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- An air traffic controller is monitoring two small planes flying at the same altitude. One isflying towards the control tower from the West at 120 miles per hour and is currently 5 milesaway from the tower. The other plane is now on top of the tower and flying South at 150miles per hour. In order to respect local safety rules the planes have to be always more than4 miles from each other, or fly at different altitudes. Should the controller order one of theplanes to change altitude, or will they always be farther than 4 miles from each other?A prisoner, 1.80 meters in height, was discharged in consideration due to his advanced in age. In order to receive full pardon, he must run as fast as he can towards the country border 100 meters from the prisoner's position to be totally free. Unknown to the prisoner, he was not meant to be discharged alive, due to the heinous crimes he has committed. An archer with an exceptional accuracy, hidden from the prisoner, was 15 meters behind him. As soon as the prisoner started running at a rate of a = 0.012t m/s², an arrow was released 30 seconds after the prisoner moved from rest, from a 2-meter high at an angle of 30 degrees above horizontal aiming at the middle of his body for a sure kill (neglect air resistance). a. What should be the initial velocity of the arrow if the prisoner was dead before reaching the country border? b. What was the distance from the country border to the dead prisoner?Data accumulated by the National Climatic Data Center shows that the average windspeed in miles per hour for St. Louis,Missouri, is 9.7. Suppose wind speed measurementsare normally distributed for a given geographic location. If 22.45% of the timethe wind speed measurements are more than 11.6 miles per hour, what is the standarddeviation of wind speed in St. Louis?
- A machine to manufacture fasteners has a setup cost of $1,500 and a unit cost of $0.003 for each fastener manufactured. A newer machine has a setup cost of $1,750 but a unit cost of only $0.0025 for each fastener manufactured. Find the break point. (Round your answer to the nearest whole unit.)An fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 130 pounds, and will sell for $0.6 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 7 pounds, while the price per pound will decrease by $0.02.A) How many weeks should the grower wait before harvesting the apples in order to maximize the sales revenue per tree? (Round your answer to the nearest tenth of a week.)Answer: (rounded to the nearest tenth)B) Use your answer in part A to find the actual maximum revenue that can be expected. (Round your answer to the nearest dollar.)Answer: dollars (rounded to the nearest dollar)A low resting heart rate can mean a high degree of physical fitness, which is associated with reducedrates of cardiac events like heart attacks. By working out regularly in the gym, the heart becomes moreefficient, pumping the lowest amount of blood one needs when in a relaxed state. Normal resting heartrate for adults ranges from 60 to 100 beats per minute but a well-trained athlete can have a normal restingheart rate as low as 40 beats per minute. Dr. Castillejo wants to know if her gym members have attainedthis average resting heart rate of athletes. Use the R commander output below to address Dr. Castillejo’sconcern . Write a brief report about the analysis by identifying the set of hypotheses to be tested, theappropriate test to use, and implications and recommendations of/from the conclusions.
- If 3% of the thermometers are rejected because they have readings that are too high and another 3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from others.should i write it with variables like x = 11, y = 11, z = 4? but it says exact number, no tolerance. thanksAn fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 126 pounds, and will sell for $4.7 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 1.8 pounds, while the price per pound will decrease by $0.06.A) How many weeks should the grower wait before harvesting the apples in order to maximize the sales revenue per tree? (Round your answer to the nearest tenth of a week.)
- Find the distance between (2,4, -1) and (0,8,3)The number of phone calls between two cities, N, during a given time period varies the directly as the populations p1 and p2 of the two cities and inversely as the distance, d, between them. If 36,000 calls are made between two cities 310 miles apart and the populations of the cities are 31,000 and a 180,000, how many calls are made between two cities with populations of 80,000 and a 150,000 that are 485 miles apart?Data were collected from a group of senior citizens, ages 65 and older, about their age and pet ownership. The results were used to calculate the model ŷ = –0.24x + 18.48, where x represents the age in years and ŷ represents the predicted number of pets owned. If a 45-year-old is predicted to have more than 7 pets, would that be a reasonable use of the model? This is not reasonable because the prediction is based on someone outside the original population. This is reasonable because the model is based on real data. This is not reasonable because it is impossible to own more than 7 pets. This is reasonable because the prediction is based on someone within the original population.