The average price for an oil change is 35$ . In random sample of 20 oil changes, find the probability that the mean cost exceeds 42$ given that the population standard deviation is 87$. Please draw everything out so I can understand

1. Now suppose that a new technology were created that lowers the costs of production, graphically illustrate and explain the changes that arise in the short-run and long-run within a perfectly competitive industry.

Please show all the work with the steps, please.

On Matlab use BFGS Method to find the minimum of the following function: f(x) = x₁³ - 2x₂x₁² + x₁² - x₁using initial point (x₀, y₀) = (1, 2)^T to start, and stop when f changes less than 0.0001

In short answer format, use no more than 100 to 150 words to answer the following questions:

3. Why have the changes made during the Civil Rights Movement of the 1950s and 1960s not eliminated the income and educational gaps between groups?

Provide an example of

What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula. .

What are the key leadership skills a manager should have?

Choose a CEO that you perceive as being a leader. Describe his leadership style and how it is impacting the success of his company.

What are the drivers of globalization? Describe the major changes for businesses.

When using r programming or statistical software:

(A) From the summary, which variables seem useful for predicting changes in independent variable?

(B) For the purpose of variable selection, does the ANOVA table provide any useful information not already in the summary?

Compare  the short run and long run for perfectly competitive firms. How do perfectly competitive firms adapt to market changes in the short run? What can perfectly competitive firms expect in the long run in terms of profits?