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Lucki1944
04.04.2020 •
Mathematics
Of the 300 students in 8th grade, 180 take PE, 80 take art. 72 take music, 33 take PE and art, 28 take PE and music, and 20 take all three
classes
M= all students taking music
A= all students taking art
P= all students taking PE
Which of the sets has more than 150 students? Select all that apply
AUM
POM
PNAM
PUAUM
1- (PNA)
Solved
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Ответ:
The sets has more than 150 students
P∪A∪M
-(P∩A)
Step-by-step explanation:
See the attached figure which represents Venn diagram for the question:
180 take PE
80 take art
72 take music
33 take PE and art
28 take PE and music
20 take all three
M= all students taking music
A= all students taking art
P= all students taking PE
Number of students taking PE and art only = 33 - 20 = 13
Number of students taking PE and music only = 28 - 20 = 8
Number of students taking PE only = 180 - (20 + 13 + 8) = 139
Number of students taking ARt only = 80 - (20 + 13) = 47
Number of students taking Music only = 72 - (20 + 8) = 44
Number of students doesn't take any thing =
300 - (20 + 13 + 8 + 139 + 47 + 44) = 29
We will check the options to find the sets has more than 150 students:
1) A∪M = 13 + 47 + 20 + 8 + 44 = 132 < 150
2) P∩M = 20 + 8 = 28 < 150
3) P∩A∩M = 20 < 150
4) P∪A∪M = 20 + 13 + 8 + 139 + 47 + 44 = 271 > 150
5) -(P∩A) = 300 - (13+20) = 267 > 150
So, The sets has more than 150 students
P∪A∪M
-(P∩A)
Ответ:
B
Step-by-step explanation:
(f+g)(x) means add f(x) and g(x) together:
(x/2)-2 + 2x^2 +x -3
collect all the like terms:
2x^2
(x/2) + x = 3/2x (explanation below)
-2 -3 = -5
x/2 + x can be turned to 1x/2 + 2/2x (2/2 = 1, so when you simplify it to 1x, it is still x)