IM 6.6.3 Lesson: Staying in Balance
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[/img][br][br][size=150]For diagram A, find:[/size][br][br]One thing that [i]must[/i] be true[br]
One thing that [i]could[/i] be true or false
One thing that [i]cannot possibly[/i] be true
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[/img][br][br][size=150]For diagram B, find:[/size][br][br]One thing that [i]must[/i] be true
One thing that [i]could[/i] be true or false
One thing that [i]cannot possibly[/i] be true
Match each hanger to an equation. Complete the equation by choosing x, y, z, or w to go in the empty box.
[img]data:image/png;base64,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[/img][br][math]\boxed{\phantom{3}} + 3 = 6[br][/math]
Find a solution to the equation. Use the hangers to explain what each solution means.
[img]data:image/png;base64,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[/img][br][br][math]3 \cdot \boxed{\phantom{3}} = 6[/math]
Find a solution to the equation. Use the hangers to explain what each solution means.
[img]data:image/png;base64,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[/img][br][math]6 =\boxed{\phantom{3}} + 1[br][/math]
Find a solution to the equation. Use the hangers to explain what each solution means.
[img]data:image/png;base64,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[/img][br][math]6 = 3 \cdot \boxed{\phantom{3}}[/math]
Find a solution to the equation. Use the hangers to explain what each solution means.
Here are some balanced hangers. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Write an equation.
Explain how to reason with the [i]diagram[/i] to find the weight of a piece with a letter.
Explain how to reason with the [i]equation[/i] to find the weight of a piece with a letter.
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[/img][br]Write an equation.
Explain how to reason with the [i]diagram[/i] to find the weight of a piece with a letter.
Explain how to reason with the [i]equation[/i] to find the weight of a piece with a letter.
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[/img][br]Write an equation.
Explain how to reason with the [i]diagram[/i] to find the weight of a piece with a letter.
Explain how to reason with the [i]equation[/i] to find the weight of a piece with a letter.
[img]data:image/png;base64,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[/img][br]Write an equation.
Explain how to reason with the [i]diagram[/i] to find the weight of a piece with a letter.
Explain how to reason with the [i]equation[/i] to find the weight of a piece with a letter.
When you have the time, visit the site [url=https://solveme.edc.org/Mobiles.html]https://solveme.edc.org/Mobiles.html[/url] to solve some trickier puzzles that use hanger diagrams like the ones in this lesson. You can even build new ones. (If you want to do this during class, check with your teacher first!)
IM 6.6.3 Practice: Staying in Balance
Select [b]all[/b] the equations that represent the hanger.[br][br][img]data:image/png;base64,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[/img]
Write an equation to represent each hanger.
[img]data:image/png;base64,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[/img]
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[/img]
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[/img]
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th/97vfOdjpfmvQoIGNHj3awe71cth1YQAfaEK8/PLLdsIJJ7j0Zl6SAj0AcX1EIdA9xMsFnZKUPmv+AhuZGO/xpk2bPK72f4pSkXY5sH7zm990VV+6zi699FJbuHCh+66iuwDbunXrXJ/6IYcc4tLdpEkTu/POOx3sYZXqxPvmm29a//79LdPkoQsQzQR6RRYL/zuB7qFxLuj0Vd90003Wpk0b5+giE5911lmu2y3oASDAwkAduszoH997770dNEOHDnXDW/N9uRAPfdb0XTdv3tyojeD1vueee2zVqlUeT+3vFPfDWXnBBRe45gXdfwcffLANGzbMNXkEuj99/V4t0D0UzAV9//33d1CPGzfOcIRRuhIuu+wy5ygLcmAK1fUXXnjBOnfu7F4qe+21l3Xp0sV5q/OFPPNIwLdgwQJXwtJWznji6XbjBcVzBnFkRhGiB34Maj6MwadGMnHiRDvuuONUogchtI84BLqHeLmg43GnyswAlOuuu86VkLQ9KW1/85vf2IcffugRS9VPASb9zP369XNDWymFGRwzffp0ByXfV/XgJfTiiy9at27dXBUa2HmJ0CcfVG2EGgg1BUpwfALUeM4991yjb/+f//yndejQQaBX1XAB/16gewhaHuiIRfX0wgsvdA4uSvVMdZjv/Dq6iHv48OGu356qLuA89NBDrq/cI5l5neLlQE2AgTX0qwMhpTsz3eh3r2otIfemQD558mRr2bKlUfvA8ff973/flixZYtROqD0I9FzViv+/QPfQvDzQKQFxklG60/ZkfDnOJhxm9F9//PHHBVWHcZ5RK6Abjb5musUYxnrXXXe5F4vfKjbXM978vvvuc7ADJIG+eaa18l0hB9dRYh9//PGuKUOcDMnF645OvGRmzZol0D3ExSZvv/223X333a6WSE0xzEDNE4cyeYvaKD4UfEBMggrzvtlxe8hQ6amySn/h4wcVgU60ZHC8y9/5zndcPzWwU1r++9//dkNOq1LFphbARJVbbrnFQU4tAQ853WgMzuElENTBW338+PGuFoKhKd2vuOIKe/fdd11tJN908zvSxQvvu9/9rouHKjsvvNmzZ+9WSxDo3tajSfXwww87n0+mCzLpf72VqPhspKCTNDI71WHavrR7qWr37t3btYerUoUHvvvvv9+aNWvmnFhUfc855xznGQ/SyZeRk7HnvESovgM7Hnn66qnC51tz4Pl4CQ0cONAYkks8lBaU7rmDiQR6Rvnd/wr03fUo77/IQSdhwPHII4+4KhCgA8/3vvc9Vx3Op3SkZjBlyhR3PS8LagYMWaU6TUbIJ47yBCrvPPECKbPJGFKbaSZQhWTiTmWw8z3NDPwU9EZwPX9pZtBtl1sDEejelsgGnVocTld6LcaMGZOIQGFyySWXuOnU9MJQWynkKOyqPO9UWdU9Oxo88bfddpurDpPpKZl5QBxr5bV9AZhS8amnnnKTUKhCU/VlQgpDRynlwzxIF+1D2tOZ8fNMknniiScc7BW9YHhJXH311bvae/gSaIcxFZV2ee4h0HMV+er/bNAZUMTIReY08LJNQuClP2/ePDfDkgKs5EEHCpxw//d//+cyP29nnHQ33HCDG6eOQXMPQGM2GmDT38wLAtAAnxFtxThIN153pr3yoqH6zQQU/AzlvWiowTCxh4FDdP1xHaP1Fi1aVG6SBbq3NNmg001L4YCvJikHhSW+nz59+uwaCl3Is8WmRCfxPBSTTGhbU0ICDbDfe++97u2c/YD89p133nETTZhwAjAMMqEJQBzFPKhV/OMf/3D96jQ9qFUMGDDAc3EI0v3444+7wS/8jnQzOpChwBX5JAS6t0UFurcuuWdjBTqJy7zBBg0a5DzxwM5yT6wIwyQTDkrRzDBRnFi0yxmLzugxnFi57dvchw7jf14uDzzwgB1++OHOR8BwX7oOWXcus14e/eEMsGFCD85CutFY9IKqGf3oFVX1Bbq31QS6ty65Z2MHOgmkjTpnzhznfaddQujRo4dbIILqOh7va6+91kFFiUipj9MCqCqCJffhg/yfFxRVxltvvdWlC4h5CVGVXLp0qatlUMVntB41EL7HcURNgJcE11d0CHRvdQS6ty65Z2MJOolkUM0zzzzj2tx44Wl/0Q7G+cVqK/Q144UEmJ/+9KfufEVV39wHD+N/YKX9TXoYsEP6SDueeLoQhwwZ4tpZnKd9TjODUr4yyEmrQPe2WFSgU6CQ38LOc+SNxLXRc02Z6Xaj6k71HAcd1V7a7xnImcoJ/Bg8DgcZAKci3W6U3LTZ+Xv00Ue76jr/U9LffvvtX+srryj9At1bnahAJ2/SQ0JTMZ8XtXfqKz+bCtB5WyIoy0Uz2w3nFbDzl5KSIaMsf4x3O6oqu5ep8BEw4u+MM85wNQ5eSryo+EsXEM+DI7EqvgSB7qW0uRd8ZmRcMbzu5EmaYix0StOLphr+lbCOVICeEY/+UFZAZXIKJSLAADmz0XB0hflGzaShqn9JF7PdWAEXxxxORUp25rXTjUaVvSqHQPdWq1glOgUJXbasinTmmWe63XxonrHYaZhduakCHZGBAy82sOBhf/TRRwMRmLh5S1O6kmnKC3xf1RcKMGdmuzFEloE19PtXFXKyuECPFnTyBY5TZiviGB4xYoQdeeSRAh2zAAaeaEo1BoVk5qMXMn+buPCqs8ECVTU8734PIMeALBxJVZr4ywu0xzLdZFW5L+lmeO6VV15p//nPf6r8ssjcS6BnlNj9L/YrRtWdJuQdd9zhxniwEQljO6hVqkQPGHTMS7cbgNOfjoH9HsTHVlH0ZTMPnG2YygusAEtpXMiBDwGnTXkj5fKJU6B7q1Qs0Kn10RZnfgI1MnbwEeg7bRJkie5tZn9nAZ2NGRjFxkKVGC4TcLTg7adtjfOPmgROmKgOge6tfLFAz707tQiBvlOVuIOeeUszCeKNN97YFVgfjvngtKnx8u+3335uVlmYTpfcjJT7v0DPVeSr/wW6ty65Z2M7YCY3ocX6n3Y7o+9YkJFqPKPyxo4d69ZtK1YavO4j0L1UKX73WiYVKtEzSoTQRs+KOpSPQI53nUknbdu2dQNz6ErB41+IIy7IRAp0bzVVonvrkntWJXqWIjhZ8Iyz2g0rvbDSDavJ4nHlJRDlIdC91Rfo3rrknhXoOxUhw7CsMiuv0ibHGTdjxgzn3Y8acpIo0HOz7lf/C3RvXXLPCvSdirAby8UXX+za5Kz2wg6mlORxOQS6tyUEurcuuWcFupnrH2X8Oc43hqtmlofGKx+XQ6B7W0Kge+uSezbVoFMlpy89s/84izMyFp3utqidb7mGEui5inz1v0D31iX3bKpBx/nG/mzsgALkrGpTyISTXFHD+F+ge6saFeiMe2egFdON/Yx49H6q/51lLEri56P/73GD/4SAlNyZjRPYRIJVbeLgePN6WoHupUp0/ejeqQn+rED3oSkwM5yVPnLWbmOdN/rOi72oZFUeQaB7qxVVie6dmuDPCnQfmrICDGuqM5EFDzs7mDKDLa6lOY8q0L0NHjbo5AlmWzIpib0HKgvkLXprqrKoiPeTfXVWoFekTjnfYTQ86b///e/tiCOO2LUjDBNbqMYzVTU7sMkCRouD912gexs1bNABlhWI2Vxk3LhxlYYbb7zRTZQKqt0u0L3tXuFZgGWaISPfWHaImWnsCMNCFqwJnxvY/5yRcoXMn68wIQV8KdC9RQsbdHpf2CmVtQpz84fX/yxayuKl1BCDOAR6ASoCOh5MVqoB9i5duriphl27dnXTVJmqmh3Yv40XA11wUR8C3dsCYYMOaFTbqd1l1/bK+8zAK6rvQeUZge5t9wrPUnUnY/C2XbJkietKozutvMCQWN7oiB31IdC9LRA26N53Ld5ZgV48rWNxJ4HubYZig05hwTRmmnP4b8IuCAS6t90Te1age5u2mKADOXC//PLLzkHHKsTsvhMm7ALd2+6JPSvQvU1bDNABnCXHGSqNP4fVX7/1rW+5NQtwvrHMGPAH5WnPflKBnq1GCj4LdG8jFwt0hrwyhZmdfulqY3HISZMm2UUXXeS212IbLjYT4aUQ5CHQg1SzBOIS6N5GKgbo3Jnde1lHECcubXSABkLWERw6dKgdc8wx9sQTTwQ+5kKge9s9sWcFurdpiwW6993NQc8mmu3bt7c777zTLQUdZKku0MtTPqHnBbq3YaMGHUccA2TatWvnhlKTHoF+wAG2cOHCWIw088428T0r0L1tEyXoDMBiQ5HTTjvNTj75ZHvuuecCH3OhEt3b7ok9K9C9TRsV6JTa7Bh0//33O2fcdddd50bOeaey8LMCvXDtSvJKge5ttqhAZ7ILzjmGTPfr189t7UVagj4EetCKxjw+ge5toChABz5WJqK6/u1vf9t9Zjx8kG3zzNMK9IwSKfkr0L0NXUzQAZnJKrTFhwwZYv3797e///3vbsfgoOaf5z6lQM9VJOH/C3RvAxcLdCBnjUGGvFKS9+nTxxgCy2g4YAzrKFnQ2XqY8cIIp5C/BjNnznSLWFarVs0OOuggt4NMWJmrlOItFuh42BnmSnucdQoYKRfGkNdc7UsS9Lp167q54D/5yU/sggsuUKiCBmeccYbbQUag745CMUAHNtrklOKsGDxt2jQ3Qo5554yMywT2Tyc9FGBBHSUJOiu61KtXz22S0KhRI1PIXwN0q1Wrlgn03REKG3SgxdE2atQoO/jgg61Vq1Y2cOBAO/vss2348OG7hTFjxrgXAGkK6igZ0HnbsVILyzU1adIkloGtkatXr25lZWUuAFT9+vVjmdamTZu6cdXs4a4j/OWeAZ1BMeeee64b5srMtfIC67y//vrrga0ug31LAnREYojg5MmT3TDBa665xuIY2rRp4/Zcy4DO8s80LeKYVvZqZ9OAlStXinMLH/SoRS4J0BEJ2HG+UbJTBYpboJ3Vq1cv15wAdKrG3bt3t+effz52ac1ox4isoNYkizoj+71/2FV3v+nze33JgO73QcO+nhfRqaeeao0bN3bVdkDv2bOnzZ8/P+xbK/4AFBDo+YkY6t5r+SUh2l8J9Gj193t3gZ6fggJdJXp+OSWmvxLo+RlGoAv0/HJKTH8l0PMzjEAX6PnllJj+Kht0uklZ040RbIzATEJ4++237amnnnKj8erUqeP8SIWYQqAL9ELyTWyuyQa9Zs2abhAWK7R26tQpEYGtoHgexk/UqFFDoBea8+SMK1S5eFyXAb1169aua5Rek6SHQpRXia4SvZB8E5trmGwyY8YM69u3rxsxyGqsSQ+FiC/QBXoh+SY211AjY9ATQ0+ZJ56GUIj4Al2gF5JvdE2JKSDQBXqJZVkltxAFBLpALyTf6JoSU0CgC/QSy7JKbiEKCHSBXki+0TUlpoBAF+gllmWV3EIUEOgCvZB8o2tKTAGBLtBLLMsquYUoEEvQWT2FVVTWrFkTemA9sJNOOmm3FWa6detmzz77bOj35vk++ugjt144K4nokAJhKRBL0JcuXWrjx4+3yy+/PPRw2WWXWcuWLXdbM46FLH/0ox+Ffm+e78orrzSel80BdEiBsBSIJehz5syxLl26uFK2YcOGof+tXbv2bqvAMgsqsyx12PdnZVyed/369WHZWPFKAYsl6My/bdu2rZuFxNS8Bg0auDXdWNctCYH17DNLTPN87MrJwo86pEBYCsQadCA49NBDbfTo0XbFFVckJlxyySVujjHrxwv0sLK24s1WINagU+r17t3bli9fnp3mkv7MbCuWvsYHQPNAoJe0OUsm8QK9yKYS6EUWXLdzCgj0ImcEgV5kwXU7gR5FHhDoUaiue6pEz8kDgBjmIdDDVFdxl6eAQN+pzI4dO9wecexxzTpkYR0CPSxlFW9FCgh0M1u7dq09+OCDbgfVW265xXnFKxLNz3cC3Y96urZQBVILOsBt27bNVqxY4YbbtmvXzpo3b279+/d35woVtLLrBHplCun7MBRILehUz9nJY8SIEdaqVSu3dTIb3Av0MLKZ4oxagVpcTgYAAAXBSURBVNSCvnXrVrvzzjutR48e9tBDD9nkyZONWWsCPeosqfuHoUBqQcf5RrX96aefdlNFn3zySbcvukAPI5spzqgVSC3oucI/88wzAj1XFP2fGAUE+k5TCvTE5Gk9iIcCAl2ge2QLnUqaAgJdoCctT+t5PBQQ6ALdI1voVNIUEOgCPWl5Ws/joYBAF+ge2UKnkqaAQBfoScvTeh4PBQS6QPfIFjqVNAUE+k6LsmHDySefbIMGDbKVK1eGZmdNaglNWkVcgQICfac4jH1nyWV2btm+fXsFkvn7SqD7009XF6aAQC9Mt4KvEugFS6cLfSgg0H2IV8ilAr0Q1XSNXwVSCTpz0ames5ljPoGZbgAaxCHQg1BRcVRVgVSCPmXKFLeB4siRIy2fMGnSJFu1alVVtfX8vUD3lEUnQ1YglaDff//9bmUZPOyVhcGDB9uECRPcnPUgbCHQg1BRcVRVgVSCzmKQ7777ri1cuDCv8OGHH9rmzZurqq3n7wW6pyw6GbICqQQ9ZE0rjF6gVyiPvgxJAYEekrDlRSvQy1NG58NUILWg40lfv369zZ8/363pfscdd9jdd9/tFop866233OCZL774InDtBXrgkirCPBRIJejA9v7779vtt9/utmU+/vjjrUuXLi507tzZ+vbta1OnTrU1a9bkIWHVfiLQq6aXfh2MAqkEnX70Bx54wDp27GgDBw60e+65x2bPnm2sBHvbbbdZy5YtrVOnTjZjxozA+s8z5hLoGSX0t5gKpBJ0YNuwYYMr1ekf5/OWLVtc4PP48eONnVvGjBnjvO1BVuEFejGzt+6VUSCVoPPwAJcJGTEy5x9//HE77rjjbPTo0bZx48ZAN10U6Nlq63OxFEgt6F4CU6UH7LFjx1qHDh2MDReZ1aYS3UstnSslBVINOqUrcDPeHaDXrVtnjz76qIOcHVteeOGFwG2pEj1wSRVhHgqkGvRNmzbZww8/7BxyJ554oh1zzDF26KGH2qhRo+yll15ypXseGlbpJwK9SnLpxwEpkGrQKcWnT59uF198sQ0fPtxtsEjbvHfv3nbjjTfa4sWLA622YzOBHlDOVTRVUiDVoFNtZww7nnf61QF71qxZDvj27du7NrqccVXKT/pxTBVINeheNqHEBXgGzVC6M/ll27ZtXj8t6JxK9IJk00U+FRDoHgIyu23EiBF2xBFH2JIlS5yjzuNnBZ0S6AXJpot8KpBK0IGN4HVwnmr8aaed5gbNvPfeeyrRvYTSuZJSIJWgs4wU1fMFCxbYO++849rojGtn3jnnx40bZ7TRzz//fKN0ZwJMUIdK9KCUVDxVUSCVoDPM9dJLL3WTWIYOHWo///nP7ZprrnHe9379+lmLFi2cQ4613ssr+asicvZvBXq2GvpcLAVSCTolNINhLr/8cjv99NOtT58+1qtXL7eBw5lnnmkTJ050TrigVpXJNqZAz1ZDn4ulQCpBBzYmsVBdX7Rokc2dO9deeeUVmzdvni1btsxV1xktF8Yh0MNQVXFWpkAqQa9MlDC/F+hhqqu4y1NAoJenTEjnBXpIwiraChUQ6BXKE/yXAj14TRVj5QoI9Mo1CvQXAj1QORVZngoI9DyFCupnAj0oJRVPVRSIPeg9e/Z0nnGmlCYlsP/6sGHDrG7dulajRg23Xh1bNuuQAmEpEGvQq1evbrVr17amTZta8+bNExOaNWtm9erVM55PoIeVtRVvtgKxBr2srMySHgR6dnbU57AUiCXoDF4ZMmSIW9KJtduSHFhHnoE6zHvXIQXCUiCWoDP/e/Xq1bZ8+fJUhKAXoAwrsyje0lUglqDjmWblVcakJz2wyg3Pq0MKhKlALEEP84EVtxRIowICPY1W1zOnTgGBnjqT64HTqIBAT6PV9cypU0Cgp87keuA0KiDQ02h1PXPqFBDoqTO5HjiNCgj0NFpdz5w6BQR66kyuB06jAgI9jVbXM6dOgf8HxaVzuQkDC40AAAAASUVORK5CYII=[/img]
Write an equation to represent the hanger.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZEAAAE8CAYAAAABo4xnAAAgAElEQVR4Ae2dB7hUxfnGMbEnsSS2oCIRFVFEQewFBGILKDbsirELasSusSK2xC72giV2VIpgAVGJBRtWEBUQYy+J3URN5v/8vvxns6x77927e8qcc97zPOe5e3fPmfJOeecr800bp0sICAEhIASEQJ0ItKnzPb0mBISAEBACQsCJRNQJhIAQEAJCoG4ERCJ1Q6cXhYAQEAJCQCSiPiAEhIAQEAJ1IyASqRs6vSgEhIAQEAIiEfUBISAEhIAQqBsBkUjd0OlFISAEhIAQEImoDwgBISAEhEDdCIhE6oZOLwoBISAEhIBIRH1ACAgBISAE6kZAJFI3dHpRCAgBISAERCLqA0JACAgBIVA3AiKRuqHTi0JACAgBISASUR8QAkJACAiBuhEQidQNnV4UAkJACAgBkYj6gBAQAkJACNSNgEikbuj0ohAQAkJACIhE1AeEgBAQAkKgbgREInVDpxeFgBAQAkJAJKI+IASEgBAQAnUjIBKpGzq9KASEgBAQAiIR9QEhIASEgBCoGwGRSN3Q6cW0EPj3v//tvv/+e/fdd9+Vbv7/4Ycf3H/+85+0iqV8hUAhERCJFLLZs1tpSOLzzz93zz77rHv66afdlClT7Ob/2bNnG6lkt3YquRDIHgIikey1WWFLDIEghTz//PPut7/9revVq5fr2bOn3fx/zjnnuM8++6yw+KjiQiANBEQiaaCuPOtCABJBZfXQQw+5hRZayM0777yuTZs2di+44IJu4MCB7sMPP6wrbb0kBIRAfQiIROrDTW+lgIBIJAXQlaUQaAEBkUgLAOnncBAQiYTTFiqJEPAIiEQ8EvobPAIikeCbSAUsIAIikQI2elarLBLJasup3HlGQCSS59bNWd1EIjlrUFUnFwiIRHLRjMWohEikGO2sWmYLAZFIttqr0KUViRS6+VX5QBEQiQTaMCrWjxEQifwYE30jBNJGQCSSdgso/5oREInUDJUeFAKJISASSQxqZdQoAiKRRhHU+0IgegREItFjqhRjQkAkEhOwSlYINICASKQB8PRqsgiIRJLFW7kJgVoQEInUgpKeCQIBkUgQzaBCCIG5EBCJzAWH/gkZAZFIyK2jshUVAZFIUVs+g/UWiWSw0VTk3CMgEsl9E+engiKR/LSlapIfBEQi+WnL3NdEJJL7JlYFM4iASCSDjVbUIotEitryqnfICIhEQm4dlW0uBEQic8Ghf4RAEAiIRIJoBhWiFgREIrWgpGeEQLIIiESSxVu5NYCASKQB8PSqEIgJAZFITMAq2egREIlEj6lSFAKNIiASaRRBvZ8YAiKRxKBWRkKgZgREIjVDpQfTRkAkknYLKH8h8GMERCI/xkTfBIqASCTQhlGxCo2ASKTQzZ+tyotEstVeKm0xEBCJFKOdc1FLkUgumlGVyBkCIpGcNWieqyMSyXPrqm5ZRUAkktWWK2C5RSIFbHRVOXgERCLBN5EK6BEQiXgk9FcIhIOASCSctlBJWkBAJNICQPpZCKSAgEgkBdCVZX0IiETqw01vCYE4ERCJxImu0o4UAZFIpHAqMSEQCQIikUhgVCJJICASSQJl5SEEWoeASKR1eOnpFBEQiaQIvrIWAk0gIBJpAhh9HR4CIpHw2kQlEgIiEfWBzCAgEslMU6mgBUJAJFKgxs56VUUiWW9BlT+PCIhE8tiqOa2TSCSnDatqZRoBkUimm69YhReJFKu9VdtsICASyUY7qZTOOZGIuoEQCA8BkUh4baISNYGASKQJYPS1EEgRAZFIiuAr69YhIBJpHV56WggkgYBIJAmUlUckCIhEIoFRiQiBSBEQiUQKpxKLEwGRSJzoKm0hUB8CIpH6cNNbKSAgEkkBdGUpBFpAQCTSAkD6ORwERCLhtIVKIgQ8AiIRj4T+Bo+ASCT4JlIBC4iASKSAjZ7VKotEstpyKneeERCJ5Ll1c1Y3kUjOGlTVyQUCIpFcNGMxKiESKUY7q5bZQkAkkq32KnRpRSKFbn5VPlAERCKBNoyK9WMERCI/xkTfCIG0ERCJpN0Cyr9mBEQiNUOlB4VAYgiIRBKDWhk1ioBIpFEE9b4QiB4BkUj0mCrFmBAQicQErJIVAg0gIBJpADy9miwCIpFk8VZuQqAWBEQitaCkZ4JAQCQSRDOoEEJgLgREInPBoX9CRkAkEnLrqGxFRSATJOInj2+//dZ9/fXX7quvvtJdQAy+/PJL98UXX7ixY8e6BRZYwP30pz91bdq0sXv++ed3u+++u5szZ476RgH7RvmcwDzx3XffuX//+99FndcTrXdmSITJ4+6773aHHXaYGzx4sO4CYjBo0CB3yCGHuG222cbNN9987ic/+UmJROadd17XqVMnt88++6hvFLBvlM8JQ4cOdVOnTnXff/99opNpUTPLBImwovjwww/d8ccf7xZZZBG38MIL6y4oBgsttJBD6oBA5plnnhKJ8BkiQUJR/yj2+Ojatau79957HRKJrvgRCJ5EUGVBIu+9954bMmSIrUC9CkN//6vKEQ7CQX3gf31gtdVWc3feeaf75ptv4p9BlYMTify/Tl2D8H+DUFgIiyz3AZFIsswmEhGJlFRCWZ44VHYRn+8DIhGRyFwItKTOQhfOjY5ctzBQHyhWHyi3i4lE5po6E/sn05IIE8biiy9u3jijR48210/cP3ULA/WBfPeBMWPGuBEjRrgePXqYnbScTCSJJMYfllGmSQRvnLZt27qrrrrK/fDDD8kip9yEgBBIDQGcbd555x232267uQUXXHAud2+RSLLNIhJJFm/lJgSEQAQIiEQiADGiJEQiEQGpZISAEEgOAZFIcli3lJNIpCWE9LsQEALBISASCadJRCLhtIVKIgSEQI0IiERqBCqBx0QiCYCsLISAEIgWAZFItHg2kppIpBH09K4QEAKpICASSQX2qpmKRKrCoi+FgBAIGQGRSDitIxIJpy1UEiEgBGpEQCRSI1AJPCYSSQBkZSEEhEC0CIhEosWzkdREIo2gp3eFgBBIBQGRSCqwV81UJFIVFn0pBIRAyAiIRMJpHZFIOG2hkggBIVAjAiKRGoFK4DGRSAIgKwshIASiRUAkEi2ejaQmEmkEPb0rBIRAKgiIRFKBvWqmIpGqsOhLISAEQkZAJBJO64hEwmkLlUQICIEaERCJ1AhUAo+JRBIAWVkIASEQLQIikWjxbCQ1kUgj6OldISAEUkFAJJIK7FUzFYlUhUVfCgEhEDICIpFwWkckEk5bqCRCQAjUiIBIpEagEnhMJJIAyMpCCAiBaBEQiUSLZyOpiUQaQU/vCgEhkAoCIpFUYK+aqUikKiz6UggIgZAREImE0zoikXDaQiURAkKgRgREIjUClcBjIpEEQFYWQkAIRIuASCRaPBtJTSTSCHp6VwgIgVQQEImkAnvVTEUiVWHRl0JACISMgEgknNYRiYTTFiqJEBACNSIgEqkRqAQeE4kkALKyEAJCIFoERCLR4tlIaiKRRtDTu0JACKSCgEgkFdirZioSqQqLvhQCQiBkBEQi4bSOSCSctlBJhIAQqBEBkUiNQCXwmEgkAZCVhRAQAtEiIBKJFs9GUhOJNIKe3hUCQiAVBEQiqcBeNdPgSOQ///mP++GHH9x3333n/vnPf7pvv/3WffHFF+61115zhxxyiJt33nldmzZt7P7pT3/qllpqKXf++ee7v//97+6bb76xd3iXNEhLlxDIIwL07X/961/uww8/dO+995579913C3W/88477rnnnnP9+/d3888/v/vJT35SmhdWXnlld80117hZs2YVCpPyPpBknw+KRPzAeP/9962DTJ482Y0ePdrdcMMN7uijj3bdunWbq7PQcX72s5+5rbbayv35z392t912m5swYYJ78sknjXQgHxFJkt1JeSWFACvxGTNmuP3339/tuuuubsCAAYW6d9ppJ9evXz/Xrl07mxPmmWeeEoksssgibsMNN3Q77LBDoTAp7wNJ9UPySY1EGATff/+9SQ5fffWVrRoeeOABd+mll7pBgwa5Hj16uDXXXNMtvvjiRhQLLLCAQ/Io7yx85jt+g0zoPO3bt3ddu3a1DnbSSScZsUyZMsV98MEHlhd5iliS7GLKK2oE6L+MnyeeeMItu+yy1vdZjRfxrpwT0FKwuOT7+eabr5CY0A+SvBInEQYANyqnOXPmuFGjRrlhw4bZimGNNdawAVFOFHQK/q/l9mou/w6daPnll3ebbbaZO/jgg911113nnnnmGQdpMQhFJkl2NeUVFQL0W9S1f/3rX02dSz/3fb+WcaJnaptPsoaT7wP8TfJKLDc6PlIAdovZs2e7Cy64wNRQnTp1cksssYRJE35VQeOxmmBwLLjggm7hhRd2P//5z92iiy5q92KLLea4+R/pg994BomEd3jXp4ENhe95ZoUVVnDrrruuif8jR450X3/9tWwnSfY25RUJAk2RCCtQL5H7MaK//50r8o4D8x9zHfNe7kjEkwdGcmwU2Dh69+7tfvWrX5XUU1Tci59M+AsttJBr27at69Wrl9tvv/3c0KFDzS7yyCOPuBdeeMG9+OKLpfv55593999/v7vwwgvdkCFD3B577OE6d+5saXhSIe1yYiF9jG8Y6qdOnWpqLhniI5nflEgCCFQjEcYQKmAke8ZE+RjR5//NF3nF4ogjjigtxHNFIt7ugecUE33fvn1tcvfSApVlgmeyZ6WAkWznnXd2I0aMcG+//bZJCkgueGhBQnijVN587724eBbp4vPPP3ePP/64O/XUU1337t0tbYijnEgoA+y90korubPOOsv97W9/s3QYoLqEQMgINEUijK+XXnrJxkDlONH/P5478oTJ2WefbfOZ915Nsv/Gos7y0sdnn33mnn76aXfssceaAdCTB5M5ojfSyGqrrebwtLjyyivdG2+8YQMAe0kjkznkRRrYPjCoP/zww2Z3wTYCUZE3ZeCmTL/4xS/Mm+PGG280d0kZ35PsgsqrtQhUIxH68jbbbOOmTZtmauPWpqnns40A3qmo7JnPciGJMAl/+umn7pZbbnEbbLCB2TXo5N5OgQSA59UxxxxjrrxIEqiTvLG7EQLxXYE0uEmTtCGVf/zjH+7WW281W8xyyy03l2QCg0MmeIZNnz7d3vNp6a8QCAkBkUhIrRFGWXJDInRuCIF9HhdffLHr0qWLqasgECZpjH5IHocddpgbM2aMbZSCcJK4/MBD3cUmpCuuuMJtvfXWbumllzb2huBgcdRqqNQmTpxoajRISJcQCAkB35fLvbMkiYTUQsmXJRckQsdmtY/n1VFHHWXqKy99QCBMzgMHDnTjxo1zH3/8cUPqqkabiLJCJhjV8RJbf/31TcVVLiltvPHG7s477zT7Cs/rEgKhICASCaUlwilHpkmEDs2N/eHll1+2XaJsEMRgDnngorvqqquWwhBgzEp7dU95KQNlweiPEX7PPfc0nSLER9lRubFvhZAqqOZQiekSAiEgIBIJoRXCKkOmSYTJFRUWxuuNNtrISIMVvZ+I11tvPXfPPfeUNviFBf1/S4P3F/GHcBGG9Ci7V8Ets8wyRiR4fqVNfiFipzIlj4BIJHnMQ88x0yTCBPzqq6/aBj4mYD/5sgmwZ8+ebtKkSbbip+OHekEOqOJwDUa9xeZHpCjIEE8u6sJudxFJqC1YrHKJRIrV3rXUNpMk4tVBb731lgVHRIXlJ91f/vKXbrfddrNAiEgqIROIbyDKWO7BtdZaa5WkEgzu7Ha/9957zdiehfr4eulv/hAQieSvTRutUSZJBK8qDOSs3Nnv4Y3SrNrZZc5mwaypf/zg/PLLL40w1l577ZLnFlIWIVMIeif7SKNdXu83goDvp/LOagTFfL2bKRKhA0MghDBhc17Hjh1Lm/Zw4SX8MoEVszrR+gEKQV599dWl+qHegiDZGElYCQiSZ3UJgaQR8H1UJJI08uHmlykSYfLEPRaPJryuvBsv3kx9+vSxKLlZk0CqdQ0vaZ1zzjkmaXmvLaSuwYMHW5iUPNSzWt31XdgIiETCbp80SpcZEqHzYjdA0oAwsBXgyYTxGRsC8bEwtOdhhU4dIBJOC2MXu4+9RZ05swQpBWlMlxBIGgGRSNKIh59fZkiESRUphGBfflIleOJvfvMb817KC4GUdxnclz/55BO3xRZbGGkikSB1cZoi+2LyQJjl9dXn8BEQiYTfRkmXMDMkAkm8/vrrZmD2eynwyiKMCaFO8jihorJiU+Kbb75p4eOpN/YR7D+XXXZZbiSvpDu98qsfAZFI/djl9c3gSYROy2TKipyzPdhHwYocjyXOMsZjCSklrxd1Zw8JR/cSpNETCd5b7JHJc93z2qZZrpdIJMutF0/ZgycRJlEmSrxB1llnndIkuuSSS7rjjjvOdqzHA00YqTJokUYIVc8GSkgEl2a8tU4++WSTRsIoqUpRBAREIkVo5dbVMXgSwZjOuRwnnniiHUnLJIpNhCCFHIJDp877BZFyPgoG9WWXXdZIBElslVVWcZMnTzaX5iLgkPd2zkL9RCJZaKVkyxg8iRDug9hYnA3CChybAOebX3LJJYVS5UCmqK8GDBhg6jzIFCJhdz4GeIhGlxCIGwGRSNwIZy/9oEmEiZHDnM477zyLcguJYFTmUCmi2xZp4mQDJdGK2WRJGBRIBJffDh06WAj8rG6wzN6QKXaJRSLFbv9qtQ+aRLCFzJw50+29994mgTBxEhuL42xZmcd1MVC4ISn/uaW8/HO805r3WkrX/076EAWeWv379y/tk+Fgq+uvvz5WPHwZ9FcI+H6oHevqCx6BoEkEt17OSe/WrVtp5b3iiivaJry4Vt4MEsiLGFbYIdjUh2G7pQviQPWGJ5V/DzVTlBdlozwY1Nm9jpcaHlu777677aGJMi+lJQSqISASqYZKsb8LmkRQZd1xxx22wc7bAPbZZ59Yw6JDBhDBTTfd5E4//XQ3bNgwN3bs2CbjcXnSYa8KqibckM844wyTlpCi+D3KC6LijBTCvqDeY8Ml7r6vvfZaodR7UWKqtGpHQCRSO1ZFeTJoEiEaL4c1seLGoP7zn//cXX755SYpRD05+wZHCoFE2MSI/YW7d+/eFq+qWp5IRJxQyLnpyy+/vKmZeOfYY4+1c9yrvePzqucvUhGbLnH39bggnXGcLmXXJQTiREAkEie62Uw7aBLBG4m9Iay48URaaaWVYg+yiCSCvWXChAnmTku+hFZBMqmcpHkWtReSCt5jxPHCc+yAAw5ws2bNalJ6aaSrUAbCvxx55JHm6oyExhnynC1PWXQJgTgREInEiW420w6aREaOHGk6f0gEKWTXXXc1iSBuqBko7E0ZOHCgqYvY2Lf//vvbGSY+bwgEqYAYVr/73e+sfKiWttlmG8dhWXHZbDzJoTrzdhGIrl+/fm769OmRq898ffVXCICASET9oBKBoEmEUOis7iERVtu4+qJqSuLCnZb9KQQ8ZJLG7oDEwcVAQlr529/+5vbdd1+TCCA5pJEXXnghVnUbeUMkeGnh6ouaD/LiPPmHHnpIJJJE5yhwHiKRAjd+E1UPmkT22msvmyQhEcKcjBo1KjFXVqQMDPtEzGWSJtjjSSedZKokfsMOQkRhTzKEox8/fnxiYUjYJ7P11lsbybJfZI011jCDO4NclxCICwGRSFzIZjfdoEkENRErbfT+TJKPPvroj+wScUHPah9PqFtvvdXiVEEkvXr1spMFCQZ58803mzrJ22owrGOrSGoSh+DwVKNcYNSuXTsLi5JU/nHhrnTDRkAkEnb7pFG6oEmkc+fORiBMksTKevbZZ2OzNVSCz2BBZcXBUHhnsdpfaqmlzAvr7rvvtl3zxPBq27atO/XUU91HH31UmUSs/6PWO+2000zVBj4Y9M8880y5+caKuhIXiagPVCIQNIn40OdM4Egl06ZNS3SSxDjOZD1ixAhTW2Gf2XTTTe0kRT6j4jrwwAPttMWkJQA8sa699tqShxaEdvTRRycqDVV2Jv2ffwREIvlv49bWMGgSadOmjUkiqGxQ3WDIRs2U1MWAYdc50YLXX399k0ZQX1EeDOl77LGHbfKDbJImEQz/48aNm2sjJq7FSERJlyWp9lA+6SMgEkm/DUIrQSZIhFX24MGDE58g/YBhYmbnOpsIITaIhFAs7GNJktTKOw/2F86Vx7DvD+nCU4yd82mVqbx8+pxPBPyYUOysfLZvPbUSiTSDGgMGTyzsInhmeRJBCjn33HPN8M4zaVwikTRQV54iEfWBSgQyQSKs/AcNGpSoJMJgYXc4rrzYHrB/4CWGuzFk0qdPH3MBFolUdin9n2cERCJ5bt366pYZEmHH+HvvvZeYqsa7+N577712ZgfGfTygkEJ8eBOCQ0I0aRCJJJH6OrzeagwBkUhj+OXx7aBJhFU/q38mbc7QmDFjRiIkwkDBcP3II4/YTnVsMgRXPPjgg90uu+xiu+f5brvttkvtcCzKR9BFbCJgRHkOPfTQVKWjPA4Q1WluBEQic+Oh/5wLmkTKT/Bjox8hReKKSeU7gx8kTz75pKmsIDAOwsKV95VXXjFjdseOHc1Ti/IhqcRdJl+28r+cK0IYGMgDEoFMOGekMkhk+Tv6LAQaRcCPDxnWG0UyP+8HTSI9evQo7Vgnmi8Te5wTNgOEg7D8Weaorgi+iP0DN19USHhqca45dhrieeF6zJ4N3k3y4uArwtX7HevLLrushclPuhxJ1ll5pY+ASCT9NgitBEGTCCf2sRsbF9ZlllnGAiDGtdJmcJD27Nmz3SGHHGLSBxM0UgdqLX6DwPDWIhQKhnaIpEuXLu6BBx6IldyqdRoM/kQ1RlLCXkOY/BtuuCFxMqtWNn2XXwREIvlt23prFjSJoONngsQ2wqTNmR5ICnFchDghJtbFF1/sOLcc9RCh1pmYIQ4GDzcG948//tg2H0IySCMcQBVXuarVlXIgEXEYFSQLkSCpsW+E33QJgbgQoH+xmJI6Ky6Es5du0CRy/fXXm84fEkGthGGbzXRRXgwKpAzUQ7fddptJHkzMEAnH3EIOlRMz9ggIDVdfbBKcMsigqnwuynL6tHx5kY6QzrCHIBFhM3rqqacSKYMvi/4WDwH6n0ikeO3eXI2DJhEM6R06dDBJhMm6e/fu5qHVXIVa+xuSBbaOiRMnuq5du9qqHimEECJIJtV2fxMKhQ2IPI80ssQSS1hYeKL+xk0kDGCIjeCL2GxQ9RFjDMM/4eF1CYE4ERCJxIluNtMOmkRmzpxpen8mSlQ27NMYPXq0rYSimKz9gMBovsMOO5jKDE8szul4/vnnm8yHiRziueSSS8x2gtprxx13tLPPoyhXc10JtRuqLE5QRGLixqg+fPjwxM5aaa58+i3fCPgxI3VWvtu5NbULmkSYLJkcIRHvxspZ4kgCUUzWpIEqi2Nlr7vuOjuPAxsIBNKSjYP35syZ41C5saP9nnvucR9++GFVyaU1DdLSs5SLc1U4BAs1H+TKWSuosiA3XUIgTgREInGim820gyYRXGcnTZrk2rdvbyTChMkxtdgkqqmZ6mkC0sFwzuSMOgqCYjJuiaT4HamA97j5TFotvVdPGcvfARPidmEPgVxRaW277bYWsj7uvMvLoc/FRIA+xviQJFLM9q9W66BJhMmdPRvlJxxyMBT7RZAEinQxeCEpwuGzax5bDCSCPeaCCy6QKqtInSHFuopEUgQ/0KyDJhEmTVRanByIBxKTJl5axNFKwogdUpuBBVLSfffd58pPfCQcy8MPPyxVVkiNleOyiERy3Lh1Vi1oEqHDEiNq5MiR5nqLDYAVOIZsNvgVSRqhrgSgZE8KhIqNCCzYTQ+hQjK6hEDcCIhE4kY4e+kHTSLAyer7jTfecHvttVdp9zr7M/CG+uCDD2K3QYTSpBDF2LFjzYgOmbIJkw2Yt99+e002nFDqoXJkGwGRSLbbL47SB08iGPEwXDNZrrzyyiUDO8Z2vKJqMYLHAVxSaTJoMdqzL4VwLDgXQCIY1IkiTPgTntElBJJAQCSSBMrZyiN4EqHTcr/zzjtmC2HyRJWDNNK3b1/bm5FnVQ51Y08KLsTsB8EuxP2b3/zGXH0hGF1CICkERCJJIZ2dfIInEaCk42IbGT9+vMWLYhJlkx1G5UsvvdRUXtmBvPaSUm9sIcTq6tevn6mwqDc2EaQSpJA8E2jtSOnJpBAQiSSFdHbyyQSJACcr7s8//9wMy969lfAkG2+8cck7iQ6ep4s6sy9k2LBhFqML8qTunTp1cpMnT05kX0qe8FRdGkdAJNI4hnlLITMkwoqbfSMvv/yyqXVQaXGzKufUQ77Pk7cWg9Wf747qzquxMKafcsop5vqct86o+oSPgEgk/DZKuoSZIRGAgUiItnvZZZc5Nh1CIkyuxNTigKa33norF+odnAVQ33Fq4qqrrmpqLOpKoEU2Xj7zzDO5IsykO73yqx8BkUj92OX1zUyRCB0YaQO11tFHH237RfBUwk5A4MShQ4fa5MtzWb7wRiOsRO/eva1ufn/Muuuu60aNGqXd6Vlu3IyXXSSS8QaMofiZIhHqjzTC3pHXX3/d7bfffqWNd7i+ckgTh0rxexYNzpQZAiEEPkfwsjvfE0i7du3cVVddpRhZMQwCJVk7AiKR2rEqypOZIxEahsmWzXdErvVxtfxkC5FQKR+kMStSSTmB/P73vzcCQVWHGgt1HQdkaU9IUYZluPUUiYTbNmmVLJMk4jsyREEsKY6G9RMu3ku4/hIynr0lWTC2QyB4Yb344ouuR48eJQmEXekY1ffdd187IAtbiS4hkCYCfuwpim+arRBW3pkkEQ8hBIEBmjM9kECYdCET/hJfC3UXZ4XgKstEHdrFgKRskCEnK7KZ0NcBOw/qrC233DJzUlVoOKs80SEgEokOy7yklGkSoUNDDkzCHCq1+uqrlzy2mIQ5UnerrbZyTzzxhKm/Qmo0yg4Jvv3226Z+w3UX1ZV3FLLLi8MAACAASURBVCDE+9577222nyxIUyFhq7LEh4BIJD5ss5pypknEg+435Y0bN848mtiE6N1/UQf17NnTSAZ1ESFE0lQLQXoY/jkFEenj8MMPd0svvXQpuCT7XpCqUMe9+eabuY8N5ttQf7OBgEgkG+2UZClzQSIARudmcuYQqz333NNcftu0aeO4UXEttthiZoQfMWKEHWubJMg+L8rIhskpU6a4E044wa255prmXebLiYfZaqutZh5m77//vgIreuD0NxgERCLBNEUwBckNiYAoEgZeW6+99po76aST3AorrFDaZ4F6CwmFVT4nA95yyy0mDcRpL2HAIXlAHBjOn3vuOfOywngOqXlpib9ITOuvv76dnfLpp5/ae7yvSwiEhECSJMJ4ZnPxmDFj3K233uruuusuN3PmzFjGBnlx5MTw4cPt+Ok//elPtieLhWlcF1gy/zDeCWN0+eWX2163gw46yJxpcKgZNGiQlef555+3eaS5sjDXsEVg9uzZ7u6777bFKJoObMOkdcQRR7iLLrrIPfjgg3Y2EXNlFFqZXJEIANMw2BDwzGLPSJcuXSzelLc3YHPAVrLSSiu5ffbZx9122222052JnvcAlcZo7QTO89y8SxqkRQdkY+Tjjz9upzOyWRDbB5IR5aBMSB+QG9ITz8XZaZvrgPpNCNSCAH2c/h2ndxZ5MH44Cvr444+3kzw7dOjgunbtauM16oUf+WFXPeaYYyw6NvZIVMxMvHwf9eUxZKxzxMWAAQOsbjjWsGmaOYG5wc8PyyyzjO0RQxVf7fJ4ffLJJzbnbbHFFm6VVVZxv/71r22uYwFNWqjKifRBFAz2od1///1WP7AmjXqv3JEIQAAIHY0JfMaMGbb6p2PQOEze3oOLsPJLLrmkYyPfDjvs4G688UZTddFYkAqDpRZweYZneQdvMfZzYMwnxlWvXr2sQ+Jp5T2vyJ+yeO8rVlpE6uX9WvKrt7H1nhBoFAHf1+MkESZXVt7bb7+9SeyMFW4mwGuuucbGCYu1qC7G3Z133mmBTdki4CdcNBbMIVFe4Mfc9Morr1j9IAi0EEzw5M1nwhuV3yw8CfWE5FB5gQN43XzzzW7ttdd2zHMsSsGLNPnMPMft82Ee4nuI8vzzz3f/+Mc/jLTrnXtySSLlQNNB/B6MAw880DoikggdBULxEgENyKSOCozOc/XVV1vo+Tlz5tiBUJyiyEQP23PzmfPfObIWDyuM9oQkwdax4YYbWicgTS91lOdDp2BVdcEFF1jaja4Eyuurz0IgTgTiIhHSZRyw8n/ooYfs2GcmPb/wYrzitk/UBsZ0FCRCnqQDYbFpmYnVj1n+7rzzzqZOiwpP8oNAyG+zzTaziZ18mOCRtDi99corrzT1HfvfuDkaHI0Ki1LqXXlBLBAB5wt5kkCaYX7huAjwGj16tJ2KeuaZZ9qREiycIRiv4kcb04jDUe5JxHcUGo8OiggHSdBoNJ4nEj/JAywdFyangelYqL7w8OJI3t13391uxMGddtrJGotG4Vne4V3S8OSB0dynzaqjW7du7qyzzjIJiTLRiSmjLiGQBQToq3GosxgHqK84H6hjx442lljU8dmTSdQkQp7YI1BjYaNk8mVyZ/wyyUZNIpAkIY0gLOYe5gpstIceeqibOnWq2TMgCuYFnuX2n5vSivA99l1wYh7adNNNTVrDMQf7CO+X3yyA0bistdZaNmdRV1T+s2bNsufr6YO5J5FyUAAc5kZyIEIuUgMNihhIB4UEvITiPaY8AZQTSzlhNPU8z9BRkGxoWGweSB4PP/ywNRZl0SUEsoZA1CRCekxySPIYkZkIWbix4GKfFMZmjsJmbKKqiVISYVF5ww032CLRkwYTOmMXbUXUJIKd9sgjjyzNNRz3zf42NBqopOpZTEKEqNBPP/10cyaaNm2a/d8U6fA89T711FPNZsK8BoHiUMD39VyFIpFKgGB6PDLwVgAIpAxYmZUP5OGJpNa/nnDQ3W6++ebmDUEnJXQ74mI9naSyzPpfCKSJQNQkwqTGKhztgNcMYBA+9thjzcvy6aeftlU2k3yUJEI9UBHh7AJhYIhmYcnkyv9RkwhzDXYXL2Vh84AgmbijmBdQ2SN51JoWuG6wwQYluwkeYdhy67kKTSJ0YBqXVQCNifvgY489ZnrIc88915gdzwl2vbMyQkXlCYXPdDT2dfAMjYBbMaLi2LFjTWzFjkLa5FFr49bTiHpHCCSFAP2YVW5UhnXSw+6IapjFF+od7AJ8x6TIAoyJN0oSofws6rBBkC7SD1oJ8hw8eLB95yUTXIwbvZhn2Fx88MEH25yBpEN933333bolkMoygWNr5hjqtfXWW1t5kPJ++9vfmq23Mt1a/i80iVQDyDcGzI6+FJ9rWBt3YPSHnkRQY9H5iK7LMxAGDSM1VTVU9V1eEGB8REki4MIiC1sBHpKPPvqoeQv5fJ599tlISYR0ISf2S+CdxDjebrvtTBrCE4sI2hBIlCRC/V566SXTcjCH4FjjjdkQTBoXGGy77bamOkSlxdlFOAvVc4lEmkDNd2IMXegy2agD2J5E6AyI3Yik3luEd7h1CYG8IuDHRVSSCDiRJnYR7JVI7pAU3zHBRkkipMmEjrYBGyhqa9RYqJmQTMifvSFRkwjp4oILeUBaffr0MRtQNW+rpPoNZerXr59JItig8FyVOisG9H1Hxo13yJAhPyKRtm3bmqFP0kcM4CvJIBFgTEQtiTRV0ahJhHKjNSAyNqpoVNRoElBl8xsEFgeJoKHg+G7sIJAIcwmeaF7NTd6QKKTib/7ne/CO4yJ6BlsRIEy84PAYrXdPjCSRZlpIJNIMOPqpkAhklUQoNyttjtVGDY0dAJd9tAxekxAXieBWyy5yVvxoM/Aw88SFBMSGaGw/qPIeeeQRi1yBeg83XYg0aiKBnNgHh/0JHCBTnIsoSz2XSKQZ1EQizYCjnwqJQFZJBDdY4m/hCMNk3rlzZ5u0WfEzUXPHRSLYS3HnRfrBw+yOO+4w+ylqtWHDhpltYr311jPbD+o1ArMS6QJ3Y2wnGPwpG2Vs9IJAkMZwX8YbDhJhmwPSUr3qNZFIM60iEmkGHP1USASySiI4x+CNBIFgm/jLX/5ikSx8I8ZJInh9csQ1qiNW/wSSJHzLJptsYsSCp2flzXYB7K7E00L9RZiUeid5X0f+IgFdccUVtveG9NkjgmszhvZ6SUokUo5wxWeRSAUg+rfwCGSNRFh5o7JiI6M3pnNWD6otpBB/xUUipIuqCHsIq34kITzAOEAPYuH/Aw44wBGS5OyzzzbbBGVlRzmSAhM90gtbCNjTBpHQBq29eAcbDOqyjTfe2MgUV2MIis2O3j7T2nR5XiTSDGoikWbA0U+FRCBLJEJZUWPddNNN5s7rVTcvv/yyEQi/+ysOEvFY3XPPPUYI2EO8IRuCgExw/cX2gTqJbQVICkzq2EnwmEIFxnuQEDG0ID+IsTUX5YAkUGP17du3FGML76zXX3+9VZsUq+UrEqmGyv9/B/h0LnlnNQOSfioUAn5ijNLFtykAGXv1uvj6sYuBmlU97ryokh544AFz5SXt8ispEkFtRVkIcY/BHTUSEzz5+xuSQEp66623LFwShINXF3YSVGPlElR5HZr6TLpE6iUiB55YSDdIQNhkMKbzeyOXSKQZ9HxHFIk0A5J+KhQCWSERJmIm6YEDB9rqH5XQiSeeaJuC+Y16lF9MpFEb1j1W5ZIIEziTOQfnkV9lOcrLhOoKVRgRenkPe86ECRNqlhx8/hjm2Z2PNEMaEAjnmCD9QGCNXiKRZhCkEehcIpFmQNJPhULAT0yhSyKosTidELuDDzOC6qgp43RSJEKkYNRrqK5aUkvxO3YQzlWhDqjCCLRI3Vp6l05JnVBXEcjS21cgpEsuucTUYvzeHInV2rFFIs0gJRJpBhz9VEgEQicRysfqevz48RZBm4mXTcFE0OYcD+whr7766o9uvJ+IJEwIFGwQ3MTMY/+Gfx47hXcJrqXx/fyB9xNSAESAazHSRC0uu0zy2EswvFMP3sfADgE1J0H4fCFNNk8ihWFb4fA9YgISs6spMq2lXpXPiEQqESn73w+Y5iQRgsXVsiooS1YfhUBmEfBjIlRJhPJhZ0BlxMSJLQGXXs4JgRS4cfWtvPmeDYHLL7+8vcN7hDUiRIl/FokAKaC5CbyyYSkP5IQtAiLAKwsSYRKHJJq7eJd4VnhrURdIBGM7xvfmysB8BOF5AoEQ8Uzj8CoIhHSjvEQizaAJ2Kw8CFHwhz/8wVYn5bGz2OlJ7CyeibphmimWfhICqSFAP2eSCpVEmJghEaLS4o3FfguM2dgUmISbu3me53jHv8cE7N9BFUVokNau4tlsyCF4EAHqJE4srGVfBnXBU4sTCr0k0hyJ0Da8gwqLgLFERabs/GWXPJGEW1v2Wjpa4UnEAw+zAzBiJsHJ8FpAbMQoxa5RViqsTjyJ+BUO4Z2ffPJJM9jxDu+SBsRCmjSqCKaWrqhnsoBA6CRC+Rh/jFdW/0zctd5M1JCGJxHGOJOwfx+1EFIAY7s1F9HACf2OXQKiYrMfZNSSBoO5g/lnjz32KBGZV2dVe5fvIAqcCbAFUW52wKPawzWY+SiOuajQJAKgNBQiKqsFdJ8jRoxwu+66q4m/iMF4M9CR6FB0Lk8ifOY7OgWNRQdZddVVLaTy4YcfbudEowajs7S207Wmg+pZIZAkAlkgESZTDrriFNGJEyfWdHOuO0dnQz4QCTdHYnM+uU+D2FaMZeaM1lwsRgn0yO5w5gxOOcVg3tK8QD2w1aBmozyQHPMTC9XKMtAueFtBMhAIz6+xxhpWfuaguAgEHApFIn4AsFJB14ibHaebIepxshqGJ0iDBqgkDU8eTf0tJxXSQAdJlEx2hBIrB70oajGkFToHZdElBLKGgB9DoaqzwJMyMskycdZ6o4VgMckqnkUjN9IDUoRPw49bP3bJgwkdaQEVEqon0vG/+7aFLJhnOnXqZHMLthbCzzdn2yANyAdPruWWW87UbIRA4fjbyjwoFwtWTmWEQDDiszeGWGHsD6H8cV6FIhHAhq3Z+o+rHIHHMKShB/Wxa7wo2xRZtPS9f9+nBxnRqOuss44Zxa699lrrCJUriTgbWWkLgagQYHJjHIVMIvXUlfHI4rI8FDwnljJfNHXx/JgxY+wdDng65ZRTzPvLk41/j7RZtHImERsN0V4QeoTNfpBQJenwP+9MmjTJbbTRRiaBMI9w6iJkUU4KPIuxnD0waE4gv65du9r5JZSddCrT9+WK6m/uSQQQWQnA+gRho6E5W9iLfEz2TPz8RQJBiuDEMyJp4pnhj76lkYi4WX4PHTrUHXPMMbaRh3ACm266qQU2Q71FWk2ljRvh9ddf72bNmvWjVUVUDat0hEAcCDAhFYVEiHTbFImAA+pvQod4+wM2E+YEyAWM/OUxgxQIuuhV5HiMEZIdjQjzk7fDMi+gvcA5ABUWN1KMD9fOnOYvpCCO5UZKgUAgKcKpIMGMHDnS1Fmo5Gq5n3rqqZpsNT5v/ze3JELDATYNil4RnSSsjrGtXFqA4ZFEsGl0797dPCFuuOEGWwWgVyXMAGIq6VRepO+N7+QxZcoUayzy6t+/vzUsaZOHJxTyZiXSvn17M5iNGjXKOlDl6qUyL/0vBEJAwE+IRZBEWiKRcePGuW7dutl4RkPBGMee2pQbMLYJnHS6dOli7zAvoAnB5kHYdwiIvxATBnFIgTRXWmkli5vFPMScQxv46+6777b0eNbPLYSdZ1d6a+/99tvP1HKoy1pz5ZJEABkXOmwQhFzGNsEqAekAoGk8QIdQ6AQcVIMHw/Tp001cpBMAJGIjk3tlw3mAPVHxDM/yDvmiR2U1gdcW9hb0rHQW3ynoGJQFNRcdBEMbqwCIirx0CYFQERCJ/LdlwAFjPOeA+AmcBSOeVKioylVOvi0Z20gcSAjrrruujX+kDD8XMUf5/STeYadjx46OvWgQCBoV8i2/WPAyh/A8RMb8xvxCWVp741TAZsxqC+byPCs/54pEfAenEdmtyeSMnhBQuT15MHmjeiKuPy5xPB+HJECakArudXhjoBJD3KTTUBZPaKi/MLbh+ufLUtlQ+l8IhICAH2NJSSJoAzASs0cDxxe8k5hMo15sUS/SxbuJvLgJF8KCstrF89gi2NTIHMO4RqWEeopJmLFf7eI9FpsscE844QSrE1oQVFzMA9ykhTH9yCOPtEkd4mlqIcvZ7WxgpAyk08iNXccb7quVvanvckUiNByAY7DybnGQB5M1rAzQrADOOecci5BJY/JOUw3UFGi1fk+HIW3yIC90npAbG4YIxcDqwa8c+Myxndhs/LGYteaj54RAUgjQp+nPSZAIdWL8MCmzGOOuthqPqu7UDQnC59UcGZAnODBW0TZgG8XuwCKwpfnEY8icwHz1+OOPOxxumIyvu+4629GOmtzXl3x4p9rl5xaeZX5p5Ka+1L+pvKrlz3e5IBEajc6FyOdFRT9Bozbyaqtjjz3WJnHAai1QTQHYmu8pJx2HPSnoRtG5srqirEgmlJXdpegmCWFNh0ijnK2pk54tFgL0xyRJJHR0/ZhmTvGL0taU2ePJuxAB6XhJKytjPxckAui4vhFcbIUVVjDVFSt8bkKT4LaHW29zjN6ahm/0WToHZUYcvuyyy8z9FyLxOk1EUkRLNj/RsbLSmRrFRe+Hj4Cf9JKSRMJHRCXMNIn4VQAqInywcc1lRY8KC4MVO8hPPvlkM3IzaYc0GVMWREc2A+G6h0eGN7yjesNugzcZZxGkJTlpeAiBSgREIpWI6P9MkwgiIKt59JH4ansDOqt6/KoxVGM4D4k8KrscZYPgMCDi3+2JBKkEImS/CuEb6tFVVual/4VAowiIRBpFMH/vZ5JEfEfGlXb48OHmPuu9r/ByYL8HJ3dhtEKFFfJFXZCoUFtxHCabGfEMoT5IJBAJ9UHagkh0CYE0EfBjT+qsNFshrLwzSSJMprjesdkHGwiTLZMuBIK7G0ZppJQsXQxOJBIkp0svvbQUL4d6YSMhRAu/hU6KWcJcZW09AiKR1mOW9zcyRyKs2nGjwy2OvR5MstyosCAQAh2GZv+otRMxQCFIfMhR0eHy692TCeiI33jo6rla66rnsomASCSb7RZnqTNFInRgCISImXgvQRxMsmzQwQZCvJmsEohvZOqIIZ06YiNBCsFZgLpyoA0NhjEeMtUlBJJGQCSSNOLh55cpEkGVwx4Lf8ogBIIUwuSKbQQbSB4uP1A5E3rLLbcshWtBbUeYFn8yWh7qqjpkCwHfN2UTyVa7xVnazJAIBIIUQox8NuR5FRbhQo4//njbJ5InewGDlc2GDFZCO3u7DxsnkVCIzaVLCCSNgEgkacTDzy8zJIKKBykEA7PfC0KMmR133NFCMtO583ahsqLebDr0HluotSBOondmXXWXt/YqQn1EIkVo5dbVMRMkQscljDJxZQhy5qWQzp0722a8rHli1dpEfsASwBFDOwTi7SPEBiNuT56kr1px0XPpIeD7pNRZ6bVBaDkHTyKsxvFY4uCW3r17m30A1Q7nFRNinUBldOy8XtSNPSTsEyHkMySCLYj6c7CVdrPnteXDrJdIJMx2SbNUwZMIBIIUcskll5gaBymEXd1IIWPHji2ElxLSBsdrcqQvNhHvkcYJjZxsJk+tNIdQsfIWiRSrvWupbfAkwiocLyVsIRAIUghxpYYMGVKYVTgDF4mDg6s4UhMciPiL++8f//hH2UZq6el6JhIERCKRwJirRIInEaQQ4vUTXJEVOGFAVlxxRTvylg5dlAtp5JNPPnF/+tOfSkZ2iITYWmxAlDRSlJ6Qbj1FIuniH2LuQZOI373NucNMmKzAsQVwLgjG9CKRCHXFG+uZZ55xPXv2NIkM+wieWmPGjFFcrRBHVw7LJBLJYaM2WKWgSQQVDnGwUOEwYaLKQiJ55ZVXYvNKYpB4Yz6TNkRWyyq//B3eQ3KImuRID0+tww8/3FR6nlQPO+ywzMUKa7Df6vWUEBCJpAR8wNkGTSLsQOesDYzJkAgG9R122MGCL9YysdeDO5P/Z599Zpv8MNw/8MADbvbs2c0SCQOLjZDE7SIoJDvKJ02a5N58883IiYTAkzfddJPr0KHDXAZ2QuLHhUk9OOqdfCIgEslnuzZSq6BJhNMK8UjyBnU2F/J/nKosTyK4DxP0kCCIAwYMMOJiAFVePM/O8gkTJrj11lvP7BVIS2yChHyqvVOZRmv+RzqbMmWKnYboDewdO3a0DYlITbqEQJwIiETiRDebaQdNIjNmzHBbbbWVkQhSCEfdcsxtnCtu0kYddcstt5jqjOCOnJDIrnEIo/LCe+zZZ59122+/vUlKeEzhevv000/HUk6IAmkEkvObDwkDc9ZZZ9l+ksry6X8hECUCIpEo0cxHWkGTyMSJEy1OFl5ZSCHs0o47ZhSDBCJBiujTp48RAxIJO8bxFPMXzyER8RwBIZFYIDoCJKLKiktagshIm7PZcTJAzQfR7bTTTu7tt9+OXPLx9dVfIQACIhH1g0oEgiaRiy++uBTuneNvOS+d0wyTuLDH3HjjjeZSjFsxxn32afiLyRyX23PPPdckFgiEHeVIMEgLDLY4Lj+IKUvbtm1LtqJNNtnEPfbYY7HlG0ddlGb2EPD9T2FPstd2cZU4aBI55JBDSmHQCUBIBF9sAklc5MPhUGuvvbYRCRP2+eefb1IA6i5USpSnffv2JoEQjp5d9XhPxUUgvt6kz94QiAPXZ9RaRPrF1TfuvH0Z9LeYCIhEitnuzdU6aBLBzuBDoGOXQE2UlPEYSQOiACDURdx4hmGnIV4XkgAGbSSQxRdf3PauEJokTntNeUNyMBUGfwgEIkEKwmtLJFKOkj5HjYBIJGpEs59e0CSyzjrrlPaHdO/e3T355JNVjdtxNAODBdsDsalWWWUVm6jbtWvnRo4cacEgUW+h5iIEy1577WX2CAgkqUkcN+RTTz3VygDRQmTnnHNOYvnHgbnSDB8BkUj4bZR0CYMmEbyOMByz0iZ21quvvprYSp+GQBrBBjNs2DCTOBZeeGG3//77m/suXljsX8H4zi7ypCQk30Gw2RACBQkJjCjbSSedZJ5l/hn9FQJRIyASiRrR7KcXNIm0adOmZDhGdTNz5sxESQTJAhdeSILNfd4TClJDCtloo41sMyJkk5QE4rscqrbx48cbebBfhPIcdNBBFu036bL4Mulv/hEQieS/jVtbw0yQCBPkoEGDzJic5ARJXkgYGNgHDx5sEzXuxthBIBVOF4zLlbelhmSDI3tXkEA8iey77752UFWSGLVUTv2eLwREIvlqzyhqkwkSQWXDJP7RRx8lvuJHGsGV9+yzzzb1FdIRdpAjjjjCoVJK62qORJIy7qdVd+WbHgIikfSwDzVnkUgzLYOaCqJgxd+pUyfzFINEWP3vsssuFu4krVW/SKSZhtNPsSEgEokN2swmnAkS8eqsJCURbw+ZPn2623DDDU2FhU2Em/KwQ50NVxBNGhckUmkTkTorjZYoVp4ikWK1dy21DZ5E0PezF4I9Gm+88UZihnUM6gSA7Nu3r3lA4YmFWy9ux6jXCMPCZkieS0MawbBOtGCkIm/wx3OMTYhplKeWzqZnso+ASCT7bRh1DYImEWwPTJB4Q2255Zbu5Zdfjp1EkEAwphMTC2M+kzTlIH/Cwo8YMaK0S33llVe24Itp2CDY8Ej8rHIX3xNPPDE1Q3/UHVPphYmASCTMdkmzVEGTCC60bKTjJjIuIdDjVh8R0uSDDz6wPRfE60J1xRG0o0ePNhsI5LL55pubdLTEEkvYTvWkQrGUdxSCQXLCI+UDH8py3nnnSQopB0mfI0dAJBI5pJlPMGgS2W677WyCRKWFS+1DDz0U26Y+PzggkIsuusgRCwtX3uWXX94NHz7cCASCQX1FDC3UW0gpG2+8sZs6dWrs5FbZ0wh7wk55H/aEc+eRkqiHLiEQFwJ+nCgAY1wIZy/doEmEzXOssvGIIgDj7bffHlsARiQc7Ax33XWXW3311W2Fz670E044wXatM3i4UV1hbMdbiwmcM07YOc5+kSQv3I4JDomqj3IgLY0aNUokkmQjFDAvkUgBG72FKgdNIqz4mSDZ4Idq6fjjj7cd2S3UqdU/Qwx4O02ePNltuummlif5cfDT+++/P5eUwSAibtWZZ55pRIM00r9/fzv3vdUZ1/GCH8RIP8stt5yRLBITqj8O7OJ3XUIgLgR8/5MkEhfC2Us3aBLhxEB0/f5QKmwRhD6J8oJAUFFxHjrxuTBUMyn36NHDjOvVYmJxnjrPcwwuzzKZX3311SalxD2JIzEh9Vx66aVzHUrFvhW8yeLOP0rslVb2EBCJZK/N4i5x0CRC2HW8onyoEU7yI5JvVBMl6WDnIKzJ4YcfbqohJAui9uKJxW/V8oJY2ITIrnVIBOLZc889LeJv3J5aPm9IA1UW3mv+eNykVWpxd06lHx4CIpHw2iTtEgVNIqysTzvtNJsosY2wN4OIulHFq2JAMCmjBtpxxx1dv3797Kz066+/3lRWTTUOREEZkJRQZW277bZGQpBe3CSCJ9iLL77o1ltvPSNXiIRzTdh4GLfnWlN46PviICASKU5b11rToEmE1f64ceMcZ5z7TYdIJhjAo5ysGRjcpMnN51quet6pJd3mnqHuV111lVthhRWMRJCCevXqZW7JtZa7ufT1mxBoDgH6GIsV2USaQ6lYvwVNIqy6MSBj7EZtgzSC/WHatGmFW3V7wmJH+oEHHmhSGcTKYVQ4HEiVVayBm1ZtRSJpIR9uvkGTCCued955x/3hD38w/b+fNFFpYa8o0sXgpc6sANl4CaFCrL/+9a/dPffcE9v+mSJhrLq2jIBIpGWMivZE0CRCh0WlxSa6tm3bltQ3qHKSPuUw7Y4BobLBkF3pbHSEi8CoDgAACQZJREFUQHB/7tKli/v73/8eqXov7boq/3AREImE2zZplSxoEgEU3G8xYG+99dZmF2EFTiyrgw8+OLXgh0k3FgMX1R5hX3r37l3Cgc2QZ511VpNeZEmXU/nlHwGRSP7buLU1DJ5E8J5iI+CFF15oe0ZQaeFWi0fShAkTajaCtxaYkJ5HCuGs9zPOOMPqjsszBnV2qROmhYGtSwgkgYBIJAmUs5VH8CSCtxREQqgRXGl9wEEMyvvss4/tYI/SUyu05mPQsrnxiSeecN26dTNbCETKRsdrr702tjAwoeGg8oSBgEgkjHYIqRTBk4gHC9sIk6a3jaDWIn4Vsa4gmbxeECQ2j0MPPbTkXEDdIVQO6UJK0SUEkkJAJJIU0tnJJzMkgk1gzpw5brfddivt1MbAPGDAADtnhM7NnafLq/Juu+02t+yyy5aM6e3atXN8F9WmyzxhprrEi4BIJF58s5h6ZkiEFTlEQjh4DOuodNitTWwtwo+8++67ufJQYrBiC3r44YfN/oM3FnVm1z4nGL711ltZ7G8qc8YREIlkvAFjKH5mSMR3XgzMxLnCvZVJFdUOsaM4A4SDmngu6xeEyZ6QF154wc4roa7epXettdayECfaXJj1Vs5m+f041I71bLZfHKXODIlQeTowLr8ff/yx22KLLczIjqcSxnZ2smMfybqKhzoicREUco899rC6eQJp3769eakhoeTZmSCOjq40o0FAJBINjnlKJVMkAvBMnngrPffcc65nz562Qkciwe0X7yW8mLJqbPYDlMCTHIaFhAVJQiIcynXUUUcZgfKcLiGQBgK+j0oSSQP9MPPMHIkAIwZnDoZC8mCvBCotiITNdxxXO3HiRLMnZGmy9TYfbB2clIjUQb0gEGxAu+66q51hklWCDLP7q1StRUAk0lrE8v98JkmEZqEz4+J68cUX23noHKHrVVvrr7++u+WWWyxkShaIhDJCjKiwcBLwEXqpD/YQdqm/9NJLmZWw8j+MilNDkUhx2rrWmmaaRLB/MPGefPLJtvmOVTs3HkxrrLGGregJ4MgqP1QygTxQz2FE50wTwt57yYoDsrp3724HcTV1QFatDa3nhEAUCIhEokAxX2lklkRoBt+h2T9y9NFHW1h0SIQVPDYS9lYcdthhRjRM1iEZoykLZeJ8EM5MwZ7jPc6oA+VHNXf//fcrzHu+xlyma+PHnGwimW7GSAufaRIBCTo1EgkRbq+88kqzizAJYyNhH8miiy5qGxRff/1183oKgUgoMx5YxL3igKkVV1yxtBudsmPb6du3rwWepG4hlDnSXqfEMouASCSzTRdbwTNPIiBDx2ZVj7GdzXmrrbaaBShEIoFIUAthZzjuuOMshDz7STBQ815Sly8jLsqQx4MPPmi77f2pjZAekggxsQYOHGg2kKKdmZJUWyif+hEQidSPXV7fzAWJ0Di+c7OHYvLkyXZeOit6Jmdu7AyQyTrrrGN7LV577TXbc5JEw1I2pIn333/fTZo0yQ0ePNgtueSSJduHJzvCmXBKIXacpEkuCRyUR/YR8ONM6qzst2VUNcgNiXhAmHyxM3AGyUEHHeSYmCttDUzgqItQfz311FM2uaNeimriZqAhGZEmUg+ENWrUKDdkyBDXuXNns3d42w1lg+w22mgjd8EFF5g0RTl0CYEQERCJhNgq6ZYpdyTi4UQVNHPmTHfNNde4/v37l9RbrPq5kU6WWWYZ16NHD7fffvu54cOHu2eeecbcgpEaGCz13LwLgbDf495773VDhw61iLsrr7yyqda8K7KXjiAVNhE++uijhTlky7eR/mYPAZFI9tos7hLnlkSYzCESQshPmzbNXXfddW7LLbcshRGBSLwXFGouPLlwp91+++1t4scraurUqSYZfPnll7Z5EVdcbBrcfEZ1RvrYYnA15uRBwtUPGjTIyGnVVVe1AJFIG97Yz18OlMJGw+mM2EawkciFN+6urvSjQEAkEgWK+UojtyRS3kwQCkQwY8YMO6McwzsutBjd/eTuJRQmfEKMMMmvssoqjoCHnN3BeR6cLMhucn8PGzbM4lttsskmdrYJXlaoyiAJnx4SB3mQFzG+CF+/0047ufvuu8998sknRh7lZdVnIRAyAiKRkFsnnbIVgkR8x8ddFukBd1/sD9ghIAwmfSZ6P/HzGUM8Ez+kAuFAADxXfvMdv/EMz/pNguXp8Mxiiy1mqrPdd9/d3XjjjVYG77pL2XQJgawg4MeSDOtZabH4y1kIEimHkUGA6ggyYW8J6qRzzz3XVF2c246LLTvevaQCMXiCwZ5RfkMW3rYBifAOJANpEPuKDYR77bWXqdKwkZCn1FblraHPWUOgGokwDvr06WMx69544w03e/Zs3QXCAI9SvxBnfkzySja3spoxELhRc+EJhSEcdReeWhdeeKEd+oT9BKM7qq8OHToYsTBYPInwGYLhUCyewXW4V69ebueddzYvrJEjR5phn7TJg7x8vmVF0UchkCkEmiIRjmLgeIZtttnGHFlwZtFdDAxWX331uRbaSXbo1EikWiWZ5FExYTDHWM6K6sUXX3SjR492N998s0kUgAVhcPN57bXXdkceeaQ988gjj9jznIdOGkgcpKlLCOQJgWokwsLKq4BR7eouFgYspllU+0V2kv09KBJpquIMGryx8PAaP368GcQxivOZ3fHE7eIZXUKgCAjQ11kcPf7442bngzBQ6eoWBr4PJDkOMkEiAMKgQbJAUmEDITefUVVJ2kiyyyivEBCgz+POjjci6lxsgLqFge8DSfbRzJBIkqAoLyEQOgJII0SFmDVrlrnNT58+3ekWBr4PJNl/RSJJoq28hIAQEAI5Q0AkkrMGVXWEgBAQAkkiIBJJEm3lJQSEgBDIGQIikZw1qKojBISAEEgSAZFIkmgrLyEgBIRAzhAQieSsQVUdISAEhECSCIhEkkRbeQkBISAEcoaASCRnDarqCAEhIASSREAkkiTayksICAEhkDMERCI5a1BVRwgIASGQJAIikSTRVl5CQAgIgZwhIBLJWYOqOkJACAiBJBEQiSSJtvISAkJACOQMAZFIzhpU1RECQkAIJInA/wFO+KBdMVjRNAAAAABJRU5ErkJggg==[/img]
Explain how to reason with the hanger to find the value of [math]x[/math].
Explain how to reason with the equation to find the value of [math]x[/math].
Andre says that [math]x[/math] is 7 because he can move the two 1s with the [math]x[/math] to the other side.[br][br][img]data:image/png;base64,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[/img][br][br]Do you agree with Andre? Explain your reasoning.
