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Ivan
3 years ago
11

A 12 N package of flour is suddenly placed on the pan of a grocer's scale. The pan is supported from below by a vertical spring

with a force constant of 325 N/m. If the pan has negligible weight and no energy is dissipated by friction, find the maximum distance the spring will be compressed.
Mathematics
1 answer:
Licemer1 [7]3 years ago
4 0

Answer:

  24/325 m ≈ 7.38 cm

Step-by-step explanation:

The equilibrium position of the package is the distance at which the package weight is balanced by the spring force. That distance is ...

  (12 N)/(325 N/m) = 12/325 m

Since the package is placed suddenly on the pan and there are no losses in the system, the position of the package will oscillate about this distance with an amplitude equal to this distance. That is, the maximum compression will be to a distance that is twice this amount, or ...

  24/325 m

__

This is the depth at which all of the potential energy of the package due to its height is transformed into the potential energy of the spring due to its compression.

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Answer:

Step-by-step explanation:

Hello!

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X₂: Number of cases of polio observed in kids that received the experimental vaccine.

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These two variables have a binomial distribution. The parameters of interest, the ones to compare, are the population proportions: p₁ vs p₂

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H₁: p₂ ≠ p₁

α: 0.05

Z= \frac{(p'_2-p'_1)-(p_2-p_1)}{\sqrt{p'[\frac{1}{n_1} +\frac{1}{n_2} ]} }

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This test is two-tailed, using the critical value approach, you have to determine two critical values:

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b)

H₀: p₂ = p₁

H₁: p₂ ≠ p₁

α: 0.01

Z= \frac{(p'_2-p'_1)-(p_2-p_1)}{\sqrt{p'[\frac{1}{n_1} +\frac{1}{n_2} ]} }

The value of Z_{H_0}= -4.76 doesn't change, since we are working with the same samples.

The only thing that changes alongside with the level of significance is the rejection region:

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c)

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Rejecting the null hypothesis using different values of α means that there is a high chance that you reached a correct decision (rejecting a false null hypothesis)

I hope this helps!

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