Solve the triangle. B = 36°, a = 41, c = 17 (5 points)

(01.02, 02.01, 06.02 MC) Peter is the owner of a hardware supply shop. He has hired you to check his machine’s calibration prior to starting production on a large order. To check this, you set the machine to create 2.0 inch nails and manufacture a random sample of 200 nails. That sample of nails has an average length of 2.024 inches with a standard deviation of 0.205 inches.Does this sample provide convincing evidence that the machine is working properly or should it be shut down for repairs?

The position of an object at time t is given by s(t) = -9 – 5t. Find the instantaneous velocity at t = 4 by finding the derivative. (5 points)

Find the derivative of f(x) = at x = -8. (6 points)

The bond that links sugar to nitrogenous base is called _________________

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 74°, a = 14 cm, c = 20 cm (5 points)

Use the given graph to determine the limit, if it exists.Find and . (7 points) 

Find an equation in standard form for the hyperbola with vertices at (0, ±4) and foci at (0, ±5). (5 points)

Two forces with magnitudes of 90 and 50 pounds act on an object at angles of 30° and 160°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. (5 points)

Find the center, vertices, and foci of the ellipse with equation 4×2 + 6y2 = 24. (5 points)