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3 years ago

If sin(1/x^2+1) is an anti derivative for f(x), then what is the limit of f(x)dx from 1 to 2?

Mathematics

1 answer:

liubo4ka [24]3 years ago

7 0

By the fundamental theorem of calculus,

$\displaystyle\int_1^2f(x)\,\mathrm dx=\sin\dfrac1{2^2+1}-\sin\dfrac1{1^2+1}$

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The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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.

Mean of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

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

By the Central Limit Theorem

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

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

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

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

3 0

3 years ago

A 16-oz bottle of water costs $1.44. What is the cost per ounce?

tia_tia [17]

Ok to get the answer you will have to divide 1.44 into 16 to see how ma cents does the ounce cost. when you do you wil get 0.09. This means that every ounce of the bottle of waters costs 0.09 cents

Hope this helped

7 0

3 years ago

Read 2 more answers

24 + 0.44x = 19 + 1.69x

lys-0071 [83]

Answer:

if it is find the value of x her it is

$24 + 0.44x = 19 + 1.69x \\ collect \: like \: terms \\ 24 - 19 = 1.69x - 0.44x \\ 5 = 1.25x \\ divide \: both \: side \: by \: 1.25 \\ \frac{5}{1.25} = \frac{1.25x}{1.25} \\ 4 = x \\ x = 4$