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Reika [66]
3 years ago
6

Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the

Mathematics
2 answers:
Simora [160]3 years ago
8 0
I’m not sure but I think it might be C so sorry if it’s wrong
Colt1911 [192]3 years ago
3 0

Answer:

<em>The stone covers 36 m in the 5th second. Correct choice: A.</em>

Step-by-step explanation:

<u>Proportions</u>

Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:

y=k.x

There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:

y=k.x^2

According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;

d=k.t^2

To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:

64=k.4^2=16k

Solving:

k=64/16=4

Substitute the value of k into the equation to get the complete model.

d=4.t^2

Now we calculate the distance when t=5 seconds:

d=4\cdot 5^2=4\cdot 25=100

The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.

Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:

distance in the 5th second = 100 m - 64 m = 36 m

The stone covers 36 m in the 5th second. Option A.

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Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increas
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Answer:

a) The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

Step-by-step explanation:

a) Develop a 90% confidence interval estimate of the population mean monthly rent.

Our sample size is 120.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

df = 120-1 = 119

Then, we need to subtract one by the confidence level \alpha and divide by 2. So:

\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 119 and 0.05 in the t-distribution table, we have T = 1.6578.

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

s = \frac{650}{\sqrt{120}} = 59.34

Now, we multiply T and s

M = T*s = 59.34*1.6578 = 98.37

The lower end of the interval is the mean subtracted by M. So it is 3486 - 98.37 = $3387.63.

The upper end of the interval is the mean added to M. So it is 3486 + 98.37 = $3584.37.

The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) Develop a 95% confidence interval estimate of the population mean monthly rent.

Now we have that \alpha = 0.95

So

\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025

With 119 and 0.025 in the t-distribution table, we have T = 1.9801.

M = T*s = 59.34*1.9801 = 117.50

The lower end of the interval is the mean subtracted by M. So it is 3486 - 117.50 = $3368.5.

The upper end of the interval is the mean added to M. So it is 3486 + 117.50 = $3603.5.

The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) Develop a 99% confidence interval estimate of the population mean monthly rent.

Now we have that \alpha = 0.99

So

\frac{1-0.95}{2} = \frac{0.05}{2} = 0.005

With 119 and 0.025 in the t-distribution table, we have T = 2.6178.

M = T*s = 59.34*2.6178 = 155.34

The lower end of the interval is the mean subtracted by M. So it is 3486 - 155.34 = $3330.66.

The upper end of the interval is the mean added to M. So it is 3486 + 155.34 = $3641.34.

The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

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Step-by-step explanation:

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