Postgraduate Mathematics I task 52: For the data set 1,2,…,7, which fraction equals its arithmetic mean before simplification?
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The sum is n(n+1)/2=28, so the mean is 28/7.
Practice China questions with answers and explanations.
Choose an option to check your answer.
The sum is n(n+1)/2=28, so the mean is 28/7.
Choose an option to check your answer.
There are 6 favourable outcomes out of 9 equally likely outcomes, so P(red)=6/9.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
An antiderivative is 4/2 x²+4x. At x=5, the value is 70.0.
The dot product is 4×4+5×6=46.
By Vieta’s formula, the sum of the roots equals the coefficient 13.
aₙ=a₁+(n−1)d=7+(16−1)×6=97.
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The sum is n(n+1)/2=21, so the mean is 21/6.
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There are 5 favourable outcomes out of 13 equally likely outcomes, so P(red)=5/13.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=12x²+8x. Substituting x=4 gives 224.
Percentage=(7/42)×100=16.67.