Hesperia Community center is buying new seating for their building. They want to purchase a combination of stools and chairs. St
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90 degrees you are looking to your side
180 degrees you are looking behind you
around origin of 0,0
the image is flipped into the negative world if it is in posiitve or vice versa
Attached is a Venn diagram of your problem.
Knowing how many likes all three will help. You know that 10 students like all three.
Rock and Jazz only:
16 like rock and jazz while 10 like all three. To get how many like jazz only, subtract 10 from 16.
16-10 = 6
Rock and Classical only:
13 like rock and classical while 10 like all three. To get how many like jazz only, subtract 10 from 13.
13-10 = 3
Jazz and classical only:
12 like jazz and classical while 10 like all three. To get how many like jazz only, subtract 10 from 12.
12-10 = 2
Now with that data you fill up the 4 intersecting areas. To get the outer, just remember that all areas within a circle should add up to the first assumption.
27 rock
24 classical
28 Jazz
All numbers in the rock circle should add up to 27.
All numbers in the classical circle should add up to 24.
All numbers in the Jazz circle should add up to 28.
Rock:
3+10+6+x = 27
19+x=27
x = 27-19
x= 8
Classical:
3+10+2+x = 24
15 + x = 24
x = 24-15
x = 9
Jazz:
10+6+2+x = 28
18 + x = 28
x = 28 - 18
x = 10
In summary: 8 liked only Rock, 9 liked only Classical, 10 liked only Jazz.
Knowing how many likes all three will help. You know that 10 students like all three.
Rock and Jazz only:
16 like rock and jazz while 10 like all three. To get how many like jazz only, subtract 10 from 16.
16-10 = 6
Rock and Classical only:
13 like rock and classical while 10 like all three. To get how many like jazz only, subtract 10 from 13.
13-10 = 3
Jazz and classical only:
12 like jazz and classical while 10 like all three. To get how many like jazz only, subtract 10 from 12.
12-10 = 2
Now with that data you fill up the 4 intersecting areas. To get the outer, just remember that all areas within a circle should add up to the first assumption.
27 rock
24 classical
28 Jazz
All numbers in the rock circle should add up to 27.
All numbers in the classical circle should add up to 24.
All numbers in the Jazz circle should add up to 28.
Rock:
3+10+6+x = 27
19+x=27
x = 27-19
x= 8
Classical:
3+10+2+x = 24
15 + x = 24
x = 24-15
x = 9
Jazz:
10+6+2+x = 28
18 + x = 28
x = 28 - 18
x = 10
In summary: 8 liked only Rock, 9 liked only Classical, 10 liked only Jazz.