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Math 141 Week in Review Week 11 Problem Set Answers 1. A. Not regular (Third column does not add up to 1.) B. Regular C. Not regular 2. A. 63.03% will drink Coke and 36.97% will drink Pepsi after 2 years. B. 62.1622% will drink Coke and 37.8378% will drink Pepsi in the long run. 3. Equilibrium Quantity: 950 guitars; Equilibrium Price: $337.50 4. "1 0 The row-reduced matrix is $ #0 1 R1 ! R1 !1% "6R + R2 ! R2 ' . The steps are: 1 1 R ! R2 !3& 15 2 2R2 + R1 ! R1 1 2 5. A. (5, −3, 8) B. No solution 7 + 113 t, 17 + 11 t,t ) , where t is C. Infinitely many solutions parameterized by (! 32 11 11 any real number. 6. a = 26, b = −13, c = 4, d = 9 7. A. $1140.41 B. $165,123.00 C. $1111.40 8. C(5, 3)·23·C(5, 4)·54 = 250, 000 9. Let x = number of vases and y = number of mugs made each week. 6x + 4 y ! 42 8x + 2y " 24 Maximize P = 12x + 3y subject to: y ! 2x x " 0, y " 0 Corner points: (2, 4), (3, 6), (7, 0), and (3, 0). Max profit: $84 when 7 vases and 0 mugs are made. There is no clay left over.; Min profit: $36 at infinitely many points along the line segment between (2, 4) and (3, 0). There are between 14 and 24 pieces of clay left over along this line segment. 10. A. 43 B. 140 C. 145 84 D. = 0.28 300 11. 12 19 10 B. 19 A. 5 10 , P(F ) = 19 19 E and F are not mutually exclusive because P(E ∩ F) ≠ 0. E and F are not independent because P(E ∩ F) ≠ P(E)·P(F). C. P ( E ) = 12. y = 0.9797x + 0.6014; about 69 13. A. 14. 0.1257 15. E(X) = −$0.28, σ = 2.3287, Var(X) = 5.4228 16. Need 25,675 units of food and 10,400 units of shelter. 17. 0.0033 18. 550 calendars 19. 0.0322 20. 3!·P(5, 3)·P(6, 4)·P(5, 2) = 2,592,000 21. 0.8123 22. N = 14.92 ≈ 15, or about 3.75 years; $1000 23. A. {2, 4} B. {1, 6} C. {1, 2, 3, 4, 6} 24. y= 25. 0.2023 C(10,3)C (24,5) + C(8,4)C (26,4 ) ! C(10,3)C(8,4)C (16,1) " 0.3312 C ( 34,8) C (27,8) " 0.8777 B. 1! C(34,8) 2 x !2 9