We are given \(P(A\cup B)=0.9\) and \(P(A\cap B)=0.4\). We need to find \(P(\overline{A})+P(\overline{B})\).

We know that \(P(A\cup B) = P(A) + P(B) - P(A\cap B)\).

So, \(0.9 = P(A) + P(B) - 0.4\).

Therefore, \(P(A) + P(B) = 0.9 + 0.4 = 1.3\).

We also know that \(P(\overline{A}) = 1 - P(A)\) and \(P(\overline{B}) = 1 - P(B)\).

So, \(P(\overline{A}) + P(\overline{B}) = (1 - P(A)) + (1 - P(B)) = 2 - (P(A) + P(B))\).

Substituting the value of \(P(A) + P(B)\), we get:

\(P(\overline{A}) + P(\overline{B}) = 2 - 1.3 = 0.7\).