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Dimas [21]
2 years ago
14

Use the babylonian method to approximate square root of 24 to the nearest hundredth.

Mathematics
1 answer:
irina [24]2 years ago
6 0
We will start with our guess of 12, since 12*2 = 24.
Divide 24 by 12; 24/12=2.  Average this answer with our guess:  (12+2)/2=7.  This is our new guess.
24/7=3.428571429.  Average this with our guess of 7:  (3.428571429+7)/2=5.214285715.  This is our new guess.
24/5.214285715=4.602739726.  Averaging with our guess:  (4.602739726+5.214285715)/2=4.90851272.  New guess!
24/4.90851272=4.889464766.  Averaging with our guess:  (4.889464766+4.90851272)/2=4.898988743.  New guess!  You can see as we go through our guesses are closer and closer to the same number...)
24/4.898988743=4.898970228.  Averaging:  (4.898970228+4.898988743)/2=4.898979486.  At this point our answer is the same every time down to the hundred-thousandth.  Our estimate to the nearest hundredth would be 4.90.
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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

Z = \frac{X - \mu}{s}

X = 205

Z = \frac{X - \mu}{s}

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

Z = \frac{X - \mu}{s}

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
Simplify (-63) ÷ (-9)
Julli [10]
Dividing two negatives equals a positive:
(-63) / (-9) = 7
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wlad13 [49]

Answer:

I think the answer is city B

Step-by-step explanation:

Hope this helps

4 0
3 years ago
Someone please help it will be much appreciated I mark brilliant
nekit [7.7K]

Answer:

A.) The graph is translated 2 units in the positive x-direction

Why?

Because it goes horizontally and vertically downwards in the opposite quadrant

4 0
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Eduardwww [97]

Answer:

-1

Step-by-step explanation:

-49-35x+x=-3x-18

-49-34x=-3x-18

-34x+3x=-18+49

-31x=31

-31x/-31=31/-31

ansx=-1

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