In a class of 550 students, students may take all, none, or a combination of courses as follows.?
Draw a Venn diagram to find how many students are not in any of these courses.
Mathematics-280
Science-200
Technology-230
Mathematics and Technology-110
Science and Technology-100
Mathematics and Science-80
Mathematics, Science, and Technology- 20
I don't what numbers will go in each section of the Venn diagram and how you get the numbers..
start by drawing 3 intersecting circles, with an overlap of all 3 circles, label them M, S, and T for the 3 subjects.
Now fill in the values from the inside out.
20 take M, T, and S, so put that in the overlap of all 3
It says 110 take M and T, but we have already placed 20 of those 110, that leaves 90 to go into the region covered by M and S but NOT by T.
Repeat this process for the other two "doubles"
You should have 90 for M and T but not S,
and 80 for S and T but not M.
Now look at M only, it said that 280 take M, but we already have 170 in the M circle. That leaves 110 in the M circle which does not overlap anything else. Fill in the rest of the S and T circles the same way.
Now adding all those entries up should give you 440.
But there 550 students in the class, which means 110 would not be in any of the circles, thus not taking any of those 3 subjects.
thank you!
But in this part, "It says 110 take M and T, but we have already placed 20 of those 110, that leaves 90 to go into the region covered by M and S but NOT by T." why can't you put it in M and T, when that was what 110 is for?
The answer is not 440 it is 430 if you add all those numbers together 110+90+20+60 by M this will give you 280. 30+90+20+90 by T will add upto 230 90+30+60+20= 200 and 30,90,60,20,30,90,110 Add upto 430 so what do you think did I made a mistake or did he/she?
To determine the numbers that go in each section of the Venn diagram, you need to follow a step-by-step process using the given information.
Step 1: Start by labeling the three intersecting circles in the Venn diagram as Mathematics, Science, and Technology.
Step 2: Begin with the information given about Mathematics. In this case, 280 students take Mathematics. So, write the number 280 inside the Mathematics circle.
Step 3: Move on to the information about Science. It states that 200 students take Science. Therefore, write 200 inside the Science circle.
Step 4: Next, focus on the Technology information. The number given is 230 students taking Technology. Place 230 inside the Technology circle.
Step 5: Now let's fill in the overlapping sections of the Venn diagram. Begin with the information about Mathematics and Technology. It states that 110 students take both Mathematics and Technology. Therefore, write 110 in the overlapping area between Mathematics and Technology.
Step 6: Proceed to the information about Science and Technology. It states that 100 students take both Science and Technology. Thus, write 100 in the overlap between Science and Technology.
Step 7: Now, consider the information about Mathematics and Science. It states that 80 students take both Mathematics and Science. Write 80 in the overlap between Mathematics and Science.
Step 8: Finally, look at the information about students taking all three courses, Mathematics, Science, and Technology. It states that 20 students take all three courses. Place 20 in the small region where all three circles overlap.
Now that you have filled in all the information, we can find how many students are not in any of these courses. To do this, add up the numbers outside the overlapping sections.
In the Venn diagram, you can see that the sections outside the overlapping areas represent students who are taking only one or no courses. We need to add those numbers together:
Number of students in Mathematics only = 280 - 110 - 80 - 20 = 70
Number of students in Science only = 200 - 80 - 100 - 20 = 0
Number of students in Technology only = 230 - 110 - 100 - 20 = 0
To find the total number of students not in any of these courses, we add the numbers outside the overlapping areas:
Total number of students not in any course = 70 + 0 + 0 = 70
Therefore, there are 70 students who are not in any of these courses.