Consider the universal set U and the sets X, Y, Z. U={1,2,3,4,5,6} X={1,4,5} Y={1,2} Z={2,3,5} What is (Z⋃X′)⋂Y?
beks73 [17]
X' = U - X
= {1,2,3,4,5,6} - {1,4,5}
= {2,3,6}
(ZUX') = {2,3,5} U {2,3,6}
= {2,3,5,6}
(Z⋃X′)⋂Y = {2,3,5,6} ⋂ {1,2}
= {2}
Let x represent the percentage change. The percentage change is a factor that the original number is multiplied to get the new number.
60*x = 35
x = 35/65 = 0.53846 = 53.846%
If we have:
logₐy = (logₓy) / (logₓa) By change of base formula.
log₁₀65 = (log₁₀₀₀65) / (log₁₀₀₀10)
(log₁₀₀₀65) = log₁₀65 * (log₁₀₀₀10)
log(₁₀₀₀10) = 1/ (log₁₀1000) = 1/(log₁₀10³) = 1/3
(log₁₀₀₀65) = (log₁₀65) * (log₁₀₀₀10)
(log₁₀₀₀65) = 1.812 * (1/3)
(log₁₀₀₀65) = 0.604
I hope this helps.
