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Fed [463]
3 years ago
7

The surface of a spherical conductor of radius a is kept at a temperature of u(φ)=300K+50K cos(φ). The temperature inside is gov

erned by the Laplace equation. Find an expression for the temperature everywhere inside the sphere. Evaluate the temperature at the center of the sphere.
Mathematics
1 answer:
Sergio039 [100]3 years ago
6 0
The surface of a spherical conductor of radius a is kept at a temperature of u(φ)=300K+50K cos(φ). The temperature inside is governed by the Laplace equation. Find an expression for the temperature everywhere inside the sphere. Evaluate the temperature at the center of the sphere.
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The composite scores of individual students on the ACT college entrance examination in 2009 followed a normal distribution with
Mumz [18]

Answer:

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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 problem, we have that:

\mu = 21.1, \sigma = 5.1

What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher?

This is the pvalue of Z when X = 23.

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

Z = \frac{23 - 21.1}{5.1}

Z = 0.37

Z = 0.37 has a pvalue of 0.6443

1 - 0.6443 = 0.3557

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher?

Now we use the central limit theorem, so n = 50, s = \frac{5.1}{\sqrt{50}} = 0.72

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

Z = \frac{23 - 21.1}{0.72}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

1 - 0.9959 = 0.0041

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

Why is it more likely that a single student would score this high instead of the sample of students?

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

5 0
3 years ago
What is the angle of rotation from / to /? Assume that the center of rotation is the origin. A. 90° counterclockwise B. 180° cou
luda_lava [24]
D.360 Countercloscwise
8 0
3 years ago
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Use given graph to determine the limit, if it exists. Find lim f(x) -2 and lim f(x) 2+ WILL GIVE BRAINLIEST
Gelneren [198K]

Answer:

it does not exist my friend

7 0
3 years ago
Tamiko got a check for 109.60 and a small bonus check for 34.15.What is the net result of her transactions using the result from
lara31 [8.8K]

a) Net result of Tamiko's transactions = $143.75

b) Total amount she can save = $86.25

Step-by-step explanation:

Step 1 :

Given,

Amount Tamiko got in her first check =  $109.60

Amount of the bonus check = $34.15

Fraction of the amount she wants to save = \frac{3}{5}

We need to find the net results of her transactions and the amount she will save

Step 2 :

The new result of her transactions can be computed by adding the amount she has received through both the check.

Total amount she received  = 109.60 + 34.15 = 143.75

Total amount she can save =   \frac{3}{5} × 143.75 = 86.25

Step 3 :

Answer :

a) Net result of Tamiko's transactions = $143.75

b) Total amount she can save = $86.25

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3 years ago
-6/5k=12 what is k? please explain
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Answer:.......

Step-by-step explanation:

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