select the correct answer.

the half-life of helium-5 is $7.6 \times 10^{-22}$ seconds, and the half-life of helium-9 is $7 \times 10^{-21}$ seconds. approximately how many times greater is the half-life of helium-9 than that of helium-5?

2 times
7 times
9 times
11 times

Question

select the correct answer.

the half-life of helium-5 is $7.6 \times 10^{-22}$ seconds, and the half-life of helium-9 is $7 \times 10^{-21}$ seconds. approximately how many times greater is the half-life of helium-9 than that of helium-5?

2 times
7 times
9 times
11 times

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Scientific Notation Arithmetic" ], "new_concepts": [], "current_concepts": [ "Scientific Notation Arithmetic", "Ratios and Proportions" ] } ## Set up the ratio of the half-lives $$ \text{Ratio} = \frac{7 \times 10^{-21}}{7.6 \times 10^{-22}} $$ ## Perform division in scientific notation $$ \begin{aligned} \text{Ratio} &= \frac{7}{7.6} \times 10^{-21 - (-22)} \ &= \frac{7}{7.6} \times 10^1 \ &\approx 0.921 \times 10 \ &= 9.21 \end{aligned} $$ ## Round to the nearest integer option $$ 9.21 \approx 9 $$

2 times

7 times

9 times

11 times

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Scientific Notation Arithmetic" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the ratio of the half-lives

Perform division in scientific notation

Round to the nearest integer option

Answer: