There are 2,000 eligible voters in a precinct. 500 of the voters are randomly selected and asked whether they planned to vote for the democratic incumbent or the republican challenger. of the 500 surveyed, 350 said they would vote for the democratic incumbent. using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the democratic incumbent?

99% confidence limits for population proportion is:

CL = P +- Z * √(P*(1-P)/N))

Where:

P = sample proportion

Z = Z-score taken at 99% confidence = 2.575

N = sample size

Calculating for the values:
P = 350/500 = 0.7 
N = 500 

Substituting know values to the CL equation:

CL = 0.7 +-  2.575* √(0.7*(1-0.7)/500))

CL = 0.647 , 0.753

Therefore confidence limits range from 0.647 to 0.753.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."