Historically, the mean yield of corn in the United States has been 120 bushels per acre with a standard deviation of 12. A survey of 40 farmers this year gives a sample mean yield of 125 bushels per acre . Let p be the mean yield of corn nationally for this year. Supposing that the past standard deviation is still correct, what is the p-value for testing a null hypothesis of mu=120 against an alternative of mu not equal to 20 ? A0.0041 B 0.0082 C 2.64 D 125

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Q.1 dr. frank needs to choose 3 students from her advanced biology course to attend a conference in hawaii. the course has 40 students. which of the following methods could dr. frank use to choose a simple, random sample of 3 students? select all that apply. 1 dr. frank could have the students line up from shortest to tallest, then use her birthdate, 2/5/39, to select 3 students from the line (the 2nd student, the 5th student, and the 39th student). 2. dr. frank could upload her class roster into a spreadsheet and use a ranom-number generating function to produce 3 random numbers. the students whose names are located in the rows with these 3 numbers on the spreadsheet would be chosen. 3. dr. frank could choose the students with the 3 highest grades in the class. 4. dr. frank could count to three, then the first students to come to the front of the classroom and grab a golden ticket from her hand would be selected. 5. dr. frank could ask all students to write their name on a card, place all of the cards in a hat, shake the hat, and then pull 3 cards out from the hat. the students whose names appear on those 3 cards will be selected. 6. dr. frank could ask for volunteers to go to the conference, then choose the first 3 students who raise their hands. q2. now, choose one of the methods that you did not select and explain why this method would not result in a simple, random sample:

22 points algebra 1//sum and product of rational and irrational numbers. dont have to do all 4 if could much : )) write an example: 1) how the product of two identical irrational numbers can be a rational number. 2) how the product of two different irrational numbers can be a rational number. 3) write a quotient of intergers that is not a real number. 4) is the set of positive irrational numbers closed for the operation of division? if not give a counter example.