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2 years ago

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1. What is a residual?

1 answer:

sladkih [1.3K]2 years ago

5 0

Answer:

1. what is a residual?

A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.

2. The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.

Step-by-step explanation:

1. What is a residual?

A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.

2. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?

The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.

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Evaluate the function for the given values to determine if the value is a root. p(−2) = p(2) = The value is a root of p(x).

bija089 [108]

<em>Note: Since you missed to mention the the expression of the function </em> $p(x)$ <em> . After a little research, I was able to find the complete question. So, I am assuming the expression as </em> $p(x)=x^4-9x^2-4x+12$ <em> and will solve the question based on this assumption expression of </em> $p(x)$ <em>, which anyways would solve your query.</em>

Answer:

As

$p\left(-2\right)=0$

Therefore, $x=-2$ is a root of the polynomial <em> </em> $p(x)=x^4-9x^2-4x+12$

As

$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial <em> </em> $p(x)=x^4-9x^2-4x+12$

Step-by-step explanation:

As we know that for any polynomial let say<em> </em> $p(x)$ <em>, </em> $c$ is the root of the polynomial if $p(c)=0$ .

In order to find which of the given values will be a root of the polynomial, $p(x)=x^4-9x^2-4x+12$ <em>, </em>we must have to evaluate <em> </em> $p(x)$ <em> </em>for each of these values to determine if the output of the function gets zero.

So,

Solving for $p\left(-2\right)$

<em> </em> $p(x)=x^4-9x^2-4x+12$

$p\left(-2\right)=\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Simplify\:}\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12:\quad 0$

$\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Apply\:rule}\:-\left(-a\right)=a$

$=\left(-2\right)^4-9\left(-2\right)^2+4\cdot \:2+12$

$\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}$

$=2^4-2^2\cdot \:9+8+12$

$=2^4+20-2^2\cdot \:9$

$=16+20-36$

$=0$

Thus,

$p\left(-2\right)=0$

Therefore, $x=-2$ is a root of the polynomial <em> </em> $p(x)=x^4-9x^2-4x+12$ <em>.</em>

Now, solving for $p\left(2\right)$

<em> </em> $p(x)=x^4-9x^2-4x+12$

$p\left(2\right)=\left(2\right)^4-9\left(2\right)^2-4\left(2\right)+12$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$p\left(2\right)=2^4-9\cdot \:2^2-4\cdot \:2+12$

$p\left(2\right)=2^4-2^2\cdot \:9-8+12$

$p\left(2\right)=2^4+4-2^2\cdot \:9$

$p\left(2\right)=16+4-36$

$p\left(2\right)=-16$

Thus,

$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial <em> </em> $p(x)=x^4-9x^2-4x+12$ <em>.</em>

Keywords: polynomial, root

Learn more about polynomial and root from brainly.com/question/8777476

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7 0

2 years ago

Read 2 more answers

Need help with number 2

salantis [7]

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7 0

3 years ago

Jason is painting a large circle on one wall of his new apartment. The largest distance across the circle will be 8 feet. Approx

Hunter-Best [27]

Answer:

a) 50.24 ft²

b) 150.72 ft²

Step-by-step explanation:

Jason is painting a large circle on one wall of his new apartment. The largest distance across the circle will be 8 feet.

The distance across a circle is also called a diameter, Hence,

D = Diameter = 8 ft

The Area of a circle = πr²

r = Diameter/2 = 8ft/2 = 4ft

π = 3.14

Hence,

The Area of the circle = π × (4 ft)²

= 50.24 ft²

a) Approximately the amount of wall the circle will cover is 50.24 ft².

b) How much area will he cover if he painted a circle on three walls?

This is calculated as:

1 wall = 50.24 ft²

3 walls = x

Cross Multiply

x = 3 × 50.24 ft²

x = 150.72 ft²

7 0

2 years ago

Dexter collected data from his classmates on whether they prefer hamburgers or hotdogs.

algol13

C) More girls than boys prefer hamburgers over hotdogs.

6 0

2 years ago

Read 2 more answers

What is the range of a function f(x)=-x+15 when the domain is {-3,-1,11}?

hodyreva [135]

Answer:

The range is the output value or the y value.

You would work backwards to find the domain.

f(x) = 4x - 1 f(x) = 4x - 1

3 = 4x - 1 7 = 4x - 1

add 1 to both sides add 1 to both sides

4 = 4x 8 = 4x

divide both sides by 4 divide both sides by 4

x = 1 x = 2

f(x) = 4x - 1 f(x) = 4x - 1

11 = 4x - 1 15 = 4x - 1

add 1 to both sides add 1 to both sides

12 = 4x 16 = 4x

divide both sides by 4 divide both sides by 4

x = 3 x = 4

Domain { 1, 2, 3, 4}

Step-by-step explanation:

4 0

2 years ago