https://file.aiquickdraw.com/mathbot/file/1727485832404z1raz59d.jpg

The regression equation provided in the image is:

\[
DD = 2.69 + 0.0138D
\]

where:
- \( DD \) is the duration of the dive in minutes.
- \( D \) is the depth of the dive in meters.

We need to find the duration for a dive to a depth of 150 meters. Substituting \( D = 150 \) in the equation:

\[
DD = 2.69 + 0.0138 \times 150
\]

Let's calculate this value.The duration of a typical dive to a depth of 150 meters, according to the regression equation, is **4.76 minutes**.

Would you like more details or have any other questions?

### Related Questions
1. How would the duration change for a dive to a depth of 200 meters?
2. What would the depth be if the dive duration lasted for 10 minutes?
3. What is the meaning of the intercept (2.69) in the context of this problem?
4. How do we interpret the slope (0.0138) of the regression line?
5. How reliable is this linear relationship for deeper dives?

**Tip**: When interpreting a regression equation, the slope tells you how much the dependent variable changes for a one-unit increase in the independent variable.

According to the regression line, how long does a typical dive to a depth of 150 meters last? Give your answer to two decimal places.

Find out how long a penguin typically dives when reaching a depth of 150 meters using the regression equation DD = 2.69 + 0.0138D. This problem covers concepts in linear regression, suitable for high school students.

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