Mathematics, 12.03.2021 18:50 jazmine8194

Mario the marriage celebrant is interested in investigating the average age at which people who attended university get married. A sample of 55 individuals who attended university and have been married once has been randomly selected and the age at which each person married was recorded. The sample mean age of marriage was calculated as 31 years old. It is known that the population standard deviation of age of marriage for all people is equal to 11 years. It is assumed that this standard deviation will also apply specifically to the age of marriage for people who attended university. Calculate the upper and lower bounds of the 95% confidence interval for the mean age of marriage for people who attended university. Give your answers in years to 2 decimal places.

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The upper bound of the 95% confidence interval for the mean age of marriage for people who attended university is 33.91 years.

The lower bound of the 95% confidence interval for the mean age of marriage for people who attended university is 28.09 years.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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 - 0.025 = 0.975 , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{11}{\sqrt{55}} = 2.91$

The lower end of the interval is the sample mean subtracted by M. So it is 31 - 2.91 = 28.09 years

The upper end of the interval is the sample mean added to M. So it is 31 + 2.91 = 33.91 years.

The upper bound of the 95% confidence interval for the mean age of marriage for people who attended university is 33.91 years.

The lower bound of the 95% confidence interval for the mean age of marriage for people who attended university is 28.09 years.

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation:

Answer from: Quest

the simplified form is

$\frac{x^2(2x+3)}{2(4x-3)}$

step-by-step explanation:

we want to simplify the expression,

$\frac{\frac{6x+9}{15x^2} }{\frac{16x-12}{10x^4} }$

let us change the middle bar to a normal division sign to obtain,

$\frac{6x+9}{15x^2}\div\frac{16x-12}{10x^4}$

we multiply the first fraction by the reciprocal of the second fraction to obtain,

$\frac{6x+9}{15x^2}\times \frac{10x^4}{16x-12}$

we factor to obtain,

$\frac{3(2x+3)}{3\times5\times x^2}\times \frac{2\times5\times x^2\times x^2}{4(4x-3)}$

we cancel the common factors to get,

$\frac{(2x+3)}{1}\times \frac{ x^2}{2(4x-3)}$

we simplify to get,

$\frac{x^2(2x+3)}{2(4x-3)}$

the correct answer is b

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