2.2 Use case 2: A consumer organization tested two paper shredders, the Piranha and the Crocodile, designed for home use. Each of 10 randomly selected volunteers shredded 100 sheets of paper with the Piranha, and then another sample of 10 randomly selected volunteers each shredded 100 sheets with the Crocodile. The Piranha took an average of 203 seconds to shred 100 sheets with a standard deviation of 6 seconds. The Crocodile took an average of 187 seconds to shred 100 sheets with a standard deviation of 5 seconds. Assume that the shredding times for both machines are approximately normally distributed with equal but unknown standard deviations. a. Construct a 99% confidence interval for the difference between the two population means. b. Using a 1% significance level, can you conclude that the mean time taken by the Piranha to shred 100 sheets is higher than that for the Crocodile? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.

The following MATLAB code plots the location of a building and the orbit of a satellite.  How much time, in hours, does the building have coverage from this satellite every day.   % At the initial time, the true anomaly is equal to zero,% and the Greenwich meridian points to the Aries point. % Initial conditionsomega_earth = rad2deg(7.2921151467e-5); % deg/ssemi_major_axis = 3096.7363; % kmeccentricity = 0.74;inclination = 63.4349; % degreesRAAN = -86.915798; % degreesargument_of_perigee = 270; % degreesn_points = 100; % number of pointscone_angle = 10; % degrees % Building coordinatesbuilding_latitude = 40.43094; % degreesbuilding_longitude = -86.915798; % degrees % Calculate time vector over one orbital periodorbital_period = 360 / omega_earth;time_vector = linspace(0, orbital_period, n_points); % Preallocate arrays for orbital elementstrue_anomaly = zeros(1, n_points);longitude = zeros(1, n_points);latitude = zeros(1, n_points); % Calculate orbital elements at each time stepfor i =…

7. The roots of the quadratic equation ax² + bx + c = 0, a 0 are given by the following formula: -b = √b² - 4ac 2a In this formula, the term b² - 4ac is called the discriminant. If b²-4ac0, then the equation has a single (repeated) root. If 200

Computer Science C++ please, use Monte Carlo integration to calculate the volume of a d-dimensional hypersphere of radius r = 1. (Note that for d=1, 2, and 3, the common names for d-dimensional volume are length, area, and volume, respectively.) Print out each volume and narrow the answer down to 4 digits with 99% confidence.  How far can you push d for this method?