Use the substitution method to slove the system of equations 2x-y=6 2x-2y=4

What is the correlation coefficient between the variables? Round to three decimal places. Enter your answer in the box. r≈ Age S

Free_Kalibri [48]

There are two data sets x and y.

X includes = 14 25 19 35 20 12 5

Y includes = 360 293 315 212 315 331 404

to solve for the correlation coefficient, we need to get the following values step by step

Step 1: Find the mean of each set.

The mean of X = 18.571

The mean of Y = 318.571

Step 2: Subtract the mean of X from every value X value (denote this with letter a). Do the same for y (denote this with letter b).

The mean of X subtracted from every X value (a):

14 - 18.571 = -4.571

25 - 18.571 = 6.429

19 - 18.571 = 0.429

35 - 18.571 = 16.429

20 - 18.571 = 1.429

12 - 18.571 = -6.571

5 - 18.571 = -13.571

The mean of Y subtracted from every value of Y (b):

360 - 318.571 = 41.429

293 - 318.571 = -25.571

315 - 318.571 = -3.571

212 = 318.571 = -106.571

315 - 318.571 = -3.571

331 - 318.571 = 12.429

404 - 318.571 = 85.429

Step 3: Calculate: a * b, a^2 and b^2 of every value.

For a*b

-189.388

-164.388

-1.531

-1750.816

-5.102

-81.673

-1159.388

Sum: -3352.286

For a²

20.898

41.327

0.184

269.898

2.041

43.184

184.184

Sum: 561.714

For b²

1716.327

653.898

12.755

11357.469

12.755

154.469

7298.041

Sum: 21205.714

Step 4: Solve using this formula

r = ∑a * b / √((a²)(b²))

r = -3352.286 / √((561.714)(21205.714))

= -0.9713

The correlation coefficient is -0.971

8 0

3 years ago

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Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.

blondinia [14]

I hope this helps you

6 0

4 years ago

You work two jobs. You earn $14.64 per hour as a salesperson and $12.20 per hour stocking shelves. Your combined earnings this m

Igoryamba

I'm assuming you have to graph a line that shows the combination of earnings.

Our equation is 14.64y + 12.20x = 219.60

We'll be solving for x and y. We'll need to substitute the variables, one at a time, to 0, in order to find their intercepts.

Let's do x first.

14.64(0) + 12.20x = 219.60

12.20x = 219.60

Divide by 12.20 on both sides.

x = 18

Now let's solve for y.

14.46y + 12.20(0) = 219.60

14.46y = 219.60

Divide both sides by 14.46.

y = 15.18

That is actually a long decmal, but since we're dealing with money, we round it down to the nearest cent.

So, now we know x = 18 and y = 15.18.

Graph those on the x coordinate plane and the y coordinate plane, and make a line connecting the two. That line represents all the solutions.

7 0

3 years ago

Use the graph of f at the right to complete each of the parts (a) through (h)

Maru [420]

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

6 0

4 years ago

Read 2 more answers

The temperature outside on a cold January evening is Syracuse was 7 degrees below zero. As the night went on, the temperature in

maks197457 [2]

Answer:4

Step-by-step explanation:

3 0

4 years ago

Use the substitution method to slove the system of equations 2x-y=6 2x-2y=4​

Use the substitution method to slove the system of equations 2x-y=6 2x-2y=4