Question
Solve: 16 = 4 + 3(x + 2)
Hint:
solve the given equation for x .
The correct answer is: x = 2
Ans :- x = 2
Explanation :-
![16 equals 4 plus 3 left parenthesis x plus 2 right parenthesis not stretchy rightwards double arrow 16 equals 4 plus 3 x plus 6](data:image/png;base64,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)
![not stretchy rightwards double arrow 16 equals 10 plus 3 x not stretchy rightwards double arrow 3 x equals 16 minus 10 not stretchy rightwards double arrow 3 x equals 6](data:image/png;base64,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)
![therefore x equals 2](data:image/png;base64,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)
Related Questions to study
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXQAAAEZCAYAAACHCd7XAAAgAElEQVR4nOy9d5Bc133n+7mp80xPngEwGOQwRGYAExjNIEoUKZGStZbWsmzLcqxde/dt+b1/XtW+et7nsF5vuUr2vtpnSbZl2QrWKjCLBEmABIhA5AnAYAaTc+jcN9/3R8+AIIkwM+jbPeCcD4ss1nTf+/vd2+d+7zm/c87vJ3me5yEQCASCWx653A4IBAKBoDgIQRcIBIJPCELQBQKB4BOCEHSBQCD4hCAEXSAQCD4hCEEXLBrPMZiZGGUyZQLg2iapyTEmk7kyeyYQLE+EoAsWhefkuXTyDb7113/N999oA8BMjPLOj7/F9149Rb7M/gkEyxEh6IJFoadmuHDmBEcOvsUbb7zLOODlU/ScfIcjHcM45XZQIFiGCEEXLBzPRVZj3HbPU3zpM3fgJoYYtcDBRKnexL777yJWbh8FgmWIEHTBwpFkghWVtGxay9rGShwzT3LCYXzwPOn6u3nm4TXl9lAgWJao5XZAcAujKITqa4naY/S1nyU3kmLn419ilWhVAkFZED10weKRAwRra1BnBjj27hHyjXfw8PaqcnslECxbhKALbgKNQDiCpM+Q8CrZe//thMrtkkCwjBGDY8FN4GHkXOpa72bf5x9nZVT0DwSCciKeQMGiSfa38/6xQbZ/7us8u6uu3O4IBMseIeiCRZHsP8WLP/kZ583VPPnkLjHUEwiWAELQBQvCcy3Gu47y43/6Z94bjPHpX/k8zcFyeyUQCEDE0AULxM4n6Ok4xxjNPP+bX+GuFYFyuyQQCGaRRAk6wfzxsMwciak0odomKgLguR6ZbAY9n6e+oaHcDgoEyxoRchEsAAktEKV+RUHMAUzL5PTp0xw4cKC8rgkEAiHogpsjnU7zzoGDnD59utyuCATLHiHogpsinUpx5PBhBvr6mZmZKbc7AsGyRgi64KaYnJikra2Nvt5ehgaHyu2OQLCsEYIuWDR6Pk97exuZTIbpqSm6urrK7ZJAsKwRgi5YNKl0mlMnT+J6LrphcPrUqXK7JBAsa4SgCxbNzPQ0589fQPIkDMOgo72dXDZbbrcEgmWLEHTBorBtm0u9vYyOjKAFNDzPY3R0lM7OznK7JhAsW4SgCxZFLp+j7dw5RkZGUFUVCZianOTIkSPldk0gWLYIQRcsilwmS++lS7iei6ZpKKqKZdtcFBOj10VszBb4SdlyuRiGwcjICNFolPr6+pLYTKfTDA4M0HrbbSWxZ1kWY2NjSMCq5uaS2Eyn0/T399Pa2oos+/e+VjWNu+++m3AozHuHD6NpGg89/DCtt7Wi6zqhkH+lLrLZLENDQ7SsbiEU9r+khuu6TE1NkUwm2bhx46LPk5iZ4fSp08RiMXbt2Y2qXvvxy+fzjIyMUFdbS2U8vmib88V1Xaanp0kmk2zYsMF3ewJ/KFsPPZ1K8c7Bg5w/f75kNkdHRvnpT35aMnu5XI5jR45w/PjxktkcHRnhJz/+Ma7r+mqntraWf/vVr/Lv/vDf09LSwsZNm/iP/+l/44tf+hKBgL8Ju6YmJ3nt5VdIJBK+2pnDcRw6OzrY//rrN3We3t5e/uLP/oxvf/tb6Lp+3e8mZmZ46803GRwqzdp+13XpunCBN9/YXxJ7An8oWw/dcRzSqRT5fL5kNk3LZHp6qmT2XNclncmgKKW7zaZpMjU15fvQXpIkABzXhdn/n7Po58gAwLJsZmZmcBzbVztzeJ5HLp8nkUze1Hmy2SyDg4PEKitueI9s2yGVTGEa5k3ZnC+e55HP50kkS/OSFPhD2QRdkiRUVUVRlJLZlCUZTStduldJktAUFbmU1yjLBLQAUonseZ5X+JdC5sVSIMsSmqZdfqmUAkVR0K4TIrkRnufhOA6BQIBoNIqmadf9viQXng+/X45XIisKmnp9vwRLm/JPipZ6kqjE9sQU2CeEm2w3nudhWzau66IqKqp2g5eDaDiCRVB+QRcIlgGe52HaFo7roqgqUsnGUILlhBB0gaAEeJ6HZVmzPfTSheAEywsh6AJBCbgy5KKoQtAF/iAEXSAoAQVBt/Bct6SrngTLCyHoAkEJ8NxZQfc8EXIR+IboKiw3PJuZ4Ut0945iKDFWrd/I2oaKKz63mBzopn8sjRyIUrd6Hc014fL5+wnBw8WyC4Ku+bzxSrB8EYK+jPAck9GLJ9n/6huc6bpE/0iSum2P8Vu/+1V2NoXANRk4e5CfvnAAM76CkDFDOriOz33lObZUCxG6GTzXw7IKG6H83kkrWL6IkEsJWCpLiu1cgv6uTrI1e/jK7/4BX7h/NW0v/B3/8FoHAJnhdn7+j//A8cwmvv4Hv8NXPn0HiUP/xP/7L4cozX7FTy6XY+hAICgEXeAPZeuhy4qCLCvXTVBUbBRFRlZK9w5T5II9tYSrGmRZQZLlq+5OlbQoG+54nNuaVlIhwSr7Md453I4qK4DFYMchDrRNcdcffYpKwFnVyj276/jrV1+l7YsPs6fu4/ZURUGWZeTZnb+lQFEUFEUp2Q5cVVVvetemJMvYroMEhOeRuExVZ6+xRDtFFVW9/FsKbl2K8gSapsn01NTlnB43QlEUJsbHSczMMDU1xczMDIZhFMOVa6KqKmNjY2TSGSbGx3Fnt6z7haLIJBJJZmZm0DSNZDLpe94aTdOYnJwgl8syPDxMQNNwPY9IJEJlZSVqKErdiiiukWG4v5N33zlJxa7n+JXP7oT8BP2dXUxbIVrWF5RbCYepXrkSabCT88OT7Kmrw7Yspqan0XUdTdMYHBxE13UkSaKvr4/Kygocx0GSZV8Efu53TKVSjI2Ooqoqtu1fThdJkrAsi6mpKVKpFOl0muwCqzIpskwmm2FmegYP0HXjuudRFIXR0VGSyQQTE+NMT09jmv6NkSRJwrZtJienSKaSJBKJGyYPuxJN04jH4yXtnAmuTlF+gYmJCV5+8SUURZmXpiuqSi6bpb29nYmJcfL5PKbPgq4oCkODQ1zq6eHnP/s5qqr4mpFQURQMw+Dc2bPIkkxFRQX5XM43ezArdqNjDA4M8NorrxR6sB5s2bqFe++7DwDXNhjtOcMvXvgJL+0/RcXtz5NLJjFrLaamEzhOhPjcHKmsEQxG0JwkY4ksUEcykWD/G28wMjJCKBhkZmaGifFxAoEAL77wcyKRCLZtoygqkXB49iVfrBenhKIojI2NcuHCBd5+801qauuwbatI57+KRUnGtm06OzsYHxvj5RdfIpdboKArCpZpceF8J67j0NPdzUsvvEg+f7X2ICErMpMTE7S3teG5LqMjoxjG/AV2oUiSjOM4XDh/gaHhIV78+QtY1o1fIB6FUFJDQwP79j1AVXWVbz4K5kdRBD2gBWhsaEBW5BtuafYoNPCkFqCqqoraujrq6+owTcvXzdCyoqDndSrjcZqampAkcF3PF5sehV5ZNpcjHo+jKAq1NbUY0Zhv1+hREHQ9rxMOhamrqy/0mDyPitiVq1g8JC3Cmu37eCYS43/94Nv83zM5/uQ/fwkVD9eTP/RSliQZSXZx7IIoK6pKY0MD4VCIQDBIJBIhEokQCAZZs2YN4UgE13FAkpAlubjXKxVCSrZtFdpObR119XXYtuNf25nrvU5NkM/lqaurJZ+PztveXHvP5XKFpGmSRE1NDXV1dYWRzcfszYbNkKiurqG6uoa6ulpfnw9JknAch+npKTLZDA0NDQVBv8F72APwPKqqqkuaZE9wbYoi6PUN9Xz2c88u6Ji5Yd3W1q3cfc89xXDjhvR09zA8MsKnn/5MSezl83k8z0ULBHjsicdLYrO7u5tLvb08c43fQ9ZCrNi4mxUbd4N5PxWpfv78569xuOeXWVMVQWaS7FzH0XOwLBObCFUVQQCqqqt59LHHLp9vdGSUt958i2g0yueee64kw+6R4WESiSRPfvop6uquEtj3gfpD9bx//PiHrn0h5PN5Ojo