Algebra, arithmetic, reasoning.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
The dot product is 2×4+2×6=20.
Rewrite the value using base 3: 27 = 3^3. Matching exponents gives x = 3.
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Use the circle-area formula A = πr². Substituting r = 7 gives A = π × 7² = 49π.
Percentage=(10/25)×100=40.00.
Subtract 9 from both sides and divide by 8: x = (65-9)/8 = 7.
By Vieta’s formula, the sum of the roots equals the coefficient 14.
aₙ=a₁+(n−1)d=8+(11−1)×1=18.
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The sum is n(n+1)/2=55, so the mean is 55/10.
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There are 3 favourable outcomes out of 6 equally likely outcomes, so P(red)=3/6.
aₙ=a₁+(n−1)d=7+(10−1)×6=61.
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The sum is n(n+1)/2=45, so the mean is 45/9.
