One number is 1/2 another number. The sum of the two numbers is 33. Find the two numbers.

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?

Consider u = {x|x is a negative real number}which is an empty set? o {x|x eu and x has a negative cube root}o {x|x eu and x has a negative square root}{x|x eu and x is equal to the product of a positive number and -1}{x|x eu and x is equal to the sum of one negative and one positive number?

For each phone call robert makes,he pays $0.10 for the first minute and $0.05 for each additional minute. what is the cost for two 5 minute calls ? a $0.60b $0.30c $0.15d $0.45 show work.