Prove that if r is a commutative ring and n = (a) is a finitely generated ideal, where a = \{a_1,\ldots, a_n\} and each a_n is nilpotent, then n is a nilpotent ideal. deduce that if the nilradical \mathfrak{n}(r) of r is finitely generated then it is a nilpotent ideal

Groups of organs that work together to complete a process in the body are called: a. cells b. tissues c. nerves d. systems

On a day when the barometer reads 75.23 cm, a reaction vessel holds 250 ml of ideal gas at 20 celsius. an oil manometer ( ρ= 810 kg/m^3) reads the pressure in the vessel to be 41 cm of oil and below atmospheric pressure. what volume will the gas occupy under s.t.p.?

1. the materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. she knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. she also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four (4) days.2. at what point should resin be reordered? a. 0 kilograms remainingb. 50 kilograms remainingc. 200 kilograms remainingd. 400 kilograms remaininge. 500 kilograms remaining3. if order size was 1,000 kilograms of resin, what would be the length of an order cycle? a. 0.05 daysb. 4 daysc. 16 daysd. 20 dayse. 50 days4. if the order size was 1,000 kilograms of resin, what would be the average inventory level? a. 50 kilogramsb. 200 kilogramsc. 500 kilogramsd. 800 kilogramse. 1,000 kilograms5. if the order size was 1,000 kilograms of resin, what would be the daily total inventory costs, excluding the cost of the resin? a. $5b. $10c. $20d. $25e. $40