Venn diagrams can us understand the relationships between groups in order to count them properly. for example, assume a music teacher charges $20 an hour but is willing to give a lesson on a different instrument for free to those students who are studying piano. he has fourteen piano students and 11 saxophone students. now suppose he wants to know if he earns $500 on those days he gives lessons to both groups?

Hanna intends to give her granddaughter, melodee, her antique hat pin. this heirloom has been kept under lock and key in the wall vault in the library of hanna's house in virginia. the hat pin is currently the only item in the vault. when hanna is visiting melodee in connecticut, hanna gives melodee the only key to the vault. melodee is grateful for the present and excitedly accepts. in this situation has there been a completed gift?

Shelby company produces three products: product x, product y, and product z. data concerning the three products follow (per unit): product x product y product z selling price $ 85 $ 65 $ 75 variable expenses: direct materials 25.50 19.50 5.25 labor and overhead 25.50 29.25 47.25 total variable expenses 51.00 48.75 52.50 contribution margin $ 34.00 $ 16.25 $ 22.50 contribution margin ratio 40 % 25 % 30 % demand for the company’s products is very strong, with far more orders each month than the company can produce with the available raw materials. the same material is used in each product. the material costs $8 per pound, with a maximum of 4,400 pounds available each month. required: a. compute contribution margin per pound of materials used. (round your intermediate calculations and final answers to 2 decimal places.) contribution margin per pound product x $ product y $ product z $ b. which orders would you advise the company to accept first, those for product x, for product y, or for product z? which orders second? third? product x product y product z

True of false: the chancellor of a university has commissioned a team to collect data on students' gpas and the amount of time they spend bar hopping every week (measured in minutes). he wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' gpas. his team should use a t test on the slope of the population regression.