Testing for a disease can be made more efficient by combining samples. if the samples from three people are combined and the mixture tests negative, then all three samples are negative. on the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. assuming the probability of a single sample testing positive is 0.2, find the probability of a positive result for three samples combined into one mixture. is the probability low enough so that further testing of the individual samples is rarely necessary?

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Water flows at a steady rate from a tap. its takes 40 seconds to fill a 4 litre watering can from the tap. the rate at which water flows from the tap is halved. complete: 4 litres into cm3

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.