C Challenge

For Exercises 45–48, use matrices P, Q, R, S, and I. Determine whether the two expressions in each pair are equal.

P = [ 3 4 1 2 ] Q = [ 1 0 3 − 2 ] R = [ 1 4 − 2 1 ] R = [ 0 1 2 0 ] I = [ 1 0 0 1 ] p equals . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 4 , row2 column 1 , 1 , column 2 2 , end matrix . q equals . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 0 , row2 column 1 , 3 , column 2 negative 2 , end matrix . r equals . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 4 , row2 column 1 , negative 2 , column 2 1 , end matrix . r equals . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 1 , row2 column 1 , 2 , column 2 0 , end matrix . i equals . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 0 , row2 column 1 , 0 , column 2 1 , end matrix

45. ( P + Q ) R  and  P R + Q R open p plus q close r , and p r plus q r
46. ( P + Q ) I  and  P I + Q I open p plus q close i , and p i plus q i
47. ( P + Q ) ( R + S )  and  ( P + Q ) R + ( P + Q ) S open p plus q close open r plus s close , and , open p plus q close r plus open p plus q close s
48. ( P + Q ) ( R + S )  and  P R + P S + Q R + Q S open p plus q close open r plus s close , and p r plus p s plus q r plus q s

Standardized Test Prep

SAT/ACT

49. Which product is NOT defined?
    1. [ − 1 2 ] [ − 1 2 ] . matrix with 2 rows and 1 column , row1 column 1 , negative 1 , row2 column 1 , 2 , end matrix . table with 1 row and 1 column , row1 column 1 , . matrix with 1 row and 2 columns , row1 column 1 , negative 1 , column 2 2 , end matrix , end table
    2. [ − 1 2 − 1 2 ] [ − 1 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 2 , row2 column 1 , negative 1 , column 2 2 , end matrix . table with 1 row and 1 column , row1 column 1 , . matrix with 1 row and 2 columns , row1 column 1 , negative 1 , column 2 2 , end matrix , end table
    3. [ − 1 2 − 1 2 ] [ 2 − 1 2 − 1 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 2 , row2 column 1 , negative 1 , column 2 2 , end matrix . table with 1 row and 1 column , row1 column 1 , . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 negative 1 , row2 column 1 , 2 , column 2 negative 1 , end matrix , end table
    4. [ − 1 2 ] [ − 1 2 ] table with 1 row and 1 column , row1 column 1 , . matrix with 1 row and 2 columns , row1 column 1 , negative 1 , column 2 2 , end matrix . matrix with 2 rows and 1 column , row1 column 1 , negative 1 , row2 column 1 , 2 , end matrix , end table
50. What is the geometric mean of 8 and 18?
    6. 12
    7. 13
    8. 26
    9. 36

51. The random number table simulates an experiment where you toss a coin 90 times. Even digits represent heads and odd digits represent tails. What is the experimental probability, to the nearest percent, of the coin coming up heads?

    Random Number Table

    31504	51648	40613
    79321	80927	42404
    15594	84675	68591
    34178	00460	31754
    49676	58733	00884
    85400	72294	22551

    1. 45%
    2. 50%
    3. 54%
    4. 56%
52. Four percent of the tenants in an apartment building live alone. Suppose five tenants are selected randomly. Which expression represents P(all live alone)?
    6. ( 0.04 ) 5 open , 0.04 , close to the fifth
    7. ( 0.4 ) 5 open 0.4 close to the fifth
    8. ( 0.96 ) 5 open , 0.96 , close to the fifth
    9. ( 5 ) 0.04 open 5 close to the 0.04

Short Response

53. Explain how to find an equation for the ellipse, centered at the origin, that is 50 units wide and 40 units high.

Mixed Review

See Lesson 12-1.

Add or subtract.

54. [ − 1 2 0 17 ] − [ 32 14 6 − 10 ] table with 1 row and 1 column , row1 column 1 , . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 2 , row2 column 1 , 0 , column 2 17 , end matrix , end table . minus . matrix with 2 rows and 2 columns , row1 column 1 , 32 , column 2 14 , row2 column 1 , 6 , column 2 negative 10 , end matrix
55. [ 0 − 1 5 6 10 12 ] + [ 9 − 5 7 − 4 10 0 ] table with 1 row and 1 column , row1 column 1 , . matrix with 2 rows and 3 columns , row1 column 1 , 0 , column 2 negative 1 , column 3 5 , row2 column 1 , 6 , column 2 10 , column 3 12 , end matrix , end table . plus . matrix with 2 rows and 3 columns , row1 column 1 , 9 , column 2 negative 5 , column 3 7 , row2 column 1 , negative 4 , column 2 10 , column 3 0 , end matrix

Get Ready! To prepare for Lesson 12-3, do Exercises 56–57.

See p. 967.

Simplify each group of expressions.

56. 1. 3(4)
    2. 2(6)
    3. 3 ( 4 ) − 2 ( 6 ) 3 open 4 close minus 2 open 6 close
57. 1. 3 ( − 4 ) 3 open negative 4 close
    2. 2 ( − 6 ) 2 open negative 6 close
    3. 3 ( − 4 ) − 2 ( − 6 ) 3 open negative 4 close minus 2 open negative 6 close

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