The current price of a non$-$dividend$-$paying stock is $$114\mathrm{.}14$ and the annual standard deviation of the rate of return on the stock is $50\%.$ A European put option on the stock has a strike price of $$90$ and expires in $0\mathrm{.}25$ years. The risk$-$free rate is $3\%($continuously compounded$).$

What is the value of the term d$1$ in the Black$-$Scholes formula?

What should be the price $($premium$)$ of the put option?

What is the put's current hedge ratio $($delta$)?$