6OHToEHfcdSe/9Pj1zzM1NYVhGOx74AG2tm5dlM2F0nC0ieix4zz+5BMlsScoPmWbATENA9M0FhyPvBkMQy+EdkqUcdEwDEzTIp/3b7j8UUzDwLFtbGseYQhPob5pJbW1ddRXV9G0somgnGZ0OFP42DLIJKdxalrY0FRz1VPouo5lWVi2TT5Xmtz2eV3H0HXfw3RzmKZJNpvFms89vQa6rqPPvuDn09PO53KFUKSPsfMrsSyLXDaHUSJ7An9YZlPas49SCfNoX2G1zLjkU2N0nDxF73hBsJNjvbQPZ9m87xke2hylYfMuNtZInDtyDABzeoyLnUM03XUf21YGr37aMlzc0rifC6OwDt0CDwKBa9zLDyGVNN/7rMlb8t4KPkBMSy8bPFKjHfzom/+Tyeb7+KV7NqLkpmDV3Xz1yWeIA/bGe/ncZ87y/SOv87NDVVQOv0efs5Ff/tKT1IkQ6U3hee7sahxJ7BQV+IYQ9GWDQmXjBu5/9F4OnBvi9BmPHXfu4/nP7qZKK0Sh1GgDD3zp6wSqXuPsyaNMRyt4/Nd/l8d2laaI9ycZ1/OwbatQUSogqgIJ/EEI+jIiHF/No1/+Ax69ymdzo3st0sS+z3+VfY6FLWuoYgxeFDzXwzQtVFUhGLzxxiKBYDEIQRdcHUUTjaOIuK6DYRiomkZoHjtFBYLFsMwmRQWC8uC4LqZpoqoqobAQdIE/CEEXCEqAYzuXBX0+uVwEgsUgBF0gKAGWZX7QQxeCLvAJIegCQQmwLAvTMISgC3xFCLpAUAIsyy700DWNYFhUgBL4gxB0gaAE2LaFac720IPz2SkqECwcIegCQQmwLAvTstA0TRSREPiGaFkCgd94HpZpYVsOkYgItwj8Qwi6QOAzHmBaJrZtEQ5Hyu2O4BOMEHSBwGc8r5Bp0bYswmJCVOAjQtAFghJgWRa24xAWIReBjwhBFwh85nIP3bZFyEXgK0LQBQKf8WYnRS3bFpOiAl8Rgi4QlADLsnBsW8TQBb4iBF0g8Bl3NtOi53mEQ0LQBf6xzAS9NMWhl4ZVwVLBdVzy+TyKohBc4nlcRFu9tSmboEuyhCzLKErpilXKslzSXXqSJCHJEkpJbcqzdktjU5ZlZKlQ0FhWSmNTmv0dS1VEea6dLtaeh4dhGiiKQjQ6v0lRWSnDNcoKsixKVN3KFKUojeM46Lo+7+8riko+r2MYBnldx7ZtDMMohivXRFVVsrkclm2Tz+fxPA/P868/oigK+VweXdfRtACe55HL5XyzB6BpGrqex7Is0uk0wWAQ13WLbmfuvqmqSjaTwXEcHNsmnU4jyzKO7RQqyPsgRqqqkstmMS2LbDaHYRizxZf9QZIkLNMkny/cV4BsNjvv42VZIZ1Ok0mlL3deHMdF1/PXPEZRFLLZLKZpXLZrmubNXch1kCQJy7LI5XJYhlkYUVzHv4/5K8sEgkGR0mAJUBRBn5qa4tC7hwo9ivkYVVXS6TTtbe1MTEwiI/ku6Iqi0NfXR++lS7z68itomuaL2F1pT9d1Ots7UBSF/W/sJ5vNzuv+LBZV0xgaHGR4eJi39r9Z5GuUQALLNEnMJLBsC1VVmZ6aYnR0lGAwyI9+8EMikQi2baNpGtU1NQURK9aLU5JQFIXBwQG6Llzg0LuHaOiqvyy0fiDJMqZpcvLECcbHxtj/+n4y2cy8f0dZUchls3R1dSHJMp0dnbz+2i8wLfPq90UqjFyHh4Y4feoUmhYgmUiQ13Xf2o4sy5iWxfvHjzE0OMTrv/jFvJ5Hj0Kt1Jraanbv2UNFRYVPHgrmS9F66OlUCvnysPT6D7CqqKQzaXK5HNlshnQ6jWH6L+jZbBZdz5POpEsm6LquoygyqVSKfC6Hn4quqiq5XLbQQ89kZq/RKdLZJSRA1/OMjAyjz+b2TqVSGKaB67oMDw8TCoVm11uH0QIaiqLiecW5zxISsqKQSWfI5/OzbSeEZfsn6LJUEPRMJkMmkyGdSZPNZOb9O8qyQiadJp1Oo8gyHh6ZTArjGj1uiYKgZzKFY9LpNOlMGj2v+9Z2ZFnGMi3SqTSpZJJ0JjMr6Nd7jiWYHeWGwkFcp1jtTHAzFEXQV6xYwa/+2lcXdEwykcC1HTZv2cJDjzxcDDduyPnOTmZmpvnVry7M18WSz+XQNI1AIMDnn/t8SWx2X7zIyPAIX/m3X/FtCOy6Lp7noSgKvZcuMToyTDQa5Y//j/+deDyO4ziFmLpP9vv7+jANg88//xxNTU2+2LgS13VZtbqZM6dO8eznnl3w8TMzM5w9c4aLXV08+alPsffuu294zMjwMKqq8sijj7J9x47FuL0gPKBl7RpOHD/O81943nd7An8oW2F3wzCQZnsspcLzPCSpdHE+wzSRwNeRwEeZi7W6juOboF553sLEnYwsK6izMWK/J7od10WSpZL1Ch3HQWLxcwKmaZLP51AUhUBgfrnQCy9M1dd5nitxbBsJCVXVSmJP4A9lncXwPLekYud5Hl4J7RVsguuWdjFYqUQAwJ0ddrueV7rr9Dy8Et5Tz/Muj0oWg2Pb5OaWLc6zuIXrztlclMkFU/gNXZwSPx+C4rLMpqXLsyRLLARb3hRWteios+G3pYxoq7c2y0zQBYLS4zgOpm4QDAZLuu9CsPwQgi4Q+IzjOBiGQSgUQlGFoAv8Qwi6QOAzjuOgG6KHLvAfIegCgc84jo0520NXRQ9d4CNC0AUCn7HtuZBLEEUp20phwTJAtK55kE6n6evtxbIsVre0UFdXV26XBLcQjmNj6DrBkAi5CPxFCPoNGB4e5p+/98+8/MILGIbBY088wa/+2ldZv359uV0T3CI4joNhmrOTouKRE/iHCLlch+npab7zd9/ir/7rfyWVShEIBvnOt77Ff/9vf0ViZqbc7gluEUzTwnUcgsHQ5d20AoEfCEG/BpZl8eYbb/AP3/kO27Zt4y//+1/xF//tL7nr7r289MIL/PM/fa/cLgpuEXQ9D5JEICBCLgJ/EYJ+DUaGR/jxj38MwG/99jd44MEHuf322/m93/99qqqr+afvfpeTJ06W2UvBUsfzIJ/TAYlQMCBCLgJfEYJ+FRzHobOjgzOnTrP79tt56jOfufzZXXv38vwXv8DQ0BAvvfhiGb0U3Aq4roNu5JEkCASDJa1eJVh+iNZ1FZLJJG+//RbZbJbHHn+MaDR6+bNoNMpjjz1GTU0N7x0+TE9PTxk9FSx1XLdQTxSYd2IugWCxCEG/CkNDQxx4+wDr1q/niSee+Njn6zds4IEHH6S9rY3Dhw6VwUPBrYLjOIVqQ5JEcJ6pcwWCxSIE/SO4rktPdzd9vb3ctfcuWtau/dh3qqurefKpp5Akif2vv04mkymDp4JbAdd10fN5JEkiEFzamRYFtz5C0D9CJpPh3JmzqKrKnj23X/U7siyzbdtt3HHnHRw/9j5nTp0usZeCWwXXcdBnQy5LPXWu4NZHCPpHSCYSvP/++zQ0NLBh08Zrfq+uvp6HHn6EVCrJW2+9WUIPBbcSjutizIZchKAL/EasofoI4+PjdHdfZPv27axubr7m98KhENu3b6Ouro6TJ05iGDrBYKiEni4Wh8RIH72DE9haBavWrGNFdfiDjz2HxGgv/SNJpGCMhtVraawUQrRY3NkYuqIoaELQBT4jBP0KTNPkwvnz5HI5Nm3eTON1ChBLsszadetYv34DPT3dnHj/BPfed18JvV04nqMz1HmMX7z8Oqc6LzGasFm799P82q9/kdvqg+BajHQe5cWX3yYTqiVopTBjm3jml59mXaVoKovBdhxy2UKx8NAt8cIX3MqIkMsVZDIZ2s61o6oaGzZeO9wyR7yqip27d5FIJjl+7Pg1v1faiqLXJjPZx/GD7zIV3sxTzz/Pg1tjHPnh3/I3338XF8iPd/LSP32bd0Yb+ZVv/DbPPdTK4Bvf4X/+6zHscjt/i+LYDtlcjkAgQCgcvvEBAsFNUFZBlyQJqYQbLSTp+pXbdV2nv7+PiliMdetunHyrsrKSvXfvRVNV2s6dI5fNXsWmhLzIavGLQ5q70I/83caRVFbu/BS/8/tf4VNPPcvX//3v88T2COcOHGUcGDl/mP0nR7jt0c/QqEHd+l3cuyPOkRdfouMaqWskSSr8C0hyia5z1mapuNxOF2HTcWxyuRxaIEB4AYIuyWW4xhLfV0HxKdo4eiEV0SVJQpZlXNdlrqy535XqJUkqVKi/4m9X2pQkiVQqxfj4OFXV1bSsabmBXx6SJLNp82aam5vp7OjgwoUudu/Zjee5SJJcsOm6l/N3eJ6Ln2V4Cw8kMFul/kr/JUkh3rCevQ0f2Hckjaq6emq0SjQvx2D7BSbNIGs3FkJNSiRM7epV8JPzdA5OsaO69vI5567rsh08HMcpnNdxPvClyNcrSRKe5zH3T8Ef/+7rZXvelW11fvYKbc4ll80R0DRCoeC8ji/YdGe/V8JrdF28j7SbhZxDUH6KIujJZJL2trZ5veE9PDRNI5VM0d3dja4b1NTUkNfzSD6KnaIodHdfZHhwkMOHDqGoyuXGOye+Z86cYXJykvr6egYH+hkfG8NxbK7+IHkoikoymaJpRROH3z3Em/v3I8sSuXwOVVHJ5XJc6ulBVVXOnTtLJp3xreF7eAS0AH29vYyPj3Ps2DE0TcVzPRoaG1i3bv1HrsIhMXKJgUmPXU8+QK2VYWRiGtuJEa+c/YqsEgpFCFjTjMxkgVpy2SxnzpzhUs8ltECAyckJxsbGCAaD/PQnPyEWi2GZFsFgkIbGhkINzSK+qxVVpa+3j77ePk6fOsX42DiGafjUdjwkWcYyTc6cOk1/Xz9tbedIp9M3tDf3e4yNjjI9PYXtOFzs6kJVC+3ieu1AURQGBgbo7OikuqYG4IbHLJ7CNdqWzYn33+fixYucPnUKXdfncaQHHsQqYqxfv4FIJOKDf4KFUBRBT6fTnD51GkVR5tXoFEUlm80wNDhEPpcnXlWFZZrFcOWayIrC8OAgkxMTnD51Gi0QuCzoc6OFE8ePk0omWbt2DZd6esnl8tcfZc++wJqaVuC4Lm+9uZ9YLDZblcbDMAwGh4ZQFJlTJ0+Rz+s+vrIK93V8bJSZmRnazp5Dng1ntba2fiyEZCUHOXHgKPrKB/ja0ztw8wOFNK+eygdRMBlJVpBkF9su3KtcLsfZs2c5cvg9tECAfC5HcmYGRVU5+PYBAoEAtuMQi0bZuHkzAU0r6uhLVhRGhocZHR2ls+M84+OTWJbl232VJBnTNOnqusj01BSnT54hm8vOy56qqoyPj5NOpwov275+8nkd8wb+yrLM8PAw/f391Nc34Loeel5fTMRnXshy4Ro7OzoZHRnh9OkzmIZxw+M8r9CTb2hsYNXKVULQlwBFEfSGhgae/+IX5t1LUjWVqclJLMtk3foNPPbYY/PqEdwMqqbS0dbOzMwMX/zlL4IkXxZ0RVXI5XKMjo7iOg4PPvQQz33hebKZj8fEr0SSJBRF4cyZM7z55pvYls3jTzxOdXUNrueSSqZQFBlN03j+C18k6/OOUi2gcb7zPCOjozzz7LMEAgFczyUU+sjqCjtJ+7EDnByL8syv/ypbYuCkVcKREBJpcrm5LzpYtolDmMpYYclddXUVzz33PJ966ik0TaO/r4+/+NM/JxKN8J/++I+Jx+NYloUsywQCWiHuXCw9lwoi2dPdg2noPPnkkzS3rMYyrSIZuIrJ2R56Q2M95zs6eP4Lz5NOp+flq6ZqdHZ08LOf/pSa6mo+89mnaW5uxjSu03mRZnvo/QOoqsr9+/ax5/Y96Hn/ng9ZlrEsi6YVTbSfa+O5558vpPy93u8mwWwHHU1Tqaio8M0/wfwpiqAHAgHq6+sXdIxtWcTjcWpra4hVxIhVxIrhynWpraslGotRe5USchKQSiUJBIPs3LWLcDg870msjZs20traStu5c2RzOdauWwcUHszKyjiqphIOhwiH/V+2Fo9XEg6HaWhsuNxD/xCeTt+545y+qHPvl77OIxsrwDXJmTKrVq8gKA8xNpaHNWE8yyCbTGBXNbO+sTD0V1SN2rpaainE023LJhwJE4lGWN2yekETf4ulrq6WWEUFtXW1xONx3+25rktdXR0DsRjBUJBgaP45WaKxKJ7nEY3FaF61isrKyhsfBBiGQVVVFdU11cRiMWIxf58P13Opr2+gMj5ILBYlFove+CDBkqNsq1xc18VxHCzLv97VR3EcB8e++gK8VCpFb08vlZWVtKxZs6DzVlRUsG3bNhIzMxw9cuTy313XxXVdbNu5Kb8Xgjs7seU6H7fpOXl6jr3Oj392EL1xOzsaLC51nuDgGy9xuMdm0647WBd3aTtayPNuJSfpOT9A3Z672b7q6i8j27EL99Vxsa3SLG60HQfHdi5PyPpuz7axLOvyiG4hpNJpbKswp6Bq2vxtWjaWbeM6pblGxy48i/ZV2o3g1mGZ7Ra5dkiosMJljHhVFQ0NDQs6aygYZMOmjQQCAU6fPLUAq6XEYeriUb77P/4Hr1+S2ZHIceFtndT0BCkzyqf+4y/xxJb7eOaJ4/zw1Mu8/H6c6OBhuvOree5rT9GwhFrK0rifN2YuMZftOASCwY+Hvm5Aya9TunXureDqLKHHtLykUimmpqe58647F/zgaYEA69evp6Gpka6uLpKJBPGqKp88XSSOgaXrxNbeyRMbAsiOje1GiFXWsX31Th7eUQHBCh798m+hxl+m/Z23iUaCPPiV3+WpvSvK7f0tyZygO7ZNKBS4eghMICgiQtBnSSaTpFIpmlc1oy6iTFjTihWsbmmhs72Ts2fOsu/BB5bOFlEAJcKKXU/yH3Y9ec2veEAg3sJjX/5tHjXymEqYkDr3iei7LZRCcQsdx7YJiFzoghIgugwUCkJPjI/jOg4rVi6uNxoJR9i8eQuZdJr29rYie1garpRsOTgn5h/9RDBfXNcll8/huK7I4yIoCULQgXw+z+DgIKFgiMamxQl6rCLG9h07QIKLXReBEm6FFyxJ5srPeXhEomLViMB/RJXRzLgAACAASURBVMiFQg6XoaEhQqHQgpdfzqGqKhs3bqSyspLu7m6GBgeJx5dYHH2JkkmnGRgYIJlMIssKdfV1NK9aReAWr8E5J+gSEBOCLigBQtAp9NBHh0eorIpTXV296PPU1NawfsMGLnZ1MdDfT83u2iJ6+cnDcRza29p46YUXeefgQcbGx9E0jTVr1/DYY4/xxKc+RfN1ctIvdeYmRT0gWoJ9FgKBEHRAz+cZHRstbKyoXPyOt3g8zu133M6R996ju7uHPXfcIcIu10DXDd7c/wZ/881vcvL9E6xfv56tW7diGAbnOzo5cvg93n33XX7vD/6AO+64o9zuLgrXcQo9dE8iFhWCLvAfIegUeujJRIqtW1qpiC1e0GOxQhzdc1062tuw7c8hyzI+J5K85TBNk1dfeYU//S//hYnxcb72G7/B05/9LBs2bMAwDc6cOs2P//Vf+cVrrzE2Msr/+X/9Z/bu3VtutxeM67roudkeuth5KSgBQtAp1BG1HZvKeCWR6OITDEmSxOrm1TQ2NdHW1k4ymUJRlJLuFF3qeJ7Hkffe4y///M9Jzszwh//hj/j6N77xobX/zc3N7Ny1ixUrVvCP//D3/Omf/Bf+nz/7U7Zs3VpGzxeO47rkDR1ZlsWkqKAkLPtVLrZtMzk5BZ5HVXX1TVeVqamrZcvWrQwODjA4MIAsy75lybsV6b54kb/95t/Q19fHb37jt/id3//9q27kal7dzL/7oz/kl7/0JY4eOcLffvNvSCZTwNJa3n89XMdB13W0gEYsIgRd4D/LXtAty2JqagrP8+adOOl6VFRUsGnLZlLJFG3nzondgVeQmJnhB9//PgfefptnPvcsX//GN1Bni39cjfr6en77936Pe++9jxdfeJEffP/7AL7mzS8mjuOi53UCmiZ66IKSsOzVxjRNpqemkCSJipuYEJ0jGAyybu06ZFnmnBD0y9i2zbvvvMs/f+97tLa28vVvfGNemRLXrVvPb//e7xCLRfjHv/8Op06dulz5Z6lj2RZ6Po8W0G4qlCcQzJdlrzaWZTE9PUUgEKBmtjrMzaBpGqtbVlNdXc2F8xdIp9Mo8rV7ocuFkeFh/vl73yOfzfG13/gNdu3aNa/jZFni/vvv56tf+xr9ff3849//PXldL1Sc8tnnm8U0TfKGTkALEBUhF0EJEIJumkxPTxMIBosi6LIss3LlSpqamhgbHaXnYjdaYP5pUz+JWJbF4UOHeOedgzz86CN8/vnnFnR8OBLh008/zY6dOzn49gEOHjiw4ARq5cA0DPS8jqZpopqPoCQIQbdsEjMJQsHg5fqNN0tlPE7z6tVMT09z4fx5tECgKOe9VRkaHOQH3/8B0UiUzz333KLEbc2aNXz22WdIJpP8/Kc/JZFIoC0gv3g5ME0TwzDQAhpREXIRlIBlL+iGoZPJZonGYkXpoQOEw2E2bNqIaZpcunRpyQuPn5imyYG33+bY0aM88uijPPLoI4s6TygU4rHHHqf1tm0cfe8IF85fWPK9dMMwMXSDYDCEfJ3JX4GgWCx7QU+nUuTzOWKxGNVVi9/2fyXRaJTNmzejaSrpdHpZ3+RLPT386w9/RE11Nc9+/vNEb2LH5KrmVTz/hecxTJPJiQnsa1SfWgp4nodpGFiWWZLyigIBLHNBd12XZDJJLlcQ9GI9eIqi0NLSQmW8Ctdzl/zknV/ous6hd9/l3Llz3LdvHw89/NBNnS8YDHL/A/u45957GB0dpe3cuSJ5Wnw8z8MwDCzLInYTu48FgoWwrAXdcRySyRRGXi96seHKyjjr1q/HddyS1b5caoyPjfHaq68RCod5/gvPEyjCXMKKFSt4+rPPkEwkePHnLxTBS3/wPA/DLAh6hc8FngWCOcos6BIl30Z5hTnHtkkkE1i2TV1dXVHNxCpibNu+DdMwSSYSRT33UkS6/J8Cruty7lwbx48dY+9dd3Hf/fcXxU44HGb3nt2sWLWK9957j+6LF4ty3huywHbqeR6GbmCYJhUVi+ihl2Hv1K2xXUtwPcom6IqqIisy2iLKvS0WVVWQr1gTLsky6VQa27ZZuWpVUW1VV1eza9cuTMukp6enqOe+HnP3dTFl9BaDpmnIsowsSx+a/E2lUrz+i9eQJInPPP30TadUuJLVLS00NzfT19vL/jf2F+2810LTNDRVXdAmMUVRCj1006SmduGT7ZqmoigKqlqayVRN01DVgk3BrUtRnvpcLsfgwACSNI8et+ehKAoTExMMDgyiKiota9ZgmmYxXLkmqqLQ3d3NxMQEF7u6UBSFVDpFf3/f5QmsgYEBdF2/aVsSICsKnuehKgrnzpylva2NUCiE4zi+jUpUVaW35xKJmQQdnR0EtABuEVM9ShQSTun5PLZto2oaw4NDJJNJTMvi+LFjVFRWIiPR09PDm6/vZ+XKFdTW19Hb24tlmjd97aqiMDg4iK7rpNNpDr/7Lvfddx+RaKQwSVrkeytJEqZp0t3dzcjwMENDQ+Sy2evakSUJwzTp6+1DlmWy2Sz9fX0Y82zjiiIzODDE4OAg3d3dRKPRwvPhU7uRJAnLsi4XZpn3czDbtkKhEI2Njbd8QZJPAkUR9KmpKV595RUUVS2I+vXwPFRVJZvN0dnRwdjoKLZtY5qGr+EXRZYZHh6mv6+Xl196iXA4TDab5fz58yiKwqVLPbz26quYxs37IVHYYDQ+Pk5tXR3t7e288LOfUVNbi2VZ/lzn7H0dHxtneGiI/W/sR1WUQvy+SPYkCpuEZqanMS2r8FJMpZicmEALBHjh5y8QiYTR8wZnT58mlUrSuu02Lpw/T9eFCzf3MvM8JEm6fF/TqRSrmldx4sQJvvPtb7P1tq1YpoXnecW7v56HLMuYlsW5s2eZmZrm9ddeI5fLXdvG3DGmyZnTp9E0jb7ePl579VWsG63KufIax8boaGtDUWQmJyYKAutTu5FlGdu2aW9vZ3R0lNdeeQXTsuZ1rOd5NDY18cgjj1AjBL3sFEXQq6qqeODBB5HmOSRVFYWZmRlSySSrmpu5f9/98+69LBZVUbh48SJjo2M8+NBDaIEAE+PjHDlylGAoyN577mb7jp1FGykoskwikaS/r5+333qL2rpa7n/gQQzDKMr5r4amqnR3d9PX38c9995LQNOK2kMH8NwPJnkVRWV4aIhL3T2EwmE++8wzxONxznd28sYbr9PQ2MSXv/Jltmzden0RnCcShVDGwMAA09MzxGJRvvsP32VmZoY779qLIss4RZ6AliUJ07IIBUP0Xurhvn37CtdyHRRZJplMcu5cG5qmccedd3LvffdhmDf+7edGdyPDw+i6wZ49t9N6W6uvz4csSVi2TTgS4WJXF/c/8MD826nnEYlERPKxJUJRBL2iooLde/Ys6Jjp6Wm6urrYsmUrW1tbi+HGDQkGg5w8cYJdu3cDMFFfTzgUIhQMcccdd7J+w4ai2jMMg2NHj/LySy+hqCpbS5DPW9MCHD50uGRVfurr64hXVRGNRtm7dy9aQKPrwnly2SwPPvwQTz/zTNFtVlVVceH8ebZt387BAwcZGR5m5coV1Nc3FN3WHPl8nryeY9OmTfP6fjKZIBqNoAU0du3exdbWhf32jQ0N9F66xJatpXs+TMMgn8uXpJ0K/KFsk6K2ZWFbFrqeL5lNy7KwzA+Gkul0mpmZGbRAgKAPuw4dx0HTNDKZDKdPni76+a+GbVu4joM9nyFzETAtC9u2sR0Hyy6kIn7jjTcwdJ3HH3vcH5umiWmYrFq1igcefIDOzk7e3P+mL7bm7On5PM4CCpVkszmmJqfQVG1RsWXDMNF1s2SbpyzLQteNG4eFBEuaZbYO/cNDfsMwyGQyBIPBxS0tmweyJOHYNsPDw6QzGV9sLAUkqZAZcWR4mKPvHWXj5k3se+hBX2x5FJYFxuNx7rjzTmRF5uCBA77YWiy2ZZNOpQmFQkQXmZir5IVRJLF08VZnmQn6hzENg1wuRzQa9S0viCRLKLNzBuc7O32xsRSQJRk9r3Pi/fcZHhrkgQcfLPra/itxXRdFUdi6dStr167l7Jkz9HR3+2ZvoViWSSabJhaLLfvkbILSsawFXdd19HyeeDyOJBe/b+J5HqqmUVdfTyaT+WQLuiIzMTnJ6794nbqGevY98IBvtiQK99YDGhsb2blzJ2Mjoxx695BvNheKaZpkMlkqKiuXdXI2QWlZ1oJuGAb5fJ7KeNyXIhSu6xIMBtm4aROOY9NTql2NJUaSJFzH5WJXF6dPnWbHjp203nab73Zdx6EyHufue+7Fdl1OnDxRWBq5BDBNk2wmTUVFBYFlng9fUDqWtaDruk4ul6OqqtKXUnGu6xIIBNi0aROBQJD+gUEyn7Q4uldYSpjJZDjw9gFs22LvPXf7Gm65bHp2DfXO3btoamri7OnTnO9YGqMg0zTJZnNUVMbQNBFyEZSG5S3o+TymaVJZWdzEXHN4rouqKDSvbqampoaB/n6GhoZ8sVU2pMImqumpKY4dOUJdXR1333N3SV1oqG/gnnvvpbfn0pLJwJjNZnFsm1isgoAQdEGJWLaC7jhOIVe5JFNRUembHc/zqKyMs3HjRkaGhxn+hAm6LEm4rsvIyAiTk5Ns3rKFPbeXZg38HFXVVex74AFMy+LosaNlD7u4rksqlUKSZaLR6LIvQSgoHctW0C3LIplMoWoqFb4VIJBwXY9oLMr2HdtJJZP09fb6ZKs8FOLnDhPj4yiKwt333FPShGtQGCFs2bKFtWvXcvL9E4yNjZbU/kexbZtUMoksycRisRunwxAIisSyFfS5h05VVV8LELiuSyQcYUtrK67nceHChSVdaWfhSHiAbhjU1NSw70H/Vrdcj/r6Om6/43YGBwc5e/pMWXyYw7ZtkskUkiTdVIUmgWChLF9BtyxSqRSKqvpeIkxRFFasWEFdXR3nOy98wiZGPRzbJqBpbNy0ic2bN5fFi2gsyo6dO7Esk8OHD5fFhzls254NuUhEIsVLGywQ3IhlK+iWbZNMJlFVhWjMz8RCHq7rUFFRwcbNm+nv62V0pLwhgWJi2zYziQQVlZXce9+9vqwWmg/BYIgtra3U1Tdw+uQp8vnSpZT4KLZtk04VRn/hRe4SFQgWw7IV9LkeejAYIhL28aHzCmGXWCzG1i1bSCRm6Oho989eidF1nZHhYWpqatixc2fZ/JAkiTUta9iwYQMDA/2ceP/9svliWxapdJpAMCiyEApKyrIVdMuyyGYyxKJRgkF/tv3DB3lHQqEQ6zesx3HcJbO0rhgMDw+TSqVobGqitq62rL5UVFawbfs2Uqk0J0+cKJsflm2TSWcIBYOLzuMiECyGZS3o6XSKaCxGMORTYv7ZxQ3ubEry1atbqK6upnOJbH65WRKJBIfefRfLsmhsbCp7dfuKigruuONONEWlo729KNWnFsPc6C8UChEVPXRBCVnmgp4pJObyu9LKbJGJVc0raVrRxPDQEAP9/f7aLAGTk5McO3oMx3EIh0Nlz1kiyzIbN2+icUUT589fKF0B6Y9g2/blLJ4i5CIoJctY0G2y2SzRaLRktRCrqqpZtaqZ6akpOm/xRF2O49Bz8SK9l3rQNA0PCvGlMlNVVcXuPXsY6O+nq6urLD7Yto2h64TCYRFyEZSUZSboH9SbNAwd27Z9TZ37UcLhMBs2bEDXdS50ni+JTb/IZDKcOHGCqalpampq8Ipc+m2xVFVVcc+995DP5zlzqjRFRT5KPq9jWRaRSJhIVAi6oHQsM0H/oGhAKpUCIBKNEixRDz0SibJ5yxYkWab3Ft8xOj01zckTJ1FVlRUrV+IukSyHqqqyZetW6urrOHHifaYmp0ruQyaTwbZtwuEwkYgIuQhKx/ITdCTwPFLpNJ7nFUIuJSpAoGoqa9euJRaNMTAwwMjwcEnsLhwPyzQwr1FyzfM8enq66WhvZ8PGDVRXV+O4SyDeMktDQwN79txO98UeLly4UFLbjuOQzWawLItwOFKy0Z9AAMtR0CUJx3VJp1Kzgl7aIXFNbS2rmlcxMDDA0FDpBd218kwMXOD4obd4652jjGQ//LmdnaTtyFu8sf8tDrz1Fsfah/hovflcNsupk6fIZDLcv28f4XAI110aPXSAeDzO7tv3kMmkOXK4tEUvHMchk8lgzfbQBYJSsuwEHUkqZFpMpQHP301Fs1zZd62orGDrbbcxOTHB4OCA77Y/6omZmabj8Kt866/+hD/75r/QlfjgU9eY4cz+H/Odf3qZ/kSawY73+Jf/7+/Y3z79obNMT8/wzsGDNK1YwZ133oWiqLhLJIYOEAyF2LJlC5WVlZw8ebKktl3XJZPJ4Do24Vtw2//SGWcJFkPZBF1WFGRFQS1hZj5FUVAVBVmWyWQySJJMNOZfHhdFlpEVGVX9oBpSdXUVu/fsxjAMLvVcKrpNWVaQZAlZuXoFJiVcRcuGVjbVB8gaLh+45jLV/T7/+sOXya9/mm/8my/w5S89TXP2GH//3Ze4MhI9NDTI+c5Odu3axaYtmy8XmijVb6koCsps+7nW5+vXr2ftunX09vbedIZLVVVRVXV+aQ08j3w2B0hUV1ffhM25ayzNI6qqhWdDKVPqBkFxKMoTaBom09NT8y5TrioK4+MTpJJJZmZmmJmexjA/OrAvLqqqMj4+Ti6fZ3houJDuVVWwZjeB5HK5otpTZIVEMkEykUDTAiSTSfR8HkVVicfjKIpC27lz9Pf3Ew6Hi5LDW1M1JicnyOVyDA8NEwhoeJ5HOBKhsrISkNBCUdZuuY1taxt5Ydz7oEdmpRk8d5SzIzZP37e3cL5YA9t2reGnP3qHs/1f5OGWINlMhvcOv0c+n2d1y2pcxyGTThMMhRgcHKSysmL2WiRkWUaSitfrkwBl9nfMZrOMjY6iKiq28+HslaqqYts2DQ31XLzYxTvvvEN1TQ25bG7BZe0lScKyLGZmZsik06RTKbLXaCuKrJBOpxkdG8XzCsemU2myuexVv3+ta5QVhbGxMTKZNJMTE0xPTWNa/j0fkiRh2zbT09NkMmkSiQSGrs/vd/NAC2jE4/GSds4EV6cov8Dk1CSvvvwKiqLcUNM9QFVUsrksnR2dTE9Po+d1DNNY6LO2IGRZYXh4mL7eXl55+WUudnUBEj3d3bz2yqvkcrn5vo9uiEehl2joBu3n2lBUlcp4JblcDmXWj6rqatrOneOFn/2MmppaTNO8KfseoKkqo6NjDA0O8frrv7hcJ3Xz5s3cfe89l7/rWDa67eBdccdtPU9/7yB5N0JTU2EiTwoGidbUEZg5Ts/YNA+3rGB8fJx3Dh5EkiQGBwd54ec/Z2hoiEAgwI9++EMi4TC2baNqGlVVVbO92uJJuqIojI+P093dzcEDB6mtrcWyrMv3zqMgrJZt4bgupmHyi1dfJaBp6LqxYF8KYufQ1dXF6MgIr16jrcy1a8PQaW9rw3UdBgeHeOXll8nn8wv4bQsvwqnpKTo7z+O5HuNj4+i6XrT2+TGLkozrOlzsusjg4CAvv/QStmVzo3vleYUJ8vr6eu67/z6qbmJEIigORRH0QCBA44qm2R6ZxHUbwmwNymQySWVlJVXV1dQ3NmCZ5oJ7TwtBUVR0QycajVJXX4dt2wQCGitXraSuvg7DMIpn3yv0srKZDBXxSlRFob6hAT2fR1YUwpEwra2tHD1yhFwuR+u2bZg3a98r9Ex1wyAcDtPQ2IiqKHh4VMQ/XJFJ4uOmbNskncniuBE+CP0qaGoAVcqRyhgADA0O0XvpEmvWrOGee+5lenoaTdPQAgGqq6uJRCI4jk0gGKS2tg5ZlvA8r0j3tiDojutc/h3r6+sL+eWlj39v7913c/TIEUZGRvGAlatWXuW7N7JY6L1OTk2SSiVpaGwoZHL86Dm8wughmUhg2zaaqrJu3TrqGuowjYW0belyqK6iooKqmmrqGup9fT4kScKxHaampkgmEjStaMI0LW748vMK36gSvfMlQ1F+hbq6Oj796U8v6JhEIkE6lWLjps3se2BfMdy4Id0XLzI6OsoTTzzJj37wQyIzUR559FG279jhi71cLodpmmiqykMPPXT575ZlMdDfz6F336WxsYlHHnmkaDa7L17kYlfXgn8PSZqNmHkOV0Z/PA88ZFRFAcfiwoXzpNNpnnzqKb76tV9jbGyME8ePE62I8Zu/9fWSbP8fGhpibHSUxx5//LrFqLdu2cL/+tG/4jgOu3bvYsuWrYu2GYvFCAYCPHjF73g1JicneeFnPycajfLEk0+wecuWRdmbnJgkmUzy4IMPsrW1dVHnWChVVVUEA0EeeeTRktgTFJ+yzYCYhoFlWYWeR6lsmha2ZZNMJshmMgQDAV83FZmGiW3ZmJb1sc9aWloIBAIcP36suDZNE8dxsK9i83qoapDqqkoUKU0yOftH18IwsthqFU31FWTSaU6dPAmSxL333QtAPp/H9Txcxy1ZMizTMLBtuzCquQ7hSIRdu3cz0N9PR/viUxabpollmvOqNJVIJJieniYciRCrWHyyMsPQC23HXNjvuFgsyypc5yeqmtbyo+xT2l4JF0pJUiHml81mMUyzkGvDx1Uul4fIH7lETdNobmmhvqGBnu6eok/I3uiWyoqMoshIkszcQhElFGH1hrVUKFl6L40VTmPozIyOIa3eTOuqKsbGRjlz+gyrm5u5a+/eD8x5XulzuczDVjwe5/Y7biefz9PR3uG3OQCymQzpdJpwJExNTc3i7ZVh/aBYsnjrU3ZBLymzFeqz2SymYRAOh4j5KejXoampidWrVzM6OlrS/OiuazM1PsLg8DgzU+MMD2UwLRvUGM077+GujdW0v/USIxmdgQsdnD2fZNcTj7OhEtra2rnU28ue22+nsbGxZD4vFlVV2bRpM/F4nDOnz5BKpny153kemUyGTCZNRUWl2CUqKDnLStAlCg9dLpfDMA1CoXDZivjGolE2bNxIOpXi7JmzJbLqYaQm6Gw/S08mzIq4TM+pg1wcSwMS1c2384VfeY419nl++rNXOXziLN6Gx/mNLzyEm0pw+MhxVEXh3vvvK5G/N099Qz1bW1u52NXF0NCgr7Y8zyObyZLP5am9TmxfIPCL5TU1LRVWXOSyOUzDJBgKoZRo48ZHiUSjtN7WCkizSyhLg6IGaVy3k+d+ZzdfUjxcNCKB2YlMNcymB5/nd1dspq1nDKXlAe7dtoOWapmuCxO8d/gQa9asYdu2bSXz92aJV1Wxc9dOTr5/gtOnTtF6222+2XJdl0w2Q17Xqa+v982OQHAtlpWgF3roLvlcDtOyiJQx10YwGGTz5s3EYlF6eroZHRmhacUKn61KBGI1bNxxndiupNK0eQ9Nm6/4m+fRc7Gb/t4+Pvvss7S0tPjsZ/EIh8Ns2boVSZY4fuw4/+bLX/bNluu6ZNJpTCHogjKxrEIucz30fD6P67hEY+VNbdrQ0Mjq1avp6+2jt6+vrL5cj0QyyeHDh1BUlZ27dt1SlewDgQDr16+nqamJjo4OMum0b7Zs22ZmJoEsK9TWLn5CVCBYLMtK0Odi6Lqu43pu2es9VsYr2bV7N5OTk/RdWrr50aempjh54gR19XVs37G93O4smBUrVrJm7drCKp0zZ3yzY5omU1NThEIhqm9ihYtAsFiWlaCDhOd65PU8nutSUeaixpUVFezavQvTNOno6FhSGQvncF2Xnu4e+vv72bhxEzt37Sq3SwsmGouyZcsW0qk0Z077V8XINE2mpybRggEh6IKysLwEXQLX89DzOo7jEqsozwqXOWRFYd369VTP5nVJXN7Rs3TIZrOcPnWKVDrNrt27b8mleLFYjB07dyDLMhfO+1fwwrrcQw9SXVXlmx2B4FosK0Ev7POZC7k4ZY+hA9TW1bH1tlYuXepheGio3O58jGQiwdkzZ4hFo9x3Cy1XvBJVVdmwaRNVVVX0XOrxrfyfYZokEgkqKyqJlDmcJ1ieLCtBh0IIQdd1JCRi0fKGXKCwm3Hnjh3MTE37Gg5YLAMDA5w7e5YNGzawa/etF26Zo7a2lk2bN9HX28elS8XPQw+g53USM0lqampKVqdWILiSZSfolmWh6zqqpi2JXlQ4HGbT5s3IsszJEyfK7c6H0A2D9vZ2JsbH2XvPPbd0weN4PM7td97JzPQ0Fy/4s+5f1/Mkkwmqq4WgC8rDshJ0D7Asm7yeR9M0Iktg+Z2mabSsXUtDUyMXOs8XUrMuERIzM7x78B0qq+Lcc0U+9VuRaDTKju2FOPq5c2dvmNhrMWSzWfL5PNU1VULQBWVhWQk6nodtmeh5HU1Tl0QMHWDlihWsWbOW4ZHhkuZ1uRHDg0McP3ac1q2tbN1amhSuftK8upmWljW0nWtjYnLqxgcsANd1mZ4u1F6NVwlBF5SHZSXoHmBaFvl8Hk3ViC6BHjpArKKCjRs3kkqmOOvjOumFoOs6J0+eIJ1Kcvudd9C0oqncLt00tXV17Nq9i6HBQk3UYmKaJhPjE8iyTFVV1WyhF4GgtCwrQccrhFwux9CXiKBHIhFab2tFlmS6fFxWtxASMzO88847VMbjt+Ta86sRjUbZtn0buq7z/vHjRT23YRiMjY6hKMpNFYcWCG6GZSXoHh727KSopqll3yk6RzAYZNPmzUQrYnT39DA6OlpulxgaGqKjvZ01a9awe8+ecrtTFILBIBs2bCReVcXpUyeLem7DMBgbGyUUConamoKysawEHT5Y5RIIBJfUJpnGxkbWrGmht/cSPd3dZfUln8tx8sQJpqem2bFzJ6tWrSqrP8VClmVa1rSwpqWFvt5eui4UbzRk6Drj4+PEKipED11QNpaXoHselmVimibRaBRZVsrt0WXiVVXcedddTIxP8P+3d95Bcl3Xnf5e6u7pnpyQZzDAIGNIJIIERIIASJlBErNEWhJtJVvSSvZarvVu2bK1ZZe95aq1ZUv2WlpbEiWtRMkWSVnMEQARiUTkGaTJfvEzRQAAIABJREFUg4k9oafTy2//6AEIkiA4A/TrxgzuVwX8Abz3zr0v/Prec88953QWheZKGB0d5fChQyiKzLr1k3Mz0QdRVlbOvPnzGRwa5vDhw1m7rmmaDEajFBcVXVWlIoHgariuBN0jU1fUMo0xQb92ul9cXMzq1Wvw8Dh86BCGD2F146W7u5tDbx+mpnbulBP0SCTMsuXLcGybE8dPZO26qVSKRCJBSUkJpWVC0AX54dpRtFzgMTZCtygsLESScxOJMN5ajXPr6phbW8uxI0fp6+vztU0fhGWaNDU20tnZwU03raGisiIv7fCLgnCYZcuWEQ6HaTl7lqHBoau+pud5DAxEMUyTktJS4XIR5I28CbokSUiShKzkzu0hSWCZmermhYWFvo/QL/RxnHaqqqtYe/MtdHV2XXE8+nmbVxo2Nzo6ylt73iISibBh48YPPV6WZWRJRs7hs5QkGUm+8j7OmjOHOTU1tLa2jiuviyzLyIrygfZs22ZocBDTMCgtLUXTrr5ujCxfXR+vxJ4iyyLccpKTlYpFjuNgGMa4XwZFUTAMA9M0MQ0D13UxdD2juD6haRq6rmNaJpZpEgwF0XUdyIywso0iyxl7poE2dv10KvWBfZQlCUVRWLxkCab17+zasZN77r13QjtHNU3DMExs2yaZShEMBHAn0DdVVWlvb+etPW9RN28e8+fPx7ZtLNO80G7P83AcB8/zUFWVRDyO49jYts1oLIaEh+04SGP9ybZAqKqKrqexbZt0Oo1lWdiWNe53R5FlNE1jybKl/Pqppzl18iQrVq7ANIxLzqQkScI0TQzDwLIs4N3PUZZlUskkvT09OI5DcXHx+46ZKIqikNZTFyKyHMfJ7Gz16fuQJAnbsjB0HcsyL9QMGC+yJKEFAteUC/N6JSuCPjw0xL69ezMPdBwvnaqqxONxmpubSafTBDQN3WefsaaqdHR0kE6lsWybgf4Btr/5JoAvecgVRUFPpzl9+jSqqrJj+3aSicRlBR1JYnhoiMLCQva+9RYvv/QSsiyPu32aqtLVdY6enh52bN+OpmnjPve88B7Yt5/+/j7qF9ZzsqmJttZWLNvOHAOkdZ3enh5Mw0DVNIaHhuju7iYQCPDkz39GOBzGsixCoRAzZ81C07Ss/mCqikJPTw8d7e3sfWsvra2tF4R2PMiShOO6qIqCaZpsf3MbFZUVSIBziXslSxK2bXPs+HG6Ojrf9xxVRUHXdY4dO4rrusRGR9m5fTuJyzzryyEBsiLT3z9AS3ML4XCYZDKBnk77JuiyJOE4Do2NjbS1trF1yxZM0/zwE8eea0lpKcsbGigqyn+yu+udrAi6ZdsMDg5mponjeOkUVSWZSJJKphgdjRONRsf3Al0FqqoSi8VwxkaPSDA8PIzrung+CLqsKBi6TjKZRFVVotEoqVSKy90dRVUpKi7OuANaWti1cxcrV60knU5f9rzzqKrKyMgIhmEwNDSEqqrj7psydu7WrVsIhyPMn1+PZVmMxGIZ25KERCZfSVdXV2Zz1tgPs2EYOK5DV1cXwWAQx7YJRyIEQyECgUBW76+iKIyMjKDrOiMjwyiqkhmhj5exmUNFRQWlJSUcPXKElatWUVpWhmVZ77vPkiRhOw7JeIJ0Ov2+56ioKslkkt6+PiRZJlxQQF9fH7phjOuZXQpZlokNj5BOp4nFRhmMRq/qeh+GNPYjF4/HSetpBqPRcf1IeozNbmUZx3F8ap1gImRF0KdPn85vf+Yz4zeqqgxEo1iWSf2CBdxx553YY6NAv1BVlRMnTvDEj57AdV1uumktjz72GI5Pgn7+B0RWFAKaxoMPPfShfTwvkH19vZw9c5bq6moeevjhcd8bVVU52dTEuXNdfPJTnyIQDOKO40M773M/cOAAP3nix8ytm8sXvvhF6ubVXdK267p4ZGYELS0tfOubf04kEuEvvvWtd4RxAmsHE0FVVZrPniUej/PxT3yCOTU1E3t3JAlVUWhva+Pg/gM0NTZx09q1rFy16pLXkWV5bCT/JsePHXvfc1RVle7ubrZt3UZhJMJ9D9zP6jVrrvx9HmtfR3s7juNw2+23s2LlCl+/D1mWsSyLXTt3cvTIET756KMTsufXsxZMnKwIuiRJqOrELuW5LoqioIwtpE30/CtBlmQ8z0OW5QvTQ0WWwaeX0fM8VEVFGrv+ePoYiURYvXo1v/j5kzQ1NeE4zoTujQcosoKmqpmFynGem06nOfz2IaIDUTbfcQd18+rG1eaApqHIMoqiEAyFkGXZ98RUiqKgyMqFtl3Ju1NZWcmKlSvYs2cPx44eZeWqVR94HUXJ2JLPu1nec1wiHmdocJDikmJqamuvuE0Xo2oaipq77yPTR+3C3oxcfI+C7JO/n1XPw/O8nNbR9DwX13VRZJmCgtzsEs30cfw+ZFmWqa9fwLRp0zjV1MSJExOMlR67rxP1Ww8ODrL3rT1oAZUNt28Y93mu573zx8nNs/SusI8XEwyFWLBwEaqmsX///g+1d35Wcqn/i0ajDAwMUF5eQVVV1RW36WJcx8V1r66PE8HzPFzPndAiuuDa47qaJ3lkZgayIlNQUJAzuxP1fVZUVXLzulto72jnWI6qGLW1tvL2wbdZuHAx69Z/JCc284mqqsydV8esWbM41XSSaDR6Rdc5nzY3NjLCnDlzstzK3COCFic315WgA2MuF4WCayTT4qUoKytjw+2349gOe/fum1AI2ZWQTCZ5+8BBotEoG27fQFGei2fnipkzZrBw4UJ6enrY99ZbV3QNx7aJDgyQTqepq6vLcgsFgolxfQm652V896pKKHjtJOZ6L5IksXDhQhYsWMDbBw/S3tbuq73BwUG2vLGFGdNncOuGW321dS0RKSzkhhtvRNd13j54ZeX/DMOg+1w3iqoyu6Ymyy0UCCbGdSXoHoAEwUCAQCCQ7+ZclsqqKm7bsIFzXV3s2b3bV1unT53m2LFjrFi1ckpUJhovkUiElStXUlhYSGNjI9GBibtdUuk0He3tFBUWMmf2bB9aKRCMn+tK0M9vhAiFQmgBLc+NuTyFhYWsWXsToVCIN7dtG3c+mIkyPDzM66+9hixL3LJ+3XW3OaSmtoZ58+dz9swZmpqaJnx+Kpmiq6uL0tJSqqdV+9BCgWD8XFeCnokYkAgVFKBp1/YIXVEU6uvrWbR4MY0nTnDUp8XRtrY2du3cQU1tDevWr/PFxrVMaVkZ69avp7+/n6bGxgmfn0wm6OnuZsbMmUQKr68fQ8G1x/Ul6ACSRGhsB+O1TnV1NatWrWJoaIgdb27P+vWTySS7d+6k+1w3t6xbz5IlS7Nu41qnsLCQNTetQVVVDh48QDKZnND5w0PDDI+MMGv2bCKRa3ehXXB9cF0JOp4HnkcwFLzmXS4ARcXF3LzuFoLBIAcO7M/kB8ki/X19vLltG5HCQu66+66sXnsyUVNby8JFizh25ChdnV3jPs80TVpaW/E8j9lzZuc0FFYguBTXlaCf3zRREAoR0K59QZdlmSVLl1K/YAHHjx5j/759Wbu2bdscP3acw4cOs3r16uvS3XKeiopy1t68lt7e3gkVj47H4zQ1NRIMhaZEDLpg8nNdCbppmOBBKFSANglcLgBVVVXcc++99Pf3s23r1qzlnYnFYrzx+us4jsPd995zza8p+EkkUsiKFStQVJXdu3aN+7xkIsmZk6coLytnzmwh6IL8c10JeiqVxMMjFCogMEkErKCggI2bNlJbW8vWLVuvKBLjUjSfPcvWLVtoaGjg1luvn9jzS6GqKvPrF1BbW8uxY8fo6hqf22VkZDizIDpjBnNEDLrgGuC6EXTXdS8seIUKrv2wxYuZOXMm937sY7S3tfHKyy9f9fVGR0d56YUXicVibNy8iVkifpoZM2awbPky+vv62Ll9x4ceb9s27e3tJJJJZs6aycxZM3PQSoHg8lw3gu44DqlkEs/zCI1lBZwsFBUXs3HzJqqqqnjlpZfp6+29qus1nWjkheefp76+nt+6jhdDL6a4pJh169fjui67du780Pze6XSa5uZmDMOgdu7cHLVSILg8k0fVrhLXcUimUgCTMhphwcKF3LrhNlpaWnjphRev+DpDg0M89+yzDAz0c9c9d7N06bIstnLyEggEWL16NTU1NRw9fJgjhw9f9nhDN2hrbUNRFRYtXpSjVgoElyfPgi75Wkf0YhzXJZVMgYfv+br9oLS0lDvuuBNVUXj99dcZHh6+ouucOnWSV195hfnz5/PgQw9luZWTm+pp07htw210dHa8L9rlvZW4YrER2lpbKSkpZckSH9Il5CHtoci0OPnJ/wg9R/mXHcfJLIpKEAhOjgXRi1FVlZtuXsvqNWvYv28fLzz3/ISvMTIywnPPPktvby/3PfAA9QsW+NDS3OCN/ckmJSUl3L55M6qqsWPHDkZGRi4y+I4113VpaWmh+exZ5s2fR938+VluyUXiKuUwP7nIhT7pyZuge56HaRrour/Foc+T8aGnkGWJYChXmRYzRQOyVW+xqqqKzzz+OIqi8MtfPMmZM2cuYXGsAMQlzj+wfz/P/udvuPHGG/nEffdnpU35wLadTEphH/Snvr6etTev5e2DBzn0diYDo+u6JFMpjLFC5ulUiuNHjzE6OspHPnJrpupVljFNk9HRGE6Oioa4rks8niARj+fEnsAf8iborueRTCYZjcVyYs9xHNLpNKqiEMqhy8V1XUwrOwWwFUVh3UfW88BDD3L0yFF++fMn33+Q5+F47vsq3Zw5c4Yf/eCH6LrOgw8/dKHE3GREN3SSiTh+KHpFRQW/ddfdpBIpnnnq6UwVH9dlZHiY1NgazNDwMLt376Kqqopb1t2S9TYApFIp+vsHsC1/a+2ex7ZtotEBBocGc2JP4A95dbm4roft5OaFPe9ykeVcCrqUGS1PoATdh1FSUsKjjz1Gff0CnvrVU7z2yqvvP2gsxcF5YrEYv/rlv7Nzxw7uvuceHnx4cvvOPdf1rXRhKBTilnXruGHFjWx/8022bdlKMBjEcZwLz7Gzo5OjR46ybPly5tfX+9IO13VxbBtfpiGXwPM8bMfJ2YzgXTg2hmG+01PPRk+lsfLRlklOXgX9fLX5XOA4DslUGnmsmHGukC78lT0WLV7C45/7HRKJBN/9x+9w/NixDzzWtm1eeeklnvz5z5hfX8/vf+UrlJWVZ7dBecG/96a2rpb7H3yAeDzOM089TTweJxgMIiuZz2XPrt3oaZ01N91ESUmJL22QyHwbUo6WKjPfonyhEPZEsEyLdDp9RXbtZJTD257ll0+9TGsCcOI07nqZJ3/+NIfacjN7n0rkTdDlMTFXxqqM+43ruhmXi6oQzlH5ufMfSbZ9rKFQkPsfeIDPPv5ZGk+c4Nt/9/ecHNtBqmoasiwTCAbHxPxlvvuP3yFUEOZrX/86N9x4Q1bbIkvyhR/mXMX2y4qCLEtIPtkLBUNs3ryZ1atXs3PnTv7z179GkmQ0TaOluZkXXniemrk13HyLP+4WAFmRkWU5ZwMeSZaQ5SuLOuvo7OCp//gVr77yCiebmhgcHKfbxjUZPHeSN199lp//6Mc8v+ssPa1H2PL6DhrPthEdzc362lRCzcZFXNfN5EkZ57ugqiqmaWFbFpZlAfhaN1NVNfR0mmQy43I5/5Hoad23gZ4iKxiGgWm+c1+y2cfi4mI+98Uv0NnVybYtW0mlUnzt61/D9Tws0+L0qVPs2b2HH/zrvzI0NMRXv/Y1PnH/fZiGietlZyqrqiqGoeO53oU1ikAwkLVF4EuhKCqGrmfspXRs28G2razakCSJ8ooKHvnUJ/nrv/orfvzDH7FqzRrwPJ5+6mna29r4zGc/y/KGBgzDeN96xdWiKAq6ruM49tj1wdD9e1dlWcZIG1iWhTPmAh3PuypJEo7jcvrUaf7pu98hmUiyaPFiGhqWs3TZMmpq5zJjxgwqKisIh8MoyrsHb45tQ6iK9fc8hpv8IW/84kdUPLCWpR//fb7YMAdVzoo8XVdk5Y51dnby9K+eQlXHdzlVUUmmkhw+fJjW1laSyWRG+HxCVVViIyP09fai6zovPv8ijScaL0Qt+IGiZAT9+PHjSIBjO2MRPdn5+GVZRlFkysvK0bQAr7/6Kk2NjSxdtozowAB//mffZN++fSTicRoaGkgmEvz0xz+54qnxpVAUheHhYc51n0PTNH78xBOEw2Fs2591kfOzgO7uc5w+fYZf/uJJysrKfLGnqirx+CilpWU0NjbS29dLSXEJqVQaSZKIx+M8+fOfZfY2ZJHzfezp6ebs2bM89+xzHDt2zNd3VZZlLMvi6JEj9PX18f1/+d64vkdZkvCA5uazJOJxYrFR9u3dy57du9FUldlz5rBw8SLmz59P3bx5LFq0iIWLFl1wUymBMNNqFjFtVhV28yv84l8OMfzpz/OZNdkPA71ekLwsDC/279vHH/3BH6IFAplp24cZlSQcx2E0NoqiqhQXF+NladT4ARYxDYPo4CCyJFFRWUkgEPDVpoSE67kk4pkc5iWlJdldyPMASSIYDKCqGoahk0qmGBgYwLIswuEwVdVVhEIhVFXDNAxMy8zqFF5CwrJthgYHkWWJiopKZEXO+oj1vTYNwyAej1NSWoqmqb7ZUxSVUChIOq0THRgglUpRUVlJaWkpeB66ofvkEpEwTYPR2ChFxUUUFBT4tgh83p7neSTicQzTpKqqapzfRqbv6XSa4aEhLMvCHVuwdl0X27aRJImqyiqW37Cc9R+5lY/e9VEWLnzPzlqrn23/7x/4myeaeOSvvsOXN9Vmv4vXCVkZoS9YuJC//bv/fcEv/mGfl6ooDA0N8dKLL1JdPY27773HtxGIRGYE0tx8lv/zT/+Mqqr84Te+QW1NDaaV3an6xSiKQjKRYMf2TKWh++6/n7RPbiVZyrh4TNPk4IGDbNu6lU9/9rPMmTMbSZYzERpXeG1JkjP+akmCsRC+80E7qqLQ093DD3/wA0KhEF/+L1+lqKjIvxE6Gf9585kzvPLyKzzyqU8yffp0LJ/sQeY5plMpXn7xJdrb2/nyV79COBy+qnt6Od55X5t58fnn+ehdd9HQ0IDu8whd13W2vvEGLc0t/PGf/Df0dPpD+ydLEq7ncfDAAb7/L99Dj8cpLCyksKiIGTNmMHvObObVzWPpsmUsWLiAisrKi9avvExkjZGgo/EoTV0Si+fJ7N+1l4dvnUkgHkcrKacgN0tsU4asCHppaSm33XbbhM4ZGhyk8UQjNTU1rFmzJhvNuCyRSARV1SgpLub2DRuoqva/oG8qlaKvtw/Pc1m1erXv9gBmzp5NT28Pn3z0U1m6okdieJCk4RIsLKG08N0hnz3d3Tzz9NNECgvZsGFDTkr7lZaWcvjQYdatX09VVZXv9izLovvcOSKFYTZt3uy7PYDy8nIO7NvPypUruXHFCt/t2bZNV0cHqWSSVatWTehcVVHYvnUbwWCIpcuXMbduLosWL2bJkiVEIpFLnuOkYpw5uJXtx3rxpADz7n6MJY2/4K9/9Et+OifImkXzuPHmciZf1qX8krdVB8M0sS0Lw0ff+Xk8zyMWi2EaBqqWuy6bpoltWzi+TpffjZ5OY9s2pmEQuKp4e4uB1iaONbYwGNexbQvLVaiYM58Vq1YyqyQj3IZp4jgOjuNg6EZOBN00DBzHwfRx1Hoxhq5jmiZWjjb5QKYYi+M4WKZ/s8iL0XUdw7Sw7YktaHueR928efyPP/tTqqqqqamtGVe0k2MkaD6wjdcOwgNf+Cp3rV1Mb7CLm+ae4tTZHjZs2kSJSC4zYfK7jCxJVxT3OlFc10VP61iWhaYFcheHPjZnnXTvpZPizL7XeOY/txIrXszmTbcwq9il4/gBtj/zBG+dOMdXv/QQM3MXzp9fxhYqcxUTng8yIcTyhENBJUmiurqa6gnOeLXiatY/9g0W3R+kdt4MAKqWbeSP/mYJZqCSOdOKJnQ9QYa8CrqiKIRyIK6u66Lr6TFB13IyigTw8HzztfqHReeRN/i/3/k3+mvv4y+/8fvUjbk9lyxfxvRIgr/8h3/jiRmL+ebDS/MmcX4uvL4XWZYpKAijKLnctuGN5eTJTT8VRaGwuCh3ezSUAGUz5lJ2cRvUMNPmTN6UFNcCeRP0YCBAXV0ds+f4Xy3H8zx0Xc+5oKuqyrTp05GkXAqBdGGzz5WQjjbz2pNPsHe0hv/5lc9fEPMMQWpXrqeh6gV2v/AC5x5eipIHRVfVzDPMlaRrmkbt3FpfQwffi6pphMMFOdtYpKoq8+rmYeYoWZ7AH/Im6MUlJWy+8w5CIf+XPTIjdAPbsjJbuHO0o7GoqIiNmzaRq3wckNnoJ13xDkODntN7eenNFhY8/HnW172/TJ+mVDCtXGO0s5m2KMzLw17jUEGI4pLinImdpmmsXL2axTksZBGJRJg+cyaalptSiaqqsmTpElF9aZKTt63/qqpSVlZGQLIYiMbwb2/hO9v+Lct632413/Ashns66OnuYThuYeQwz9AVy5w+Qs+JQzSb1axsWMSlJt8eLo6byebo+fnQLoNEJkY8N3LukY71093exnDcZFTPTadlRSagBXxLb3ApwuEwlZXlJIajjCTESH0yklcfuh3vYtfzz3EoOY8vfOkuin2ykxH0FKZl5mR07loxzhzazZY39nC2qx8rOIvb7nuET2xcwrW8jujqBtGefqyiYiorKi55jKkP0DOgEyqaRlUluF05buR5cuFDdy36W4+y7bUtHDnVzpAeYMlH7uWRhzYzM+zve+S5Y+sEOV2AcRk8u59nf7OLio2f4r7Vonj4ZCN/2Ra9FKf3vcoPvv8Tth/vxM/gLNd1Ses6pmkh+z1Cdw16zhxm25b9pApns7h+JqMnX+Of//67vHEy6a/tq0WSkFQFCT5gZKgz2HGS030mNQ1rqVfAmVwrvhMiEW1n7xuvc3okwPwlCykxmvmP732bH7/4wdktJzPOaDvbnv4JP/zZS7SO+JdbSeAfeRqh20TbG9m5+whxN0hpYdDXXxbXdUmnUjiOM67UBFeDY5qkDYXFGx/l9lsWAQ4blhfzX//039my7QgfW7zeV/tXgxyOMKOujmJ9N939A/CuGASwRnrY98YOouF6fvv+TSjA1M1YbWEYBpHZN/OV39tIpQSJj97At/74m2x5/k2+/MiNXHoOMznxzGFOvr2HPScHCReHCQXEFs3JSF5G6OloB4f2HkaqW8vNS6bjmpavM8tMcYsUsiwj++x5lYMR5jasGxNzAI/IrFpmlxajqtf4R6KVMnfVRjbMkzmwYyutF+XxclMD7HvtN7x2NM7tn/4yH19+6R2AUweV0lmL2HBXRswBiFRQUzOLSD5Ce/zEM+g6fYSDpxM0bN5MbcjFmspTrylMzgXdNQY5eXAPZ9Mz2bRhFWFPx/b53XFsm/SYoOOzD12S5HcLt5Mm2tJKsng2q9cs9dX21SNTNe9mPv2lR5k2eIinfvE8bx89wfHDB3j9xWd5/a0Olj7wVb7++G3krohfvpBQZJV3HqVLYuAcfTFYsv7mKTU6H+1pZv/eRoqWbWDdghLSRu52xAqySxZdLi5WepS+vkF027toB6iH50kEwqVMm1nMwOmjHDqT4qZHP0O9fBLLlVBUzVeBsGyb5HlBvxo8FyMZo38giuHIvOO98fCQCUTKmDGtDPWiAVys8zR79rRQc/tD3L1iEux+0yIs/+jjfKO6ji17TnH44DBBxcW0g9z66T9g4+o6rvF5hi84yV6O7t5HvHwNX7zf/9xDucJJ93Pq8AGiwUU8/pHFDO45iCTLaDmsuyvIHlkUdJPo2d1877s/5eSg844PznNx3ABzGu7k8c+v58Rvfs1BfSlLOw/ySutxOofijJin2HPsJMtq5jKjJPtxIKZpkkqOuVyuJnbZMeg5upXv/etPORMPUqCNXct1sKQQtWvv57//4SNUjYUO2/EuDux8k96iVXzu8Y/5FsWTdaQANSs287kVm3HSCVKuRlHkOv7A3RRn3t7J3jaJux7/PCsr81q5MXt4Ou1H3uTpZ7ZRsfFxTu3bRuPB08RScVoOv8XxipuoW1jDVHeuTSWyKOgSihKksKiUUschoMljIVcerqtRFNawkil0TyFo97DlxRfRY720DYwyGDvN7jcPUPKJ6f4IumFe8KFLV7MoKkkogRCFJaWUyEEKtLEuug62FKIoctHirhXj1KH9nBkt577Hf5sl5eA6Fo6noKmTRxCUgkImwbzCR2x6Th3iwPF+ln/8d/nEyirAxjQhEJjkFXVMA300gRcuJNG6mxeadQY6TjOUinPm4D72VJZTtaCGyBRbMpjKZPGNDFK99A7+9Nt3fPAhnseqb/49ruuAohLvepvv93dytOpuvv71z1LuU2yxYRqkUyk0Vb263YVKiDlr7uUv1tx72cM8M0bj7ld4dV8vS3/rERrKdc61ttDZM0hF3VoWzMhN6gHBVeLZ9J7cw8uvvoU3bxP3r57GUE8r5851EA8uY31DZb5beHUESljy0c/xt3f+Lo7joigmjVt/Sf+ZGOt+5yv83oa6HMfBC66W3A4xLhSGlrFSg5w9cZyW7n6iZgsnuwdZVV1OyIcWmaaJbuiEIxFkn/OqeFaCpu3P8N3v/JSO8BJ076fsfXqU4f5e0oUL+MKf3OqrfUG2cIiefosff+fbvNaicNOtNv986Hlig31ERz3Wf+l/ce0GoI4TKVMBCklClTxivW2cOnWK3ugQHadOcm55NTPLI1M4x+TUIz9zRs8mPthNZ2cflTesozwUofVQMws2lRLyIbTPNAwM3aCouNj3rdS2kWIoOkxgxmKWFgXp7+rCdhxcpYyGm25l8XRfzQuyhaOTHOkjrlazfEkYa7CHHsfBsWRmLl7LbavL893CrOKYKXrbWumJqay48zZKEj2c7hhkennkulwEn6zkR9AllfI5DTz4ew08mAP3vhCXAAAH10lEQVRzhmGg6zrTpk9H8VnQtcJqbn3sj7n1sQ86wmMSZki//lAi1N78MH9z88P5bklOUIJFLFr3MRat+1i+myK4CvK2OmdZFj09PYyMjPhuyzAMDF2nqKgoZxn6ILOhqb+/n4GBgYv+VYj5ZMPzPEaGhznXla/ENf7jeR6xkRHOdZ3Ld1MEV0HeBD02MsIbr73OsWP+5sXwPO9CCbGioqKcZq9LJBLs3LGDXTt35symIPvYts3Ro0d5/rnn8t0U33BsmxPHT/DCCy/kuymCqyBvcVeO4xCPj6Lr/iYBchyHVDKFJ0FhUWHOcqFDJodMIpHIXcpegS94nkda14mNjua7Kb7hAbqhMzoay3dTBFdB3gRdkiRUVfXdp23bNvF4HFVRCYcjOXW5SJKEqqhC0LNMPiLpFFlGU3P7ueS6n7KioKm5Kagh8Ie8Cbqqqiiq6ns5OEmSSOnpTEGN8rKcFvrN9FFBzaEQKKqKLMuoOap0o6kaiqJkBC+QO5uqqubsvmqBAIFAwP/Uy++yqaGNvT85sadpBDRNDD4mOVn5IpLJJJ0dHZnR7zhGwIosE41G6evtpaCggNaWFkwr+xnRZVkmEY9zrqsLWZZJp9OYhklLczO2bfs6ApJlmdFYjJ7ubrRAgPa2tox7yccZgqqqtDY3MzwyzInjxwkEArjZ3qzlnS9eDKqi0NXVRSqVwnVdGhtPUBgpxHHdTE71cb4PE0FRFDo7OhgaGuTUqVOMxuM4jn9VhCQys7yuri6iAwN0dHSQTqc/9LyrQZFlent7GYwO0NrcTEFBAZZp+vbuSGRck50dnUQHBmhrbcMwx1GxaOzdChUUMH36dIIi/0veyYqgD0ajvPzSSyiKMi6XhqIopNNpTp08RXQgSnx0FNM0s9GUdyHLMqlUiqbGJgDa29rR02lefOEFZFnGdf3L5q0oCoZhcOLECVRFJRQM+i4EqqoyMDDAua5zvPH666iqmvU+Zuqz6ji2g6IqjIyM0NfbixbQeP7Z5ygIFWA7NoqiUFCQ/SLHiqIwODhI89lmdu7YQVlZGbbtX3ZASZJwHIeW1laiff28+sor6H4+x7GNd8PDwzQ1ncQwTXp6enwtUC1JEq7r0dbaSm9vLy+//BL2OAdYnucxbfp07rjzTiHo1wBZEfTyigo2bd487ggSVVEYHh4mkUhQU1PLuo+s9+WFVRSF6MAA+/cfIBAM0tDQQH9fHxs3bgKJ7I9e32M7EY9jWhaaqnH7pk2kUinf7AFoqkpLcwudnV3ctmEDWiCQVUGXyAh6KpXCth00VaWnp4djR44SKgixbv16igqLsB0HVVUvVK3P1l2WyLiUOjs6GBke4eZbbmHGjBlYPgu6bVkUFhZyNnSWTZs2kfTxOWbqpSr09PSg6zorV65i6fJlvgq6LEnYtk1xcTGhUIhNmzdjGsZln5vE+VRNHuFIhEhEpPC6FsiKoBcWFnLjihUTOmdoaIjTp05Rv3ABixb5V029v7+fUDBAQUGI+gX1SLLE8hsafLN3MYlEgva2NlRNo76+Pic2VVWlsrKSlatW5cRed3c3v37mGSKFEW6//XYCORilFRcVcezoUZY3LKe6eprv9gDi8TiJRIL5OXqOlVVVnD1zlkWLF/v6fVxMKpUiHo/nzJ4g++QtDt22LGzbxvRx5AGZlzQ2Mko4HMnkkDGt3BQYJuN7tW0H0/SzYur7bbqOM+4p89VimiaO4+A4LoaRfbfZJW1aFrZlY1u5KcRgmuaFfuYK0zAz/fRx9nExlmVl7OWwj4LsM3nyuF4htmWTTCaIhMNogUCmknqOEXtDs8v1cj/z0c/r5d5OVaa+oNsWqWSScCQyFvUxdcsaC3wkh/sXBIIrJW+C7pFZYPNzYRLANC2GR0YIBgJompazaToAnofrujg+RtO836SH4zg525TieR62bePYNl6OrF7oYw5nW67r5tTlAuf7mMN3J+d9FGSb/G0sUhRKS0uJhMO+2tE0jdlz5lBTW0tRUREVFeU5G23JikJxcTGykrvfzUAwSFV1dc52xGqaxswZMwlHwjlLq6BpASoqK3O2eUqSJAojEcrLc1caWlU1ysrKCAazX8HrUkiSRLggTHl5WU7sCfxB8vLhVCaTAbG3t5dIOExlVZVvdmKxGG8ffJvy8jJqamsZ6Otn4eLcrOJblkVfXx+SBLNmzc6JzXg8TmdnB0uWLM2JqKdSKZpONKKqKssaludk92YqleJc1znm1MwhFPJf8FzXZXBwkNHYKPPr5/tuD0DXdbq7e6isqKC4xP9qtK7rMjQ0xGgsxrz5uemjIPvkTdAFAoFAkF2m/KKoQCAQXC8IQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCIIQRcIBIIpghB0gUAgmCL8fy4iqoZbNxSXAAAAAElFTkSuQmCC)
The graph of the function f is shown in the xy-plane above, where y =f
. Which of the following functions could define f ?
Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.
![](data:image/png;base64,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)
The graph of the function f is shown in the xy-plane above, where y =f
. Which of the following functions could define f ?
Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?
f(x) =2x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?
f(x) =2x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?
![2000 minus 61 k equals 48](data:image/png;base64,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)
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.
![2000 minus 61 k equals 48](data:image/png;base64,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)
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
Which of the following is equivalent to
?
Which of the following is equivalent to
?
![](data:image/png;base64,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)
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
![](data:image/png;base64,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)
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
![8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x](data:image/png;base64,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)
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x
![8 x minus 2 x left parenthesis c plus 1 right parenthesis equals x](data:image/png;base64,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)
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x