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3 years ago

Which graph represents the solution to the system of inequalities?

Mathematics

2 answers:

sattari [20]3 years ago

6 0

Here is an image of that

diamong [38]3 years ago

3 0

Solution:

we are given with the system of equation:

x + y ≥ 4

2x + 3y < 12

we have been asked to find the graph representing the solution of the given system of equation.

To find the the solution of the given system of inequalities, we can draw the graph using a graphing calculator and thereafter , the point of intersection will give the solution of the given system of equation.

As we can see, the graph is intersecting at only one point at (0,4).

The given system of inequalities will have infinite number of solutions and it will fall in the region shaded with green.

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What is the value of the correlation coefficient r of the data set?

enyata [817]

The correct option will be: C) 0.84

Explanation

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

(Please refer to the attached image for the table )

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

Read 2 more answers

(2x +1) -7 (-6x+9) what is the answer if using the Distributive Property?

Margarita [4]

Answer:

Step-by-step explanation:

Distributive property: a(b +c) = a*b + a*c

(2x + 1) - 7(-6x + 9) = (2x + 1) + (-7)*(-6x) + (-7)*9

= 2x + 1 + 42x - 63 {Combine like terms}

= 2x + 42x + 1 - 63

= 44x - 62

5 0

3 years ago

Can someone help me there is a picture of problem

german

Answer:

8 interior angles

Step-by-step explanation:

There is a simple trick to finding the number of interior angles
For instance, a triangle has 3 sides, and how many angles are in a triangle? 3
A square has 4 sides and 4 interior angles
A pentagon has 5 sides and 5 interior angles
So an octagon, the shape we have here, has 8 sides so 8 interior angles

8 0

3 years ago

A class is selling magazines as a fundraiser. Of the 200 magazines sold, Ananda sold 1/8 of them. Gina sold 0.065 of the magazin

Zina [86]

To figure out which sold the most magazines, multiply each number by 200 to find the answer. Let's start with 1/8. 200 * 1/8 = 25. Then 0.065 * 200 = 13.

3/100 * 200 = 6

200 * 0.105 = 21.

Fatima sold the most magazines.

5 0

3 years ago

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. first, find

Alja [10]

Given

Endpoints of the diameter (5,2) and (-7,4)

Step One

Find the center

Center = (x2 + x1)/2 , (y2 + y1)/2

x2 = -7; x1 = 5; y2 = 4; y1 = 2

Center = (-7 + 5)/2 ; (4 + 2)/2;

Center = (-1 , 3)

Step Two

Find the radius squared using the distance formula. Use (5,2) as the second point. The other point is the center.

Distance squared = (5 - - 1)^2 + (2 - 3)^2

Distance squared = ( 6)^2 + (-1 )^2

Distance squared = 37

Step Three

State the circle's formula

(x - - 1 )^2 + (y - 3)^2 = 37

(x + 1)^2 + (y - 3)^2 = 37

4 0

3 years ago