Question Consider the differential equation dy dx = x? (y – 1). Sketch a slope field for the given differential equation on your paper for the domain (-3, 3] and the range (-3, 3). Part A: List five coordinates and the corresponding slope of their segments. (5 points) Part B: Using the slope field that you drew, describe all points in the xy-plane for which the slopes are negative. (5 points)

What evidence supports the conclusion that the SLC24A5 gene contributes to the production of melanin in humans in the same way it does in fish? Select all that apply. Hint: Review the section of the paper entitled “Conservation of golden gene structure and function in vertebrate evolution.” A)Injection of golden zebrafish larva with human SLC24A5 messenger RNA (mRNA) restores the fish’s ability to make melanin. B.)The slc24a5 protein produced by the gene in the zebrafish is 68 – 69% similar to the SLC24A5 protein in humans. C)At least 93% of East Asians share the same G allele of the SLC24A5 gene with Africans, yet East Asians are usually light skinned. D)The zebrafish slc24a5 gene and the human SLC24A5 gene are both expressed at high levels in skin and eyes.

(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.

2.31 Let R be the region bounded above by the graph of the function f(x) = ?? and below by the x-axis over the interval (0,2] . Find the centroid of the region. 2.32 Let R be the region bounded above by the graph of the function f(x) = 6 - 2² and below by the graph of the function g(x) = 3 - 2x. Find the centroid of the region. 2.33 Let R be the region bounded above by the graph of the function f(x) = 1-2 and below by r -axis. Find the centroid of the region.