Show that the value of `((2000),(2))+((2000), (5))+((2000),(8))+…((2000),(2000))=(2^(2000)-1)/(3)`

Write the number in short form: 10000+ 2000+ 300+80+9

The following table gives the distribution of the life - time of 400 neon lamps. {:("Lif time (in hours)","Number of lamps"),(1500-2000,14),(2000-2500,56),(2500-3000,60),(3000-3500,86),(3500-4000,74),(4000-4500,62),(4500-5000,48):} Find the median life -time of a lamp .

The following data gives the distribution of total monthly household expenditure of 200 families of a village .. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure: {:("Expenditure (Rs)","Number of families"),(1000-1500,24),(1500-2000,40),(2000-2500,33),(2500-3000,28),(3000-3500,30),(3500-4000,22),(4000-4500,16),(4500-5000,7):}

For the reaction, following data is given: AtoB,K_(1)=10^(15)"exp"^(((-2000)/T)),CtoD,K_(2)=10^(14)"exp"^(((-1000)/T)) The temperature at which K_(1)=K_(2) is

For the reaction, following data is given AtoB:K_(1)=10^(15) exp ((-2000)/T)" "CtoD,K_(2)=10^(14) exp ((-1000)/T) The temperature at whilch K_(1)=K_(2) is

Write the numbers in short form: 10000+2000+300+50+1

Short form of 10000+ 2000+300+ 50+1 is

The ratio of energies of photons with wavelengths 2000A^(0) and 4000A^(0) is