Algebra, arithmetic, reasoning.
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There are 2 favourable outcomes out of 10 equally likely outcomes, so P(red)=2/10.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=3x²+14x. Substituting x=2 gives 40.
An antiderivative is 2/2 x²+1x. At x=3, the value is 12.0.
Percentage=(9/24)×100=37.50.
Subtract 8 from both sides and divide by 7: x = (50-8)/7 = 6.
By Vieta’s formula, the sum of the roots equals the coefficient 11.
aₙ=a₁+(n−1)d=6+(9−1)×5=46.
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The sum is n(n+1)/2=36, so the mean is 36/8.
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There are 6 favourable outcomes out of 13 equally likely outcomes, so P(red)=6/13.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=15x²+12x. Substituting x=1 gives 27.
