Let a, b = R. Let f : [a, b] → R be an integrable function. Let g: [a, b] → R be a function which agrees with f at all points in [a, b] except for one, i.e. assume there exists a c = [a, b] such that g(x) = f(x) for all x = [a, b]\{c}. And g(c) < f(c). Prove that g is integrable on [a, b] and that fog(x)dx = So f(x)dx. Hint: Prove that g(x) - f(x) is integrable and the integral is 0.

answer part 2 frq styed please and show work 1. Because of the constantly evolving political climate around the United States, Gallup (who regularly conducts polls in the U.S.) conducted a poll just after the inauguration asking U.S. adults if they approve of the initiatives President Biden had implemented in his first few days in office. Another Gallup poll was conducted now that President Biden has been in office for a month asking U.S. adults if they approve of the initiatives President Biden had implemented after his first month in office.   According to the first Gallup poll of 1500 randomly selected U.S. adults, 64% approved of the initiatives President Biden had implemented in his first few days in office.  And according to the second Gallop poll of 1700 U.S. adults, 54% approved of the initiatives President Biden had implemented after his first month in office. Construct and interpret a 95% confidence interval for the change (difference) in the true proportion of U.S. adults…

For this exercise please refer to the downloaded Excel Workbook (See Excel Workbook Instructions) from the JB Learning website with your access code. Please upload your answers as an excel file with properly labeled answers. At the end of the chapter 5 workbook you will find Practice problems. Please answer in excel only under practice problems 5.4 questions: 1, 2, 3, 4, 5. If help is needed, tutorials are found in the workbook with relevant problems. Note: These pictures will give you an idea where it is in the workbook. You are responsible to use the workbook. #1. Total cholesterol in children aged 10­15 years is assumed to follow a normal distribution with a mean of 191 and a standard deviation of 22.4. what proportion of children 10­15 years of age hfave total cholesterol between 180­-190? What proportion of children 10-15 years would be classified as hyperlipidemia(assume that hyperlipidemia is defined as a total cholesterol level over 200)? What is the 90th percentile of total…

Please help me with these 2 questions.Help is very much appreciated!!

Please answer all parts of the question, thank you