Question
The pollution level in the centre of a city at 6 am is 30 ppm (parts per million) and it grows in a linear fashion by 25 ppm (parts per million) every hour. If y is pollution and t is the time elapsed after 6 am, then determine the function that relates y with t .
Hint:
To form of function we will use the pollution at 6 am & the constant increase in the pollution .
The correct answer is: ![y equals 30 plus 25 t](data:image/png;base64,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)
STEP BY STEP SOLUTION
The pollution level at 6am = 30ppm
It grows per hour = 25ppm
y= pollution & t = time
The function that relates y with t.
y = pollution level at 6am + It grows pr hour
Time
y= 30 + 25t
Related Questions to study
A car rental charge is 100 dollars per day plus 0.30 dollars per miles traveled. Determine the function of the line that represents the daily cost by the number of miles traveled.
For such questions, we should know about the concept of function.
A car rental charge is 100 dollars per day plus 0.30 dollars per miles traveled. Determine the function of the line that represents the daily cost by the number of miles traveled.
For such questions, we should know about the concept of function.
Evaluate the function ![p left parenthesis x right parenthesis equals negative left parenthesis x minus 1 right parenthesis text for end text x equals 0 text and end text x equals 5](data:image/png;base64,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)
For such questions, we should know the concept of the function.
Evaluate the function ![p left parenthesis x right parenthesis equals negative left parenthesis x minus 1 right parenthesis text for end text x equals 0 text and end text x equals 5](data:image/png;base64,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)
For such questions, we should know the concept of the function.
Identify the function that is linear.
For such questions, we should know the concept of linear functions.
Identify the function that is linear.
For such questions, we should know the concept of linear functions.
Ramona’s garage charges the following labor rates. All the customers are charged for at least 0.5 hr.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPoAAABSCAYAAAB9o8m+AAAgAElEQVR4nOy9eZxdVZX3/V1rn3PvrapUksqcQAJhDGEKIigqioAooIIj4tQObevz2Pb7qN2Ordj92I/aag8+Yisq3Q6tqIgDIMo8iIwyhBkCGZgyVIaa773n7L3eP/Y+tyqQhASw+/O+1MonSdUdztlnn732Gn+/I2ZmTMqkTMr/r0X/uwcwKZMyKX96mVT0SZmU54BMKvqkTMpzQLKd/WAVylf/iwgi8qcZ1aRMyqTsUMwMM0NECCF09HF7OimTybhJmZT/70ql8LBj47tLFn1wcJCBgQFarRZAZyeZlEmZlP9aybKM3t5eZsyYgarivcc5t/3P7+yBV65cyT333MPatWsZGRnBez+p5JMyKf9N0mg0mDlzJnvttRdLly6lXq/v8PPbVPQnevOrVq3ihhtu4KqrruLmm29mdHQUM0N1Mpc3KZPy3yFZlrHPPvvwspe9DDNj2bJlZNn27fYOLbqI0Gw2WbFiBTfccANXXHHFVgoeQnh2Rz8pkzIpOyXNZpPbb78dM6Ovr4/ddtuN+fPnb/fzT2mSh4aG6O/v595778V7j6p2XPbJPN6kTMp/vVTZducc999/P48//jgDAwM7/M52Fb1S4rIsaTabtNvtTlavyvRNuu6TMin/9VIZWhGhLEuKoqAsyx1+Z6c0VUQ6lnxiKv+5aNGDAQGMgAkEhM4sBMAMA540MyG+Grb1ngEIYfwQ6Z8w/vbWB0uvjn9m/FDVeNLRwnj/gwlpzHR+iEdQAhL/miAhvhfiVWJSnS5gGIaAgZhHgid+EsLE+bCApGHG3+OZwoSRdv6zCddk1X/x3OPvT5iFzoDCNubmuSMT6+hPJdtU9Eqxq58nFucnKv1zTQwwEUQCilFimGlHO4WABKFUwYum78TFqASwAJI2StOoMAQUAXOAUGogiKF4hJKQ3uus9aBR+dLRTaqf43m8RKUV8zjzCAKmIBAo8RbABLE4Jo9glhPI05gFFxTMCGL4pLzxOx4EvDkwIQ8ljhYQCFJtY2k3id8i4AgCgo/Xb7LVhmFk6Tp85xUImFTbXto6rFJsxVDEAs48INhzsMFzYs18Z4zuTpfXJspz0ZIDCCBiBPN4b1FZQonXgqBGLg0ERUJALFqodCvwqpgENHgkLX6r3kv/ulDiAUQwcxiKVyMLPn5KQE3wZEkhkrpIiUfQIPF8YohPG4cDL6Dk1HKH+AIry3hGAWeBPLQxoNCASLTg4tL2ZOB9ixAUBXwowUHQjOAbBPF4FEwRDBeiegc1CgFMMQyvkAXIQpyTUpVSFMSDBCqzEeLlI8ER3QYfldscmjYIxDATAhli1tk8J2X78rQU/bkrhvlA6O5j5szZ9Bq4UDAaxtgyuIn2aAu1OpnFhRvVMFrJIJXViVbKoh0Hok2SZEEd2QT336Hm42ImehPR6ileDGeGC8l26vgYwVA0/SSMSZ39DziYPz/l5ay6+2bO/cUFNKVOECUPnszalJosJYKoB8ui5c5z5syZx6K5C8AVDG5aR/9j/QwXhpcs2lsJqEUFrv56iJtfKXgTgjgChrNxq1y5384CmMYQQmM8IWTpSK0Y1EgWNz8JyduJio6Unc10UrYvk4q+i+IN9jv4SD74l+9jYW83XSKUZZsH77uNs7/5dR5YuRYVRzAjkEVXX0s0CIajRFDxSCgxE8QRXdlgeCeoKUoZPWAzCCVBFJUMQ/AuRKssUZFDMEwz1Oi4uBagtAJEcCEnSM5RL38Vb3vHG/n1d/s513tK5yAYFgIlgUKVIA5F8aVQkNHVN4vXv/n1vPr449htxgyolYwNPM5FPzmPs370a0qMgMdCO7rW6qLyoVgQXDDUe8xKvIMSwUv0X0R83BTMUFMkCJY8AS9GFpJyS4ZYGefBBFFBzVKEEDe9bWUxJmVrmVT0XRETLCg9U2ew/wH7My8rWHXfgyxcvC9LD9ofbQ3xyc98kWEf6O7uoafeTVm0aI1uAXF4zdFaF6E9Snc9I1cYGhsDVXqndNNqtShbTYLLaXmhnmV0dzewdpuxsTFwOUEy6lmDPICXNo3enGK0oCw8QRQzoWdKF5kGms0W7bEmPfWpHLzvXvjmCNdcdyOjBXhXo6e7QU0K2s1hzEqEArOMttShayrv+cD7+fO3v5FeK7l7+Z2s3zLC3otnsXCP2YgazcLIu3J66zlZ2aY5MobH0dI6WW0KWbtFVlO68pyhkTGk3kVX7xSC97RHhmKOQGq0Qs6UWk5XDQabY9RcRqYlTW+0Qw3FMbUnwwi0BwcRFQrN8UIKawR7DuaMdkUmFX2XxMgsEIJHNbBx9b187q8/xrITT+cTH30/ey45gL4pPez9vBdx3DEvY/HcOQysf4wbrrqEq2+8kYUHHcwxLz2WoY39zJk3l76ejGuvu5Ep0/t44eGHsmHNKn7+4+9z79oR5u5zMK87+XiW7L0HQxvX8Ycrf8fvr78Veufwxjecwox6g3Y5xl77LmT1Pffw65+fy4aywbEnnMyLn38w3V2wevUafvvzn7O6fxT1o9y5/A7uun81OmU2Lz/2lRx39JF012vcdf01XHDhL9jUGgFt0A6Og553BK9/4ylMzQp+dtZX+Pb3L2CwKcyZ2UOWlZQq7LvsMI4/9iXsv8dulIMD3H79tVx66VW43ffkVa99Nbq5nxkzp9EeGuCyK37PsSe9hr33WkxzdJC7briO3/3uItY2YY/9DuKNp76SBTN7uO/eh+jtmcLY5tWc+5tL2TDW4FUnHM+xL15G6T03XfobLrvsSppaB9UqMMLYfp/3pEwq+i5JFXeLFWgwnNbpmTKdufPnkQFbNjxOM3je/mfv4yWHHcCWjRvZ7diX8bKjDqP5qU+w+/Oezzv//N10hZKiLOlt1DnxxFdTBujq6aa7JnQzylf+43zO+PvPcdwLD2XT4+vond7LK457CV/6/Fe4dU2LN771dJbuPpeRwWHyRoPsFa/EFVu48MaVfPBDH6TLmhSZ8qqTXsuR++7F//qbv+GsM79Ktwhr1jd56Umn8KlPf5i+rGRsrM3ivi5+f/UlrBsbJUuu8bLDljF3ajer77iab/37D1nXajBj1gKGwjA2NEoXDY5/1Wt4+2mvZmxDPzPnzOGE419Oe2CYgRm7cfo738HudajnOdddcSVSm8I73/tu+h9dy7y5sznllUcjTjjvstv4Xx/9MCcdezijmwY4/rjX0Ntb4+4/XsaFV9/Ma1/1Sj7z1x8kjA5Q5r286pgXY+GjXHD5dRi9nUrIpOxYJhV9FySWrwRUKYKxcM8D+KdvnUXXjNmsffgezvvJ99jSHONXv/gdl573CzZvepS/+uhHeOHSPTl4yb4MKmSZsObue/nF+Vfw1necxp7z+jjnx+exhTofePsbWLL0EF5xQpOXveBg+lfeycc++QWOfu2b+Iu3voYTTz6FB751PrUQKEbW858//CXZzD14z2mv4ICDlvKj397M2Wd9hzUP3MHMhYv5+09/nEMOO4i+KY677r4DlW5M6uyz/34smtnH9Zf8iv/4/g9wJmweaeKyBlgO5Ow+ZxZdBNY+/jAr1hec9M5388H3vwtpbuLxB+/m85/4Ctdeei2PP3A/jzx4L6f9+Z/zxhNeyLJD9uPm/haqIGWLn5/zI6646ibWj46xeuPneejOezntbe/ktDe8iiUHH8oBDxsvfcFhrFv1AP/8j//GYS86lre//WS8BfrmL+aUU15Dw0b47N+dQe/iZZzxsQ9x7LFHc83llzPsuwjOYYTnYIFt12RS0XdFREAyypCBwUirycbBMRbPEqQ9wvI778I3+pg7azqnnnAyfdO7mTF3HoV3uKwRE1fFCMuvu4YLz/8dLzr+OGbVWvzm17+iv2sBb3/z68F1MX/R7jREePiuP/LHm29ky5TdOO2tpzBz9jxm9zTIQslA/2NcctFvYeFhvP71L8eyLvqm9bL34oWcduqJ5N1T6e6qEcqAaY26dIFztGly/wP38vjgGIe9+BgGhkb4/tlnMzwygrocLDa1tNttAoLXDIdRNguGx0oO3fsAuqwNdcfcqXVed+Lx9M1+HT1z5lOYIc7jaJOJ8fjKBzjz619n9UbPS447jlcdfzwLTnsL9b7ZMbFY72HW/HlMrSsr16zi6suuYlCn8prTXkEoldlzd2PBbruTZyXveNe7yGfsDsA+e+3N3GkNBgZKcHkqsU1a9R3J5Ea4SyKYKaJCnsH6x1ZwxqfP4N77VzJv8b4ceMSxHHjEK/jkR/8HS+bP4HcX/45bH1yFieBCG5e6y8rWUMou55TBCG1Puy2pmaUkcw6futTwnrIsY1HNiNlqF0tRGFD62IdCjbe+/W2868/ewtjYKD857wK2DAwiYjGJaEpQwWnJ5Zf8jr/9/Je565FNHP+60/nUpz/OQYt3R9slDo8yxqrH1zKMsGivJRy4YCpX/OTf+ciHPsXGzaOEwrFo6SH81V+/n2WHLuSPN/2BW2+9m1AaogFSCSyUIwyXBdMX7cUn/vaTvOTww7n5huu44qprgBxvNVBDJCChpKBk1EosONQEJx51wlghbB4aYtV9d3DhBedz84230PSGd0pmAfcc7evYFZlU9F0SwygRCyiOLAiPrVrBVbfdjuk0jn75iey7eDdmdGfcdeMf+MXPzmVwZAxxBW2KVN2ujpPaFgUcGTUPom2UFuvXrmcUmL/vYSw96CBOOPpQphEYHN7E+tExvMUavClkkhpRGlNYuHgvMoFzf34OF19zPWVwSAhoGCK4QCEZYl0sWrCA/sce4qyvf40Vqx9h3wP2Z5+9FgGCmJK7guuuuZrVj21i4V6H8OFPfZznHbGMPXbbjZoaEgpmz57HrDmzWHnvHfzqnJ+w7vF1OHEEEbzmmDhECkxg6qw5LFg4h8cefYSzvn02Kx99DAHyVpMtj62j2S6Zu8eeHH3yKzniqOfRWwfVgi1bNrKhvx91juuvvopv/NM/86vzfsp5l17Bo6OBTAMqGWEyEfeUMum675IEVAKZGo0sp8zrZKHJNddfx3tPP5Ujj3ghK1ady1CzzYte9Uq+fdCh7Lb3AdS1Rde0aQzlNepZNzVXQzDqdUfe6EGdImpkeZ1aTw9/uOwqTnnrezh8ycF87dvfpG96H8VwPxdfcjFDBo1GHVfkUdldTr1WQyyw9rF1BJSPfPSjvLvMmT+nDxscpdHoBoZRaVB65dUnn8z7/uJdDPZvZP78efSvuou1/Zso1chMcJLx2IoVnPWN7/C5v/4Ax578Nl5w7Gtpl46+3m6G1gqbNg+yeXCMQ55/NF/9l92Ztfte5HmdWs80Mt1Cd1ZjNO8CcQxt2cLGDYMs3mc/vv3d7zJ90WIA+urGugfu5Nrl9/CKFxzOl77wBUwzHJ7ghccfuo/LLr6YZR/6AH/58U/zhtNXsdee8/j2N89m+e0P4FRp4nGqExEHk7INcZ/73Oc+t6MPDA8Ps2LFCpYvX87g4OBzssd9XAwzqDV6qOeOB+9Yzs033sD6gRFcXmNww1ouvOB8HnxoFY1GjQ0b1nHFFVey5uFHWX7rbaxet4F2a4zbb7yZ+1Y/RvfUKfSveZDrr72JgXZJo1d48LbbuPTSa7n51uVkOZSl8cAD9/Ojfz+bX/76QnzeYHp3zur77uYPN93OiPd05YHbb7qZn/7il3gRMhHuued2br35NlavXMN1N93C5sFBRBWkxtS+qTRqGc2RUe5efhvf+9ZZ3HjLrXjVZB3roMa9dy3nlttuo/Ce9sgWBjet5+47buOySy7hokt+z5p1/XTVc4YHNvL7a69m9UP3c+ddd3PfQw+Dee5ffhs33nI3a/s3sWbVGnq6corWKFdffRWrVt/PfXfdxXU33sS1d93BaKvFyhUrWbNqDfvuuZgHlt/KJRf9jhtuvZPHNg8QMsV8wQN33MKVF1/Ow2vWY3lOcBI7C/+7l8Z/k4gIhxxyCEuWLGHu3Lnb/9xTkUOuXbuWiy66iB/+8Ic88sgjz2loqhEBHWaBotUkE6GeZ5QCzcJDgEYtpyha9DRqlKHFaBkQn9GdesiboUDyDHXdlO02uR+jnnfR1m5Gi2EarsTlXZQlSOnp6uml2R5AfEEtb9A08K2S3MDVcgo12kVJTjeae8pQ0F1r4Msh2q0APqPeyHDO8CZ4uiitRM3TVatTFCOYL8nVoS6jNEdLM0Riu2pZBAiB3p4MyZTRZgvfKshcF60AtVxxUtJsjoAZTjMsy/FFm9w8UuvFXE6r9ORqdLmSYrTAW5tS6iza5xBOe8ep3Pz7q3lk3Qgf/OAHOfWVL+b8f/8Wf/elf2ELNcZ8m3oto1tz2sNbcEBW76KQ2H2oQqdN+LkkFdDsbW97G6eccgoHH3zwdj876brvoqjE/uy85hAcpoHcQPIa5hzqCxqNOk3zZM7RIzmmdZyAUdDlajFaN0+t7lBrRMCICo16g0zbOITMZZSa0SpGqYmC1vAG4pSuei0hwyBTIWvUyUojCJA7yrKgJhmupljWoExJPhEjo0AjOI2ibINkaM0RgkBQTARVg+BRCzSygAVotkrKNgRtoHmNXFrUVShRSoOsawpqAYLDiUfqOYFezBSzNo3cYSYUwXC1bpzUEC90d3Vx8smv4QN/9m6MuCDXr1zOpVddzkDh0VpguvP4oqQErDaV4KAdWqgZEdf3XLXnOy+Tir4LEgEbJSHV0tU8pVTLE8BHdJuAqRBCRh4UFSjF8OpAIPMBEZ+OKZgqhQREQQK44CnN4R0RwGGCaEZQIebbLdbzBRQjGAhFRM6ZIGpYyFEV2hbwGtFedR+bYUo1vFoEsIQcsZIgUIgDDbiyjYp2kHCmAlJLYJ0Aqngq2C5oqkZYBWFO8NHY0x6z6iEYKi726ItikkFW8sgjK/jiP3yZFz7/SKZP7WZgwyquuOiX3HLHXbhaF0ZAUDKFwjyoEkxw5ICP6DeEybzyjmVS0XdZqpgwYsG9OlwJGZ7SBC8OtRKHYdTxIjhrA7XkXkbFqSCdQQQTcAQkGODwEktUWVShWBqTCPfU5KEGSYpqGktoGhe8wwE+Rq0msfQvCe/t4xgkqaklIIwhERorWyHEx9NbEtFmGT7CciWjdIqYohbSMR2+Y1grpatYI6pkWUBECVJSSqQla7WGuOj8X3Hp+b+JpcMwhkiJ5vVYdjPw1AABKVAibDUgOCLgJfF2TMoOZHIb3EWJ6hV/8gIeTTXuyIbikyXMAlSYb68lQUsU0EDCokvHIorFz+cWrXyIkDacxYUeFIJIslvjZbkgkkgYDCSkVlCJEE6N5xFTNETMehx1Fp1di5tGkBA9FBNcwtELEtliBNTGldY6118RSEgHlmoQ5wCfqCLiNVTEGJ2xBUA9ogEjhgdduSN3hlNB8y6sNhWjjiYmGROHkaMoziyW7bQgYHGjm1zGTyk7Z9EtBv4hhM4y387HdrixPvH9bf3OUxxjV8V4lpumLOLEo32KcNNgGWIZBEMpiDqvaPAgRgmUUpBZhpqg3jBRSgJmATWHhkDQIrWgaqq0B7wSrbgl2ys+Ms6EaNWrDcEShj1QMY8YmO8oNaURLLLQWDKBZiFiwMXIDJwZXj1mEBIDTmSTCQgFZbXZWKgciAnsTwGxAhNHME0eTSTSUEibCeTBsJDhnMesIJgmjyCAprAo5OAVLxkmHqSI7DT4uFGFAFKCKb5DK/Xck10hgNkpRReBrJZRb9SekHXvkIml36Tzk22j5DH+/tafr17bNrL4mSVbpFrQYSLn2JM+BJ0Rbz2q8fNXFimRSVTurARUHIKSE+KqtoipEgPEU2qGE0kMK5GEwbRStIAzJQsB7xxmdWKarSBIhmlOFgIaAHExeRYykEDQ6D5nFqLrT4aX6PBLRVsV6WLiBtK5dxnW2SSSomeSQgGJ5yMjqOvQTom08WpgGm21gUmOWAwVFFDLUojhcIkOSkRwgai0puQaUGqItRAFr5FQAjwoESxEDAXQBqgnxDRcxPabIw+K4DHn8BpS+CJPWoXjlmN81VWBV1xRFddatfKeeq09HQbkcQNm6d+KKuOJXG/GrjjZE+ndnkq2q+gTiee6pnTxuje8htJaE+ZBqSZIKOLAg8NweI0UQWKerPLyENRc5FfRyEiiweHJCM4Q2mSVVep8Pjq40R22dIOiy2nVOGz8Isf500BMIolCERgZGiFzOZnLqG7oRO8h6nmIdWTJ4mKzQFCIFE/Ripca3eB49YJQ4iXgyROXXCSYqGYlSsWnFhVEDEofaLXbNBoN0NjaqhaSha7G6BO5RORHUwvJW1YkaLR8W9M6UtKIngTlhIXcmSgmLqJIyTSuFkW7hS8Dja46DghWYbxjgg9pxxi+6sojjqXihwNQc0BJkJAShZ6AQ4PgqRHEkVkbwyWWmBA3BqmOMWGrDUq7KAnmqddzRCsPykVoqkUoi0nAmRDEKBxocGQhdNZNvFexK9FSKGOWgXhMfNrcXDq3p2IEiuN5stJVjyOr1WuJ6298IW1P9SNppqVWXRcJPsxS7sYmsA/5dP93pLhp9iURhxpMmzbjKQkin9Kim0FeyzjksIOYMrVBkMg3ZpYRJGaB81CkC1JKHCYZah6l6MSYMQZMLCkaOdCy4OICUANpxe9Yhk/sKVrxkKadPF5jSImwaH3E4tIwAqbjChwVzjEyPMrYYJMDlx7I9N7pmG39ueiKxhtbqiSXm7jYJXKUuSCoCYWrNppkMyQSHgbJCClx5ExjpvpJEymEAM4p/f39rFy5kqVLD6Snp3vnrIMkylbinId064QybpxBE7VSsuZPdV+xzuapoqxevZpNmzZx8MEHk2VZGlM1LodI5JXDoqKZBIK5uCTFY6Y4y4ASr5HfLiYf88SuI3i1yJ5jlTLt4HJFWPHgg4w1mxywZAnOKeCf8L0qtwCleorMyEJG7uOmWEocn7N2ylcIEON9owQtwBwSspj7kDI1DElSJBk3JAbqlLvuuguA/fffH1cRqPIEJX/C/bekmBridVtVHRFPIMQNM31yR6ExNp4RCVaiLiZSrrjimmeu6CKgIlgIeO8JVTnDYsLHLKDpJF5DzBiHlESSFGmGNLzEKxasjAsFh4aY/TUtoxKaUkq0cgGLyiaRglgrhY6rK7qUBhAwDZifEAhYnOBgHh88zmW4PIPwZEWPjKxQk0RdrBmC4CjxaZNxnYRX3Ai8g1KUmocc4oIBUKHUbXRqmRCCkWVZx9XKMpeUasc3KVrPaOkz82luQuRsk3q0Qc5igwrR+3hqqfLqiorinMPMcG7imCzdOAHyCfNenUWJmfRqPj1mGU5yOtY51BD1CC0y9clNT8q0AxEZZxpWdWTOAfrkr1kkpszEo1riEJxEjj5JtFZKrDwwYZOOlYYYeog6JBkUrXy8SvkqQ5Lmpvo/z/PxXMiTBr+1osdyo2Kao5Q4KwhklJpHjyzldGKpcpywu7pPW19vNb4s5lrUpfna8XxuV9HHY5GJju5WZ0wXYJQy7sRHwEeISRmq/HS8kJRDHVdCEtGfpfOYJupETxAhDyDmKJXEs0ZykVL8a+PLdTzGmsiFrnSMpRnB+87PW02lxdG44AkCpaSkkUTLhQnBKlZyjZtNujkxmRQ63kUpluLfJ00XEB9jVVnwECrm9J1QdIu2wJthlqGUKC0CdYLloAVSzSXuKTOQ4xTeyban38f/VrtzLJ/FbP04GEfMocTSVjBFxOPFovoH6XDYxbAuZtir5N/WOZDtDpCQwkeoHg0c572zqKOL0fkjwZAQCBLwxPhOzSLQJo6aWJePY5KgnZJn5K8PaXuqXk8nScoVQugoewix72Gb+9UTdROA2DAUaax9mnMFSjTlQYI+UdO2NU9p4wmpVBk8ok8zRt/6ecvb+aZELs8YfyTXB0UiBSCC4slSfF6VaaKzWHlDiqSLc6kmmyZbiRZSIqFAmXbySE+ect5iKfEzHoNuldyQKvUxfi9EZIKSh867cZOKW1FI54rVoJj06SiDaFr0MYHWKe2kmnYpmsKSbc/XxFVRzfHOuO1VcBLPLbSdkgclS98ttEyejcbuuKewlp256Mzc1rz9T5YUryavJghkFiL1tMTQzJl0ynxqkCX9MClirsNc2iwqd/cprrszjJRTscSp+6QW7NiQA6RYu+pN8GTB4yzgRSklS58uiTSVlkKKVOHQamOrzjlxLBadG9HxDXKr3MeEsUz83aq5dojlEATTithTk0EsCdQmUGKlcRrpujoZEcZX84R7lcq62zbG47ITWfftHMBIddjowos4nNSxsolagSm4rE5hHgsFWFyopcbSkguGhti1VaiQe4dYdP0lWeJgIcWmSiQTF0xLAmVqDAlpegRN4xyflojn7uyJ1eOktnE91dNRxGKNuKFxAgsycHW8b8eHIVgsQSmx2SO4Rir4KL40isROWiUMnxRvmSEqWz8IY/sz/ISvpjjFEne6GZJlZFrDAvjQjt1yRuz93oljxmlJ2fbKg3vSaNJspvyA12j/shAQV0eyiJwz3yQLBUF8h7E2oFitlsIdwRmROdYXOzW+KtyrrkbkiUoOpERktASOgKMkJgKVAnE5lZJIVsf7FoSCvOMlQMc93AmpNsQnX0AyMom3nqSEea2GBYnP7qhltEJGsJhAVAATMhyqNcxZp4eiLNrRiJklYxvD5RhyJN8kWMea7zC2ZzuKvrMItSDpgtoFV195Nav6Rzj2+KNZPLubFffcz5U3LGevZct43mFLqEmJBI+mrGPMrBqJjaHamDAM5w21SO9rmsU9N0SVDmaginkPEimKTaJLm6I4qoQHpDjvKQn+LcV0UJM2d9/2R/7zZxfQKoWXnPBqjjnmxXRJ3KyCU1qDg1zwiwu5e+UGCisx3+bQFx/FK046ia4QM+jScQsmzms819MTJYQyUjSZkWfC8huu5dJrb+eFJ5zKYQfthfjh1LTy1K77+JieaolEqSoezmJoopny+MoVnPObK9nzgDKwlXMAACAASURBVIM58WXPRyQnupWeTNtsePQRvv+Li+gfGAFviGtwyuvezBGH7ouVzZ0YHB2lkomu2YT3o3MXqLLZ8cWY/W+ODHLFJZdx/a3LGfOOQ444mhNfczI9eQZWEMuO8eqe+r5Y6jLc+vRYZxuK/0o1WzA0MsLFPz+PW29dTpA6hx35Uo456Vi663WyMiaVsyzjpssu5urfX8cmU8qgzJszm7e+9XRmTJuaXPNtlbR3diuPsvMtsFvteqnjSTRG3q0WN111NZff8zBLnn8I+86fwtoHV/CLH/2UY7MaBy7bjx5KMoVMlDYZXgKWGRZa1DRDM4f3AUXJNe5ehSmYI0Oia6WGhJQVVwgu3v3CYv93pFqZuEuHznh3fCNT4sjlrHvoXj7z8U9w3xZjjxlTuOTqGznjS//Iyccsw9oFKkIxPMSvzz2X2x8d5IB9FzPWHKWxaB7HEOjtxKDbOOO2FuvOSHLLRXOi21lwzcWX8vnPnsFNK/r5xJy9OeSQfaj7aqt8prJVKimFLdGqC4YqPHjPcr7w6f/NOZffyuve9V6Of+kLUOeSe+TBlfSvf5gzz/wO83ffk3lzZ9KyjMOPWseRhy3ZxTHahM26+l+e+Ak6D5MTwWnOw4+t5Xvf+w8GWm1Gt4zwk3N/y3DheOfpr8SCT/33xJyKVKHndiRmbXegYxNeNEOdY83qNXznu99FzRgeanHOuRfyt7Wv8KbXvAJlDMEhmXD7jdfwnW9+m0UvPoZG1mBTfz9jo2NI3/Q4l9u40l1V9qfd6y4IVobYg2FlbBxxOUpOJkbNGc4BLsfIcFIwNjzCo6tXMeIzpu+xOzNn99JowvDaTWxsFcycP4dGaPPouk2UjV7mzphKGB6gf7BFPqXO6i1b2G1mH/N7uln96Fr6B4fomT6VBbvNj4ssNVZ0UoA7+agexVALZKpcfvnlrHh4A3931jkcMSfjPe//CBdccD5Hv+hQesnIzZDgKWvKye95B2d88H+QmTJiJbkp4i31BTwdjd62mFTPShRqJowNbuY/zzmH9VuGmTZ1OuqNnNjDEDTs+n4iE+aqsnCdA0jKoRhqhseBL7jiN7/kxltvZd68RbEkqg7zzRh3JhCMpwvrmsdn/u7LnPTyIxluDoOAb48+g9l5wgKX8W4CMU9GzOyH4JizYBEf+8xn2GfJvqxf8RBv/Yu/56o/3MLpbzmRmstQnyyl+PFDV30C21s7+uTzd7Yeq+xMfJTV/AW78Q//5wscuN+erLjzNt73l5/krjtv5+QTXkZv5WiGDAvCfgceylf/40csmNZLGBtF06O/tHNvnphx2jV5RqAWSeAMTcwrKrEmO7H2aKZkrs6D993Dmf9yJiuWP8SY5WQL5/P+v3ofJx16KF854yvcs2kjZ3z5c8ywMT71qX+kb8kRnPH/vJUrz/sB55x/HdLTyyNt4SPvPY3Wynv58S8vY3NzjK6+KfzDF/6Bg5fuhwSfEho7ay/GLb1aCa1h7n3wYerzl3LkEYezgC285KA9uWXVvTw2OMa+fdPwqcnBB8+jj6/ljzfdxO4LFzN30W5QtCFFI0GqhotnR+EzYvmwVMi7p/Hhv/kkDy2/lb//x2/FTDwRxRYTiM/eJsP4tgmQmpWM17zudRy09Pn8729exJjP8Che6xhNqkx1bKv1PHTfvdw8JWPRPouZ1teFtdvPcITVfauKUS6FFh61Ijru3tGYMp1lL3gRTgts9nTmzOjDiNRTpQ9kpim+H18HOxm0TpiTrZOalT8fCEybMYPnz56FSJu5c2fTXc8RdZQuJ5iRhQQTFhgdHeSPt97C0Ly57LfXYjJn4AuqfgcY79z807ruTxADTFIaJETIwfC6tfzbV7/KzxrG5vWDDLcCuXMwOshPv/s9/vjHBznxdaeyeM40vvXdb/P9b36Lg774RQZGWwxvaRNKQaSg3DLEyOAIIUBzeJTH122knCa89Oij6Q1tfvnbS8m7ZvPxD7+d9UPr6J1ex1mB84rpeENNEIdRMN5osC2JYQKagx+gQOnunc2UXDEPs2f00ugfpDChFMhSMnFK3s0Vv76Qu395HvWeObzrbz7OW95yCnnRjJlTsyefcudzPluP0OLSQWNCKuQ5+x90MGX/Y+S+iUmkoXYpK7zLWhRvZmc6SEmg6jgWn3qIT4kxCRlzFy3BZTWUFiZuHGwiMZ9CosfqYZSzvvZ/OLNdsOdBh/OZL36ew/fbA8rWTo6LCfdv2wtcxtsk8RL56jI8Hk/TlB6pcccfb+WhlXfxgXe/l7oqUgjgEXUES/cLHT9F51SVpyPjf9O5xp/ymqVQNpXvNMQnWwbB0ybTEa6/8ToeGfC8eb8lTMkFX8RkZR0lz7tY98gjnPHhvyRrGkeddCp//9m/Zl6Xw1tE+7mgqcJh5CGkbrqJ4cKOp/JZgP3EemBsN22xqX8TgwNjjI2VlN5AlNGBzTyycg0903bnde95N6efdhIvWbKQ0Q0bWPHY41Br4KjhEkIpx1FHybzEjq+8xolvOZ1Pf/KjHHnQEpzL2Dw4wOaBAU5+9SnssWgPfChSjTKOSbZS7h0oeRWDptJQKY5WIanVNZBlVZNKurG+TU/fLP7qox/jpz/8Hv/0lS8zxUb5py9+mYfXbkbyWId/0o2YcL6nMcVxEXUWYKxgW/BkqUmmOuzT8yG2Nc4Jv1lMhJpWPQIZWB6fuUaBWOwny0wQr6gqpYfdFu/HN/71S5xzzr/zsQ+9h1uuuYKvf+9ntIKiO5EsFCbOmGz71RTSSLKmPiUExTyYUVNjw8Mr+dpZP2D2nnvyyle8BELAEUunpBw9kiVPqLKgE6G2TzxvKsFinWpPx76LQOolySS27Dz64Eq+c/Y5zD/oMI558Qvp9WOolVjm8O2C4199Kt/9wQ/52fe+zXFHHcy55/ycX//2CqTWhfksdptoLO+qCaTHVu/oDj5RnkGMXrVQxnpOYSVT5yzgL//mExy931yuv/hivnr2TyiAlo+tsSGrQTAaqsydNZP2qnUMDw4lCxxTIc4cbcnxZCjR9ctrNfrmzCfkyqz5c3jXu07nWz84j3/72tf4/Y238+GPfYiF87sQH0kaXBAyM7xEVpKnvpb4+GDSFakm1BYwMjJKKD01AjlCLUCoT+WQo47Cq1F//iFsWX8v//Oz32T9+kH2mZdBmazMn+RxvtGKRCsv6dnjVRLyT3E+xtd3x7pWcWPsIXD42ERijkxjq6o3oWf6PF563FwMz4EHLOKaP/yBa++8h81DI/T2ZrGC8gzFpCqyGi7EOYiYAUdNIQxv4gdnnsl1dz/GGf/0NRbMmwVFfKa7agz0qkRcRAeGnXbio0crVK68YBDithMTxiWjA4N841s/4Z61JZ/+6J+xaNZUsnIkYhVEwJcs2G8/5i09GKdtPv6x9/P72/6WFfc/wmjIyPJY3/dYKlA5StGEYtz5+XtGFl1So0gQxZxCrcGUmXOYPauX2VMMJ20QQfMaLs/w7TGaQwMMjIzxwCPrcY0pzJ/ZF8kGrEUYbbH+4fVsHmvRdpHIQERiSaeMSK8mgWNPeBlf/crnOObFL+X6q27hgvMvx9UblBq79GI1oFLenen7lthQkU1h3tQaY4/ew7p162m3Cpav3IB1z6CvnlGMbGagGWiHGqFZkgcPYZgNA5uhK8c1FDUlD9mfRsfTaCu7HSSCOapyXuWf/KkkHn9iTFqBQVIDigrWHmNocJRmCd4XtNqRIoLRYTZv2Uzf1JnUs/xZqQ10xiFVu1O07EFyvAhajnLBj3/M93/8a972vg/x2lNPSs23EfQTqt7sKkbYFkZhR+fdagcE0gjUaiiKtUf55U/O4We/upw3vvt/8qbjj6FBoDRotUoGhiOkuVV4ytiMz6YtW2iWnu7uHkSF0kqwQO4tAZvC0zIgz4xhxmJTSxCjHQJlKAm+oAwlhW/jfRsrWkybNpUDD9yfux+8ih997zssnDGFP658nMXLns/ee8xn97nTWH73fXzzm98ga25iaGwQZyWY0DajDKm9UwP9GzbwvW/+Gwv32hungChdjQaW2nE7cSXstA8bARA5Il0c+4Ln8fMf/oQzv/6vHLDbNK6/51He86E3wfBGPv25M+haeDAfetc7ueGS86n19bBl83rOPPt89lp2OAvmTycrMnzwfwJKjyq9m+Jki/2HbR+QFFpUH/uTSQfMU3VsKRZK8G2CBDQ3brv6Sj77r2fzng99kCMXz+B3ly5n0eI53HT177jh1hW8+2//B9N6ugh++NkaVEqoRXhsbFl2qPM8cNvNfPffvk3once8+XO49IILmTd7Oi98/jKCkHIaTMhq00lP7OSp4xc0jHs6ELs8Rblt+a383zO/Tk99NvP6ernwwl8wc8FcjjpoKf/xrW/z8xvv5zv/+llW3XwjG/oH6Z3Zyw++9302l57DjziUjDZe43P+shBBQaa+0168K9y3z0jRgxGL+QpTZvQxf06guwalgeudztwF85nRk1OvK298yxsYGGly4123cGdQ9jvscN71F+9l9oypHHfCy7l39aM88ugaluyziEOWdTNzZjdkGd0zZ7Ng/iymdQmOAu9LHl/Xz/W33gnSy6tOeBmvePlRaLvdUYRxR2rnY+IIvsk47MgX8Z73vZN//s/zubooOfaVr+XNbzyVcmAVG/s3MWtO3FFvvvk6LrrySgqDRUtfzEc+9nF26+kmlM2dAWc9LRmPUuNqrHf3sGCPhUzv7aFCVAeznYp/d0k6YUiVgY+hlssbzJ8/j945famd0xhujjG4eTOZGO2yzS9/eg4P9z9Oyzxv/rP38L43nYwLxa54nTuUTtgVYlecSYkmZNfGwRGkMRVpOc76xldpj41w3LEv54hlB1Fv5HSwRJXCVuFI58g7HmQV0Y9vwPFVjyGqDI6NUJ86hfZwwdn/94s0yyGOO/VNPG//fRnYvIXBoTFMavRv7uerX/oyLcvpmjmPj3z0r3jJUQdhxSiaeuor6HbEkpTYLmZjnpLu+bHHHuWGm69j9vzpdE+pJ/QagIsPpqckCwUDW4YYKXOmz5jOlLygNTzCpqEWbup0pnTX6AklI0NjrBscol0KU6dPZ8bMXhwFWatk3frNjBaBaX3TCH6MMe1hxtQeGNrE4GiBTp9Nb4+SN4cY3DTIltESVce0Gbszpa+O+C2AYuISQiniqdvDTUYHxjjs0Ocxfeq0iJCTCpyRHF4TPCVZyHCUFMUoq9ZtIZQZM+bMY+q0OtIeYPP6AYqumczqzWhufpwNW0ZoS87UWbszb/p0XDlMkbURaoms4QmTaYKqY926dTz00EMccsgh8fnnO+MwGsmSGsFyMgw/NsCGLUPotAVM76qRkTDj22wV3cYhzVIbrrJy5So2bNjAssOWkWd59JCq8QcluDYSIsFG7PUP4Jus3dQm5F3MntGNECiHhti0ZYhps2fQyAIbH9/MxmaTkHex29zdmN6dE0L7KdeoiHD/fStoNpssXboUl1Utz0+eGDGPWJaqLLHE6lVoj4wy3L8x5onMEMlo1LuYO2c2WKDqZLXkJXVosoCYf6hCPwFTnMtYvnw5ICw9cEknlDE8FbYiRgAOk4J2a4CNGwewdgbqaWVQ75nLvCndjA5upL/M2X1WHza6mY3r1tNqK653GrMXzCbPStRHMo9Sy7TXSoegM0gFihEuv+wqFsxfyKGHLdvufD59i14lZkQQB9NnzaYXB1ZQADplOvOmOkoLBEpaCF3Tp7PHjFmoGuKbhDBMm4yQdzF3YQ/BYg605rpo4/AB6n3TmNKntC3HfIusVmPmgvnMkAZYQRmU4EfIUlknbLWAdtZ/rvqTIZjD1Rvsu9eeBBqEUGC+idMa83abT1scGpp0z57LtHl1QkLpaTGGaRvEJ2SR49lNjm0dD1qAWr2LBQunMmZ1xPsID37WPYm0+NPpO/BjE5zWmD93GqVmhNAmWKxdL5o2nRACwQvz9uhlpgsgNVwR8H4E0fFm5WdjfJCBgKONEShUCeTUe6YzdcoUhDZBM4wa5sGXZWzqgfEyoliq1OzauCq/MYy/EDHmJjS6p7F7z4wE5/W0ncPKHFcG+mb2Mc0ZVhquZxpT9ukDiR5J8GMRv2B1gmR4EYImAhTLqMg9d0WegesuETNMhBWUoeLmtHHWEF9BMGONsY2hZUmgwEmEOIpkeIy2byMJTlgUAZcuxqtQilCakYliJnhfEmQUJxHt40QSACZLXlgCYey0fxgd3yASEUMm+HaJ6WgC0MRW3DKUIG0IgcIygjdMxiJcMQTIBI+jlmCO9qwr3fh4IxsqFL5EiE1KkviiKwv1bEknZKgIIYWINwhCMB8xC+ZRlMKIHZOJPqoMRezw8u1ECb31MZ+xGAQcQomjSFBnF9F0wVOIJzOjEI9IMYF0RzuQUYFxdt1dCPcqX6AijpAU7xslKo5QZKCGEZPShVeyUKAmETLtC7xE3Kf4hMKzNiqAZYg4gkUEnobxSovHUQFvd1Z2WtErhFMn6yrSgUaKaOqIiwkRSU0rKoKZJNqjBBtNVjNoJFKoYiyVFHWYgNSBNpnEp4iWpjhxqEWWVdMS8BAiPUSQlNntUB/F1AxSjZsOWsxCytJK56pIuNgY44qglkfKIm2hzqM+Q8gJFaeZGEFd3OjMyCSLjReQ4uMIsRV9wkZjcQwV1LIzpu0112x1A6Q6BGoV57oDrWgcInVWkOpRjjKev0sH7NSjOz0g4657h+RB9Elj0mpT11hViE+AENCY6dZEE61aRGowsvhwRzEgR8TIFDTUMBc9BJk4NptYLRhfXzCO8nsSPNUmhNYJwBQVzpFbhPCaJgSdxPsXD1mmJpkK6tkBJ3fqGZ3ZkvF4XUxQrRCQxJ9TeVnExfEnpqKoqIJJHSgQ5/Fk1EPEeiBCoTmmQuYDwRQyTUnc+KCOiG0IMbQNgoRYS/euuiPjiMKdkW0qegiMI3VMwMPw4Cjtdiu2dlqc3KofODKAjVFxxGpnjQRKiZ+ASNnkAnjVSCZBIKtQaKaoVig2l6ioQiINUERaEQKoE7i+gsRYUkGswKLPEPuyk4VutwrazTaPPfYYmzdtgdQuWo09VlcSrt1KgnpMHZnPENp4BSzDWUbQEgmRFtkrtF3klst8Pe62UsTGBqJ7pU/WVkSUgcFBRkZHefiRR6jX6onkYWIdXCb8nfAyIZEjZOmdyIjjLIusrYnCieCSux0Sy0/KkVsCbpgjMppEq6Di2NDfz/DICKvXrME5nUAlFXvcW+pQc2TmE52YorjIyKqChni/Wi4iCrPk4WF5zH+YgOU0M8itnTzBqnXVIpecgJEjBl5h0+YtlGXJ6jVrEkPMRDLHTo67MzdV1UWCw5niRSLsWUrUR2W0lHAL5gnOxTUYPEYtqruWqdkmEV0KnbWo4tg8MEgAVq5ak6yqYNQR2hGuKykdZzlGN0IbJPLk5T5eg5ectjqClkzxY6gpLalRqMXt2uIaMinJrEUWSHRZQlszJHkwVTdfs9Wc0Cy2bdm2RZ+QYa2msd1sUfiUvSCSDMTEnEuspCWlRlZRFyLFEFrQFsWINMfOIszRi+BVUlmoAtsnq6pxq3YhbhpBKv7zijywWvWadrQWnVIoCWVFVVsVfOkpC8/GTZup52OYTaQ+qsKzxBVnAe9KSg3UyjztvBFHn3mhdLE7rVYYqKedRbJEDRVFc4FIEWG4NsH7SRIRtsro6AitdpuNmzaRuZxx1HxqQBKB1LDTQUpUjK4I4ClTjFnzIeK8pYbXMiaQLCpQ3Y8/lcVZ5HmJMaWLRJ463rM9NDREq9mif+PGJ1AkRSKJghrRf4rsLKHCsXc2obgmfOqe086Qx7n9AkqRWeSPr1hWcIg5HK2IZcehQSmdMjQ6hvmC9RvW4zRet5nEWHbC2jTxSEI6dvjqNeAlbSRSTmimSevTAoVTRCK2HqvFtaYFLpRARiGRPstZfI4c4hgeGSOIsmHjRpyViRorx6QEwjhjjTjEtqTNJTZyZYnbLlJi14GSYcZwJnjyDj4iRkjRG1aLPHvxXgpjLkMtEoAmux7Dt6dFJTXhO7HzDabNmE5PbxfjVEIVLY5AIgU0reh5oqKb+oQRJu12qWWwuvESe3cxIffRH/Bu3KebOPRxwACJaGLCWtzuNSijw03Ghlss2X9/pvZOjUeqWGaksnTJDTOldIEgJVlwYHHXdRZwQWmrw6tR80R6Zg1p/JGyOF5fkTgHJsZ64xZIVVm/fj2rV61m6dKldDe6U4bbOiFEVNZ0a6Qc37hMY1hBi1Kj51PzHge0pRYXmxSxFGM1GqWmPviUwBPFtBkXo+Ux655c8jWr17Chv5+DDzpwK3LIyD4Tw4LxbqzEQithgkcUFydYJOkI8ekywbXRkGEmExiDKiqsIlpRq6cHRngyC+QBCpexYsUqms0RDjhgf5zEkNDM4iYoEMk543EtsbuqKZl5Slckvr88VUCK2ICF4Hy8N97FjLkLIZF6hkjeQbwdpWSp7bTE4VGpsfzu+zERDliyNypxPJlZ/CySYn2Jz7oPgpfockfijagDQQQxxYVAqXF9qBkikXMvSDSSEhSzOl49DR8wHO0sstpKiEy5qLJ58+anZCraNvHERBVLsaaqIG6coS2S7lfJd5/inARRxDB82tnTAwbE4zXyfjiLXT50FksC9aOd2C1aZEvxdkVKHFsOJb03QffZeltISiWGy+Kzz/LcUatlRB7LimAyOo7RiYhAgRo5WI64kEIAB5bhM6hpvDJxGRKERqI2to6bF/m/IsO7bCMZJ6g48ixHRcicI8+zzpxG5a4UPUXeKUzBsuicakBDRhaj4shhRgTbYBlI5LDLgtJuxLnOTSjJ47VoO2XN8872o+JwqpF7PsueVF6LOSbBJTy2kXUUM1rkxEwrSsCTBSEzFx/AmBkuuLSZFh1l18Qm6yw+26XlaiB18tKTawkO1BmiRp5nOKmBRALR/7e9846zq6j7/3tmzjn33r3bskk2ZDedJEBAQkBAEYOigBRFmqIgiJQgVQR8VBSwUSyIgAVRSigiKiKEEkjoSSCSAIEAMYX0simbrbecMzO/P2bO3U2D5Xl8fvi8Xszrtfvae/fec+ZM+c63fT5fkVJiu6PbjbdwcFU3/pasVRUQiDQKiFAuYxcpcaxGOAeisAHKaKevqLT0VZqP4H0uVqGCCCGdfZ4JAyqmE8aZMVZ5DcYS2RijrPdJRAjjzBNpJbF0QiE02pmrKCfkvfkWpgPvGYhiFToTidCnYscQBGjj1sgWPHo7aH2ikrLWeu8hHqSPY3yxKZdb4tan1y4tBoR2j29FJVVW2wArAmfjCceMKZAVUkbj89utsJUfabwGQBob9/zcOLvW+Yy29JSmp7WT8q6/iSca6H1SpZ821lUoETZCGbegDbEj86ucrI7cMBUKsQgwNiA0CTa1x22CERpts6TCLt3glZ4Jgaug4vLTre2JTLgqLS5261R/Z++5EzPAYMAW/YIOnfdWWLQ0qXSsCAtLjKDsN2OIMCHKuKdOpPSb16vuwlWMSbvo+uRNhl7jaYyzDt133Y5JEChv5yKcZmI9nZNFI41CGFMxTrzbDKzPZPBgIXcrA65+TTqBznlrDEqmC9r6frvxdgIwdCEt4T37fuuBBuuYgSwKYdKot5tzReLNNo9gE9o7wtJ+ab9OrHOYGe/AM8aFMrE+q9JvCOti/ZIYLL64pZPbEksiBKEVnsfOjbHQ0tFzCacJOTpsVRGm0mrCRFNSzoEYGRclSKzBSgXWpx7/d070LVtK6tjLREz/9l5GL0uxwsHqkL24Pq31LKE429BL/zAM0DJLEoOy3QgJFumzlXoSWtKN6K6fJglQSfaoJDvYrRJFKrvdf7ZCfJiqAakrxz2UFQKpDYGNsdZVTcGTHqYCIxAJQkQu8GcFiQycWicswiq0ERiROLJEeoseKq+8MuzGQ7oTi5QXLe2z11rSTSCAEhYrFcq66IKxoIQTfGnugEI4khUhMEoRGEeS6MolOc3LCEmaamXpGRfhbaFUu+otnKQVaJsACm0kSFcjXlhQ/oR2I6kJrMRYp6or4U03WfKCLQQrUFajlUR7KiehjUcHeuHtza40yiOFY1B1jndBSt3slqCgjFPlI18yLJYutTUUzjdhRUpd6othuAAcwtFUuHUnDUIqrAywxqvHGG8WCE/EJ53wsc5kkd7HEAuBsAlCJIQYrC5TDrNeRVc9MFoRYIVBetYY7b3+0o+3FF5JIUALi5HO9+Aq7Po1Iax3TrtRT/kO+7KLt2lbno+i56eCx+35hMV1LkKgZBZU5Dzn1osIIUAEJEJhMESiTM50s+DVuTw69RmWrOvEBBkwZYQpYUi8uuqoe93EuonSxkc5rV9cxrg8XJue1P40TH9SIj/eifHFbbLABGSUJUm6+OOtt7Khq4yJ8pRw8MwgCAlshC4bbJhFBgGBLaNCjdGWgg4gUwtksCLpdZqn9/CjWRE4aUsFmnAqkbC+7wkSjVIZlr69gj/fdy8EIQQ1WBMShhIVCgwKGdRgVQawBDYmEwrKiaVscxDWowmdhuUZSJWVpPy5W/TFa1Fs1T1hIJvJMnfeq9z/0MOE2SqQGbCGyBbJSpCZahIV+hgvZCKFCkKstsiwGiMj0jCYjAK0hdgqUHm0ipCiTOBLPxvSZCOfg+FPcrcaDS5mb1FhjrkvvcLDUx8jjPIImfdRm5hsFBGGtSSiisRapI2RClSUIcyERKFyxRxVDiliwtDVLUh0AGGOWEROKdep5tUzVumQWSvASKxxwjaUGmkTHrj/AeYvXoIMakEHCAyBgJzKumvLyBUGMKACyAiLSBJskCeWeRIDodJkpEEbS1lVI1UG5anCtfBMt36q+pIkteMTvbdbE3qpz/5/3gEjhKCrvY27Jv+ZTSbLMSd9kaaBtcjEgnSbTVtPlaw0whQJ43Yeuvce/vTsAi6++npG0G6zrgAAIABJREFUDd+LoNCOQuPKATteOIEHzUi3CZy9HvvEAVvZOMZqL+G2pNuVFYXxnVtKT7y5ZQ3X/+o67pv6FH99biZfPvVUjjviEGRcZP7sl7nl93eyZv06Ms1DmHTOWUz80EhefWEGN9z8J1a1GQ49/AjOPO0kQhIqzKS+J5Uxrfz0ZuIR/jNpyqV1ISEZ8NLMf3L9dTfw+sKFPPfSXM445wL2HzuCRfNe4pbb7mDB8jUMHjGGM88+i712bkaVu7jv1snc/ehTiGwtp3/9HD5x4P5QbnfYdaO8E1L3ZHNV1H63ESt9FG4MA2F58IGH+emNv6Kjvcis2fO49JKLGNwYYgvd/P0vD/L0nIWcfPYZjBszlLBzE3+56y9Mmf4M3d0JQ8aN5/wLz2doQ55Axjw8ZSq33HkXYVjF8ceeyGGf/yxZigTG8+WLdH5TB6WgN92T9OG9xx54ghtv/A2r21t5/p+vcN6kSYxtqkaWO7nvtnuZ9erbnHTOWew1ehCi2Mkfb7mdJ2fMRakYk3Sx8z4H852LvkG13sz0xx/l93c9SMFmOe5LJ3H0Z49AGO3s+srKTzUsR3MuhXThVpxGVNq8icl/uINb7r2ffHMzRx93El874Xjqc4LWtSu5+eY7KNUN5rQzz6ApG5CR3bz47FNMvm0y61q7GDB6T8755iXs2lyDbmvh1tvu4OGnZ9MwZCyTJp3BvuPGInSJlH2+Dwd5r72woya2ftmjRorer6XFFIvMe+FFnpz+PC0b270TQyJ1gpSWQCmUdI4ipPOCRgJyUYYoyCIIsTJHoiJXrctaMlaSISKjskgVYYQrNxQAkZQEKkIEzumFCCqqTA/xztYPsz2x5xwtSmjQbVzx/R9w8+1/RVtJaGD9ug0oBK/PfoELv34+z736Bs2jRhIIQVxoZ9nCN7j0ou+zaGULDbUhP7niu9zz4FRUUIWocNLKre639XsAzsPvPOxO+xAKli5ZyAXnfoMXZ75EJpdjc1eB9o4ONq1eyPcu+z6PTptBY/8annzsr1z+41+wubWDJ6Y8zBU//jlhdRVda5by9XO/wasrWyAMSUmmXNSht2a29fj0JIoEAcyZMZ1zLrmMeUtWk6nK0d3dQaJLJMV27rjtj1xy0cX8/f4HWbhyA8iQQucmpjx6P5tLnWSx3Pnr33P1z26gFAjemPMCF33rSjoKJWTcyo9+eDnTZs7FBnmc9hYjhWdoReLOIjc2HuyNDAWzZ83kwvMuZtFbi6nJ5tnU0cHGuEShu5PJ19/E9y65lMn3/pXFy1uc+p908cKMF3nptUUEtQPo39APIQWh0Mx7eQ7fvOQK2otlZGkzV11xGU/OmI0NsgiR5iyISn6GW2cSDc7WNmUC083tv/kNP7vmJjZ1GMIgS8umVhISNi5byJUXf5Orrr2Gv015itaOMkGYsG7RK1x0wbeZ9cYyGgcPYurf7uW/Lr+K1rZW7r79Lm666VYaGup5a86zfPuHP2ZRy2aUDH1Uqw/HeK/WhxPdq5K9tk96WlnvhAgE5IIQFToObyyEKDCapaveZtmydZQKmv47NbHL2FHkZBUWQaATutauY9bTbcS2xG7jxzGwNoMoGTaubWXx4uV0lMsMHN7E0JFDyYchG9etZdWK1VT168+KNSsZMWIEQ4YM8TagBz6IlA4gJYzc0SZPvZuW7sI6FixcwsQDDmPImJGc9/3LqM0ags61PDJlGi22jt/84SYO2mcC5aSISlq5b/KdLGwPuO2GaznoQwM4+thTue/+aZxw1KepVi5W2zOeO5gYm4rNVCPp6d369WvZtGEzx3z+OBp2G81Xzz+P2qSLlx//C2+tWMdp3/wvLj7989xy/c+56p6ZzHllHlOefJb63ffllpt/R+srz3L4SZfxxMPPM2HSUb6ijiXx2Vmpo3P7up/3GQjNonmzKYTVHH7c5/nk7kP52pdPwugyG1bO59lZsxk8bBjdpSxIRZmYXG0/rrzqVzSOGEaVSfjK577MyiX/orVU4tEpU8jUDuCmX99Mo2jl+JPO4aGpT3Pwx/YiEKrC7OOcDaZH8/Eef2fUG1asXE5S1nzpyyczct8JHPXlE4l0N5uWvsnTM+cwYtRIZKcvsCEjrI3RSjDx0KO49ZffR+DIHGTXGqZNm0Z73TDuue56BiTr+crZ3+Lhx59i4v77EEmJMTFI5frQy9Ry0YuYrFKYUjtLFi9mxMjdmfCpwzjqq8eyy9ix1MgyM96Yz4IlKxi/6yhsJnTRCxGzdMnbrOiU/OAHP+Zrxx7Kj751AZOfX8CyBfN59LnZjDv4c9z6u58w9W/3ceFP72LmnDcY/dkDoZTwXjHpfUyB3UKH978FBkeXk/q3lAydd1NYpCizduUyrr76ehYvXk3GSoo25NhTT+XcLx4MIiQpWG791Y2EZhOJNBx89LFccM6pLH1tLr/6xR95a8UGUJYoijjh9NM4+YTDeXzKw9w5+T5UfX82tG7m29+9hGEjh5PECdJXfHHhsx5bU2z1JHaLZ3EiTOWq6FdXxbKF/0LV1VESivpcSNvilcx/8zXG778/m9eu4U//WMqECfuy6+AMC996jcFjd2HIsCZENuYTH/8YP7/vNboLJaprZB91K+fccYTVgT8nXMw8n68mE8S8Nv8Vxo8cjgwUVcKidZmwX38GjdgZkIweNgxbmMbKJYv419Jl7HXQMVRHWfIjd2L0zk28Oe8VAo7C03j2cvr1tiV2NPWW/oPqyHS3sXD+AvYePYwwyJAkZQY0DeNHV1/N848/x69uvANjEnd6RlWM3Hks1hQQtp2SjMnmqpCxZcmKlTSOGsOgESOpbYXxY4azsGUVXR3d1OaVL+DRu28+9owrASUAjKKuphaSTl5/Yx4DJ+xNRgqqjKV68GCuuuEXvDBtKlfdeBdGuzmWwhKImLffeJW777mPxqFD2XfvPanT3cxfuICR4/dhUGMj/RLNuHF78MrCFZSK3YgqiZAZ77TTnuhDkDL6KBX6Uk0Z6uqr2dQyh7cX/4uSVdRFIaJUZN8DD+J3t+/GHb/9JU8v6HAZg0YyYPAQ8lXw2twXWbFnM6/Me50hQ4Zjih2sXNvCkZ85iSCQ7LLbCBqq61i+eDnWUiluWlnRlfncceuD6p6GtagMfnpdl7duKuAW7ePKxjqEU3VNNUccciRX/fAqLrnwQuqzWWbO/ieb2lpR0gFh9jvgI1xx+SWMHdSPF5+aycsvL+L5x59gwaIVHPGFE7n00gtpyOS4/96HefvtZQQC4qLGmJDPH3cio0aPRZsYB07o0T62UODtVo/U+00s2iiC7EBOPvXLdHWtYsYzj/OPP/+V1raS85SWO5j97OP87KqruebyK7ng4st4fcFKEIK6+mrCTAgioH//nZAmJq1Jt/WG2VGzwoAvQCj8CCc2ZPjIXTnhC59j3rzZPDX1UZ6Z/hyJzVBd24Du2MjMaVNZvngF05+aTWdbO5HUSGVo6NeATQxhVRVV/WoQOnYcab4CLn7L90QgttsrEBatBR89+HMcOWFXFj73CA8/8gjPzn2dRFVhwjxDhzXRUKWQOnV3ughFEhcRAuY8P4O5y9Yybr8DGJB150omk/VhVEldbUQkYsfdID2nIr7GO8J5An21HgeQhdhE7LX3fnzmMxOZNfNpHnnwAV6aO58yEWSqaB42mJqcBO1Qas57HtI8YADlTav47Y0/Z9Lpp3Ptjb+nTAYENNbXE6oAFYXkaxtcWFAkbh+Z1E/gU1yFcytGVqASh8UwYT+OOPYYdhqUY+YzD/OPv/ydZas3YkRELt+P5iGDUDLBemLHRCh23mMPTj36k9zzhxv47HFfZM78f3HaaScxoLERIaBffQ0gyFVXkc9nkNqxzVTWUsV5uyPTtKf9z7CCxoW9pJUOQqcSn4YZom2GMFfLTg39efnlObwy/2VCUwIdY5IYZcpEGcveB3+cTxz1CT681x4UNnbx9sJVLF+2geohI/nYoR/nyMP3ZcLuI+hs2cyGljZAoRPFYUcczfkXnsvYMSOwOqmcAimHWMVp2IdmUSS6isOOP47rb7qa5mr46Xe/y/W/u42ycWyPIlPDN7//Ha745tdYPv8VHpgyjW4ylMlibITL3Nc+rGbeZdjT+zqvuREuMyqysU8JdkIwV13Hxd++jO9+62JWvzaH75x/EQ9Nm8tu4w/kuE/szzP/+BNnfP0ipjwxk0RlfS60pejTUIXWhLECnSEh9AkdCcgyaU37d2taR+T7jeZn11/HeacczuszpnDuJZfy/JuLMTIDtoywMdK6xB3tufeCQNGxbgM3Xn8n2X5DOOb4o4noItAFwiSpkFDFQnmEojscXO0261NmA6xwVW0D6zMEESTa0jh4CD+59mecfsqXeGn6Q3zr4ot58bUlJCqL1hKpcRlvGISJsZl6vnzGOdx+96384bc/58Ddm7njjnt5Y9FqMiIiTqSvBKw98jCNoacz1TsE6pqwGmVjl09gAiYc8Gl+dtOv2Xf3nZl848/44U+uZm1bEaNCEqsJbIJnpgMkG9auZfHSNTQ2DWPC3ntSnQt4+81FdLeXiVVISbgol9Iuhp8o60qQm9TZ2/f2P9rorlSMxWrtwkZWEYqISAWExvL840/y0+tu4rm5r1I2higTYETOJabYEEuECQK0gUBEYCSlQkKceHSPsIRCk4lc9ppOYi/EFNV1/RHKAiWkcbWnLR4rLTyKro8OC+Ez9YSKmDjx03x8v/0YM7aZJ56Zzpr1rRRVHbvs8zE+ceBHOeLwg9l9191oWbsBoTW60IHWDiK7eXO7gxbKbeEsO765k8ZpZmFanzsQFqtjcg0DOewzh/PRfXfHqCJTZrxIXD2A8y+5hB99/1K+dPTBnH7qcfRraEDakDAWlNs7QSpKiaGtXEZHIRoXXVA2qdSR60uzwqBlQv3QkRx82OeYuOfusPJtnnx6FsgQhANbpAAZIRRSKnSxncm33cIj85dz1rnns9uQQdgkQQhPDWZAakN3ZzfGCBCuCmugXYVdLfBoNFGZH+1PLoXjuK9vHsFhhx7CAR/eg7Xr1jLzpfmgA5QMKohFYRyTcCxCdh43lhE7D2O3vfbi1JOOQ9syC5YsJUtEqavsorVG011ox/qUHys8LNdaD2hysXSXGYgTTEYjpEWTYdz4j3Dwxz/Gh/ccw8wX/snC5auxSqGlm9fQJoTGEgiYMf1xHpuznAsu/yk3//oXnHHyF7jzj39i2dvLUIGgUCiACCkVEkplV89QCI2U736Cb93+2xvdW0+kLLCJEIhiQml9O+0tG9m4dg0L5r9Fl7GceuZZnHb6V8kPqCPRgoQMliy6LGhZvYZCazub2luxOahrrCZXm6W8uZXWVS2sW9vOqpZN2JwiX5dDWYMwgsQKLDGKMgHCF5nvFervc3N1X0XSztrVm+koKzL1WZpHDSHRGhWF9BtYT3vbZoqFmM2bu2ht70RlFTuPGsLyN99gybJVxMWY2S/MYPjYYeQyuT5C4VNTw6VzaAIS4QAyITHlrnY2rt1AoqFpyDD6DWigYLroirupru/PsSeeyFdOOYF1a5ZTX51jtz32ZMjgocyb8SJdxTIrVqxmwfIFjN6tmRCNIPY+DFc9py8tQNOxcSVtm9tJVJ7Ro0ZTl8vQ0dmNixZkcIk3BUISMgiULvLwAw/w27v+xpFfOYVjjjmSyIJUOQY2DmDZ8uWsXtNCR9tGli5YyKC6flTlqivMu2lqaVpcwQqXXKNFhABCEjrbNtK2oRWEYuTI0eSrq+mOi25hamdDJ7gCnsaGSKPp6Gx1vAW6zLIFC5AkNA0dwuDhw1nw8kusbdnE+tZO3vrXfEaMbCLMRthKjsa2sQkHglFus8cFNq1fR0dHF5lcnmGjdsaokHISIym7bDjvZXDapqG7fTPZKGCnpiaiqv6M3nkMxe6EsEoxoK6KubNmU4wlC/71Nu3tGxg5dBDCGBeu/rd53SvNbvG3SxxwvgjnEHWbvGQ1m9es5o6bbuSR+hz5mjxSacpJiekPTeXFwPLWouXUjx5IiRIFkaCTIs/8428U589i5szXaB47jj33GUNN927Mmv0GD0y+h1mNVcxdsISxe3+EpqEDWDyrREmX0FY7yKpOPIY9tW59ks17kGFSWkrdG/jpD35JVX0jT734Km+tauPTRx7PkNG7MPEjH2LWjXdwzbXXUty8nmVr1vHVffZh/zG1DL9nCn+44Sc8N7yJF19bxHk/ONtV5EjeXTUWOOioC3c5T7gRLttOCMOSRQu49pe30Nx/AI9Ne4HWsIYTx44iKLRy2733sblQYuXKFUx9YgbHn3wme+w5jkM/NZFZ11zPNVf9kE3Ll5IEeQ45ZCKBLoIs4BI7I2ylGu07NxUGzJr+OA89MRebDXls6tPI6kHsPWEXl9BkFSRQLhUdSQKW9SuX8ptf/4a1GzvJFbq466bryNU1cPJJx3HokZ/jz4/9kGuu+B41kWbp5jLHffIgqiOLiku4fL0AkQI9rHV5l8IVUQxsjJCWF2bO4O77HqQ+m+GBx6ejG4exy5hmQmkgNsTGUjJlLA52bIud3H/XPbS3G3SpwOS7/8ye4yey5x7jyXRu5M77H+S6a39ETWRZvaGTkz71cXJRCLHuiYpCTwQAh4QrW4sSBpGUmXzL71i9dhNLFy3iubcWMPLDn6R5UAOhjjFGk2hDl4Wyh/aNGbcH+dK93HzNlSw+aD8e+vtDDNllNLvsMYHDPvomf7h7Clf+IOStV19lwNBh7Lv37gQmwZVv7uWM60N71/rotsdMASEcmwiOYMEaT+qQyTByj10pRbVYD+ULaus46NMHQ5hlxeJVZJuGMfGgT9OdCSEs07RLMwe0xwwdOpzFb7zJqN324vAvHM/IEYMYlj2Icpvl2X++xqqWjez/yYM46oQTGDSwkQHNTXxo//E0DW7wJZhcOmglQlQJw/hB6MPJagCVjRjcmOexac/Q0lLk8MOPZdJ5Z5Gv789Rn/0sLetW89jzL0KY5+xzJnHIoYcyMFfiskvP5I93/5VZL23ii6dN4oTPfsJj4/smc3usP5+Q4W10jKKmvj/aGJ59/jlEvpbTT5nEl474DFnbxrIVy3n2hVcQQS0nfO1cJp16Apkww1FHHsaaFQt4YvZcbFLD5d+7nAljRkK5HSG0g0NWIsN96aBlQHMzrWsf5a3lS+nXNJRTJ53PERP3AV3AioD+jUOZ8JH9aaivRZOgLew8eiyqppmVr85lcdxG/7G7ceRxn2fvAw/lv85dyd33P8aSsJoTz72UT33q40jdQWBLGEKXGkuP+SN65f6n9m3DwEZaW9t4c/nb9NtpCCeffwGHHLAPwsSgBHXNw9lv/31prs0jTIwKApLuIk888gxlEbLXJz/D2edeSL4qx4QP78O3v3EK9zw4jdWihlPOOJeDD/woUmvveE4PkLAya3gTEesAMCJQNDb258knnmXpmjXss/9HmXThuYxsGog2ZRARo8aMY59sgVwkSIxmwgETufI7F/Gn+x/lyWnPUN80jIu+cRGDh4/mS8efQNuGjTw/Zyb5/iM4/8xJDB8yGJM4/LqrAW8r+/PdNMjtkkP23ugrV65k9pxZNA6up6omiybBWosSoaO3wWCEplAqYIqR8+dKg1SSTFVA0p1QLJQJsxGhVBRtkUxeQqmESCQirKKrqw0lcuRq6yAskdUJshvaijFdwhBVVVGdrULYmKRQoFyWUFVDFJU8IigAArTQjnwBHAzQBhQ6i3S3vzM5pONBK1IuWNpXbeKWP97Ol847myHDB6ASl9RZLnZT7ChgZEhQ30AQBQS6DCamq62bsrZkazJk81lk7DzE2xjCW5FDfmjPPcnlq7DW+GowTr0zUoKnaCoXysz752yefPk1zrjwEvqHEpI2ugpFil0abES2oY6qrCYoO4W8mLSzubuMsBn61dU4jj5r0QLn+wCXJdcHckiLQesY3WGYOv0JWtpaOPP0M5355HPHiYt0lQqIfC2ZQBCWCxS7CxRt5MWJQQSSbL4aRUgQF2ht76QoQ2rq6omUIDRlJI64w2XtK95cuJhyscD43cYQSEiEZ5ExBmMscXeR6Y89wvJCmVNOP4t8UkKaMlop4lKRcqFMLpsnCgxGxpRKgs52Q2IN+bqAXFUWk0CoDDop0tZeRltJrrbeza8pE1iBwZGbKBEy/5U3ECJhlz3GOV+QMbjKcxCXEzo2tXP7XXex1yGf4qP7HYCKY4RNUEaTFAqUDIT5HCpICNCIWNLRVSbWFhFKsvV5lBFERlPsKtJWKmGyin7V/Rwhp8Vj4GPH4GMl06c/TfOQ4YwfP36HG32H9dGNceCGCtuIkD7VVLgsSZtCPAVGQlhTjcxVIZBYWSawJUSSoPM5cnVVWONQWGHqSczkEBmLFoq6fD+UDkBrtLYYIkwWqqojstITF8SJqy+Wy1FTJTAkLs3dQxTxhBMpbxd9PlOdlS5sjmxOUTWqmrMuOJ2GxlqEdoSHBshGWaoG1jrWGoCkiERjwpD6fgNQQqNFTDlJQETeUdAHdSIlKvAnVZqjr6VDstXWBHx4v33Zec+9qAk0se1GKUOuuor6mghhBSVrMFp7RJQkytTRmIFYgdRlpHHEEfj5Sm3gvp3pAhVmCOsVhx52GKVyJ4IEaxzFEzZBZjJU5WowOibQFiED8nX1RCrEqIRAS2QCxgqH6Y8i+jf2x3iuudSZawhJufZ0hYHVVtK1FIYEiZYRUmhqa/N86tBD6ZSKjIkRRqOFJcEQZHLkogzCltHCES1GWUX/XMbdR3QSJDGxgARFIKrp3+CcigYwJnaAGG2dKyL1uldGxU2vksIh24QgzEY0NFVxymlfIayvRumCS+X2eUlhdS0Z74x0e1aiVZaaujxSGDQao8tYoSjbgEx1PxprNYkqEpScKRhLAcLBpCsmND1+hB21HdroqSpcVVWFUoru7m6qauodisk6tJhWEm28YyDRQAm8VzJBIpRB2xIiccLD0yx66KILZyShxeoEayyKAGlcccREuSlWsXaLU6R8aBZrYq/YZR1EUWqHKBKpCqx7Nnkf1rJ3+SBtghGSxqZm0AUS6wr2KaPBWIrSIEyKVfbwUm0gcZtcB8ZPwnZO8+2NsZtq3JUCtJAEuOKD1miUsNikTJirprEqQOsSWmkEAegQYx001MrAxcmFQHt1ThpHomCsdMRD0kUuAhPjcrX7VtNFWIFMEqzU5GpqiUQNZVNwnGzW4cYNIBJfslgqtHGQSp0kYFy1EceUEhBox3uvtYd6CsfBF4sA69cH1gFNla+fpn2Ks6IE1uDwWwabxOTrGshKsEnZaUxCue9hSSykOH4hFMKUQSSUZYZAW6TIIHSZEIvVxjmXJb6mnV9LUhFjMdZxwW253fFlpTzTC27aBwwcSCxisMbj8DVWGIz2gBSpAIXQqbMxIUZ7hqbQcbmToI03VawjcxHCOLNQSA/yEbS1tZHECdXV1e84j9vf6NY6W1wKqquradppMEtXLSWTzVBdmyfFhhtrEdJlo4XetnSSznlJjVAoYVyM3QhXJke4zzv4oXChMVIVz5FMaus5z6wiIEBYh1d3lptz0kjpwmw97C2iQlIBgeecl0jruMidJuK0CQd/7A1p9Smo1sNrrUDKqEKG6AB4jolFWY+Rlw5lFVhH2uBEkMtuc+y0Yish4197skPrSfmEUCis5yR3HnFhDYFwY2BFgPXEiEq4kKG1EilCpNBYKVEopMd8Sx/ylL7CqZSB/65T35V17CZCSipVxoRESNcfmf5tfaRbgDIBRjgvtkGgREigHK+bTWdAOphwggAVIn3aSwWUElgwEFkHarb+fk7xcXxsVqjKJncEEu7UklJhpcRaR/AYeqJQawOMlEiMK+FtlctlEClRp7+/37RKuudQ0sFUrQ2RAS7JSSmMdAIQ6TwE1ho35yJ0s6ukv5zDK6Rr3+HdrU8c8wlJIgDjyDxSp7VbJ27tGX8QKmsqAkUKgQ+Uo6QTPMYqhAixSoDQKCEx1p3q3V3dvPnWArK5PI2Ng95xo2+/gIMnaPBEn3R0dDBn7kusW7+OqnyOKJtFSokxGuFJ6XocJb0zCtKb+P3U602B7Xndy4FWuU4auyT1pm/53VS2puSC6f97/nZ2elJOKJdimpqayGQi72DsLZf9UrX0SmZg6yfx1xXb/N3TtpT12wvxWU8S0NHRwaZNmxg8eDBRGG7nw+m1etxR27vHdu7wHv7vx8nLu82bNtPR2UFz85BtGFdFhYCiZ2ze3TDZeox7rxCx1edg634LIVi/voVyEjNo0CCH25beGSy2vJawae96z/6210zvla6vHqVrq7mrfLXnfS+XWbN6LQhobGz0uSPvLcy142a3czhs+xlwY1Asltm4cRNJkrD33nvT1NS0LVNur7Z9Z5wxFS97+sDdxQLLly2lZX0LXcUujPH0zJWO9Z7ULW6x1fvv9nrr93a04N/9tUjzug0IKXy5ovRz224eYd/pXlv37Z370ZMy3PN/6/HxvUMjovL7v/OM24qjvn7X9pq3HsZXsQ3pBKQboi/X3npzb+9zfX+mHo3Db+neUaCtr2a3eNWrvfd1Z8X2nin1cHvTKKXs3ubQ2NG9+jonO/p/7+eRRFGG2toahg0bRkNDQ4XnYEeUUjv0um8jHf1oxklMHMeA9Y6vf5dE+99oAizbLI4dDsa/8c7vdNrZCjNPqs3//x/DtH+p03XLDb5le79m2OEoeoRk7w3Wu/27+7ejubOVtdRD3/TvrHPXF59J2qSURFHkHeem8t572uhAxYtXOYV6K8/Cn0L/NrXlf7H16mKa7PN+tw/68d5a73Dv+9uPnvFKd8371aVUQPdoifYdT/TtF3DoFYWv0Ocgeuxb++7W4H9K63mUdGDevwXTW6T2/vv9W7/Waxc9r9/vzbR1633gpO39m7//nFWfDkEPvdU792v7qnvg/rmmAAAAPUlEQVTvD7zDl9+LqvH+tPeaEfxB+89rfZnB//yV+O9v721lv2vZ5A/aB+2D9n+//c/w6B+0D9oH7f9E+3+pShTRYQxGrgAAAABJRU5ErkJggg==)
Write the linear function for the data in the table.
