The graph below shows the U.S. federal expenses for 2012. A) estimate the fraction of the total expenses that were spent on Medicare. Write your answer as the closest fraction whose denominator is 100. B) estimate the fraction of the total expenses that were spent on Medicare and Medicaid. Write your answer as the closest fraction, whose denominator is 100.

Do not use the Residue Theorem. Thank you.

Evaluate the line integral sin z dz, So sin where C is the portion of the curve y = x² from 0 to −1 + i.

Let f(z) be complex differentiable everywhere in C. Fix two distinct complex numbers a and b and a circle C of radius R with |a| < R,|b| < R traversed in the counter-clockwise direction. Evaluate the integral Sc − f(z)dz (z - a)(z – b) in terms of a, b and the values of f at those points.

| Let C be a circle (with a positive radius) such that z = 1 lies in its interior. Evaluate the contour integral So Tz zez (z - 1)³ = where C is traversed in the clockwise direction. dz

not use ai please

If you are using chatgpt leave it I will downvote .

Temperature measurements are based on the transfer of heat between the sensor of a measuring device (such as an ordinary thermometer or the gasket of a thermocouple) and the medium whose temperature is to be measured. Once the sensor or thermometer is brought into contact with the medium, the sensor quickly receives (or loses, if warmer) heat and reaches thermal equilibrium with the medium. At that point the medium and the sensor are at the same temperature. The time required for thermal equilibrium to be established can vary from a fraction of a second to several minutes. Due to its small size and high conductivity it can be assumed that the sensor is at a uniform temperature at all times, and Newton's cooling law is applicable. Thermocouples are commonly used to measure the temperature of gas streams. The characteristics of the thermocouple junction and the gas stream are such that λ = hA/mc 0.02s-1. Initially, the thermocouple junction is at a temperature Ti and the gas stream at…

3) Recall that the power set of a set A is the set of all subsets of A: PA = {S: SC A}. Prove the following proposition. АСВ РАСРВ