Certainly! Let's walk through the detailed, step-by-step solution to determine the number of heart beats per minute for someone who has 247 heart beats in [tex]\(6 \frac{1}{2}\)[/tex] minutes.
### Step 1: Understanding the Problem
We need to find the rate of heart beats per minute given a total of 247 beats over a span of [tex]\(6 \frac{1}{2}\)[/tex] minutes.
### Step 2: Convert Mixed Number to Decimal
First, we need to convert the mixed number [tex]\(6 \frac{1}{2}\)[/tex] into a decimal. A mixed number consists of a whole number and a fraction. Here, the whole number is 6 and the fraction is [tex]\(\frac{1}{2}\)[/tex].
To convert [tex]\(6 \frac{1}{2}\)[/tex] to a decimal:
[tex]\[ 6 + \frac{1}{2} = 6 + 0.5 = 6.5 \][/tex]
So, [tex]\(6 \frac{1}{2}\)[/tex] minutes is equal to 6.5 minutes.
### Step 3: Calculate the Beats Per Minute
To find the number of beats per minute, we divide the total number of beats by the total number of minutes.
- Total beats: 247
- Total time in minutes: 6.5
Now, let's do the division:
[tex]\[ \text{Beats per minute} = \frac{\text{Total beats}}{\text{Total minutes}} = \frac{247}{6.5} \][/tex]
Performing the division:
[tex]\[ \frac{247}{6.5} = 38.0 \][/tex]
Thus, the rate of heart beats per minute is 38.0.
### Final Answer
The heart rate is 38.0 beats per minute.
