Write the dual for each of the following primal problems: (a) Maximize z = 66x1 – 22x2 subject to -X1 + x2 s -2 2x, + 3x, s 5 X1, X, 2 0 (b) Minimize z = 6x1 + 3x2 subject to 6x1 - 3x2 + xạ 2 25 3x1 + 4x2 + X3 55 X1, X2, X3 2 0 (c) Maximize z = x1 + x2 subject to 2x, + x, = 5 3x, - x, = 6 X1, x2 unrestricted

Q: Solve: a 5X-1 = 7x

A: We have to solve for x.

Q: -4) 12x+30= 3xー12

A: we first distribute the equation, Then combine like term on same side.

Q: Solve 2X1 + 4X2= 80 and 3X1 + 1X2 = 60

A: 2X1 + 4X2= 80 rewrite equation as X1 + 2X2= 40..................(i) 3X1 + 1X2 = 60..............(ii)…

Q: Solve for points (-2,0) , (0,2) , (2,3)

A:

Q: X-X-30-0

A: x2 – x – 30 = 0Solve by completing the square.

Q: Solve by using u substitution and factoring:  x+x^1/2-20=0

A:

Q: Solve Vr + 5+1 = x

A:

Q: Solve for r  us = -rtv

A: Given,            us = -rtv

Q: 2 * = 8

A: Given query is to find the value of x.

Q: Solve 7 = ex+1.

A: Given function  - 7 = ex+1Taking ln on both sides - ln7 = lnex+1ln7 = x+1lne…

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.