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A physical therapist is evaluating a direct access patient with that complains of lumbopelvic pain.  The patient is a 60 y/o male that points to the lower abdominal and sacrum regions when asked where the pain is located.  He reports that he cannot recall a specific incident where he may have injured his back.  He does report a history of back pain 5 years ago following shoveling snow after a heavy storm, but it resolved in about 2 weeks with rest and Advil.  He reports a past medical history of diabetes mellitus, lung cancer 8 years ago successfully treated with chemotherapy, and a left knee replacement 2 years ago.  Which of the following is the MOST appropriate examination procedure to initially incorporate?  

Compute the upper limit of the 95% confidence intervals for the inventory of a series of [CC] replications of the simulation of a system, where the average inventory is [AA] units and the SAMPLE standard deviation is [BB]

Using the graph above, state:  a) Domain of the graph b) Range of the graph c) List any relative maximums or minimums of the function.  d) State the intervals in which the function is increasing, decreasing or constant. 

Factor f (x) = 6×3 + 31×2 – 29x + 6 as a product of linear factors given that -6 is a zero.

Use the graph of y = 3x to graph the function f (x) = 3x + 5 + 2 on your submission paper.  Also, state the domain and range in interval notation.

Explain why a polynomial with real coefficients of degree 8 could have no real zeros. 

Explain why a polynomial with real coefficients of degree 5 must have at least one real zero. 

Given , find

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary.

Graph the function on your submission paper. State the domain and range.  g(x) = – (x – 1)2 + 2