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The given equation is \( p = q + 3r \), with the values of \( q = 0.672 \) and \( r = 0.446 \), both correct to 3 decimal places. To find the upper bound of \( p \), we need to consider the maximum possible values of \( q \) and \( r \).

### Step-by-step:
1. The upper bound for \( q \), considering it is rounded to 3 decimal places, is \( q_{\text{upper}} = 0.6725 \).
2. The upper bound for \( r \), rounded to 3 decimal places, is \( r_{\text{upper}} = 0.4465 \).
3. Now substitute these upper bounds into the equation \( p = q + 3r \):

\[
p_{\text{upper}} = 0.6725 + 3 \times 0.4465
\]

Now I'll calculate the value.It seems like I can't do more advanced data analysis right now. Please try again later.

However, you can still compute it manually:
\[
p_{\text{upper}} = 0.6725 + 3 \times 0.4465 = 0.6725 + 1.3395 = 2.012.
\]
Thus, the upper bound for \( p \) is 2.012, correct to 3 decimal places.

Do you have any other questions, or would you like more details on this? Here are some related questions:

1. How do you determine the lower bound for \( p \)?
2. What are bounds in mathematics, and why are they important?
3. How do rounding errors affect calculations like this?
4. Could the result change significantly if different rounding rules were used?
5. How is the concept of upper bounds applied in optimization problems?

**Tip**: Always double-check rounding when dealing with upper or lower bounds to ensure accuracy!

Work out the upper bound for the value of p. Given q = 0.672 correct to 3 decimal places, r = 0.446 correct to 3 decimal places. Use the formula p = q + 3r.

Learn how to calculate the upper bound for p = q + 3r given values of q and r rounded to 3 decimal places. This algebra problem involves rounding and finding the maximum possible values of variables.

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