Key to In Class Final Exam Review

1.

2. y = 2.38x + 69.1 thousand dollars, prediction for 2010 is $100,040

3. a)

4. a)

b)

5. a) no solution

b) (2-3z, 7+5z ,z) Particular solutions possibilities are infinite but two are (2, 7, 0) , (-1, 12, 1)

c) (-1,3)

6. When the number of variables is equal to the number of equations and the solution is unique it can be solved with an inverse. RREF always works.

7.

8. $54.107 billion of energy and $33.214 billion of manufacturing.

$24.107 billion of energy and $21.214 billion of manufacturing are used up.

9. See picture from class. Remember that x=6 is a vertical line and y=4 is a horizontal line.

10. a) Pmax=$405 producing 0 of A and 9 of B. Leftovers are 3 hours in parts and 4 hours in assembly, no leftover finishing hours.

b) Pmax=$390 producing 9 of A and 4 of B or 13 of A and 0 of B or at any point on the line segment connecting these.

c) Pmax=$390 producing 13 of A and 0 of B. Leftovers are 4 hours in parts and 5 hours in finishing. No leftover assembly hours.

11. 4 do none of the three. The numbers in the diagram would be a=10 b=8 c=2 d=2 e=3 f=6 g=5 h=4

12. a) 120 b) 720 c) 360

13. a) 32768 b) 6720

14.

15. a) 0.02475 b) 0.03 c) 0.4242

16. x 0 1 2 3

p 4/35 18/35 12/35 1/35 E(X)= 9/7

17. x 0 1 2 3

p 2/3 1/4 3/42 1/84 E(X)= 3/7

18. mean=15.942 median=15.9 mode=15.9 st.dev.=0.1291

19. mean=3.0909 median=3 mode=3 st.dev.=1.4640

20. a) 0.1474 b) 0.8089 c) 0.8079

21. a) 0.5671 b) 0.7257 c) 0.2743 d) 67.6 inches e) 64.87 inches