, 0.62, 0.17, -0.24, 0.89, 0.09, 0.18 and -0.7

Read more about residuals at:

brainly.com/question/16180255

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1 year ago

Can you please help me with this question please help and i will give you a Brainiest

patriot [66]

Answer:

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Step-by-step explanation:

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2 years ago

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36 is _______% less than 60?

Arte-miy333 [17]

60*(1-x)=36
60-60x=36
-60x=36-60
-60x=-24
x=24/60
x=4/10
x=2/5
x=0.4

36 is 40% less than 60

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3 years ago

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Please help asap!!! i dont understand it

pshichka [43]

Answer:

Step-by-step explanation:

A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.

Calculate slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)

m = $\frac{13-1}{9-(-7)}$ = $\frac{12}{9+7}$ = $\frac{12}{16}$ = $\frac{3}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{4} }$ = - $\frac{4}{3}$ ← slope of perpendicular bisector

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ )

using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then

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The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{4}{3}$ , then

y = - $\frac{4}{3}$ x + c ← is the partial equation

To find c substitute the midpoint (1, 7) into the partial equation

7 = - $\frac{4}{3}$ + c ⇒ c = $\frac{21}{3}$ + $\frac{4}{3}$ = $\frac{25}{3}$

y = - $\frac{4}{3}$ x + $\frac{25}{3}$ ← equation of perpendicular bisector

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Answer:

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Step-by-step explanation:

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