5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e. g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will . (5 points)

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.

Proving the congruent supplements theorem

Write each improper fraction as a mixed number. 9/4. 8/3. 23/6. 11/2. 17/5. 15/8. 33/10. 29/12.