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1 year ago

14

He slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFractio

n
The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.

1 answer:

Kryger [21]1 year ago

8 0

Answer:

-1

Step-by-step explanation:

The product of these slopes is -1 ... when dealing with perpendicularity

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2 years ago

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

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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

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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.

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1 year ago

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Answer: The correct option is A, itis the product of the initial population and the growth factor after h hours.

Explanation:

From the given information,

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Increasing rate or growth rate = 30% every hour.

No of population increase in every hour is,

$1000\times \frac{30}{100} =1000\times 0.3$

Total population after h hours is,

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It is in the form of,

$P(t)=P_0(t)(1+r)^t$

Where $P_0(t)$ is the initial population, r is increasing rate, t is time and [tex(1+r)^t[/tex] is the growth factor after time t.

In the above equation 1000 is the initial population and $(1+0.3)^h$ is the growth factor after h hours. So the equation is product of of the initial population and the growth factor after h hours.

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1 year ago

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Explain and discuss why engineers usually want the minimum variance unbiased estimator achieved by using the MVUE in making engi

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Answer:

Since the name indicates Minimum Variance Unbiased Estimator-first of all it is a parameter estimator. Secondly, it is an unbiased estimator so that the sample is carried out randomly. I.e. whenever a sample is chosen, there is no personal bias.

Then we can consider more than one sample-based unbiased estimator but sometimes they can vary in variation. But we have always intended to select an estimator that has minimal variance.

Therefore if the unbiased estimator has minimal variation between all unbiased class estimators then it is known as a good estimator.

The advantage of MVUE is that it is impartial and has a minimal variance of all unbiased estimators amongst the groups.

At times we get an estimator such as MLE which is not unbiased because the sample can be personally biased. Now let us assume an instructor needs to find the lowest marks in a physics class. Presume an instructor picks a sample and interprets the lowest possible marks.

Again the mistake could be that the instructor may choose his favorite sample learners because the sample might not be selected randomly. Therefore it is important to select an unbiased estimate with a minimum variance.

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To solve this we are going to use the simple interest formula: $A=P(a+rt)$
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2 years ago

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