Pages 134 and 135 of a Pre-Algebra textbook displaying answer keys for sections on misleading statistics and introduction to counting.

The image provided is a teacher's answer key for a Pre-Algebra textbook (Glencoe/McGraw-Hill), specifically covering sections 10-4 Misleading Statistics and 10-5 Counting. Since there is no specific question asked, I will explain the solutions for the visible problems on these pages to help you understand the concepts.

Section 10-4: Misleading Statistics (Pages 505–508)

This section focuses on how graphs and data can be presented in ways that trick the viewer.

Problem 1 & 2: Identifying Missing Information
* Concept: A good graph must have labels so we know what we are looking at.
* Solution: The sample answers point out that the axes might not be marked uniformly (equal spacing) or might lack titles. For surveys, it is crucial to know *who* was surveyed and *how many* people were involved to judge if the data is reliable.

Problem 3: Inconsistent Scales
* Answer: Khandi.
* Reasoning: The scale is not consistent in length and width, which distorts the visual representation of the data.

Problem 5: Visual Distortion in Graphs
* 5a: The value is about 1.1.
* 5b: The second car appears shorter in both length and width visually, even if the data says otherwise.
* 5c: Yes. The actual number of cars sold in 1992 is only 1.1 times greater than in 1991. However, because the graph changes *both* dimensions (making the car icon longer AND wider), it looks much larger than it actually is. This is a common misleading tactic. To be accurate, only one dimension (like height or length) should change to represent the increase.

Problem 7: Mean vs. Median
* 7a: Use the Median. When there are large and small values (outliers), the median gives a better "middle" picture because it isn't pulled up or down by extreme numbers.
* 7b: Use the Mean. High values will raise the center of the data, making the average look higher.

Problem 13: Comparing Company Salaries
* Data Table:
* Company A: Mean: $\$22,413.79$, Median: $\$15,000$, Mode: $\$15,000$.
* Company B: Mean: $\$21,935.48$, Median: $\$20,000$, Mode: $\$20,000$.
* Analysis: Although Company A has a slightly higher *mean* (average), Company B has a higher *median* and *mode*.
* Conclusion: You would probably prefer to work for Company B. The median and mode suggest that the typical worker earns $\$20,000$, whereas at Company A, the typical worker earns only $\$15,000$. The high mean at Company A is likely caused by one or two very high salaries skewing the average.

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Section 10-5: Counting (Pages 511–513)

This section deals with probability and counting outcomes.

Problem 1: Outcomes of Dice and Spinners
* 1a: The question asks for outcomes from tossing two three-colored dice or spinning a three-choice spinner.
* 1b: If the colors are Green (G), Blue (B), and Yellow (Y), the possible combinations when rolling two dice are:
* GG, GB, GY
* BG, BB, BY
* YG, YB, YY
*(Note: The text lists GG, GB, GY, BG, BB, BY, YG, YB, YY)*.

Problem 2: Fundamental Counting Principle
* Concept: This principle states that if you have $m$ ways to do one thing and $n$ ways to do another, there are $m \times n$ ways to do both.
* Answer: Using the Fundamental Counting Principle is faster and takes less space than listing every single possibility manually.

Problem 15b: Reading a Line Graph
* The graph shows population increases over 6 years.
* Looking at the grid lines, the population starts around 2,000 and rises steadily to roughly 4,000.

Problem 17: Money Calculations
* These appear to be simple arithmetic or currency conversion problems based on previous context not fully shown.
* Answers:
* 17a: $\$58$
* 17b: $\$25$
* 17c: $\$35$
* 17d: $\$15$
* 17e: $\$20$
* 17f: $\$12, \$70$
* 17g: $\$0$ and $\$65$
* 17h: $\$70$

Problem 19: Fractions and Large Numbers
* 19a: The fraction is $\frac{8}{11}$.
* 19b: The number is $1,965,955$.

Problem 21: Positive and Negative Integers
* Answer: $-6, 6$.

Problem 20: Large Number Estimation
* Answer: $1,000,000$.

Problem 16: Measures of Central Tendency
* 16a: Use the mode or median because they make the current salaries look lower (which might be useful for a union negotiation, for example). The mean is often higher due to outliers.
* 16b: Answers will vary, but both sides should agree to use the same measure of central tendency to be fair.

Final Answer:
The provided image contains answer keys for Pre-Algebra problems regarding Misleading Statistics and Counting Principles. Key takeaways include:
1. Misleading Graphs: Be careful when both dimensions of an object in a graph are changed to represent data; this exaggerates the difference. Always check if scales are uniform.
2. Mean vs. Median: Use the median to find the typical value when there are outliers (extreme high or low numbers). Use the mean if you want to include the effect of those high values. In Problem 13, Company B is the better choice for a typical worker because its median salary ($\$20,000$) is higher than Company A's ($\$15,000$), despite Company A having a higher average.
3. Counting: The Fundamental Counting Principle allows you to multiply options to find total outcomes quickly instead of listing them all. For two 3-colored dice, there are $3 \times 3 = 9$ outcomes.