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3 years ago

Estimate the correlation coefficient for each of the above scatter plots?

Mathematics

1 answer:

nasty-shy [4]3 years ago

4 0

Answer:

Negative Correlation

Step-by-step explanation:

We see that the overall trend is going from up to down. If you were to draw a best line of fit, it would have a negative slope. Therefore, our correlation is negative.

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Find the domain and range of the function. f(x)=24+x^2

masya89 [10]

<h2>Domain and Range of a Function</h2><h3>Answer:</h3>

Domain: $x \in \mathbb{R}$

Range: $y \in \{ \mathbb{R} | y \geqslant 24 \}$

<h3>Step-by-step explanation:</h3>

Domain:

In finding the Domain of a function, the values for the input of the function should not make the output of the function undefined or complex. Because of this, we can think of the values for the input that make the output of the function undefined or complex so that we will not include them in our Domain. We can only make the output undefined if the input makes the denominator $0$ . In $f(x)$ , there's no value for $x$ that makes the denominator $0$ as it is constant, $1$ (Note: All expressions implicitly have $1$ as their denominator even though it's not written). We can only make the output of the function complex if the value of $x$ makes the function take the $n\text{th}$ root of a negative number where $n \in \mathbb{E}$ . There's no radical sign in $f(x)$ so we shouldn't worry about the output of $f(x)$ being complex. Because there's no value for the input, $x$ , that can make the output of $f(x)$ undefined or complex, its Domain can be any number.

Domain: $x \in \{\mathbb{R}\}$

Range:

In finding the Range, it is actually the same logic as finding the Domain but first, we'll have to do a bit of rewriting for the given function.

Let $y = f(x)$ so $y = 24 +x^2$ .

First, we need to make $x$ the subject of the equation.

Making $x$ the subject:

$y = 24 +x^2 \\ y -24 = 24 +x^2 -24 \\ y -24 = x^2 \\ \pm \sqrt{y -24} = \sqrt{x^2} \\ x = \pm \sqrt{y -24}$ .

In the Domain, we'll have to think of the value for the input, $x$ , that makes the output undefined or complex. In the Range, the same logic for the Domain, we'll have to think for the value of $y$ , that makes the $x$ undefined or complex. That's why we made $x$ in the equation the subject. In our rewritten equation, we can see that $y -24$ is under the square root. Which means if $y -24$ is negative, $x$ will be complex. So we have to make $y -24$ be greater than or equal to $0$ ( $y -24 \geqslant 0$ ) so that $x$ won't be complex.

Solving for the inequality, $y -24 \geqslant 0$

$y -24 \geqslant 0 \\ y -24 +24 \geqslant 0 +24 \\ y \geqslant 24$

Range: $y \in \{ \mathbb{R} | y \geqslant 24 \}$

6 0

2 years ago

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current reve

Olin [163]

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

Answer: A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈ $1388.89

7 0

3 years ago

Toni is a plumber she charges 30$ to come to a house and 20 $ for every hour she works write an equation to model the situation

gregori [183]

Answer:

y=20x+30

Step-by-step explanation:

30 is the cost she charges to come to the house, 20 is the amount she charges for every hour she is there

7 0

3 years ago

Read 2 more answers

Ratio of two volume cylinders (Geometry)

Masteriza [31]

The ratio of the lengths is 75 : 25 or 3 : 1

The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2
(In working out the area the radius is squared)

The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3
(In working out the volume the radius is cubed)

Hopefully this explains it

3 0

3 years ago

Read 2 more answers

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4,

Stells [14]

Writing it in perpendicular form is easy as 1, 2, 3.

First you should put it in y = mx + b Form (Slope intercept)

#1: y = x + 7

Simply flip the reciprocals

#2: y = -x + 7

7 0

3 years ago