For a weighted geometric mean where w $=<0\mathrm{.}4,0\mathrm{.}5,0,0\mathrm{.}1>$ and x $=<0\mathrm{.}3,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}2>,$ which of the following is true? $[$Multiple answers could be selected$]$

Question $4$ options:

The first and second inputs usually $($for most vectors x$)$ have a relatively higher influence on the function than the third and fourth inputs.

The output of the function will be zero because the third weight is zero.

The third variable has no influence on the output of the function.

Although it will not be the case this time, the function usually tends towards higher values.