a 46 gram sample of substance that'a a by product of fireworks has a k value of 0.1368 N = N0e -kt N0 = initial mass ( at time t =0)
N= mass at time t
K = a positive constant that depends on the substance itself and on the units used to measure time.
t = time in days
find the substances half life, in days. round your answer to the nearest tenth.

Atoy company is considering a cube or sphere-shaped container for packaging a new product. the height of the cube would equal the diameter of the sphere . compare the volume to surface area ratios of the containers. which packaging will be more efficient? for a sphere, sa =4πr²

If x-1 and x+3 are the factors of x3+10x2+ax+b find a and b

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)