Average (mean) = (sum of all the data) / (# of data)
sum of all the data = (average)(# of data)
Thus for 100 students with an average of 93,
sum of all data = (93)(100) = 9300
and for 300 students with an average of 75,
sum of all data = (75)(300) = 22500
Therefore you would expect the overall average to be
(9300 + 22500) / (100 + 300) = 79.5 %
Now if there are x # of advanced students and y # of regular students, then
x + y = 90 (total # of students) and 93x + 75y = 87(x + y) (overall average)
The second equation can be simplified to x - 2y = 0
Subtracting the two equations yields
x = 60 and y = 90
Therefore you would need 60 advanced and 30 regular students.
(2x²<span> + 3x - 4) + (8 - 3x) + (-5x</span>²<span> + 2)
= </span> 2x² + 3x - 4 + 8 - 3x - 5x² + 2
= -3x² + 6
= 3(-x² + 2)
<u>First let's calculate the exponents.</u>
<u>Now we should multiply and divide.</u>
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<u>Now we should add and subtract.</u>
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<u>Convert the improper fractions into mixed numbers.</u>
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<u>Answer : </u>
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