During the last 2 months, your department has compared 94 in…

During the last 2 months, your department has compared 94 internal carotid arteries evaluated by carotid duplex with angiography. The results showed 50 vessels had a hemodynamically significant lesion by either method. 40 vessels had no lesion by either method. In 1 case, the noninvasive ultrasound was negative, but the angiogram showed a 70-99% diameter reduction.  In 3 cases, the noninvasive studies were consistent with a >50% diameter reduction, but the invasive study was read as normal. What is the negative predictive value?

James is a tomato farmer who grows tomatoes. If James plants…

James is a tomato farmer who grows tomatoes. If James plants no seeds on his farm, then he will have no tomatoes. If he plants 1 bag of tomato seeds, he will get 5 tomato plants; if he plants 2 bags of tomato seeds, he will get 9 tomato plants; if he plants 3 bags of tomato seeds, he will get 12 tomato plants. The cost of a bag of tomato seeds is $120 and he has no other costs. James’s production function exhibits James’s total-cost curve is