Solve the Problem $R$ Is the Parallelepiped Enclosed by the Planes $5 x + y - z = 1,5 x + y - z = 3 , - x + 8 y + z = - 2 , - x + 8 y + z = 5$

question 144

Multiple Choice

Solve the problem.
-Evaluate


where $R$ is the parallelepiped enclosed by the planes $5 x + y - z = 1,5 x + y - z = 3 , - x + 8 y + z = - 2 , - x + 8 y + z = 5$ $x - y + 2 z = - 1 , x - y + 2 z = 6$

• A) \(\frac { 45 } { 19 }\)
• B) \(\frac { 256 } { 95 }\)
• C) \(\frac { 324 } { 95 }\)
• D) \(\frac { 294 } { 95 }\)

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Definitions:

Openness to Experience

A personality trait characterized by an appreciation for art, emotion, adventure, unusual ideas, imagination, curiosity, and variety of experience.

Conscientiousness

A personality trait characterized by diligence, carefulness, and a high level of organization and responsibility.

Emotional Stability

A personality trait signifying the consistency of an individual's mood and temperament; opposite of high neuroticism.

Agreeableness

A personality trait characterized by kindness, warmth, cooperation, and a tendency to avoid conflict.