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2 years ago

How many ball bearings, each with a diameter of 1 cm, can be made using 5.24 cm3 of molten steel? A) 4. B) 7. C) 8. D) 10

1 answer:

4 0

First, solve for the volume of the ball bearings by the equation,
V = πd³ / 6
Substituting the value of diameter given,
V = π(1 cm)³ / 6 = π/6 cm³ = 0.5236 cm³
Divide the amount of material given by this volume,
n = 5.24 cm³ / 0.5236 cm³ = 10
Therefore, there are 10 ball bearings that may be formed.

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A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

7 0

2 years ago

Which of these are duties of the SEC? Check all that apply.

DaniilM [7]

overseeing the actions of brokers and financial advisers
 ensuring the security and fairness of mutual funds and exchanges
bringing suits against businesses that are not following securities laws

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3 years ago

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Round 7097284 to a tenth of a million

kondor19780726 [428]

The nearest tenth of a million for the number 7,097,284 is 7.1 million. Hope I hlped!

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2 years ago

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Sara works for a hair salon and receives tips from her customers. The weekly tips

Monica [59]

Answer:

mean: 107.86

median: 100

range: 140

mode: 100

Step-by-step explanation:

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2 years ago

Which of the following could be the equation of the graph shown below? Check all that apply.

Mashutka [201]

Answer:

y = -2x + 5

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y = 5

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2 years ago