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2 years ago

There is a bell at the top of a tower that is 45m high. The bell weighs 190 kg. How much potential energy does the bell have?

Mathematics

1 answer:

Slav-nsk [51]2 years ago

7 0

Answer:

83.79 kJ

Step-by-step explanation:

The potential energy is the product of weight and height, where weight is in newtons.

PE = Mgh = (190 kg)(9.8 m/s^2)(45 m) = 83,790 J

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Which three-dimensional figure has half the number of vertices as the rectangular prism?

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Answer:

1. The rectangular prism is a right prism with rectangular bases (check the picture)

2. It has 8 vertices, so we are looking for 3d figures with 4 vertices.

3. A face can have at least 3 vertices, and the 4th must be outside of the plane determined by the first 3 vertices. This makes 4 vertices in total.

4. The 3d figure described in step 3 is a pyramid.

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The weights of certain machine components are normally distributed with a mean of 8.01 g and a standard deviation of 0.06 g. Fin

Free_Kalibri [48]

Answer:

Option D) 7.90 g and 8.12 g

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 8.01 g

Standard Deviation, σ = 0.06 g

We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.03

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 8.01}{0.06})=0.03$

$= 1 -P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.03$

$=P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.97$

Calculation the value from standard normal z table, we have,

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$P( X < x) = P( z < \displaystyle\frac{x - 8.01}{0.06})=0.03$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 8.01}{0.06} = -1.881\\\\x = 7.90$

Thus, 7.90 separates the bottom 3% of the weights.

Thus, the correct answer is

Option D) 7.90 g and 8.12 g

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2 years ago

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