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Vika [28.1K]
3 years ago
10

Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 9 toothpicks for th

e project.  Mrs. Wendel knows that there is already a bag of 50 toothpicks in the class storage room. She plans to buy x additional toothpicks this afternoon to make sure her class will have enough. If her class has 30 students, which number sentence represents this situation?
Mathematics
1 answer:
Anna007 [38]3 years ago
7 0

1)  Each student must use at least 9 toothpicks for the project and her class has 30 students, so

at least 9*30 toothpicks are needed.

2)  Mrs. Wendel has already 50 toothpicks,

so she needs to buy at least (9*30 - 50).

x ≥ 9*30 - 50

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e = 2.71828 is the Euler number

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P(X = x) = \frac{e^{-6}*6^{x}}{(x)!}

b. Compute f (2).

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P(X = x) = \frac{e^{-6}*6^{x}}{(x)!}

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c. Compute f (1).

This is P(X = 1). So

P(X = x) = \frac{e^{-6}*6^{x}}{(x)!}

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So f(1) = 0.01487.

d. Compute P(x≥2)

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P(X \geq 2) = 1 - P(X < 2)

In which:

P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = \frac{e^{-6}*6^{x}}{(x)!}

P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.00248

P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.01487

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Then

P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00248 + 0.01487 + 0.04462 = 0.06197

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.06197 = 0.93803

So

P(X \geq 2) = 0.93803

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