A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function P(t) = ­16t² + 300t  a. Find the height of the projectile when t = 1 second. b. Find the height of the projectile when t = 5 seconds.  c. How long will it be until the object hits the ground?2. A board has length (3x⁴ + 6x² ­ 18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length. a. Find the length of each piece.  b. Find the area of each piece. c. Find the area of the board before it is cut. d. How is the area of each piece of the board related to the area of the board before it is cut?3. A cubic equation has zeros at -­2, 1, and 3. a. Write an equation for a polynomial function that meets the given conditions. b. Draw the graph of a polynomial function that meets the given conditions. 4. Alice was having a conversation with her friend Trina, who had a discovery to share:  Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle. a. Write an equation that models this conjecture using the variables x and y. b. Investigate this conjecture for at least three pairs of integers. Does her trick appear to work in all cases, or only in some cases? Explain. c. Use Trina’s trick to find an example of a right triangle in which all of the sides have integer length, all three sides are longer than 100 units, and the three side lengths do not have common factors. If Trina’s conjecture is true, use the equation found in part a to prove the conjecture. If it is not true, modify it so it is a true statement, and prove the new statement.

Understanding: Two pillars have been delivered for the support of a shade structure in the backyard. They are both 10 feet tall, but unfortunately the makers of the pillars did not create the same-shaped pillars. In two to three sentences, describe steps you can take to determine whether the pillars have the same volume. Design: Your client wants you to design a spherical fountain for a new garden bed. It is hard to find a manufacturer that can create perfect curved surfaces. You will need to modify the sphere to a series of cylindrical slabs with gradually decreasing radii.

SuperFun Toys Case StudyPurpose of Assignment The purpose of this assignment is for students to learn how to make managerial decisions using a case study on Normal Distribution. This case uses concepts from Weeks 1 and 2. It provides students an opportunity to perform sensitivity analysis and make a decision while providing their own rationale. This assignment also shows students that statistics is rarely used by itself. It shows tight integration of statistics with product management. Assignment Steps Resources: Microsoft Excel®, SuperFun Toys Case Study, SuperFun Toys Case Study Data Set Review the SuperFun Toys Case Study and Data Set. Develop a 1,050-word case study analysis including the following: Use the sales forecaster's prediction to describe a normal probability distribution that can be used to approximate the demand distribution.Sketch the distribution and show its mean and standard deviation. Hint: To find the standard deviation, think Empirical Rule covered in Week 1.Compute the probability of a stock-out for the order quantities suggested by members of the management team (i.e. 15,000; 18,000; 24,000; 28,000).Compute the projected profit for the order quantities suggested by the management team under three scenarios: pessimistic in which sales are 10,000 units, most likely case in which sales are 20,000 units, and optimistic in which sales are 30,000 units.One of SuperFun's managers felt the profit potential was so great the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock- outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios?Format your assignment consistent with APA format and work must also be shown in excel speadsheet10 days agoATTACHMENTS qnt561_r9_lta_superfun_toys_case_study_grading_guide_week3.doc qnt561_r9_superfun_case_study_week_3.doc qnt561_r9_superfun