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Medicina

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As colunas da tabela estão impressas com as notas dos estudantes na primeira prova (P1), segunda prova (P2) e com a nota final (NF), que é a média aritmética simples das notas da P1 e da P2. No entanto, por um erro de impressão, algumas notas não puderam ser visualizadas. Essas notas estão identificadas por “???” na tabela.

Estudante P1 P2 NF

Ana 8,5 9,0 8,75

Bruno 9,0 7,5 8,25

Carla 7,0 5,5 6,25

Daniel 4,5 5,0 4,75

Elaine 6,0 ??? 6,25

Fábio ??? ??? ???

Sabendo que a média aritmética simples da turma na prova P1 foi de 7,5 e que a média aritmética simples da turma na prova P2 foi 7, a nota final do estudante Fábio foi
(A) 10,00.
(B) 9,00.
(C) 9,75.
(D) 9,50.
(E) 9,25.
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Vamos resolver passo a passo. 1. Temos as notas de 5 estudantes: Ana, Bruno, Carla, Daniel, Elaine e Fábio. 2. Notas conhecidas: | Estudante | P1 | P2 | NF | |-----------|-----|-----|------| | Ana | 8,5 | 9,0 | 8,75 | | Bruno | 9,0 | 7,5 | 8,25 | | Carla | 7,0 | 5,5 | 6,25 | | Daniel | 4,5 | 5,0 | 4,75 | | Elaine | 6,0 | ??? | 6,25 | | Fábio | ??? | ??? | ??? | 3. A nota final (NF) é a média aritmética simples de P1 e P2: NF = (P1 + P2) / 2 4. Médias da turma: - Média P1 = 7,5 - Média P2 = 7,0 5. Vamos calcular a soma total das notas de P1 e P2 para os 6 estudantes: - Soma P1 = 7,5 × 6 = 45 - Soma P2 = 7,0 × 6 = 42 6. Somando as notas conhecidas de P1: Ana (8,5) + Bruno (9,0) + Carla (7,0) + Daniel (4,5) + Elaine (6,0) = 8,5 + 9,0 + 7,0 + 4,5 + 6,0 = 35 Logo, P1 de Fábio = 45 - 35 = 10 7. Somando as notas conhecidas de P2: Ana (9,0) + Bruno (7,5) + Carla (5,5) + Daniel (5,0) + Elaine (P2 desconhecido) = ? Sabemos que NF de Elaine = 6,25, então: NF = (P1 + P2) / 2 → 6,25 = (6,0 + P2) / 2 Multiplicando ambos os lados por 2: 12,5 = 6,0 + P2 → P2 = 12,5 - 6,0 = 6,5 Agora somamos as notas de P2 conhecidas: 9,0 + 7,5 + 5,5 + 5,0 + 6,5 = 33,5 Logo, P2 de Fábio = 42 - 33,5 = 8,5 8. Agora temos as notas de Fábio: P1 = 10 P2 = 8,5 9. Calculando a nota final de Fábio: NF = (10 + 8,5) / 2 = 18,5 / 2 = 9,25 Resposta correta: (E) 9,25

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