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allsm [11]
3 years ago
12

8. H={all numbers of the form 3n+1, for n a natural number} under multiplication?

Mathematics
1 answer:
poizon [28]3 years ago
8 0

Answer and Step-by-step explanation:

H= {all numbers of the form 3n+1, for n natural number} under multiplication:

Sol: all number of the form 3n+1, for n natural number so, put n=2, 3(2) +1 = 7, which is a natural number. A natural number under multiplication does not form a group because its inverse does not exist.

J= {all number of the form 3n+2, for n natural number} under multiplication:

Sol: all the number of the form 3n+2, n is the natural number does not form a group under multiplication because the identity element does not form in this set, and inverse does not exist.

K= {perfect squares of integers} under addition:

Sol: perfect square of integers under addition does not form a group because the inverse does not exist. For example, for any element x, inverse (-x) does not exist because of a square integer.

L= {perfect squares of integers} under multiplication:

Sol: a set of the perfect square of integers under multiplication is not a set, because it does not have the inverse property

M= {all numbers of the form 2, for n natural number} under addition:

Sol: natural number in the form of 2n, n is a natural number under addition is not a group as it does not have identity property. Identity property, under addition, is zero.

N= {all number of the form 2n, n is natural number} under multiplication:

All number of the form 2n, n is the natural number under multiplication is not a group. Because its inverse does not exist. For example, an element x belongs to a natural number; its inverse (1/x) does not exist in this set.

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A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca
blondinia [14]

The confidence interval for mean of the "before-after" differences is \fbox{(-0.4037,1.8037)}

Further explanation:

Find the difference between the before pain and the after pain.

Difference = before-after

Kindly refer to the Table for the difference of between the before and after pain.

Sum of difference = 5.6

Total number of observation = 8

Mean of difference = 0.7

Sample standard deviation s = 1.3201

Level of significance = 5\%

Formula for confidence interval = \left( \bar{X} \pm t_{n-1, \frac{\alpha}{2}\%} \frac{s}{\sqrt{n}} \right)

confidence interval = \left( 0.7 \pm t_{8-1, \frac{5}{2}\%} \frac{1.3201}{\sqrt{8}} \right)

confidence interval = \left( 0.7 \pm t_{7, \frac{5}{2}\%} \frac{1.3201}{\sqrt{8}} \right)

From the t-table.

The value of t_{7, \frac{5}{2}\%=2.365

Confidence interval = ( 0.7 \pm 2.365}\times \frac{1.3201}{\sqrt{8}}) \right)

Confidence interval = \left( 0.7 - 2.365}\times \0.4667,0.7 + 2.365}\times \0.4667) \right

Confidence interval = (0.7-1.1037,0.7+1.1037)

Confidence interval = \fbox{(-0.4037,1.8037)}

The 95\% confidence interval tells us about that 95\% chances of the true mean or population mean lies in the interval.

Yes, the hypnotism appear to be effective in reducing pain as confidence interval include includes the positive deviation from the mean.

Learn More:

1. Learn more about equation of circle brainly.com/question/1506955

2. Learn more about line segments brainly.com/question/909890  

Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Confidence Interval

Keywords:

Probability, Statistics, Speed dating, Females rating, Confidence interval, t-test, Level of significance , Normal distribution, Central Limit Theorem, t-table, Population mean, Sample mean, Standard deviation, Symmetric, Variance.

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