Since the given interval is
[tex]\lbrack0,\infty)[/tex]Then any number starting from zero to infinty belongs to it
The interval has zero and all positive real numbers
1) The given number is
[tex]-4.2\times10^5[/tex]Since the number is negative, then it does not belong to the given interval
[tex]-4.2\times10^5\notin\lbrack0,\infty)[/tex]2) The given number is
[tex]10^{-3}[/tex]Reciprocal it to change the sign of the power from negative to positive
[tex]10^{-3}=\frac{1}{10^3}=\frac{1}{1000}[/tex]Since the number is positive, then it belongs to the given interval
[tex]10^{-3}\in\lbrack0,\infty)[/tex]3) The given number is
[tex]\lvert-8.5\rvert[/tex]Since the absolute neglect the sign of the number, then
[tex]\lvert-8.5\rvert=8.5[/tex]Then the number is positive, so it belongs to the given interval
[tex]\lvert-8.5\rvert\in\lbrack0,\infty)[/tex]