A gas mixture containing 85.0 mole% N2 and the balance n-hexane flows through a pipe at a rate of 100.0 m3/h. The pressure is 2.

Answer:

  M_o = 18.84 N*m clockwise.  

Explanation:

Given:

- Force F = 120 N

- Length b = 610 mm

- Height h = 330 mm

Required:

Calculate the moment M_o at the origin and its direction:

Solution:

- The force is divided into components F_x and F_y along the base b and height h, respectively:

                    F_x = F*cos(Q)

                    F_x = F*(h / sqrt(h² + b²))

                    F_x = 120*(330 / sqrt(330² + 610²))

                    F_x = 57.098 N

- The F_y component can be excluded as it passes through the origin, resulting in zero moment.

- The moment at point O is calculated as:

                     M_o = F_x * h

                     M_o = 57.098*.33

                    M_o = 18.84 N*m clockwise.  

Answer:

The response is presented below

Explanation:

Central Limit Theorem: The CLT is a statistical principle asserting that if a sample size is sufficiently large and shows minimal variation from the population, the average of all samples will approximate the mean of that population. Furthermore, all distributions can be modeled as nearly normal.

This principle is illustrated by the central limit theorem. Specifically, if we gather independent random samples of size n from any kind of population, a large n will yield a sample distribution that aligns with a normal distribution pattern.

mean of the sample means

                    .............1

while the standard deviation of the sample means is

                      .........2

and This theory has findings applicable elsewhere in statistical studies. Although it may initially seem theoretical and lacking real-world utility, the Central Limit Theorem is crucial for applying statistics effectively in practice.