A linear function forms a straight line in a graph. It is usually a polynomial function with a degree of 1 or 0, and the equation f(x) = mx + b, where b and m are real numbers. Isn't it similar to the slope-intercept form of a line, which is written as y = mx + b? Yes, because a linear function represents a line.
¶Examples from daily life
1. To print logos on T-shirts, a t-shirt company charges a one-time charge of $50 and $7 per T-shirt. As a result, the total cost is given as a linear function f(x) = 7x + 50, where 'x' is the total number of t-shirts.
2. In linear programming problems, linear functions represent an objective function to minimize costs or maximize profits.
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Ramona’s garage charges the following labor rates. All the customers are charged for at least 0.5 hr.
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fVgi1bNrKhvx91juuvvopv/NM/86vzfsp5l17Bo6OBTAMqGWEyEfeUMum675IEVAKZGo0sp8zrZKHJNddfx3tPP5Ujj3ghK1ady1CzzYte9Uq+fdCh7Lb3AdS1Rde0aQzlNepZNzVXQzDqdUfe6EGdImpkeZ1aTw9/uOwqTnnrezh8ycF87dvfpG96H8VwPxdfcjFDBo1GHVfkUdldTr1WQyyw9rF1BJSPfPSjvLvMmT+nDxscpdHoBoZRaVB65dUnn8z7/uJdDPZvZP78efSvuou1/Zso1chMcJLx2IoVnPWN7/C5v/4Ax578Nl5w7Gtpl46+3m6G1gqbNg+yeXCMQ55/NF/9l92Ztfte5HmdWs80Mt1Cd1ZjNO8CcQxt2cLGDYMs3mc/vv3d7zJ90WIA+urGugfu5Nrl9/CKFxzOl77wBUwzHJ7ghccfuo/LLr6YZR/6AH/58U/zhtNXsdee8/j2N89m+e0P4FRp4nGqExEHk7INcZ/73Oc+t6MPDA8Ps2LFCpYvX87g4OBzssd9XAwzqDV6qOeOB+9Yzs033sD6gRFcXmNww1ouvOB8HnxoFY1GjQ0b1nHFFVey5uFHWX7rbaxet4F2a4zbb7yZ+1Y/RvfUKfSveZDrr72JgXZJo1d48LbbuPTSa7n51uVkOZSl8cAD9/Ojfz+bX/76QnzeYHp3zur77uYPN93OiPd05YHbb7qZn/7il3gRMhHuued2br35NlavXMN1N93C5sFBRBWkxtS+qTRqGc2RUe5efhvf+9ZZ3HjLrXjVZB3roMa9dy3nlttuo/Ce9sgWBjet5+47buOySy7hokt+z5p1/XTVc4YHNvL7a69m9UP3c+ddd3PfQw+Dee5ffhs33nI3a/s3sWbVGnq6corWKFdffRWrVt/PfXfdxXU33sS1d93BaKvFyhUrWbNqDfvuuZgHlt/KJRf9jhtuvZPHNg8QMsV8wQN33MKVF1/Ow2vWY3lOcBI7C/+7l8Z/k4gIhxxyCEuWLGHu3Lnb/9xTkUOuXbuWiy66iB/+8Ic88sgjz2loqhEBHWaBotUkE6GeZ5QCzcJDgEYtpyha9DRqlKHFaBkQn9GdesiboUDyDHXdlO02uR+jnnfR1m5Gi2EarsTlXZQlSOnp6uml2R5AfEEtb9A08K2S3MDVcgo12kVJTjeae8pQ0F1r4Msh2q0APqPeyHDO8CZ4uiitRM3TVatTFCOYL8nVoS6jNEdLM0Riu2pZBAiB3p4MyZTRZgvfKshcF60AtVxxUtJsjoAZTjMsy/FFm9w8UuvFXE6r9ORqdLmSYrTAW5tS6iza5xBOe8ep3Pz7q3lk3Qgf/OAHOfWVL+b8f/8Wf/elf2ELNcZ8m3oto1tz2sNbcEBW76KQ2H2oQqdN+LkkFdDsbW97G6eccgoHH3zwdj876brvoqjE/uy85hAcpoHcQPIa5hzqCxqNOk3zZM7RIzmmdZyAUdDlajFaN0+t7lBrRMCICo16g0zbOITMZZSa0SpGqYmC1vAG4pSuei0hwyBTIWvUyUojCJA7yrKgJhmupljWoExJPhEjo0AjOI2ibINkaM0RgkBQTARVg+BRCzSygAVotkrKNgRtoHmNXFrUVShRSoOsawpqAYLDiUfqOYFezBSzNo3cYSYUwXC1bpzUEC90d3Vx8smv4QN/9m6MuCDXr1zOpVddzkDh0VpguvP4oqQErDaV4KAdWqgZEdf3XLXnOy+Tir4LEgEbJSHV0tU8pVTLE8BHdJuAqRBCRh4UFSjF8OpAIPMBEZ+OKZgqhQREQQK44CnN4R0RwGGCaEZQIebbLdbzBRQjGAhFRM6ZIGpYyFEV2hbwGtFedR+bYUo1vFoEsIQcsZIgUIgDDbiyjYp2kHCmAlJLYJ0Aqngq2C5oqkZYBWFO8NHY0x6z6iEYKi726ItikkFW8sgjK/jiP3yZFz7/SKZP7WZgwyquuOiX3HLHXbhaF0ZAUDKFwjyoEkxw5ICP6DeEybzyjmVS0XdZqpgwYsG9OlwJGZ7SBC8OtRKHYdTxIjhrA7XkXkbFqSCdQQQTcAQkGODwEktUWVShWBqTCPfU5KEGSYpqGktoGhe8wwE+Rq0msfQvCe/t4xgkqaklIIwhERorWyHEx9NbEtFmGT7CciWjdIqYohbSMR2+Y1grpatYI6pkWUBECVJSSqQla7WGuOj8X3Hp+b+JpcMwhkiJ5vVYdjPw1AABKVAibDUgOCLgJfF2TMoOZHIb3EWJ6hV/8gIeTTXuyIbikyXMAlSYb68lQUsU0EDCokvHIorFz+cWrXyIkDacxYUeFIJIslvjZbkgkkgYDCSkVlCJEE6N5xFTNETMehx1Fp1di5tGkBA9FBNcwtELEtliBNTGldY6118RSEgHlmoQ5wCfqCLiNVTEGJ2xBUA9ogEjhgdduSN3hlNB8y6sNhWjjiYmGROHkaMoziyW7bQgYHGjm1zGTyk7Z9EtBv4hhM4y387HdrixPvH9bf3OUxxjV8V4lpumLOLEo32KcNNgGWIZBEMpiDqvaPAgRgmUUpBZhpqg3jBRSgJmATWHhkDQIrWgaqq0B7wSrbgl2ys+Ms6EaNWrDcEShj1QMY8YmO8oNaURLLLQWDKBZiFiwMXIDJwZXj1mEBIDTmSTCQgFZbXZWKgciAnsTwGxAhNHME0eTSTSUEibCeTBsJDhnMesIJgmjyCAprAo5OAVLxkmHqSI7DT4uFGFAFKCKb5DK/Xck10hgNkpRReBrJZRb9SekHXvkIml36Tzk22j5DH+/tafr17bNrL4mSVbpFrQYSLn2JM+BJ0Rbz2q8fNXFimRSVTurARUHIKSE+KqtoipEgPEU2qGE0kMK5GEwbRStIAzJQsB7xxmdWKarSBIhmlOFgIaAHExeRYykEDQ6D5nFqLrT4aX6PBLRVsV6WLiBtK5dxnW2SSSomeSQgGJ5yMjqOvQTom08WpgGm21gUmOWAwVFFDLUojhcIkOSkRwgai0puQaUGqItRAFr5FQAjwoESxEDAXQBqgnxDRcxPabIw+K4DHn8BpS+CJPWoXjlmN81VWBV1xRFddatfKeeq09HQbkcQNm6d+KKuOJXG/GrjjZE+ndnkq2q+gTiee6pnTxuje8htJaE+ZBqSZIKOLAg8NweI0UQWKerPLyENRc5FfRyEiiweHJCM4Q2mSVVep8Pjq40R22dIOiy2nVOGz8Isf500BMIolCERgZGiFzOZnLqG7oRO8h6nmIdWTJ4mKzQFCIFE/Ripca3eB49YJQ4iXgyROXXCSYqGYlSsWnFhVEDEofaLXbNBoN0NjaqhaSha7G6BO5RORHUwvJW1YkaLR8W9M6UtKIngTlhIXcmSgmLqJIyTSuFkW7hS8Dja46DghWYbxjgg9pxxi+6sojjqXihwNQc0BJkJAShZ6AQ4PgqRHEkVkbwyWWmBA3BqmOMWGrDUq7KAnmqddzRCsPykVoqkUoi0nAmRDEKBxocGQhdNZNvFexK9FSKGOWgXhMfNrcXDq3p2IEiuN5stJVjyOr1WuJ6298IW1P9SNppqVWXRcJPsxS7sYmsA/5dP93pLhp9iURhxpMmzbjKQkin9Kim0FeyzjksIOYMrVBkMg3ZpYRJGaB81CkC1JKHCYZah6l6MSYMQZMLCkaOdCy4OICUANpxe9Yhk/sKVrxkKadPF5jSImwaH3E4tIwAqbjChwVzjEyPMrYYJMDlx7I9N7pmG39ueiKxhtbqiSXm7jYJXKUuSCoCYWrNppkMyQSHgbJCClx5ExjpvpJEymEAM4p/f39rFy5kqVLD6Snp3vnrIMkylbinId064QybpxBE7VSsuZPdV+xzuapoqxevZpNmzZx8MEHk2VZGlM1LodI5JXDoqKZBIK5uCTFY6Y4y4ASr5HfLiYf88SuI3i1yJ5jlTLt4HJFWPHgg4w1mxywZAnOKeCf8L0qtwCleorMyEJG7uOmWEocn7N2ylcIEON9owQtwBwSspj7kDI1DElSJBk3JAbqlLvuuguA/fffH1cRqPIEJX/C/bekmBridVtVHRFPIMQNM31yR6ExNp4RCVaiLiZSrrjimmeu6CKgIlgIeO8JVTnDYsLHLKDpJF5DzBiHlESSFGmGNLzEKxasjAsFh4aY/TUtoxKaUkq0cgGLyiaRglgrhY6rK7qUBhAwDZifEAhYnOBgHh88zmW4PIPwZEWPjKxQk0RdrBmC4CjxaZNxnYRX3Ai8g1KUmocc4oIBUKHUbXRqmRCCkWVZx9XKMpeUasc3KVrPaOkz82luQuRsk3q0Qc5igwrR+3hqqfLqiorinMPMcG7imCzdOAHyCfNenUWJmfRqPj1mGU5yOtY51BD1CC0y9clNT8q0AxEZZxpWdWTOAfrkr1kkpszEo1riEJxEjj5JtFZKrDwwYZOOlYYYeog6JBkUrXy8SvkqQ5Lmpvo/z/PxXMiTBr+1osdyo2Kao5Q4KwhklJpHjyzldGKpcpywu7pPW19vNb4s5lrUpfna8XxuV9HHY5GJju5WZ0wXYJQy7sRHwEeISRmq/HS8kJRDHVdCEtGfpfOYJupETxAhDyDmKJXEs0ZykVL8a+PLdTzGmsiFrnSMpRnB+87PW02lxdG44AkCpaSkkUTLhQnBKlZyjZtNujkxmRQ63kUpluLfJ00XEB9jVVnwECrm9J1QdIu2wJthlqGUKC0CdYLloAVSzSXuKTOQ4xTeyban38f/VrtzLJ/FbP04GEfMocTSVjBFxOPFovoH6XDYxbAuZtir5N/WOZDtDpCQwkeoHg0c572zqKOL0fkjwZAQCBLwxPhOzSLQJo6aWJePY5KgnZJn5K8PaXuqXk8nScoVQugoewix72Gb+9UTdROA2DAUaax9mnMFSjTlQYI+UdO2NU9p4wmpVBk8ok8zRt/6ecvb+aZELs8YfyTXB0UiBSCC4slSfF6VaaKzWHlDiqSLc6kmmyZbiRZSIqFAmXbySE+ect5iKfEzHoNuldyQKvUxfi9EZIKSh867cZOKW1FI54rVoJj06SiDaFr0MYHWKe2kmnYpmsKSbc/XxFVRzfHOuO1VcBLPLbSdkgclS98ttEyejcbuuKewlp256Mzc1rz9T5YUryavJghkFiL1tMTQzJl0ynxqkCX9MClirsNc2iwqd/cprrszjJRTscSp+6QW7NiQA6RYu+pN8GTB4yzgRSklS58uiTSVlkKKVOHQamOrzjlxLBadG9HxDXKr3MeEsUz83aq5dojlEATTithTk0EsCdQmUGKlcRrpujoZEcZX84R7lcq62zbG47ITWfftHMBIddjowos4nNSxsolagSm4rE5hHgsFWFyopcbSkguGhti1VaiQe4dYdP0lWeJgIcWmSiQTF0xLAmVqDAlpegRN4xyflojn7uyJ1eOktnE91dNRxGKNuKFxAgsycHW8b8eHIVgsQSmx2SO4Rir4KL40isROWiUMnxRvmSEqWz8IY/sz/ISvpjjFEne6GZJlZFrDAvjQjt1yRuz93oljxmlJ2fbKg3vSaNJspvyA12j/shAQV0eyiJwz3yQLBUF8h7E2oFitlsIdwRmROdYXOzW+KtyrrkbkiUoOpERktASOgKMkJgKVAnE5lZJIVsf7FoSCvOMlQMc93AmpNsQnX0AyMom3nqSEea2GBYnP7qhltEJGsJhAVAATMhyqNcxZp4eiLNrRiJklYxvD5RhyJN8kWMea7zC2ZzuKvrMItSDpgtoFV195Nav6Rzj2+KNZPLubFffcz5U3LGevZct43mFLqEmJBI+mrGPMrBqJjaHamDAM5w21SO9rmsU9N0SVDmaginkPEimKTaJLm6I4qoQHpDjvKQn+LcV0UJM2d9/2R/7zZxfQKoWXnPBqjjnmxXRJ3KyCU1qDg1zwiwu5e+UGCisx3+bQFx/FK046ia4QM+jScQsmzms819MTJYQyUjSZkWfC8huu5dJrb+eFJ5zKYQfthfjh1LTy1K77+JieaolEqSoezmJoopny+MoVnPObK9nzgDKwlXMAACAASURBVIM58WXPRyQnupWeTNtsePQRvv+Li+gfGAFviGtwyuvezBGH7ouVzZ0YHB2lkomu2YT3o3MXqLLZ8cWY/W+ODHLFJZdx/a3LGfOOQ444mhNfczI9eQZWEMuO8eqe+r5Y6jLc+vRYZxuK/0o1WzA0MsLFPz+PW29dTpA6hx35Uo456Vi663WyMiaVsyzjpssu5urfX8cmU8qgzJszm7e+9XRmTJuaXPNtlbR3diuPsvMtsFvteqnjSTRG3q0WN111NZff8zBLnn8I+86fwtoHV/CLH/2UY7MaBy7bjx5KMoVMlDYZXgKWGRZa1DRDM4f3AUXJNe5ehSmYI0Oia6WGhJQVVwgu3v3CYv93pFqZuEuHznh3fCNT4sjlrHvoXj7z8U9w3xZjjxlTuOTqGznjS//Iyccsw9oFKkIxPMSvzz2X2x8d5IB9FzPWHKWxaB7HEOjtxKDbOOO2FuvOSHLLRXOi21lwzcWX8vnPnsFNK/r5xJy9OeSQfaj7aqt8prJVKimFLdGqC4YqPHjPcr7w6f/NOZffyuve9V6Of+kLUOeSe+TBlfSvf5gzz/wO83ffk3lzZ9KyjMOPWseRhy3ZxTHahM26+l+e+Ak6D5MTwWnOw4+t5Xvf+w8GWm1Gt4zwk3N/y3DheOfpr8SCT/33xJyKVKHndiRmbXegYxNeNEOdY83qNXznu99FzRgeanHOuRfyt7Wv8KbXvAJlDMEhmXD7jdfwnW9+m0UvPoZG1mBTfz9jo2NI3/Q4l9u40l1V9qfd6y4IVobYg2FlbBxxOUpOJkbNGc4BLsfIcFIwNjzCo6tXMeIzpu+xOzNn99JowvDaTWxsFcycP4dGaPPouk2UjV7mzphKGB6gf7BFPqXO6i1b2G1mH/N7uln96Fr6B4fomT6VBbvNj4ssNVZ0UoA7+agexVALZKpcfvnlrHh4A3931jkcMSfjPe//CBdccD5Hv+hQesnIzZDgKWvKye95B2d88H+QmTJiJbkp4i31BTwdjd62mFTPShRqJowNbuY/zzmH9VuGmTZ1OuqNnNjDEDTs+n4iE+aqsnCdA0jKoRhqhseBL7jiN7/kxltvZd68RbEkqg7zzRh3JhCMpwvrmsdn/u7LnPTyIxluDoOAb48+g9l5wgKX8W4CMU9GzOyH4JizYBEf+8xn2GfJvqxf8RBv/Yu/56o/3MLpbzmRmstQnyyl+PFDV30C21s7+uTzd7Yeq+xMfJTV/AW78Q//5wscuN+erLjzNt73l5/krjtv5+QTXkZv5WiGDAvCfgceylf/40csmNZLGBtF06O/tHNvnphx2jV5RqAWSeAMTcwrKrEmO7H2aKZkrs6D993Dmf9yJiuWP8SY5WQL5/P+v3ofJx16KF854yvcs2kjZ3z5c8ywMT71qX+kb8kRnPH/vJUrz/sB55x/HdLTyyNt4SPvPY3Wynv58S8vY3NzjK6+KfzDF/6Bg5fuhwSfEho7ay/GLb1aCa1h7n3wYerzl3LkEYezgC285KA9uWXVvTw2OMa+fdPwqcnBB8+jj6/ljzfdxO4LFzN30W5QtCFFI0GqhotnR+EzYvmwVMi7p/Hhv/kkDy2/lb//x2/FTDwRxRYTiM/eJsP4tgmQmpWM17zudRy09Pn8729exJjP8Che6xhNqkx1bKv1PHTfvdw8JWPRPouZ1teFtdvPcITVfauKUS6FFh61Ijru3tGYMp1lL3gRTgts9nTmzOjDiNRTpQ9