Suppose you decide to start a cupcake business. you are able to bake and sell the cupcakes at your own house, so you don't have to pay for a place to run the business. you have $1000 to start the business. now it is time to purchase the ingredients to get started. in the beginning, you decide to make only one kind of cupcakes. the following recipe shows the ingredients for 12 cupcakes. chunky chocolate cupcake recipe 1.5 cup flour 2 teaspoons baking powder 3/4 cup coca powder 1/4 cup vegetable oil 1 cup sugar 1 egg 1/2 cup milk 1 cup butter 4 cups powdered sugar for frosting 1 teaspoon vanilla let x be the dozens of cupcakes. the following table shows the cost of the ingredients. flour $0.60 per cup baking powder $0.20 per teaspoon coca powder $1.60 per cup vegetable oil $0.80 per cup sugar $0.30 per cup eggs $0.30 per egg milk $0.40 per cup butter $0.80 per cup powdered sugar $0.60 per cup vanilla $1.00 per teaspoon let y be the cost, and x be the dozens of cupcakes. set up a cost function. remember, you can spend at most $1000 on the ingredients. set up an inequality. solve your inequality to find out how many dozens of chunky chocolate cupcakes can you make

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: