Question

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as quantidades de inscritos necessárias para cada categoria podem ser escritas pelas expressões listadas abaixo.

expressões:
\\(a = 1\text{ milhão}\\)
\\(b = 10^8\\)
\\(c = \frac{10^9}{10^2}\\)
\\(d = \sqrt{10^{10}}\\)

associe cada categoria à expressão numérica que representa a quantidade.

prata: \\(100\\ 000 =\\)
ouro: \\(1\\ 000\\ 000 =\\)
diamante: \\(10\\ 000\\ 000 =\\)
diamante vermelho: \\(100\\ 000\\ 000 =\\)

Explanation:

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<reasoning>

简化给定的数学表达式

计算每个字母代表的数值大小。

• \(A = 1\text{ milhão} = 1,000,000 = 10^6\)
• \(B = 10^8 = 100,000,000\)
• \(C = \frac{10^9}{10^2} = 10^{9-2} = 10^7 = 10,000,000\)
• \(D = \sqrt{10^{10}} = (10^{10})^{\frac{1}{2}} = 10^5 = 100,000\)

匹配类别与对应的表达式

将计算出的数值与题目中的类别数量进行一一对应。

• Prata: \(100,000 = 10^5\)，对应表达式为 D。
• Ouro: \(1,000,000 = 10^6\)，对应表达式为 A。
• Diamante: \(10,000,000 = 10^7\)，对应表达式为 C。
• Diamante Vermelho: \(100,000,000 = 10^8\)，对应表达式为 B。

</reasoning>

<answer>
将每个类别与代表其数量的数值表达式进行匹配：

• Prata: 100 000 = <blank>D</blank>
• Ouro: 1 000 000 = <blank>A</blank>
• Diamante: 10 000 000 = <blank>C</blank>
• Diamante Vermelho: 100 000 000 = <blank>B</blank>

</answer>

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Answer:

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<reasoning>

简化给定的数学表达式

计算每个字母代表的数值大小。

• \(A = 1\text{ milhão} = 1,000,000 = 10^6\)
• \(B = 10^8 = 100,000,000\)
• \(C = \frac{10^9}{10^2} = 10^{9-2} = 10^7 = 10,000,000\)
• \(D = \sqrt{10^{10}} = (10^{10})^{\frac{1}{2}} = 10^5 = 100,000\)

匹配类别与对应的表达式

将计算出的数值与题目中的类别数量进行一一对应。

• Prata: \(100,000 = 10^5\)，对应表达式为 D。
• Ouro: \(1,000,000 = 10^6\)，对应表达式为 A。
• Diamante: \(10,000,000 = 10^7\)，对应表达式为 C。
• Diamante Vermelho: \(100,000,000 = 10^8\)，对应表达式为 B。

</reasoning>

<answer>
将每个类别与代表其数量的数值表达式进行匹配：

• Prata: 100 000 = <blank>D</blank>
• Ouro: 1 000 000 = <blank>A</blank>
• Diamante: 10 000 000 = <blank>C</blank>
• Diamante Vermelho: 100 000 000 = <blank>B</blank>

</answer>

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