A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Poisson distribution. The probability that there will be less than $$4$$ penalties in a day is ________.

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0.21 $$m^3/s$$. Allowable velocity through the main is 0.75 m/s. Assume f = 0.01, g = 9.81 $$m/s^2$$. The minimum gradient (in cm/100m length) to be given to this gravity main so that the required amount of water flows without any difficulty is _____.

Some of the nontoxic metals normally found in natural water are

For a sample of water with the ionic composition shown in the figure below, the carbonate and noncarbonate hardness concentrations (in mg/l as $${\mathrm{CaCO}}_3$$), respectively are: