31. Error Analysis A student made the frequency table below using the data below. Describe and correct the error.

    
    Image Long Description

    40 21 28 53 24 48 50 55 42 29 22 52 43 26 44

C Challenge

32. Make a histogram for a set of 200 data values. The histogram must have 40% of the values lie in the interval 20–29. The remaining values should be evenly divided among the intervals 0–9, 10–19, 30–39, and 40–49.

33. Copy and complete the cumulative frequency table below.

    Interval	Frequency	Cumulative Frequency
    0–9	□ white square	6
    10–19	□ white square	17
    20–29	□ white square	26
    30–39	□ white square	35

Standardized Test Prep

SAT/ACT

34. What is the shape of the histogram below?

    
    Image Long Description

    1. symmetric
    2. proportional
    3. skewed
    4. uniform
35. What is the solution of ( − 4 x − 6 ) + ( 6 x + 1 ) = − 13 ? open negative 4 x minus 6 close plus open 6 x plus 1 close equals negative 13 question mark
    6. − 4 negative 4
    7. 5
    8. 6
    9. 9
36. What is the factored form of x 2 − 6 x − 16 ? x squared , minus 6 x minus 16 question mark
    1. ( x + 2 ) ( x + 8 ) open x plus 2 close open x plus 8 close
    2. ( x − 2 ) ( x + 8 ) open x minus 2 close open x plus 8 close
    3. ( x + 2 ) ( x − 8 ) open x plus 2 close open x minus 8 close
    4. ( x − 2 ) ( x − 8 ) open x minus 2 close open x minus 8 close

Short Response

37. Between what two integer values of x do the graphs of y = 20 ( 0.5 ) x y equals 20 . open 0.5 close to the x  and y = 0.5 · 4 x y equals 0.5 middle dot , 4 to the x  intersect? Show your work.

Mixed Review

See Lesson 12-1.

Find each sum or difference.

38. [ 4 6 5 7 ] + [ 8 10 7 11 ] . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 6 , row2 column 1 , 5 , column 2 7 , end matrix . plus . matrix with 2 rows and 2 columns , row1 column 1 , 8 , column 2 10 , row2 column 1 , 7 , column 2 11 , end matrix
39. [ 0.2 0.6 0.8 0.5 ] − [ 2.3 5.9 7.5 1.0 ] . matrix with 2 rows and 2 columns , row1 column 1 , 0.2 , column 2 0.6 , row2 column 1 , 0.8 , column 2 0.5 , end matrix . minus . matrix with 2 rows and 2 columns , row1 column 1 , 2.3 , column 2 5.9 , row2 column 1 , 7.5 , column 2 1.0 , end matrix

Get Ready! To prepare for Lesson 12-3, do Exercises 40 and 41.

See Lesson 1-3.

Order the numbers in each exercise from least to greatest.

40. 13, 5 4 , − 4 , − 16 , 5 fourths , comma negative 4 comma negative 16 comma  0, 2, 16, 1 2 1 half
41. 0.9, − 0 . 2 , negative 0 . 2 comma  1.2, 5, − 1 , negative 1 comma  0, 0.1, 2

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