kpim+H18HOxm0TpiTrZOalT8fCEybMYPnz56FSJu5c2fTXc8RdZQuJ5iRhQQTFhgdHeSPt97C0Ly57LfXYjJn4AuqfgcY79z807ruTxADTFIaJETIwfC6tfzbV7/KzxrG5vWDDLcCuXMwOshPv/s9/vjHBznxdaeyeM40vvXdb/P9b36Lg774RQZGWwxvaRNKQaSg3DLEyOAIIUBzeJTH122knCa89Oij6Q1tfvnbS8m7ZvPxD7+d9UPr6J1ex1mB84rpeENNEIdRMN5osC2JYQKagx+gQOnunc2UXDEPs2f00ugfpDChFMhSMnFK3s0Vv76Qu395HvWeObzrbz7OW95yCnnRjJlTsyefcudzPluP0OLSQWNCKuQ5+x90MGX/Y+S+iUmkoXYpK7zLWhRvZmc6SEmg6jgWn3qIT4kxCRlzFy3BZTWUFiZuHGwiMZ9CosfqYZSzvvZ/OLNdsOdBh/OZL36ew/fbA8rWTo6LCfdv2wtcxtsk8RL56jI8Hk/TlB6pcccfb+WhlXfxgXe/l7oqUgjgEXUES/cLHT9F51SVpyPjf9O5xp/ymqVQNpXvNMQnWwbB0ybTEa6/8ToeGfC8eb8lTMkFX8RkZR0lz7tY98gjnPHhvyRrGkeddCp//9m/Zl6Xw1tE+7mgqcJh5CGkbrqJ4cKOp/JZgP3EemBsN22xqX8TgwNjjI2VlN5AlNGBzTyycg0903bnde95N6efdhIvWbKQ0Q0bWPHY41Br4KjhEkIpx1FHybzEjq+8xolvOZ1Pf/KjHHnQEpzL2Dw4wOaBAU5+9SnssWgPfChSjTKOSbZS7h0oeRWDptJQKY5WIanVNZBlVZNKurG+TU/fLP7qox/jpz/8Hv/0lS8zxUb5py9+mYfXbkbyWId/0o2YcL6nMcVxEXUWYKxgW/BkqUmmOuzT8yG2Nc4Jv1lMhJpWPQIZWB6fuUaBWOwny0wQr6gqpYfdFu/HN/71S5xzzr/zsQ+9h1uuuYKvf+9ntIKiO5EsFCbOmGz71RTSSLKmPiUExTyYUVNjw8Mr+dpZP2D2nnvyyle8BELAEUunpBw9kiVPqLKgE6G2TzxvKsFinWpPx76LQOolySS27Dz64Eq+c/Y5zD/oMI558Qvp9WOolVjm8O2C4199Kt/9wQ/52fe+zXFHHcy55/ycX//2CqTWhfksdptoLO+qCaTHVu/oDj5RnkGMXrVQxnpOYSVT5yzgL//mExy931yuv/hivnr2TyiAlo+tsSGrQTAaqsydNZP2qnUMDw4lCxxTIc4cbcnxZCjR9ctrNfrmzCfkyqz5c3jXu07nWz84j3/72tf4/Y238+GPfYiF87sQH0kaXBAyM7xEVpKnvpb4+GDSFakm1BYwMjJKKD01AjlCLUCoT+WQo47Cq1F//iFsWX8v//Oz32T9+kH2mZdBmazMn+RxvtGKRCsv6dnjVRLyT3E+xtd3x7pWcWPsIXD42ERijkxjq6o3oWf6PF563FwMz4EHLOKaP/yBa++8h81DI/T2ZrGC8gzFpCqyGi7EOYiYAUdNIQxv4gdnnsl1dz/GGf/0NRbMmwVFfKa7agz0qkRcRAeGnXbio0crVK68YBDithMTxiWjA4N841s/4Z61JZ/+6J+xaNZUsnIkYhVEwJcs2G8/5i09GKdtPv6x9/P72/6WFfc/wmjIyPJY3/dYKlA5StGEYtz5+XtGFl1So0gQxZxCrcGUmXOYPauX2VMMJ20QQfMaLs/w7TGaQwMMjIzxwCPrcY0pzJ/ZF8kGrEUYbbH+4fVsHmvRdpHIQERiSaeMSK8mgWNPeBlf/crnOObFL+X6q27hgvMvx9UblBq79GI1oFLenen7lthQkU1h3tQaY4/ew7p162m3Cpav3IB1z6CvnlGMbGagGWiHGqFZkgcPYZgNA5uhK8c1FDUlD9mfRsfTaCu7HSSCOapyXuWf/KkkHn9iTFqBQVIDigrWHmNocJRmCd4XtNqRIoLRYTZv2Uzf1JnUs/xZqQ10xiFVu1O07EFyvAhajnLBj3/M93/8a972vg/x2lNPSs23EfQTqt7sKkbYFkZhR+fdagcE0gjUaiiKtUf55U/O4We/upw3vvt/8qbjj6FBoDRotUoGhiOkuVV4ytiMz6YtW2iWnu7uHkSF0kqwQO4tAZvC0zIgz4xhxmJTSxCjHQJlKAm+oAwlhW/jfRsrWkybNpUDD9yfux+8ih997zssnDGFP658nMXLns/ee8xn97nTWH73fXzzm98ga25iaGwQZyWY0DajDKm9UwP9GzbwvW/+Gwv32hungChdjQaW2nE7cSXstA8bARA5Il0c+4Ln8fMf/oQzv/6vHLDbNK6/51He86E3wfBGPv25M+haeDAfetc7ueGS86n19bBl83rOPPt89lp2OAvmTycrMnzwfwJKjyq9m+Jki/2HbR+QFFpUH/uTSQfMU3VsKRZK8G2CBDQ3brv6Sj77r2fzng99kCMXz+B3ly5n0eI53HT177jh1hW8+2//B9N6ugh++NkaVEqoRXhsbFl2qPM8cNvNfPffvk3once8+XO49IILmTd7Oi98/jKCkHIaTMhq00lP7OSp4xc0jHs6ELs8Rblt+a383zO/Tk99NvP6ernwwl8wc8FcjjpoKf/xrW/z8xvv5zv/+llW3XwjG/oH6Z3Zyw++9302l57DjziUjDZe43P+shBBQaa+0168K9y3z0jRgxGL+QpTZvQxf06guwalgeudztwF85nRk1OvK298yxsYGGly4123cGdQ9jvscN71F+9l9oypHHfCy7l39aM88ugaluyziEOWdTNzZjdkGd0zZ7Ng/iymdQmOAu9LHl/Xz/W33gnSy6tOeBmvePlRaLvdUYRxR2rnY+IIvsk47MgX8Z73vZN//s/zubooOfaVr+XNbzyVcmAVG/s3MWtO3FFvvvk6LrrySgqDRUtfzEc+9nF26+kmlM2dAWc9LRmPUuNqrHf3sGCPhUzv7aFCVAeznYp/d0k6YUiVgY+hlssbzJ8/j945famd0xhujjG4eTOZGO2yzS9/eg4P9z9Oyzxv/rP38L43nYwLxa54nTuUTtgVYlecSYkmZNfGwRGkMRVpOc76xldpj41w3LEv54hlB1Fv5HSwRJXCVuFI58g7HmQV0Y9vwPFVjyGqDI6NUJ86hfZwwdn/94s0yyGOO/VNPG//fRnYvIXBoTFMavRv7uerX/oyLcvpmjmPj3z0r3jJUQdhxSiaeuor6HbEkpTYLmZjnpLu+bHHHuWGm69j9vzpdE+pJ/QagIsPpqckCwUDW4YYKXOmz5jOlLygNTzCpqEWbup0pnTX6AklI0NjrBscol0KU6dPZ8bMXhwFWatk3frNjBaBaX3TCH6MMe1hxtQeGNrE4GiBTp9Nb4+SN4cY3DTIltESVce0Gbszpa+O+C2AYuISQiniqdvDTUYHxjjs0Ocxfeq0iJCTCpyRHF4TPCVZyHCUFMUoq9ZtIZQZM+bMY+q0OtIeYPP6AYqumczqzWhufpwNW0ZoS87UWbszb/p0XDlMkbURaoms4QmTaYKqY926dTz00EMccsgh8fnnO+MwGsmSGsFyMgw/NsCGLUPotAVM76qRkTDj22wV3cYhzVIbrrJy5So2bNjAssOWkWd59JCq8QcluDYSIsFG7PUP4Jus3dQm5F3MntGNECiHhti0ZYhps2fQyAIbH9/MxmaTkHex29zdmN6dE0L7KdeoiHD/fStoNpssXboUl1Utz0+eGDGPWJaqLLHE6lVoj4wy3L8x5onMEMlo1LuYO2c2WKDqZLXkJXVosoCYf6hCPwFTnMtYvnw5ICw9cEknlDE8FbYiRgAOk4J2a4CNGwewdgbqaWVQ75nLvCndjA5upL/M2X1WHza6mY3r1tNqK653GrMXzCbPStRHMo9Sy7TXSoegM0gFihEuv+wqFsxfyKGHLdvufD59i14lZkQQB9NnzaYXB1ZQADplOvOmOkoLBEpaCF3Tp7PHjFmoGuKbhDBMm4yQdzF3YQ/BYg605rpo4/AB6n3TmNKntC3HfIusVmPmgvnMkAZYQRmU4EfIUlknbLWAdtZ/rvqTIZjD1Rvsu9eeBBqEUGC+idMa83abT1scGpp0z57LtHl1QkLpaTGGaRvEJ2SR49lNjm0dD1qAWr2LBQunMmZ1xPsID37WPYm0+NPpO/BjE5zWmD93GqVmhNAmWKxdL5o2nRACwQvz9uhlpgsgNVwR8H4E0fFm5WdjfJCBgKONEShUCeTUe6YzdcoUhDZBM4wa5sGXZWzqgfEyoliq1OzauCq/MYy/EDHmJjS6p7F7z4wE5/W0ncPKHFcG+mb2Mc0ZVhquZxpT9ukDiR5J8GMRv2B1gmR4EYImAhTLqMg9d0WegesuETNMhBWUoeLmtHHWEF9BMGONsY2hZUmgwEmEOIpkeIy2byMJTlgUAZcuxqtQilCakYliJnhfEmQUJxHt40QSACZLXlgCYey0fxgd3yASEUMm+HaJ6WgC0MRW3DKUIG0IgcIygjdMxiJcMQTIBI+jlmCO9qwr3fh4IxsqFL5EiE1KkviiKwv1bEknZKgIIYWINwhCMB8xC+ZRlMKIHZOJPqoMRezw8u1ECb31MZ+xGAQcQomjSFBnF9F0wVOIJzOjEI9IMYF0RzuQUYFxdt1dCPcqX6AijpAU7xslKo5QZKCGEZPShVeyUKAmETLtC7xE3Kf4hMKzNiqAZYg4gkUEnobxSovHUQFvd1Z2WtErhFMn6yrSgUaKaOqIiwkRSU0rKoKZJNqjBBtNVjNoJFKoYiyVFHWYgNSBNpnEp4iWpjhxqEWWVdMS8BAiPUSQlNntUB/F1AxSjZsOWsxCytJK56pIuNgY44qglkfKIm2hzqM+Q8gJFaeZGEFd3OjMyCSLjReQ4uMIsRV9wkZjcQwV1LIzpu0112x1A6Q6BGoV57oDrWgcInVWkOpRjjKev0sH7NSjOz0g4657h+RB9Elj0mpT11hViE+AENCY6dZEE61aRGowsvhwRzEgR8TIFDTUMBc9BJk4NptYLRhfXzCO8nsSPNUmhNYJwBQVzpFbhPCaJgSdxPsXD1mmJpkK6tkBJ3fqGZ3ZkvF4XUxQrRCQxJ9TeVnExfEnpqKoqIJJHSgQ5/Fk1EPEeiBCoTmmQuYDwRQyTUnc+KCOiG0IMbQNgoRYS/euuiPjiMKdkW0qegiMI3VMwMPw4Cjtdiu2dlqc3KofODKAjVFxxGpnjQRKiZ+ASNnkAnjVSCZBIKtQaKaoVig2l6ioQiINUERaEQKoE7i+gsRYUkGswKLPEPuyk4VutwrazTaPPfYYmzdtgdQuWo09VlcSrt1KgnpMHZnPENp4BSzDWUbQEgmRFtkrtF3klst8Pe62UsTGBqJ7pU/WVkSUgcFBRkZHefiRR6jX6onkYWIdXCb8nfAyIZEjZOmdyIjjLIusrYnCieCSux0Sy0/KkVsCbpgjMppEq6Di2NDfz/DICKvXrME5nUAlFXvcW+pQc2TmE52YorjIyKqChni/Wi4iCrPk4WF5zH+YgOU0M8itnTzBqnXVIpecgJEjBl5h0+YtlGXJ6jVrEkPMRDLHTo67MzdV1UWCw5niRSLsWUrUR2W0lHAL5gnOxTUYPEYtqruWqdkmEV0KnbWo4tg8MEgAVq5ak6yqYNQR2hGuKykdZzlGN0IbJPLk5T5eg5ectjqClkzxY6gpLalRqMXt2uIaMinJrEUWSHRZQlszJHkwVTdfs9Wc0Cy2bdm2RZ+QYa2msd1sUfiUvSCSDMTEnEuspCWlRlZRFyLFEFrQFsWINMfOIszRi+BVUlmoAtsnq6pxq3YhbhpBKv7zijywWvWadrQWnVIoCWVFVVsVfOkpC8/GTZup52OYTaQ+qsKzxBVnAe9KSg3UyjztvBFHn3mhdLE7rVYYqKedRbJEDRVFc4FIEWG4NsH7SRIRtsro6AitdpuNmzaRuZxx1HxqQBKB1LDTQUpUjK4I4ClTjFnzIeK8pYbXMiaQLCpQ3Y8/lcVZ5HmJMaWLRJ463rM9NDREq9mif+PGJ1AkRSKJghrRf4rsLKHCsXc2obgmfOqe086Qx7n9AkqRWeSPr1hWcIg5HK2IZcehQSmdMjQ6hvmC9RvW4zRet5nEWHbC2jTxSEI6dvjqNeAlbSRSTmimSevTAoVTRCK2HqvFtaYFLpRARiGRPstZfI4c4hgeGSOIsmHjRpyViRorx6QEwjhjjTjEtqTNJTZyZYnbLlJi14GSYcZwJnjyDj4iRkjRG1aLPHvxXgpjLkMtEoAmux7Dt6dFJTXhO7HzDabNmE5PbxfjVEIVLY5AIgU0reh5oqKb+oQRJu12qWWwuvESe3cxIffRH/Bu3KebOPRxwACJaGLCWtzuNSijw03Ghlss2X9/pvZOjUeqWGaksnTJDTOldIEgJVlwYHHXdRZwQWmrw6tR80R6Zg1p/JGyOF5fkTgHJsZ64xZIVVm/fj2rV61m6dKldDe6U4bbOiFEVNZ0a6Qc37hMY1hBi1Kj51PzHge0pRYXmxSxFGM1GqWmPviUwBPFtBkXo+Ux655c8jWr17Chv5+DDzpwK3LIyD4Tw4LxbqzEQithgkcUFydYJOkI8ekywbXRkGEmExiDKiqsIlpRq6cHRngyC+QBCpexYsUqms0RDjhgf5zEkNDM4iYoEMk543EtsbuqKZl5Slckvr88VUCK2ICF4Hy8N97FjLkLIZF6hkjeQbwdpWSp7bTE4VGpsfzu+zERDliyNypxPJlZ/CySYn2Jz7oPgpfockfijagDQQQxxYVAqXF9qBkikXMvSDSSEhSzOl49DR8wHO0sstpKiEy5qLJ58+anZCraNvHERBVLsaaqIG6coS2S7lfJd5/inARRxDB82tnTAwbE4zXyfjiLXT50FksC9aOd2C1aZEvxdkVKHFsOJb03QffZeltISiWGy+Kzz/LcUatlRB7LimAyOo7RiYhAgRo5WI64kEIAB5bhM6hpvDJxGRKERqI2to6bF/m/IsO7bCMZJ6g48ixHRcicI8+zzpxG5a4UPUXeKUzBsuicakBDRhaj4shhRgTbYBlI5LDLgtJuxLnOTSjJ47VoO2XN8872o+JwqpF7PsueVF6LOSbBJTy2kXUUM1rkxEwrSsCTBSEzFx/AmBkuuLSZFh1l18Qm6yw+26XlaiB18tKTawkO1BmiRp5nOKmBRALR/7e9846zq6j7/3tmzjn33r3bskk2ZDedJEBAQkBAEYOigBRFmqIgiJQgVQR8VBSwUSyIgAVRSigiKiKEEkjoSSCSAIEAMYX0simbrbecMzO/P2bO3U2D5Xl8fvi8Xszrtfvae/fec+ZM+c63fT5fkVJiu6PbjbdwcFU3/pasVRUQiDQKiFAuYxcpcaxGOAeisAHKaKevqLT0VZqP4H0uVqGCCCGdfZ4JAyqmE8aZMVZ5DcYS2RijrPdJRAjjzBNpJbF0QiE02pmrKCfkvfkWpgPvGYhiFToTidCnYscQBGjj1sgWPHo7aH2ikrLWeu8hHqSPY3yxKZdb4tan1y4tBoR2j29FJVVW2wArAmfjCceMKZAVUkbj89utsJUfabwGQBob9/zcOLvW+Yy29JSmp7WT8q6/iSca6H1SpZ821lUoETZCGbegDbEj86ucrI7cMBUKsQgwNiA0CTa1x22CERpts6TCLt3glZ4Jgaug4vLTre2JTLgqLS5261R/Z++5EzPAYMAW/YIOnfdWWLQ0qXSsCAtLjKDsN2OIMCHKuKdOpPSb16vuwlWMSbvo+uRNhl7jaYyzDt133Y5JEChv5yKcZmI9nZNFI41CGFMxTrzbDKzPZPBgIXcrA65+TTqBznlrDEqmC9r6frvxdgIwdCEt4T37fuuBBuuYgSwKYdKot5tzReLNNo9gE9o7wtJ+ab9OrHOYGe/AM8aFMrE+q9JvCOti/ZIYLL64pZPbEksiBKEVnsfOjbHQ0tFzCacJOTpsVRGm0mrCRFNSzoEYGRclSKzBSgXWpx7/d070LVtK6tjLREz/9l5GL0uxwsHqkL24Pq31LKE429BL/zAM0DJLEoOy3QgJFumzlXoSWtKN6K6fJglQSfaoJDvYrRJFKrvdf7ZCfJiqAakrxz2UFQKpDYGNsdZVTcGTHqYCIxAJQkQu8GcFiQycWicswiq0ERiROLJEeoseKq+8MuzGQ7oTi5QXLe2z11rSTSCAEhYrFcq66IKxoIQTfGnugEI4khUhMEoRGEeS6MolOc3LCEmaamXpGRfhbaFUu+otnKQVaJsACm0kSFcjXlhQ/oR2I6kJrMRYp6or4U03WfKCLQQrUFajlUR7KiehjUcHeuHtza40yiOFY1B1jndBSt3slqCgjFPlI18yLJYutTUUzjdhRUpd6othuAAcwtFUuHUnDUIqrAywxqvHGG8WCE/EJ53wsc5kkd7HEAuBsAlCJIQYrC5TDrNeRVc9MFoRYIVBetYY7b3+0o+3FF5JIUALi5HO9+Aq7Po1Iax3TrtRT/kO+7KLt2lbno+i56eCx+35hMV1LkKgZBZU5Dzn1osIIUAEJEJhMESiTM50s+DVuTw69RmWrOvEBBkwZYQpYUi8uuqoe93EuonSxkc5rV9cxrg8XJue1P40TH9SIj/eifHFbbLABGSUJUm