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Unformatted text preview: Name: ID number: Time: 1 hour Math 204 1/11/06
Quiz I
Fall Semester (ﬁ/Og
Instructor: Mrs. Muna Jurdak Section 9: Thurs 3:30 pm. Section 10: Tues. 2:00 pm.
Section 11 Tues. 12:30 pm. Section 12: Tues. 11:00 am. Instructions:
1. Write your name and ID number clearly where indicated. 2. Circle your section number above, according to the time of the
problem solving session in which you are enrolled. 3. Solve the problems on this, the white guestion sheet. Use the
colored sheets for scratch work only. You may use the back of a white sheet to complete the solution of a problem.
4. Write your name on the colored scratch sheet also. 5. Calculate the nCr's and the nPr's. You may leave probabilities as fractions. 6. Show your work in all the problems. 7. If you fail to write your name; ID number, or to circle your section
number, you will lose grades ' m
— /100 (10%) 1. Using Cramcr‘s Rule, ﬁnd x2 for the following system of
equations:
2x1+ x2+ 3x; = 3
3X2 + 8X3 = *4
4x;  x2 x 12 (10%) 2. For which value(s) of p does the matrix equation P] [x]: {‘15) M to have a unique solution? Justify your
‘5 4 y 25 answer. (Q (12%) 3‘ Use the Gaussian procedure to ﬁnd the inverse of the
following matrix, if an inverse exists. Hi :3) ( )(
( )( Lt) vv (18%) 4. Given the system of equations X1 + X2 + X3 = 1
2x1  x; + 3X3 =
2X2 4X3 3 9
Write this system as a matrix equation AX = B, and solve this system, using matrices. (14%) 5. ln how many ways can a committee of 8 peeple be selected
from a group of 7 men and 9 women:
(a) If there are no restrictions? (b) If there are to be exactly 5 men on the committee? (16%) 6. ln how many ways can 7 girls and 9 boys be lined up in a
row:
(a) If all the girls must to be next to each other, and all the boys
must be next to each other“? (’b)lf all the girls must be next to each other and any boy can be in
any place in the row. U1 (20%) 7. In a group of 70 students, 35 are studying art, 22 are studying
music, and 10 are studying both art and music.
Hint: Draw a Venn diagram (a). If a student is chosen at random from the group, ﬁnd the probability that the student is studying:
(i) Art or music or both. (ii) Neither art nor music. (b)i Consider the events:
E = the student is studying alt.
F = the student is studying music.
G —‘= the student is studying neither art nor music.
(i) Are the events E, F, G mutually exclusive? Give a reason. (ii) Are the events E, F, G collectively exhaustive? Give a reason? ...
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 Three '10
 RomyArbid
 Math, matrix equation, ID NUMBER, Mrs. Muna Jurdak, white guestion sheet

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