Question

In list T, consists of 30 positive decimals. None of which are integers. The sum of the 30 decimals is S. The estimated sum of the 30 decimals is E. The estimated sum is calculated as follows: Each decimal in T whose tenth digit is even is rounded up to nearest integer, and each decimal in T whose tenth digit is odd is rounded down to a nearest integer. E is a sum. If 1/3 of decimals in T have even tenth digit that is even, what is a range of E-S?

Answer 1

Answer: E - S = (-16 and 6)

Step-by-step explanation:1/3 of the 30 decimals in T have an even tenths digit, it follows that 1/3*(30)=10 decimals in T have an even tenths digit.

Hence: Te =list of 10 decimals

Se = sum of all 10 decimals in Te

Ee =estimated sum of all 10 decimals in Te after rounding up.

Remaining 20 decimals in T all have an odd tenths digits.

To =list of this 20 decimals

So = sum of all 20 decimals in To

Eo = estimated sum of 20 decimals in To

Hence,

E = Ee + Eo and S =Se +So, hence:

E-S, =(Ee+Eo) - (Se+So) =(Ee-Se) +(Eo-So)

Ee-Se >10 (0.1)=1

S=10(1.8)+20(1.9) =18+38=56

E=10(2)+20(1)=40

E-S =40-56=-16.

AlsoS=10(1.2)+20(1.1)=34

E=10(2)+20(1)=40

E-S=40-34=6