6+OOtt7Khq4yJ8pRw8MwgCAlshC4bbJhFBgGBLaNCjdGWgg4gUwtksCLpdZqn9/CjWRE4aUsFmnAqkbC+7wkSjVIZlr69gj/fdy8EIQQ1WBMShhIVCgwKGdRgVQawBDYmEwrKiaVscxDWowmdhuUZSJWVpPy5W/TFa1Fs1T1hIJvJMnfeq9z/0MOE2SqQGbCGyBbJSpCZahIV+hgvZCKFCkKstsiwGiMj0jCYjAK0hdgqUHm0ipCiTOBLPxvSZCOfg+FPcrcaDS5mb1FhjrkvvcLDUx8jjPIImfdRm5hsFBGGtSSiisRapI2RClSUIcyERKFyxRxVDiliwtDVLUh0AGGOWEROKdep5tUzVumQWSvASKxxwjaUGmkTHrj/AeYvXoIMakEHCAyBgJzKumvLyBUGMKACyAiLSBJskCeWeRIDodJkpEEbS1lVI1UG5anCtfBMt36q+pIkteMTvbdbE3qpz/5/3gEjhKCrvY27Jv+ZTSbLMSd9kaaBtcjEgnSbTVtPlaw0whQJ43Yeuvce/vTsAi6++npG0G6zrgAAIABJREFUDd+LoNCOQuPKATteOIEHzUi3CZy9HvvEAVvZOMZqL+G2pNuVFYXxnVtKT7y5ZQ3X/+o67pv6FH99biZfPvVUjjviEGRcZP7sl7nl93eyZv06Ms1DmHTOWUz80EhefWEGN9z8J1a1GQ49/AjOPO0kQhIqzKS+J5Uxrfz0ZuIR/jNpyqV1ISEZ8NLMf3L9dTfw+sKFPPfSXM445wL2HzuCRfNe4pbb7mDB8jUMHjGGM88+i712bkaVu7jv1snc/ehTiGwtp3/9HD5x4P5QbnfYdaO8E1L3ZHNV1H63ESt9FG4MA2F58IGH+emNv6Kjvcis2fO49JKLGNwYYgvd/P0vD/L0nIWcfPYZjBszlLBzE3+56y9Mmf4M3d0JQ8aN5/wLz2doQ55Axjw8ZSq33HkXYVjF8ceeyGGf/yxZigTG8+WLdH5TB6WgN92T9OG9xx54ghtv/A2r21t5/p+vcN6kSYxtqkaWO7nvtnuZ9erbnHTOWew1ehCi2Mkfb7mdJ2fMRakYk3Sx8z4H852LvkG13sz0xx/l93c9SMFmOe5LJ3H0Z49AGO3s+srKTzUsR3MuhXThVpxGVNq8icl/uINb7r2ffHMzRx93El874Xjqc4LWtSu5+eY7KNUN5rQzz6ApG5CR3bz47FNMvm0y61q7GDB6T8755iXs2lyDbmvh1tvu4OGnZ9MwZCyTJp3BvuPGInSJlH2+Dwd5r72woya2ftmjRorer6XFFIvMe+FFnpz+PC0b270TQyJ1gpSWQCmUdI4ipPOCRgJyUYYoyCIIsTJHoiJXrctaMlaSISKjskgVYYQrNxQAkZQEKkIEzumFCCqqTA/xztYPsz2x5xwtSmjQbVzx/R9w8+1/RVtJaGD9ug0oBK/PfoELv34+z736Bs2jRhIIQVxoZ9nCN7j0ou+zaGULDbUhP7niu9zz4FRUUIWocNLKre639XsAzsPvPOxO+xAKli5ZyAXnfoMXZ75EJpdjc1eB9o4ONq1eyPcu+z6PTptBY/8annzsr1z+41+wubWDJ6Y8zBU//jlhdRVda5by9XO/wasrWyAMSUmmXNSht2a29fj0JIoEAcyZMZ1zLrmMeUtWk6nK0d3dQaJLJMV27rjtj1xy0cX8/f4HWbhyA8iQQucmpjx6P5tLnWSx3Pnr33P1z26gFAjemPMCF33rSjoKJWTcyo9+eDnTZs7FBnmc9hYjhWdoReLOIjc2HuyNDAWzZ83kwvMuZtFbi6nJ5tnU0cHGuEShu5PJ19/E9y65lMn3/pXFy1uc+p908cKMF3nptUUEtQPo39APIQWh0Mx7eQ7fvOQK2otlZGkzV11xGU/OmI0NsgiR5iyISn6GW2cSDc7WNmUC083tv/kNP7vmJjZ1GMIgS8umVhISNi5byJUXf5Orrr2Gv015itaOMkGYsG7RK1x0wbeZ9cYyGgcPYurf7uW/Lr+K1rZW7r79Lm666VYaGup5a86zfPuHP2ZRy2aUDH1Uqw/HeK/WhxPdq5K9tk96WlnvhAgE5IIQFToObyyEKDCapaveZtmydZQKmv47NbHL2FHkZBUWQaATutauY9bTbcS2xG7jxzGwNoMoGTaubWXx4uV0lMsMHN7E0JFDyYchG9etZdWK1VT168+KNSsZMWIEQ4YM8TagBz6IlA4gJYzc0SZPvZuW7sI6FixcwsQDDmPImJGc9/3LqM0ags61PDJlGi22jt/84SYO2mcC5aSISlq5b/KdLGwPuO2GaznoQwM4+thTue/+aZxw1KepVi5W2zOeO5gYm4rNVCPp6d369WvZtGEzx3z+OBp2G81Xzz+P2qSLlx//C2+tWMdp3/wvLj7989xy/c+56p6ZzHllHlOefJb63ffllpt/R+srz3L4SZfxxMPPM2HSUb6ijiXx2Vmpo3P7up/3GQjNonmzKYTVHH7c5/nk7kP52pdPwugyG1bO59lZsxk8bBjdpSxIRZmYXG0/rrzqVzSOGEaVSfjK577MyiX/orVU4tEpU8jUDuCmX99Mo2jl+JPO4aGpT3Pwx/YiEKrC7OOcDaZH8/Eef2fUG1asXE5S1nzpyyczct8JHPXlE4l0N5uWvsnTM+cwYtRIZKcvsCEjrI3RSjDx0KO49ZffR+DIHGTXGqZNm0Z73TDuue56BiTr+crZ3+Lhx59i4v77EEmJMTFI5frQy9Ry0YuYrFKYUjtLFi9mxMjdmfCpwzjqq8eyy9ix1MgyM96Yz4IlKxi/6yhsJnTRCxGzdMnbrOiU/OAHP+Zrxx7Kj751AZOfX8CyBfN59LnZjDv4c9z6u58w9W/3ceFP72LmnDcY/dkDoZTwXjHpfUyB3UKH978FBkeXk/q3lAydd1NYpCizduUyrr76ehYvXk3GSoo25NhTT+XcLx4MIiQpWG791Y2EZhOJNBx89LFccM6pLH1tLr/6xR95a8UGUJYoijjh9NM4+YTDeXzKw9w5+T5UfX82tG7m29+9hGEjh5PECdJXfHHhsx5bU2z1JHaLZ3EiTOWq6FdXxbKF/0LV1VESivpcSNvilcx/8zXG778/m9eu4U//WMqECfuy6+AMC996jcFjd2HIsCZENuYTH/8YP7/vNboLJaprZB91K+fccYTVgT8nXMw8n68mE8S8Nv8Vxo8cjgwUVcKidZmwX38GjdgZkIweNgxbmMbKJYv419Jl7HXQMVRHWfIjd2L0zk28Oe8VAo7C03j2cvr1tiV2NPWW/oPqyHS3sXD+AvYePYwwyJAkZQY0DeNHV1/N848/x69uvANjEnd6RlWM3Hks1hQQtp2SjMnmqpCxZcmKlTSOGsOgESOpbYXxY4azsGUVXR3d1OaVL+DRu28+9owrASUAjKKuphaSTl5/Yx4DJ+xNRgqqjKV68GCuuuEXvDBtKlfdeBdGuzmWwhKImLffeJW777mPxqFD2XfvPanT3cxfuICR4/dhUGMj/RLNuHF78MrCFZSK3YgqiZAZ77TTnuhDkDL6KBX6Uk0Z6uqr2dQyh7cX/4uSVdRFIaJUZN8DD+J3t+/GHb/9JU8v6HAZg0YyYPAQ8lXw2twXWbFnM6/Me50hQ4Zjih2sXNvCkZ85iSCQ7LLbCBqq61i+eDnWUiluWlnRlfncceuD6p6GtagMfnpdl7duKuAW7ePKxjqEU3VNNUccciRX/fAqLrnwQuqzWWbO/ieb2lpR0gFh9jvgI1xx+SWMHdSPF5+aycsvL+L5x59gwaIVHPGFE7n00gtpyOS4/96HefvtZQQC4qLGmJDPH3cio0aPRZsYB07o0T62UODtVo/U+00s2iiC7EBOPvXLdHWtYsYzj/OPP/+V1raS85SWO5j97OP87KqruebyK7ng4st4fcFKEIK6+mrCTAgioH//nZAmJq1Jt/WG2VGzwoAvQCj8CCc2ZPjIXTnhC59j3rzZPDX1UZ6Z/hyJzVBd24Du2MjMaVNZvngF05+aTWdbO5HUSGVo6NeATQxhVRVV/WoQOnYcab4CLn7L90QgttsrEBatBR89+HMcOWFXFj73CA8/8gjPzn2dRFVhwjxDhzXRUKWQOnV3ughFEhcRAuY8P4O5y9Yybr8DGJB150omk/VhVEldbUQkYsfdID2nIr7GO8J5An21HgeQhdhE7LX3fnzmMxOZNfNpHnnwAV6aO58yEWSqaB42mJqcBO1Qas57HtI8YADlTav47Y0/Z9Lpp3Ptjb+nTAYENNbXE6oAFYXkaxtcWFAkbh+Z1E/gU1yFcytGVqASh8UwYT+OOPYYdhqUY+YzD/OPv/ydZas3YkRELt+P5iGDUDLBemLHRCh23mMPTj36k9zzhxv47HFfZM78f3HaaScxoLERIaBffQ0gyFVXkc9nkNqxzVTWUsV5uyPTtKf9z7CCxoW9pJUOQqcSn4YZom2GMFfLTg39efnlObwy/2VCUwIdY5IYZcpEGcveB3+cTxz1CT681x4UNnbx9sJVLF+2geohI/nYoR/nyMP3ZcLuI+hs2cyGljZAoRPFYUcczfkXnsvYMSOwOqmcAimHWMVp2IdmUSS6isOOP47rb7qa5mr46Xe/y/W/u42ycWyPIlPDN7//Ha745tdYPv8VHpgyjW4ylMlibITL3Nc+rGbeZdjT+zqvuREuMyqysU8JdkIwV13Hxd++jO9+62JWvzaH75x/EQ9Nm8tu4w/kuE/szzP/+BNnfP0ipjwxk0RlfS60pejTUIXWhLECnSEh9AkdCcgyaU37d2taR+T7jeZn11/HeacczuszpnDuJZfy/JuLMTIDtoywMdK6xB3tufeCQNGxbgM3Xn8n2X5DOOb4o4noItAFwiSpkFDFQnmEojscXO0261NmA6xwVW0D6zMEESTa0jh4CD+59mecfsqXeGn6Q3zr4ot58bUlJCqL1hKpcRlvGISJsZl6vnzGOdx+96384bc/58Ddm7njjnt5Y9FqMiIiTqSvBKw98jCNoacz1TsE6pqwGmVjl09gAiYc8Gl+dtOv2Xf3nZl848/44U+uZm1bEaNCEqsJbIJnpgMkG9auZfHSNTQ2DWPC3ntSnQt4+81FdLeXiVVISbgol9Iuhp8o60qQm9TZ2/f2P9rorlSMxWrtwkZWEYqISAWExvL840/y0+tu4rm5r1I2higTYETOJabYEEuECQK0gUBEYCSlQkKceHSPsIRCk4lc9ppOYi/EFNV1/RHKAiWkcbWnLR4rLTyKro8OC+Ez9YSKmDjx03x8v/0YM7aZJ56Zzpr1rRRVHbvs8zE+ceBHOeLwg9l9191oWbsBoTW60IHWDiK7eXO7gxbKbeEsO765k8ZpZmFanzsQFqtjcg0DOewzh/PRfXfHqCJTZrxIXD2A8y+5hB99/1K+dPTBnH7qcfRraEDakDAWlNs7QSpKiaGtXEZHIRoXXVA2qdSR60uzwqBlQv3QkRx82OeYuOfusPJtnnx6FsgQhANbpAAZIRRSKnSxncm33cIj85dz1rnns9uQQdgkQQhPDWZAakN3ZzfGCBCuCmugXYVdLfBoNFGZH+1PLoXjuK9vHsFhhx7CAR/eg7Xr1jLzpfmgA5QMKohFYRyTcCxCdh43lhE7D2O3vfbi1JOOQ9syC5YsJUtEqavsorVG011ox/qUHys8LNdaD2hysXSXGYgTTEYjpEWTYdz4j3Dwxz/Gh/ccw8wX/snC5auxSqGlm9fQJoTGEgiYMf1xHpuznAsu/yk3//oXnHHyF7jzj39i2dvLUIGgUCiACCkVEkplV89QCI2U736Cb93+2xvdW0+kLLCJEIhiQml9O+0tG9m4dg0L5r9Fl7GceuZZnHb6V8kPqCPRgoQMliy6LGhZvYZCazub2luxOahrrCZXm6W8uZXWVS2sW9vOqpZN2JwiX5dDWYMwgsQKLDGKMgHCF5nvFervc3N1X0XSztrVm+koKzL1WZpHDSHRGhWF9BtYT3vbZoqFmM2bu2ht70RlFTuPGsLyN99gybJVxMWY2S/MYPjYYeQyuT5C4VNTw6VzaAIS4QAyITHlrnY2rt1AoqFpyDD6DWigYLroirupru/PsSeeyFdOOYF1a5ZTX51jtz32ZMjgocyb8SJdxTIrVqxmwfIFjN6tmRCNIPY+DFc9py8tQNOxcSVtm9tJVJ7Ro0ZTl8vQ0dmNixZkcIk3BUISMgiULvLwAw/w27v+xpFfOYVjjjmSyIJUOQY2DmDZ8uWsXtNCR9tGli5YyKC6flTlqivMu2lqaVpcwQqXXKNFhABCEjrbNtK2oRWEYuTI0eSrq+mOi25hamdDJ7gCnsaGSKPp6Gx1vAW6zLIFC5AkNA0dwuDhw1nw8kusbdnE+tZO3vrXfEaMbCLMRthKjsa2sQkHglFus8cFNq1fR0dHF5lcnmGjdsaokHISIym7bDjvZXDapqG7fTPZKGCnpiaiqv6M3nkMxe6EsEoxoK6KubNmU4wlC/71Nu3tGxg5dBDCGBeu/rd53SvNbvG3SxxwvgjnEHWbvGQ1m9es5o6bbuSR+hz5mjxSacpJiekPTeXFwPLWouXUjx5IiRIFkaCTIs/8428U589i5szXaB47jj33GUNN927Mmv0GD0y+h1mNVcxdsISxe3+EpqEDWDyrREmX0FY7yKpOPIY9tW59ks17kGFSWkrdG/jpD35JVX0jT734Km+tauPTRx7PkNG7MPEjH2LWjXdwzbXXUty8nmVr1vHVffZh/zG1DL9nCn+44Sc8N7yJF19bxHk/ONtV5EjeXTUWOOioC3c5T7gRLttOCMOSRQu49pe30Nx/AI9Ne4HWsIYTx44iKLRy2733sblQYuXKFUx9YgbHn3wme+w5jkM/NZFZ11zPNVf9kE3Ll5IEeQ45ZCKBLoIs4BI7I2ylGu07NxUGzJr+OA89MRebDXls6tPI6kHsPWEXl9BkFSRQLhUdSQKW9SuX8ptf/4a1GzvJFbq466bryNU1cPJJx3HokZ/jz4/9kGuu+B41kWbp5jLHffIgqiOLiku4fL0AkQI9rHV5l8IVUQxsjJCWF2bO4O77HqQ+m+GBx6ejG4exy5hmQmkgNsTGUjJlLA52bIud3H/XPbS3G3SpwOS7/8ye4yey5x7jyXRu5M77H+S6a39ETWRZvaGTkz71cXJRCLHuiYpCTwQAh4QrW4sSBpGUmXzL71i9dhNLFy3iubcWMPLDn6R5UAOhjjFGk2hDl4Wyh/aNGbcH+dK93HzNlSw+aD8e+vtDDNllNLvsMYHDPvomf7h7Clf+IOStV19lwNBh7Lv37gQmwZVv7uWM60N71/rotsdMASEcmwiOYMEaT+qQyTByj10pRbVYD+ULaus46NMHQ5hlxeJVZJuGMfGgT9OdCSEs07RLMwe0xwwdOpzFb7zJqN324vAvHM/IEYMYlj2Icpvl2X++xqqWjez/yYM46oQTGDSwkQHNTXxo//E0DW7wJZhcOmglQlQJw/hB6MPJagCVjRjcmOexac/Q0lLk8MOPZdJ5Z5Gv789Rn/0sLetW89jzL0KY5+xzJnHIoYcyMFfiskvP5I93/5VZL23ii6dN4oTPfsJj4/smc3usP5+Q4W10jKKmvj/aGJ59/jlEvpbTT5nEl474DFnbxrIVy3n2hVcQQS0nfO1cJp16Apkww1FHHsaaFQt4YvZcbFLD5d+7nAljRkK5HSG0g0NWIsN96aBlQHMzrWsf5a3lS+nXNJRTJ53PERP3AV3AioD+jUOZ8JH9aaivRZOgLew8eiyqppmVr85lcdxG/7G7ceRxn2fvAw/lv85dyd33P8aSsJoTz72UT33q40jdQWBLGEKXGkuP+SN65f6n9m3DwEZaW9t4c/nb9NtpCCeffwGHHLAPwsSgBHXNw9lv/31prs0jTIwKApLuIk888gxlEbLXJz/D2edeSL4qx4QP78O3v3EK9zw4jdWihlPOOJeDD/woUmvveE4PkLAya3gTEesAMCJQNDb258knnmXpmjXss/9HmXThuYxsGog2ZRARo8aMY59sgVwkSIxmwgETufI7F/Gn+x/lyWnPUN80jIu+cRGDh4/mS8efQNuGjTw/Zyb5/iM4/8xJDB8yGJM4/LqrAW8r+/PdNMjtkkP23ugrV65k9pxZNA6up6omiybBWosSoaO3wWCEplAqYIqR8+dKg1SSTFVA0p1QLJQJsxGhVBRtkUxeQqmESCQirKKrqw0lcuRq6yAskdUJshvaijFdwhBVVVGdrULYmKRQoFyWUFVDFJU8IigAArTQjnwBHAzQBhQ6i3S3vzM5pONBK1IuWNpXbeKWP97Ol847myHDB6ASl9RZLnZT7ChgZEhQ30AQBQS6DCamq62bsrZkazJk81lk7DzE2xjCW5FDfmjPPcnlq7DW+GowTr0zUoKnaCoXysz752yefPk1zrjwEvqHEpI2ugpFil0abES2oY6qrCYoO4W8mLSzubuMsBn61dU4jj5r0QLn+wCXJdcHckiLQesY3WGYOv0JWtpaOPP0M5355HPHiYt0lQqIfC2ZQBCWCxS7CxRt5MWJQQSSbL4aRUgQF2ht76QoQ2rq6omUIDRlJI64w2XtK95cuJhyscD43cYQSEiEZ5ExBmMscXeR6Y89wvJCmVNOP4t8UkKaMlop4lKRcqFMLpsnCgxGxpRKgs52Q2IN+bqAXFUWk0CoDDop0tZeRltJrrbeza8pE1iBwZGbKBEy/5U3ECJhlz3GOV+QMbjKcxCXEzo2tXP7XXex1yGf4qP7HYCKY4RNUEaTFAqUDIT5HCpICNCIWNLRVSbWFhFKsvV5lBFERlPsKtJWKmGyin7V/Rwhp8Vj4GPH4GMl06c/TfOQ4YwfP36HG32H9dGNceCGCtuIkD7VVLgsSZtCPAVGQlhTjcxVIZBYWSawJUSSoPM5cnVVWONQWGHqSczkEBmLFoq6fD+UDkBrtLYYIkwWqqojstITF8SJqy+Wy1FTJTAkLs3dQxTxhBMpbxd9PlOdlS5sjmxOUTWqmrMuOJ2GxlqEdoSHBshGWaoG1jrWGoCkiERjwpD6fgNQQqNFTDlJQETeUdAHdSIlKvAnVZqjr6VDstXWBHx4v33Zec+9qAk0se1GKUOuuor6mghhBSVrMFp7RJQkytTRmIFYgdRlpHHEEfj5Sm3gvp3pAhVmCOsVhx52GKVyJ4IEaxzFEzZBZjJU5WowOibQFiED8nX1RCrEqIRAS2QCxgqH6Y8i+jf2x3iuudSZawhJufZ0hYHVVtK1FIYEiZYRUmhqa/N86tBD6ZSKjIkRRqOFJcEQZHLkogzCltHCES1GWUX/XMbdR3QSJDGxgARFIKrp3+CcigYwJnaAGG2dKyL1uldGxU2vksIh24QgzEY0NFVxymlfIayvRumCS+X2eUlhdS0Z74x0e1aiVZaaujxSGDQao8tYoSjbgEx1PxprNYkqEpScKRhLAcLBpCsmND1+hB21HdroqSpcVVWFUoru7m6qauodisk6tJhWEm28YyDRQAm8VzJBIpRB2xIiccLD0yx66KILZyShxeoEayyKAGlcccREuSlWsXaLU6R8aBZrYq/YZR1EUWqHKBKpCqx7Nnkf1rJ3+SBtghGSxqZm0AUS6wr2KaPBWIrSIEyKVfbwUm0gcZtcB8ZPwnZO8+2NsZtq3JUCtJAEuOKD1miUsNikTJirprEqQOsSWmkEAegQYx001MrAxcmFQHt1ThpHomCsdMRD0kUuAhPjcrX7VtNFWIFMEqzU5GpqiUQNZVNwnGzW4cYNIBJfslgqtHGQSp0kYFy1EceUEhBox3uvtYd6CsfBF4sA69cH1gFNla+fpn2Ks6IE1uDwWwabxOTrGshKsEnZaUxCue9hSSykOH4hFMKUQSSUZYZAW6TIIHSZEIvVxjmXJb6mnV9LUhFjMdZxwW253fFlpTzTC27aBwwcSCxisMbj8DVWGIz2gBSpAIXQqbMxIUZ7hqbQcbmToI03VawjcxHCOLNQSA/yEbS1tZHECdXV1e84j9vf6NY6W1wKqquradppMEtXLSWTzVBdmyfFhhtrEdJlo4XetnSSznlJjVAoYVyM3QhXJke4zzv4oXChMVIVz5FMaus5z6wiIEBYh1d3lptz0kjpwmw97C2iQlIBgeecl0jruMidJuK0CQd/7A1p9Smo1sNrrUDKqEKG6AB4jolFWY+Rlw5lFVhH2uBEkMtuc+y0Yish4197skPrSfmEUCis5yR3HnFhDYFwY2BFgPXEiEq4kKG1EilCpNBYKVEopMd8Sx/ylL7CqZSB/65T35V17CZCSipVxoRESNcfmf5tfaRbgDIBRjgvtkGgREigHK+bTWdAOphwggAVIn3aSwWUElgwEFkHarb+fk7xcXxsVqjKJncEEu7UklJhpcRaR/AYeqJQawOMlEiMK+FtlctlEClRp7+/37RKuudQ0sFUrQ2RAS7JSSmMdAIQ6TwE1ho35yJ0s6ukv5zDK6Rr3+HdrU8c8wlJIgDjyDxSp7VbJ27tGX8QKmsqAkUKgQ+Uo6QTPMYqhAixSoDQKCEx1p3q3V3dvPnWArK5PI2Ng95xo2+/gIMnaPBEn3R0dDBn7kusW7+OqnyOKJtFSokxGuFJ6XocJb0zCtKb+P3U602B7Xndy4FWuU4auyT1pm/53VS2puSC6f97/nZ2elJOKJdimpqayGQi72DsLZf9UrX0SmZg6yfx1xXb/N3TtpT12wvxWU8S0NHRwaZNmxg8eDBRGG7nw+m1etxR27vHdu7wHv7vx8nLu82bNtPR2UFz85BtGFdFhYCiZ2ze3TDZeox7rxCx1edg634LIVi/voVyEjNo0CCH25beGSy2vJawae96z/6210zvla6vHqVrq7mrfLXnfS+XWbN6LQhobGz0uSPvLcy142a3czhs+xlwY1Asltm4cRNJkrD33nvT1NS0LVNur7Z9Z5wxFS97+sDdxQLLly2lZX0LXcUujPH0zJWO9Z7ULW6x1fvv9nrr93a04N/9tUjzug0IKXy5ovRz224eYd/pXlv37Z370ZMy3PN/6/HxvUMjovL7v/OM24qjvn7X9pq3HsZXsQ3pBKQboi/X3npzb+9zfX+mHo3Db+neUaCtr2a3eNWrvfd1Z8X2nin1cHvTKKXs3ubQ2NG9+jonO/p/7+eRRFGG2toahg0bRkNDQ4XnYEeUUjv0um8jHf1oxklMHMeA9Y6vf5dE+99oAizbLI4dDsa/8c7vdNrZCjNPqs3//x/DtH+p03XLDb5le79m2OEoeoRk7w3Wu/27+7ejubOVtdRD3/TvrHPXF59J2qSURFHkHeem8t572uhAxYtXOYV6K8/Cn0L/NrXlf7H16mKa7PN+tw/68d5a73Dv+9uPnvFKd8371aVUQPdoifYdT/TtF3DoFYWv0Ocgeuxb++7W4H9K63mUdGDevwXTW6T2/vv9W7/Waxc9r9/vzbR1633gpO39m7//nFWfDkEPvdU792v7qnvg/rmmAAAAPUlEQVTvD7zDl9+LqvH+tPeaEfxB+89rfZnB//yV+O9v721lv2vZ5A/aB+2D9n+//c/w6B+0D9oH7f9E+3+pShTRYQxGrgAAAABJRU5ErkJggg==)
Write the linear function for the data in the table.
A linear function forms a straight line in a graph. It is usually a polynomial function with a degree of 1 or 0, and the equation f(x) = mx + b, where b and m are real numbers. Isn't it similar to the slope-intercept form of a line, which is written as y = mx + b? Yes, because a linear function represents a line.
¶Examples from daily life
1. To print logos on T-shirts, a t-shirt company charges a one-time charge of $50 and $7 per T-shirt. As a result, the total cost is given as a linear function f(x) = 7x + 50, where 'x' is the total number of t-shirts.
2. In linear programming problems, linear functions represent an objective function to minimize costs or maximize profits.
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A copy shop can produce a course reader at a cost of $25 per copy. The monthly fixed costs are $10,000. Determine the total monthly cost as a function of the number of copies produced.
A copy shop can produce a course reader at a cost of $25 per copy. The monthly fixed costs are $10,000. Determine the total monthly cost as a function of the number of copies produced.
A chemical plant was found to be discharging toxic waste into a waterway. The state in which the chemical plant was located fined the company $125,000 plus $1,000 per day for each day on which the company continued to violate water pollution regulation. Express the total fine as a function of the number of days in which the company remains in non-compliance.
For such questions, we should know the concept of function.
A chemical plant was found to be discharging toxic waste into a waterway. The state in which the chemical plant was located fined the company $125,000 plus $1,000 per day for each day on which the company continued to violate water pollution regulation. Express the total fine as a function of the number of days in which the company remains in non-compliance.
For such questions, we should know the concept of function.
When digging into the earth, the temperature rises according to the following linear function t = 15 + 0.01h,t,h is the depth in meters. Calculate what will be the temperature at 100 m depth?
For such questions, we should know the concept of function.
When digging into the earth, the temperature rises according to the following linear function t = 15 + 0.01h,t,h is the depth in meters. Calculate what will be the temperature at 100 m depth?
For such questions, we should know the concept of function.
For the function ![f left parenthesis x right parenthesis equals 5 x minus 7 comma f left parenthesis 0 right parenthesis minus f left parenthesis 1 right parenthesis](data:image/png;base64,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)
For the function ![f left parenthesis x right parenthesis equals 5 x minus 7 comma f left parenthesis 0 right parenthesis minus f left parenthesis 1 right parenthesis](data:image/png;base64,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)
Find the value of f (-1) for the function ![f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator 3 end fraction](data:image/png;base64,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)
For such questions, we should know the concept of the function.
Find the value of f (-1) for the function ![f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator 3 end fraction](data:image/png;base64,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)
For such questions, we should know the concept of the function.
For the set of ordered pair shown, identify the domain.
{(-5,0); (-2,4); (-1,-3); (2,4); (4,-1)}
For the set of ordered pair shown, identify the domain.
{(-5,0); (-2,4); (-1,-3); (2,4); (4,-1)}
For the function
, find the value of ![g left parenthesis negative 1 right parenthesis plus g left parenthesis 1 right parenthesis](data:image/png;base64,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)
For the function
, find the value of ![g left parenthesis negative 1 right parenthesis plus g left parenthesis 1 right parenthesis](data:image/png;base64,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)
For the function ![f left parenthesis x right parenthesis equals 1 half x plus 1 comma text find end text f left parenthesis negative 2 right parenthesis](data:image/png;base64,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)
For such questions, we should know the concept of the function.
For the function ![f left parenthesis x right parenthesis equals 1 half x plus 1 comma text find end text f left parenthesis negative 2 right parenthesis](data:image/png;base64,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)
For such questions, we should know the concept of the function.
For a given function
, find the value of ![g left parenthesis negative 2 right parenthesis](data:image/png;base64,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)
For such questions, we should know the concept of the function.
For a given function
, find the value of ![g left parenthesis negative 2 right parenthesis](data:image/png;base64,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)
For such questions, we should know the concept of the function.
Find the value of f (3) for the function ![f left parenthesis x right parenthesis equals negative 3 x plus 12](data:image/png;base64,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)
For such questions, we should know the concept of functions.
Find the value of f (3) for the function ![f left parenthesis x right parenthesis equals negative 3 x plus 12](data:image/png;base64,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)
For such questions, we should know the concept of functions.