Acohort study of breast cancer among elderly women followed 1,400 women (65–79 years of age) with no evidence of breast cancer at baseline over several years. follow-up visits occurred every two years at which time, investigators screened all women for breast cancer. the results were as follows: 12 new cases at the first follow-up visit, 11 new cases at the second follow-up visit, 23 new cases at the third follow-up visit, and 28 new cases at the fourth (final) follow-up visit. the investigators also noted that 35 of the women had withdrawn from the study after the third evaluation (these women were present for visits 1 - 3 but missed the 4th visit). based on this information, calculate and interpret the incidence density (per 1,000 person-years) of breast cancer in this group.

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?