Please Put in Word Document.1.Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x(1/3) + 3x(4/3). You must justify your answer using an analysis of f '(x) and f "(x). (10 points)2.What is the maximum volume in cubic inches of an open box to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give one decimal place in your final answer. (10 points)3.The position function of a particle in rectilinear motion is given by s(t) = t3 - 12t2 + 45t + 4 for t ≥ 0 with t measured in seconds and s(t) measured in feet. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer. (10 points)4.A circle is growing so that the radius is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the instant the radius is 12 cm? Include units in your answer. (10 points)5.The side of a square is measured to be 12 ft with a possible error of ±0.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your answer. (10 points)

What are some ways that you can think of to apply probability theory in business or even in one’s personal life? For example, if you were playing a game of poker with your friends, it would be helpful to know how the probability for winning a hand with a pair of aces in your hand is different than if you were holding a two of clubs and nine of hearts. When investing your money, you might need to choose between an investment that has a 95% chance to earn 3% or one that has a 65% chance to earn 30%. Business owners and managers make numerous decisions throughout the life of the business that are based on the probability of an event happening, consumer tastes changing or remaining the same, a production goal being met on time, and so on.In this Assignment, you will respond to a set of questions that focus on probability theory, including how the concept informs decision making and can be used by organizations.To prepare for this Assignment: Review this week’s Learning Resources.Refer to the Academic Writing Expectations for 2000/3000-Level Courses as you compose your Assignment.By Day 7Submit your responses to the following prompts.A midsized company recently divided all employees into four divisions. Division 1 makes up 43% of the company, Division 2 makes up 40%, Division 3 makes up 12%, and Division 4 makes up 5%. Choose one employee at random. Find the probability for each of the following statements. (75 words, or 1 paragraph)The employee belongs to Division 1.The employee belongs to either Division 2 or Division 3.The employee does not belong to Division 1 or Division 2.Jasmine Robbins wants to open an independent coffee shop in a town that already has 9 coffee shops: 3 Mocha Moose, 2 Elkhorn Coffee, and 4 Morning JoJo. She is trying to determine the probability of choices that potential customers may make. Here is one of her questions: If a person selects one shop at random to purchase coffee, find the probability that it is either a Mocha Moose or a Morning JoJo. Explain your answer. (75 words, or 1 paragraph)The following chart shows the number of customer complaints from three regions of an organization for two separate years. 20182017Northeast region6,4933,401Southeast region7322,513Central region3,7061,082Find the probability for each question. (75 words, or 1 paragraph)What is the probability that a complaint was from the Southeast region, given it was in 2017?What is the probability that a complaint was from the Central region, given it was in 2018?What is the probability that a given complaint did not occur in 2018 and was not from the Southeast region?What is the probability that two complaints chosen at random were both from the Northeast region? A management consulting team needs a team of four to analyze the operations of a new client. The team should comprise an accountant, a production specialist, a finance specialist, and a management specialist. On its staff, the consulting firm has available six accountants, five production specialists, three finance specialists, and eight management specialists. How many different teams could be formed from the available individuals? (75 words, or 1 paragraph)In a batch of 20 television picture tubes, 5 are known to be defective. What is the probability that a random sample of 5 (without replacement) will result in each of the following? (75 words, or 1 paragraph)Exactly 1 defectiveNo defectivesTwo or fewer defectivesThe board of directors for a particular company consists of 10 members, 6 of whom are loyal to the current company president and 4 of whom want to fire the president. Suppose the chair of the board (who is a loyal supporter of the current president) suggests to randomly select 4 other board members to serve on a committee to decide the president’s fate. Find the probability for the first 3 questions and explain your answer for the fourth question. (75–150 words, or 1–2 paragraphs)What is the probability that all 5 committee members will vote to keep the president in place, if no one changes their minds? What is the probability that a majority of the committee will vote to keep the president in place, if no one changes their minds? What is the probability that the vote is 4 to 1 to replace the president, if no one changes their minds? Imagine that you were the president of the company and you hoped to keep your position. Considering the various probabilities, would you consider the chair of the board’s suggestion to be in your favor or not? If the choice was yours, would you allow the suggestion to proceed? Dave has just left an interview with a prospective employer. The hiring manager told Dave that she will tolerate one mistake during his first year but will fire him if he makes two mistakes. Based on Dave’s research and understanding of the job, he estimates that he will have to make five critical decisions during the year, and with his knowledge of the processes, figures that he will have about an 80% chance of making any of those five decisions correctly. Dave does not want to run any more than a 25% chance of being fired. If each of the decisions is independent of the others, should Dave risk taking the job if offered? Explain why or why not. (75 words, or 1 paragraph)