Math Problem Statement

Based on the scatterplot, what is the best prediction of the speed of sound when the air temperature is 50°C?

Solution

To solve the problem, let’s analyze the scatterplot step-by-step:

  1. Identify the trend in the scatterplot:
    The scatterplot shows a positive correlation between the air temperature (x-axis) and the speed of sound (y-axis). As the temperature increases, the speed of sound also increases.

  2. Find the approximate pattern:
    The data points appear to increase at a roughly constant rate. From 0°C to 40°C:

    • At 0°C, the speed of sound is about 331 m/s.
    • At 40°C, the speed of sound is around 355 m/s.

    The pattern suggests that the speed of sound increases by approximately 6 m/s for every 10°C.

  3. Predict the speed of sound at 50°C:
    To extend this trend to 50°C:

    • From 40°C to 50°C is an increase of 10°C.
    • The speed of sound will increase by another 6 m/s.

    Starting from 355 m/s at 40°C, adding 6 m/s gives:
    355+6=361m/s.355 + 6 = 361 \, \text{m/s}.

  4. Select the closest answer:
    The closest option to 361 m/s is 360 m/s.

Final Answer: 360 m/s


Do you want me to explain the relationship further or analyze any specific part?

Here are 5 related questions for practice:

  1. How would the speed of sound change if the air temperature reached 60°C?
  2. What type of correlation exists in the scatterplot (linear, exponential, or none)?
  3. If the speed of sound increases by 6 m/s per 10°C, what is the speed of sound at -10°C?
  4. How do you interpret the y-intercept of the scatterplot in this context?
  5. What mathematical equation might represent the relationship between air temperature and speed of sound?

Tip: When predicting from scatterplots, extend the trend line carefully while checking the data’s consistency.

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Math Problem Analysis

Mathematical Concepts

Scatterplots
Linear Relationships
Prediction using Data Trends

Formulas

Rate of Change = Δy / Δx

Theorems

Linear Trend Approximation

Suitable Grade Level

Grades 6-8