3. A tire company claims the lifetimes of its tires average 50,000 miles. The standard deviation of lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypotheses that the mean tire lifetime is 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500. a) State the null and alternative hypotheses. Which hypothesis is true? b) It is decided to reject Ho if the sample mean is less than 49,400. Find the level and power of this test.

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Consider the continued proportionality 70 Y 9 28 x Y Identify two curves whose intersection corresponds to a solution (x, y) of this system of equations.

Michael drove from home to work at an average speed of 50 mph. His return trip home took 30 minutes longer because he could only drive at 40 mph. Find the distance from his home to his work. A. Define variables to represent the unknowns and setup the necessary equations to answer the question. B. Algebraically solve the equation you created and express your final answer using a complete sentence and appropriate units.

Find the solution(s) to each equation, or explain why there is no solution. A: x2 + 6 = 55 B: x2 + 16 = 0 C: x2 – 3.25 = 21.75

14) Solve the equation. Check for extraneous solutions: