The table shows the results of a survey at a local school. The survey asked 7th and 8th graders if they pack their lunches or if they buy their lunches in the school cafeteria. Here are the results. 47 seventh graders were surveyed and 19 of them pack their lunches.
52 eighth graders were surveyed and 33 of them buy their lunches.
Construct a two-way frequency table for the data.

The table is shown in the attached image

The commas are not to be entered in any of the boxes. Just the numbers only.

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Explanation:

"47 seventh graders were surveyed" means that 47 goes in the last value of the first row. This is the total of the 7th graders. Of this total, 19 pack their lunches (ie bring them from home). That indicates 47-19 = 28 seventh graders buy their lunch.

For row one, we have the values: 19, 28, 47 in that exact order when going from left to right.

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We use the same idea for the 8th graders.

52 total eighth graders, 33 buy their lunch

52-33 = 19 pack their lunch

For row two, the values from left to right are: 19, 33, 52 in that exact order.

To get the values in row 3, we add up everything that's over top of it.

Meaning for column 1, we have 19+19 = 38 total students who pack their lunch. In column 2, there are 28+33 = 61 people who buy their lunch. Lastly, column 3 we have 47+52 = 99 students overall.

For row three, the values from left to right are: 38, 61, 99

Note that adding the first two items of row three gets us 38+61 = 99

It's not a coincidence that this is happening. This is just another way to get the grand total of 99. You could also add up the four values that are not in the total column or total row to get 19+28+19+33 = 99. Again, this is not a coincidence we end up with 99.

Refer to the table below to see a summary.

no, because the sides are not congruent

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.