Suppose you have just made node $3$ permanent with the distance label d$[3]=12.$ After making node $3$ permanent, you consider the arc $(3,7)$ with a length of $5.$ Currently, the distance label of node $7$ is d$[7]=24$ and the predecessor of node $7$ is pred$[7]=5.$

After considering the arc $(3,7)$ and making any necessary updates, what will be the value of d$[7]?$

$($Enter a numerical value. Your answer must be correct within $+/-0\mathrm{.}01.)$