Arandom sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 284. this test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 275. assume that the population standard deviation is 32. at α=0.04, is there enough evidence to support the administrator's claim a) h0: μ≤275 ha: μ> 275(claim) b) find the standarized test statistic z and its corresponding area c) find the p value d) describe whether to reject or fail the null hypothesis e) interpret your decision in the context of the original claim

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?