Question A 12-ft-tall fence runs parallel to a wall of a house at a distance of 30 ft. Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house and the horizontal ground have infinite extent. The length of the shortest ladder is ft. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)

Suppose that f : R → R is differentiable at c and that f(c) = 0. Show that g(x) = If(x)I is differentiable at c if and only if f’(c) = 0 (Real Analysis)

please fill in the blanks. Module 6 Problem Set eBook Show Me How Dividends Per Share 1. BE.12.08.ALGO 2. BE.11.07 Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 80,000 shares of cumulative preferred 3% stock, $20 par and 410,000 shares of $25 par common. 3. BE.12.03.ALGO During its first four years of operations, the following amounts were distributed as dividends: first year, $33,000; second year, $72,000; third year, $90,000; fourth year, $100,000. 4. BE.12.01.ALGO Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00". 5. BE.12.07 1st Year 2nd Year 3rd Year 4th Year 6. EX.12.01.ALGO Preferred stock (dividends per share) 0.41 х х Х 7. BE.12.06.ALGO Common stock (dividends per share) 8. EX.11.01 Feedback

(1 point) Determine the average rate of change of the following function between the given values of the variable: f(x) = x4 - - X; x = -2, x = 3 Average rate of change = .

Question Suppose three point masses are placed in the xy-plane as follows (assume coordinates are given in meters): mi = 5 kg, placed at (-2, -3) m2 = 3 kg, placed at (2,3) 'm3 = 2 kg, placed at (-3, -2) Find the center of mass of the system. Write your answer as an ordered pair Provide your answer below:

let f(x)= x^2-5, g(x)= 2x^3+x and p(x)= f(x)g(x). a) computedp/dx b) compute f'(x)g'(x)

Suppose that a company is developing a new touch-screen cell phone. Historically, 70% of their new phones have resulted in high consumer demand, whereas 30% have resulted in low consumer demand. The company has the decision of choosing between two models with different features that require different amount of investment and have different sales potential. Estimated profit/loss are shown in the payoff table below. State of Nature High demand, ($) Low demand, ($) Model 1 300,000 -40,000 Model 2 275,000 -15000 Now suppose the firm conducts a market research study to obtain sample information and better understand the nature of consumer demand. The market research cost $10,000 Analysis of past market research studies, conducted prior to introducing similar products, has found that the survey response will be either high or low. There is a 69% chance that the survey will return a high survey response (results) and there is a 31% chance that the survey will result in lo-demand response (results). The relevant conditional probabilities are as follows: P (high consumer demand, high survey response = 0.913) P (low consumer demand, low survey response = 0.087) P (high consumer demand, high survey response = 0.226) P (low consumer demand, low survey response = 0.774) Calculate the expected value of sample information (EVSI). Develop a decision tree and analyze using QM for Windows. Determine the optimal solution.