Question
the average human heart beats about 3.5 x 10^7 times per year. the current population of Massachusetts is about how many heartbeats occur in Massachusetts. write your answer in scientific notation. express the answer to the exact decimal place.
Answers
Answer
wrong
Answered by
GPT-4o mini
To calculate the total number of heartbeats in Massachusetts, we need to know both the average number of heartbeats per person per year and the population of Massachusetts.
1. The average number of heartbeats per person in one year is given as \(3.5 \times 10^7\).
2. The population of Massachusetts (as of the latest data, around 2023) is approximately 6.9 million, or \(6.9 \times 10^6\).
Now, we can calculate the total number of heartbeats occurring in Massachusetts by multiplying the average heartbeats per person by the population:
\[
\text{Total Heartbeats} = (\text{Average Heartbeats per person per year}) \times (\text{Population})
\]
\[
\text{Total Heartbeats} = (3.5 \times 10^7) \times (6.9 \times 10^6)
\]
Using the properties of multiplication with scientific notation:
\[
= 3.5 \times 6.9 \times 10^{7 + 6}
\]
\[
= 24.15 \times 10^{13}
\]
Next, we convert \(24.15\) to scientific notation:
\[
24.15 = 2.415 \times 10^1
\]
Therefore:
\[
24.15 \times 10^{13} = 2.415 \times 10^{14}
\]
Thus, the total number of heartbeats occurring in Massachusetts is:
\[
\boxed{2.415 \times 10^{14}}
\]
1. The average number of heartbeats per person in one year is given as \(3.5 \times 10^7\).
2. The population of Massachusetts (as of the latest data, around 2023) is approximately 6.9 million, or \(6.9 \times 10^6\).
Now, we can calculate the total number of heartbeats occurring in Massachusetts by multiplying the average heartbeats per person by the population:
\[
\text{Total Heartbeats} = (\text{Average Heartbeats per person per year}) \times (\text{Population})
\]
\[
\text{Total Heartbeats} = (3.5 \times 10^7) \times (6.9 \times 10^6)
\]
Using the properties of multiplication with scientific notation:
\[
= 3.5 \times 6.9 \times 10^{7 + 6}
\]
\[
= 24.15 \times 10^{13}
\]
Next, we convert \(24.15\) to scientific notation:
\[
24.15 = 2.415 \times 10^1
\]
Therefore:
\[
24.15 \times 10^{13} = 2.415 \times 10^{14}
\]
Thus, the total number of heartbeats occurring in Massachusetts is:
\[
\boxed{2.415 \times 10^{14}}
\]
Answered by
GPT-4o mini
Let's go through the calculation again step by step to ensure accuracy.
1. **Average heartbeats per person per year**: \(3.5 \times 10^7\)
2. **Population of Massachusetts**: Approximately \(6.9 \times 10^6\) (6.9 million)
Now, we multiply the two values:
\[
\text{Total Heartbeats} = (3.5 \times 10^7) \times (6.9 \times 10^6)
\]
First, let's multiply the coefficients:
\[
3.5 \times 6.9 = 24.15
\]
Next, we add the exponents in the powers of ten:
\[
10^7 \times 10^6 = 10^{7 + 6} = 10^{13}
\]
Putting it all together:
\[
\text{Total Heartbeats} = 24.15 \times 10^{13}
\]
Now to express \(24.15\) in scientific notation, we rewrite \(24.15\):
\[
24.15 = 2.415 \times 10^1
\]
Substituting back into our equation:
\[
\text{Total Heartbeats} = 2.415 \times 10^1 \times 10^{13} = 2.415 \times 10^{14}
\]
Thus, the total number of heartbeats occurring in Massachusetts is:
\[
\boxed{2.415 \times 10^{14}}
\]
If there was a misunderstanding or if the population estimate was different from what was assumed, please let me know, and I can adjust the calculations accordingly.
1. **Average heartbeats per person per year**: \(3.5 \times 10^7\)
2. **Population of Massachusetts**: Approximately \(6.9 \times 10^6\) (6.9 million)
Now, we multiply the two values:
\[
\text{Total Heartbeats} = (3.5 \times 10^7) \times (6.9 \times 10^6)
\]
First, let's multiply the coefficients:
\[
3.5 \times 6.9 = 24.15
\]
Next, we add the exponents in the powers of ten:
\[
10^7 \times 10^6 = 10^{7 + 6} = 10^{13}
\]
Putting it all together:
\[
\text{Total Heartbeats} = 24.15 \times 10^{13}
\]
Now to express \(24.15\) in scientific notation, we rewrite \(24.15\):
\[
24.15 = 2.415 \times 10^1
\]
Substituting back into our equation:
\[
\text{Total Heartbeats} = 2.415 \times 10^1 \times 10^{13} = 2.415 \times 10^{14}
\]
Thus, the total number of heartbeats occurring in Massachusetts is:
\[
\boxed{2.415 \times 10^{14}}
\]
If there was a misunderstanding or if the population estimate was different from what was assumed, please let me know, and I can adjust the calculations accordingly.
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