Problems 21-30 refer to the table below of the six basic solutions to the e-system 2 x 1 + 3 x 2 + s 1 = 24 4 x 1 + 3 x 2 + s 2 = 36 x 1 x 2 s 1 s 2 A 0 0 24 36 B 0 8 0 12 C 0 12 − 12 0 D 12 0 0 − 12 E 9 0 6 0 F 6 4 0 0 Describe geometrically the set of all points in the plane such that s 1 > 0 .
Problems 21-30 refer to the table below of the six basic solutions to the e-system 2 x 1 + 3 x 2 + s 1 = 24 4 x 1 + 3 x 2 + s 2 = 36 x 1 x 2 s 1 s 2 A 0 0 24 36 B 0 8 0 12 C 0 12 − 12 0 D 12 0 0 − 12 E 9 0 6 0 F 6 4 0 0 Describe geometrically the set of all points in the plane such that s 1 > 0 .
Solution Summary: The author calculates the set of all points in the plane geometrically if s_1>0 is all the points below the line.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
4. Solve the system of equations and express your solution using vectors.
2x1 +5x2+x3 + 3x4 = 9
-x2+x3 + x4 = 1
-x1-6x2+3x3 + 2x4
= -1
3. Simplify the matrix expression
A(A-B) - (A+B)B-2(A - B)2 + (A + B) 2
Chapter 6 Solutions
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY