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bija089 [108]
3 years ago
10

H varies directly to the cube of c. When H = 40, C = 2. (a) Express H in terms of c.

Mathematics
1 answer:
Alecsey [184]3 years ago
4 0

Answer:

H in terms of c is H = 5c³.

Step-by-step explanation:

Given that:

H = 40 and c = 2

H varies directly to the cube of c.

Which means that,

H ∝ c³

Let,

k be the proportionality constant.

H = kc³

Putting H=40 and c=2

40=k(2)^3\\40=k(8)\\40=8k\\8k=40

Dividing both sides by 8,

\frac{8k}{8}=\frac{40}{8}\\k=5

Now,

H in terms of c.

H = 5c³

Hence,

H in terms of c is H = 5c³.

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Assume that a computer was used to generate the given confidence interval for the population mean. Find the sample mean or margi
stealth61 [152]

Answer:

The sample mean is

b.3.55

The margin of error is

0.32

Step-by-step explanation:

Deep explanation about a confidence interval

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

\alpha = \frac{1-0.9}{2} = 0.05

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

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find 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 = 1.645*215 = 353.675

The lower end of the interval is the mean subtracted by M. So it is 6.4 - 0.3944 = 6.01 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 6.74 hours.

In this problem:

The deep explanation is not that important.

We just have to recognize that the interval has a lower end and an upper end. The distance from both the upper and the lower end to the mean is M. This means that the sample mean is the halfway point between the lower end and the upper end.

The margin of error is the distance of these two points(lower and upper end) to the mean.

In our interval

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Upper end: 3.87

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So the correct answer is:

b.3.55

The margin of error is

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3 years ago
A rectangle has a length of 0.4m and a width of 5cm less than its length.what is the perimeter of the rectangle
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Answer:

150cm

Step-by-step explanation:

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