Researchers are trying to determine the proportion of people…

Researchers are trying to determine the proportion of people who get hip replacements that go on to have a full recovery. Out of a sample of 300 individuals, 102 made a full recovery. a)  Construct and interpret a 95% confidence interval for the proportion of patients that made a full recovery.   b)  Previous estimates of patients who recovered fully from the surgery sit at a proportion of 0.5. Has the population proportion changed? Please explain.   Only show final answers below BUT show ALL work on the page you scan and submit at the end of this exam.

Gauss’s law: The cube of insulating material shown in the fi…

Gauss’s law: The cube of insulating material shown in the figure has one corner at the origin. Each side of the cube has length 0.080 m so the top face of the cube is parallel to the xz-plane and is at y = 0.080 m. It is observed that there is an electric field = (3280 N/C ∙ m)y that is in the +y direction and whose magnitude depends only on y. Use Gauss’s law to calculate the net charge enclosed by the cube. (ε0 = 8.85 × 10-12 C2/N ∙ m2) 1.

Spheres of charge: Two concentric spheres are shown in the f…

Spheres of charge: Two concentric spheres are shown in the figure. The inner sphere is a solid nonconductor and carries a charge of +5.00 µC uniformly distributed over its outer surface. The outer sphere is a conducting shell that carries a net charge of -8.00 µC. No other charges are present. The radii shown in the figure have the values R1 = 10.0 cm, R2 = 20.0 cm, and R3 = 30.0 cm. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)(a) Find the total excess charge on the inner and outer surfaces of the conducting sphere.(b) Find the magnitude and direction of the electric field at the following distances r from the center of the inner sphere: (i) r = 9.5 cm, (ii) r = 15.0 cm, (iii) r = 27.0 cm, (iv) r = 35.0 cm.