Math Problem Statement
Solution
To solve the problem, let’s analyze the scatterplot step-by-step:
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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. -
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.
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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:
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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:
- How would the speed of sound change if the air temperature reached 60°C?
- What type of correlation exists in the scatterplot (linear, exponential, or none)?
- If the speed of sound increases by 6 m/s per 10°C, what is the speed of sound at -10°C?
- How do you interpret the y-intercept of the scatterplot in this context?
- 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