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Oduvanchick [21]
3 years ago
14

Each of the 108 students attending a conservatory of music plays at least one of the​ piano, harp, and clarinet. 67 play the​ pi

ano, 46 play the​ harp, 32 play the​ clarinet, 19 play the piano and the​ harp, 13 play the harp and the​ clarinet, and 8 play the piano and the clarinet. How many play all three​ instruments? Hint​: Let x represent the number of students who play all three instruments.
Mathematics
1 answer:
Marrrta [24]3 years ago
3 0

Answer: 76

Step-by-step explanation:

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Anonymous 3 years ago
amm1812
Two angles are said to be complementary, if the sum of the measures of the to angles is equal to 90 degrees.

Thus, given that HFG is complementary to ACB, them mHFG + mACB = 90 degrees.

From the figure, given that the line from point F meats line CE at point P, then HFG = CFP.
But mCFE = 90 degrees and mCFE = mCFP + mPFE
Also PFE = DFH

Thus, mCFE = mCFP + mPFE = mHFG + mDFH = 90 degrees

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Thus, mHFG + mACB = mHFG + mDFH

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