Explain why the function is differentiable at the given point. f(x, y) = 2 + x ln(xy − 5), (2, 3) the partial derivatives are fx(x, y) = correct: your answer is correct. and fy(x, y) = correct: your answer is correct. , so fx(2, 3) = 6 correct: your answer is correct. and fy(2, 3) = 4 correct: your answer is correct. both fx and fy are continuous functions for xy > 3 incorrect: your answer is incorrect. and f is differentiable at (2, 3). find the linearization l(x, y) of f(x, y) at (2, 3). l(x, y) = incorrect: your answer is incorrect.

Bruce is getting materials for a chemistry experiment his teacher gives him a container that has 0.25 liter of liquid in it.bruce need to use 0.4 of this liquid for the experiment. how much liquid will bruce use?

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?

Overproduction of uric acid in the body can be an indication of cell breakdown. this may be an advance indication of illness such as gout, leukemia, or lymphoma.† over a period of months, an adult male patient has taken nine blood tests for uric acid. the mean concentration was x = 5.35 mg/dl. the distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.87 mg/dl. (a) find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. what is the margin of error? (round your answers to two decimal places.) lower limit upper limit margin of error (b) what conditions are necessary for your calculations? (select all that apply.) σ is unknown n is large σ is known normal distribution of uric acid uniform distribution of uric acid (c) interpret your results in the context of this problem. there is not enough information to make an interpretation. the probability that this interval contains the true average uric acid level for this patient is 0.05. the probability that this interval contains the true average uric acid level for this patient is 0.95. there is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. there is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. (d) find the sample size necessary for a 95% confidence level with maximal margin of error e = 1.10 for the mean concentration of uric acid in this patient's blood. (round your answer up to the nearest whole number.) blood tests