John muir was an american naturalist born in scotland on april 21, 1838. as one of the first advocates of the united states' wilderness preservation, muir spent his career writing letters, essays and books about many of his experiences in the sierra nevada mountains, located in northern california. muir's influence on the history of american wilderness continues to live on past his death (in the early twentieth century) as people of all ages visit and hike through the 221 miles of the john muir trail, named in muir's honor. the trail begins in yosemite national park and concludes at mount whitney, which contains the highest peak of the continental united states. the following table compares mount whitney"s height, in meters, to other monumental peaks of the world. mountain location height (in meters) of highest peak mount whitney california, united states 4,418.38 meters mount fuji fuji-hakone-izu national park, japan 3,775.86 meters mount everest great himalayas of southern asia 8,849.87 meters mount kilimanjaro tanzania, africa 5,894.83 meters mount olympus mytikas, greece 2,919.07 meters use the data in the table to complete parts a, b, and c. in your final answers, include your work for all estimates and calculations. part a: use scientific notation to estimate the following: how many times greater is mount everest's highest peak than mount olympus's? part b: use scientific notation to calculate the following: how many times greater is mount everest's highest peak than mount olympus's? part c: given the calculation in part b comparing the highest peaks of mount everest and mount olympus, can you conclude that the estimate in part a is reasonable? answer in complete sentences.

Which of the following graphs represents the function f(x) = 2^x

This task builds on important concepts you've learned in this unit and allows you to apply those concepts to a variety of situations. the task has several parts, each in its own section. mr. hill's seventh grade math class has been learning about random sampling and how it tends to produce samples that are representative of an entire population. they've also learned that if a sample is representative of the entire population, then estimates or predictions made based on the sample usually apply to the population as well. today, in class, they are also learning about variation in random sampling. that, although predictions and estimates about the population can be made from a random sample, different random samples will often produce slightly different predictions or estimates. to demonstrate this concept to his students, mr. hill is going to use simulation. he begins the lesson by explaining to the class that a certain university in the united states has a student enrollment of 19,100. mr. hill knows the percentage of students that are male and the percentage of students that are female. using simulation and random sampling, he wants his seventh grade students to estimate both the percentage of male students and the number of male students that are enrolled in this university. to conduct the simulation, mr. hill has placed one hundred colored chips in a bag, using the appropriate percentages of enrolled male and female university students. red chips represent males, and yellow chips represent females. each seventh grade student will randomly select twenty chips, record the colors they selected, and put the chips back in the bag. at this point, each seventh grade student will only know the results of their own random sample. before you begin, it's a good idea to look over each part to get oriented to the whole task. additionally, it's best to complete the sections in order, since they build on each other. finally, the work you complete will be a combination of computer-graded problems and written work that your teacher will grade. in some cases, you will need to complete work outside of the problem (in a word processing document or on paper, for example) and upload it for grading. to get started click work on questions. questions: 1. suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. based on this sample, what is a good estimate for the percentage of enrolled university students that are male? 2. suppose a student reaches in the bag and randomly selects nine red chips and eleven yellow chips. based on this sample, what is a good estimate for the number of enrolled university students that are male? 3. suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are male. how many yellow chips were in their sample? 4. suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are male. based on this sample, what is a good estimate for the number of enrolled university students that are female? 5. based on your dot plot, make a new estimate of both the percentage and number of males that attend this university. use complete sentences in your answer and explain your reasoning. 6. compare your estimates for the percentage of male university students from part a and part b. which estimate do you think is more representative of the population? use complete sentences in your answer and explain your reasoning. 7. once you have created both sets of numbers, complete the following tasks. in each task, make sure to clearly label which set you are identifying or describing. identify the elements of each set that you created. calculate the mean of each set. show your work in your answer. calculate the mean absolute deviation of each set. show your work in your answer. describe the process you used to create your sets of numbers under the given conditions.

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297