The national assessment of educational progress (naep) is administered annually to 4th, 8th, and 12th graders in the united states. on the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. believing that the true mean score is much higher, a researcher takes a random sample of 500 young men between the ages of 18 and 20 and calculates the mean naep math score of the sample to be 280. the standard deviation of math scores for the sample of young men was 25.what are the appropriate null and alternative hypotheses?

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?