Give one real life example of each correlation: positive, negative, and no correlation.

For each of these examples, I have attached an image provide showing work to fully understand the problem.

Positive correlation

The number of kids at the playground and the number of swings being used

As the number of kids at the playground increases, the number of swings being used will increase. When both variables increase, they have a positive correlation. Thus, the situation in this problem has a positive correlation.

If we sketch a scatter plot for this situation, notice that the number of kids at the playground would be on the x-axis and the number of swings being used would be on the y-axis.

We can predict that if the number of kids at the playground increases, then the number of swings being used would also increase. Since this is only a sketch, it's not important exactly where our points are. Instead, we simply want to draw the points so our scatter plot has a line of best fit line with an upward of positive slope.

The image for this correlation is the first attachment.

Negative correlation

The amount of time Diaco spends goofing off in class and the grade Dicaco earns in the class

Notice that if the amount of time that Diaco spends goofing off increases, his grade is likely to decrease. When one variable increases and the other decreases, they have a negative correlation. Thus, the situation in this problem has a negative correlation.

If we sketch a scatter plot for this situation, notice that the time goofing off would be on the x-axis and Diaco's grade would be on the y-axis.

We can predict that if Diaco spends little or no time goofing off, his grade will be high and if he spends a lot of time goofing off, his grade will be low. Since this is only a sketch, it's not important exactly where our points are. Instead, we want to simply draw the points so our scatter plot has a line of best fit with a downward or negative slope.

The image for this correlation is the second attachment.

No correlation

The number of pets a family has and the number of kids in the family

Notice that in most cases, the number of pets a family has is not related to the number of kids in the family. Thus, there is no correlation between the number of pets a family has and the number of kids in the family.

If we sketch a scatter plot for this situation, notice that the number of pets a family has would be on the x-axis and the number of kids in the family would be on the y-axis.

Since there is no correlation between the variables, the data points will be spread out and there will be no best fit line.

The image for "no correlation" is the third attachment.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative