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- There are 100 file folders, each 0.45 inches thick, that will be placed in drawers. Each drawer can hold file folders with a combined thickness of no more than 7.5 inches. No folder is split between 2 drawers. All but one drawer will hold the maximum number of folders. What is the combined thickness, in inches, of the folders that are in the partially filled drawer? F. 1.8 G. 2.0 H. 2.7 J. 4.0 K. 6.0A 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?the number of banks in the country for selected years from 1980 to 2009 is given by y=-383.7x+18,499 where x is the number of years after 1980. If this model is accurate after 2009, in what year would the number of banks be 3918
- Choose a quantity to be represented by a variable, then write a mathematical expression for each. Donot solve.1. Angelo’s age in 5 years 2. A three-digit number whose hundreds digit is half the tens digit and the tens digit is 2 more thanthe units digit 3. The total interest earned after one year when Php 100 000 is invested, part of 6% annual interestrate and the remaining part at 7.5% annual interest rate 9. The perimeter of a rectangle whose length is twice the width 10. The sum of three consecutive even integers 11. A three-digit number whose hundreds digit is twice the tens digit and the tens digit is 3 more thatthe units digitAn 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.)We found that the estimated rate of increase in the cost when x = 60,000 is $438 per game system. We are asked to compare this estimate to the exact cost of producing the 60,001st game system. In order to find the exact cost of producing the 60,001st game system, we can find the exact cost of producing 60,000 game systems in an hour and the exact cost of producing 60,001 game systems in an hour and take the difference of the two numbers. Recall that the cost for the company to produce x game systems per hour is given by the cost function C(x) = 900,000 + 390x + 0.0004x2. So the cost for the company to produce 60,000 game systems in an hour is given by the following. C(x) = 900,000 + 390x + 0.0004x2 C(60,000) = 900,000 + 390(60,000) + 0.0004(60,000)2 = 25740000 The cost for the company to produce 60,001 game systems in an hour is given by the following. C(x) = 900,000 + 390x + 0.0004x2 C(60,001) = 900,000 + 390(60,001) +…
- Total prize money of $1,480 is to be divided among 8 contestants so that the lowest will receive $10 and each of the others a fixed amount more than the preceding person. What prize money goes to the winner?The number of days a barrel of water lasts varies inversely with the people who consume it. If a barrel of water lasts four days for five people, how long will it last if the consumer will be ten people? 1. As you have observed on your solution, what happen to the number of days a barrel of water could last as the number of persons increases from 5 up to 10 people? 2. Dealing with the same problem, crrate your ow questio regarding the number of days the barrel could last if there is a certain number of consumers. Also show your solution to your problem.The table shown below gives the number of radioactive nuclei in a radioactive sample over a period of 5 minutes. Time (min) Number of radioactive nuclei (millions) 0 500 1 250 2 125 3 63 4 31 5 16 Write down an algebraic rule linking the number of nuclei present at a particular time to the number present one minute previously. Write down an expression for the number of nuclei present after t minutes Calculate the number of nuclei present after a quarter of an hour. Find the time for the number of nuclei to reach 100.
- Only last partthe percentage of electricity generated from nature gas was 23% in 2010 and has increased by about 0.8 percentage points per year. the percentage of electricity generated from coal was 47% in 2010 and has decreased by about 0.7 percentage point per year. predict when the percentage of electricity generated from natural gas will be equal to that from coal. what is that percentage?The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10 .Assuming X and Y to be independent, find σM.