Acollege professor surveyed his class to see how many hours each student studied. the professor used each student's grade with how many hours they studied to create a scatter plot of the data. he determined that the correlation coefficient was 0.90. select the true statement based on the professor's correlation coefficient. there is a negative correlation between the number of hours studied and the student's grade. there is no correlation between the number of hours studied and the student's grade. there is a strong correlation between the number of hours studied and the student's grade. there is a weak correlation between the number of hours studied and the student's grade.

Step-by-step explanation:

We know by given that the correlation coeffcient was 0.90.

Now, the correlation is weak when is close to 0, and it's strong in the opposite case.

So, basically, this coefficient represents a positive strong correlation.

If you observe each choice, the third one is the only one that expresses a strong correlation, therefore that's the answer.

There is a strong correlation between the number of hours studied and the student's grade.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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