Find the matching equation to the diagram.[br][br][img]data:image/png;base64,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[/img]
Find the matching equation to the diagram.[br][br][img]data:image/png;base64,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[/img]
Find the matching equation to the diagram.[br][br][img]data:image/png;base64,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[/img]
Find the matching equation to the diagram.[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQsAAACtCAYAAACnZ1oVAAAfq0lEQVR4Ae2dB7gVxRXHUbF3RUQFRFFRLKhRUSxYUImKBUWNsXeiYO8VO8ZYMPbexZaYGKPYUFQsJIqKBSwoFhBBRVGxnXy/ifO+Zdl73+zcwlvef75v37v37szu2f+c+c+ZMzNnW5iSEBACQiAAgRYBeZRFCAgBIWAiCymBEBACQQiILIJgUiYhIAREFtIBISAEghAQWQTBpExCQAiILKQDQkAIBCGQSRY//vijff755zZs2DB77LHHyh5PP/20vfDCC/bGG2/Yp59+at9++639/PPPQTdXJiEgBIqDQCZZTJ061R5++GFbddVVbemlly57rLTSSta9e3fbY4897JJLLnHlRo8ebV9++aVIozh6IEmFQKMIZJLFN998Y/fff7+1atXKWrRoYS1btrQFFljAFlxwwRmO+eef3+aZZx6ba665bM4557S2bdvafvvtZ08++aRNmjRJhNFoFSiDECgGAkFk0alTJzv11FNt4MCBduGFF7qDz2effbb169fPdtppJ+vSpYstssgijjTmnXdeW3nlle2CCy6wiRMn2k8//VQMNCSlEBACJREIIguGGWPGjHFDi6+//tr8wVADPwXnXnzxRRswYIB17drVllhiCWdtYGWcf/75Nm7cOPvll19KCqETQkAINH0Egshiiy22sM8++6xsg8d6gEQYfvTp08fatGnjhi8dOnSwwYMH2+TJk5s+GpJQCAiBkghUjSz8HX799VcbNWqUG5rgy5htttls0003tZEjRxrnlISAECgmAlUnC2DAynj00Ued3wLn6EILLeSGI0zJKgkBIVBMBGpCFlgQn3zyifXv39/mm28+m2OOOWzHHXe0Dz/8UNZFMfVEUguB7F2n6anTEJ9FGsvvvvvOhgwZYosuuqgbiqy77ro2fPjwsn6P9DX0XQgIgaaDQE0sCx4P62LChAnWvn175+hcdtll7b777tO6i6ZT95JECORCoGZkgRRMrW655ZZuKNK6dWu3LkNLwXPVjzILgSaDQE3J4quvvnKzIqz+ZDhy6KGHaoFWk6l6CSIE8iFQc7Lo3bu3WyLO6s6DDz5YZJGvfpRbCDQZBGpOFiwFx7JYbLHFrG/fviKLJlP1EkQI5EOgpmSBz6JXr17GZjN8FieffLIcnPnqR7mFQJNBoGZkwWwIm8jY5s5u1Hbt2tm1114rsmgyVS9BhEA+BGpGFt9//7298sorbvjBku/OnTvb0KFDtc4iX/0otxBoMgjUjCyItHXxxRe7Icjss8/uplDZnar9IU2m7iWIEMiFQE3Igj0gWBVsICMoDj4LnJuE3FMSAkKgmAjUhCzYzk7gG/aFMAQheA6rN2VVFFNJJLUQAIGqkgWrMz/66CO7/PLLnUOTDWRYFccdd5xb+i3IhYAQKC4C0WSBlcBWdDaMMUUKSRAtC2Lo2LGji5TF1vSePXu6IYm2pxdXSSS5EACBILLo1q2bjRgxwj744AO3zZyt5nx+/fXX7bnnnrMHH3zQzj33XNtoo43cak2C3rCuAp8FrwqQr0LKJgSKj0AQWbCvY4MNNrBNNtmk4YAY1lxzTVt++eXdvg+GHPgnWFOxzDLLuAjfvEuk1hvHsHCI76lDGDRHHagnBQWRBUSAtZA8iODNwesBIBPeL7L22mvbQQcdZPfcc4/zUUybNq2mTk2GP88884xdf/31OoRBs9SBmU4WP/zwg2uE22+/vRH4Juvo0aOHbbvttrb//vvb8ccfbzfeeKM9//zzNnbsWDfsqEc0748//tgOO+wwI1aGDmHQHHVgppMFDZ0VmOPHj3fh8QiRl3XwGgCWdBPVm/z1Tu+//77tvvvu7kVILPzCocqLkXQIg1lZB7DwefkXRz1Tfe9W5SfzZIGvhDUdBNrZZ599dAiDWVoHeGWoyCInmXiywKpYcskl3XtWp0yZYjqEwaysA3SIIosKyGKppZayp556KucVlF0IFA+BAw88UGSRt9qSloXIIi96yl9UBEQWETUnsogATUUKj4DIIqIKRRYRoKlI4REQWURUocgiAjQVKTwCIouIKhRZRICmIoVHQGQRUYUiiwjQVKTwCIgsIqpQZBEBmooUHgGRRUQViiwiQFORwiMgsoioQpFFBGiBRQgtwH6fb775xghcFBoSkXzkp9ykSZPc7mOCN/MqSzYohl4nUMxmmU1kEVHtIosI0AKKQBJEPnv44Ydd7NS333670Y2CbD6cOnWqsbmQiGmEKRg0aJALijRw4EC3K5kVtgROIp9II6AiSmQRWZQAptzPIoty6OQ/560CcD3zzDNdECNildDYv/jii7IXxJIYNWqUDRgwwAVoZq8Ou4CJecImP95126FDB0PRX331VUc+IoyykJY8KbIoCU3pEyKL0tjkPUPDJZ7qs88+a7vssot7ORRRzwh8dNZZZxlDiVKJIctNN91kG264oStHIKTNNtvMBUI64YQTrH///i4mCkvyIQ2irvGqCO6nlB8BkUV+zExkEQFaRhECLxNI6M477zTirWIBEC4R64Dt/1gZ5cgCornssstcyMXNN9/cDTnefPNNN5ThtRDEQuH7SSedZMstt5yLrnbIIYe48xni6KdGEBBZNAJQ1mmRRRYq+X+jQdPYV1ttNWvbtq3ttttuduGFF1qXLl2M7f+NkQV3JIDz4MGD7eWXX86MlIZPY/To0bbnnntay5Yt3Ttwhw8fnl9YlXBDOW1Rz6kIIoucgJXIjiOTYMxt2rRxgZbfeustFyKxa9euwWSBdQEhlPNDMBsCoWCtMBx55JFHSkikn8shIMuiHDolzoksSgCT82cCxfA6B6wLhhsMS7AQ8pBFyC0hkiFDhjiywPH50EMPhRRTnhQCIosUICFfRRYhKDWeBwcl73ZhXYR/dUMtyIIp2Xvvvdc5Tdu3b29Dhw5tXDjlmAEBkcUMkDT+g8iicYxic9SCLMaNG2fHHHOMe1l29+7dbeTIkbHiNetyIouI6hdZRIAWWKTaZMGqTnwUa6yxhlt/cdppp+n9t4F1kc4mskgjEvBdZBEAUmSWapIFvooJEybYvvvuawsssICbln3nnXfcsvBI8Zp1MZFFRPWLLCJACyxSLbJghoTVneecc45bv7Hiiiu6dRj4SMrNnASK2SyziSwiql1kEQFaYJFqkAXOUiyKa665xhFFx44d7YgjjnAvpvKO1EBxlC2BgMgiAUboR5FFKFL581VKFpABi714rWWnTp3cu3D79etn7777bn5hVGI6BEQW08ER9kVkEYZTTK5KyILhBVvSr7vuOmdRsJGsd+/ebqOZhh4xtTF9GZHF9HgEfRNZBMEUlSmWLPxW9csvv9w6d+5srVu3tr322svY5s4KTqXKERBZRGAosogALbBIDFkw9GAr+1VXXeWGHryTk70gbF1nQZasikDwG8kmsmgEoKzTIossVKrzW16ywKLAmXnLLbc4osCZyQKsMWPGuD0j1ZFKVwEBkUWEHogsIkALLJKHLLyPguhYq6++uotpcfjhh7tdpuwzweIodcjaCKyQRDaRRQKM0I8ii1Ck8ucLJQsa+7Rp01wsDFZnLrzwwq7nI7jN+PHj3TTpxIkTM//7uJz5pWveJUQWEfUvsogALbBIKFlgObDHg70ezHrMNddcbrv7DjvsYH369Cl7MJU6YsSIQImUzSMgsvBI5PgvssgBVs6sxMns0aOHtWrVqmwMTvZ8DBs2zNZff31bfPHFXX4C6LRr167RgzB8jz/+eE7JlF1kEaEDIosI0AKLEIX7oosucvEzCY7Dku2shGVBsByWc+OnyHMQ2/O1117Luqx+K4OAyKIMOKVOiSxKIaPfZ2UERBYRtSuyiABNRQqPgMgiogpFFhGgqUjhERBZRFShyCICNBUpPAIii4gqFFlEgKYihUdAZBFRhSKLCNBUpPAIiCwiqlBkEQGaihQeAZFFRBWKLCJAU5HCIyCyiKhCkUUEaCpSeAREFhFVKLKIAE1FCo+AyCKiCpNkwRu/eQVfqR2O+j1756dwKR4uBBTSi5FzEoYnC160O//881uvXr2sb9++OoTBLK0DhCsUWUSQxR/+8Af37syWLVvaPPPM40gD4tAhDGZVHSAMwOyzz+6OnE2mouwtKio9kwuPHTvW9tlnnwZi4G1XOoRBc9ABT4T1bIKFJgu2TQ8fPtwGDx6sQxg0Sx0QWQQiQFxHokZPmTJFhzBoljoQ2FSqkq3QlkVVENBFhIAQCEJAZBEEkzIJASEgspAOCAEhEISAyCIIJmUSAkJAZCEdEAJCIAgBkUUQTMokBISAyEI6IASEQBACIosgmJRJCAgBkYV0QAgIgSAERBZBMCmTEBACIgvpgBAQAkEIiCyCYFImISAERBbSASEgBIIQEFkEwaRMQkAIiCykA0JACAQhILIIgkmZhIAQEFlIB4SAEAhCQGQRBJMyCQEhUGiy+OWXX+zHH3+07777TocwaJY6UE8KKzRZELD35ZdftgceeECHMGiWOiCyCETg448/tj/96U/WoUMHHcKgWepAYFOpSrZCWxb+jWS8nYmXrsw777y24IILFuaYe+65G94shey876Io8iM7mPM2OF56w3ssiiI7cvJCKuRHd+acc06bb775CiM/eOuNZDn5z5MFCktlb7fddnbAAQcU5lh//fUbKn3LLbe0fffdtzCyb7TRRq7BzTHHHLbCCivYHnvsURjZ0ZGtttrKERyNjvfk7rrrroWRf6WVVmrQm5xNpqLss4RlQQ/Rpk0b+/e//234MYpyXHDBBQ2Vfvfdd9vnn39eGNkvu+wy18jooXmF5DvvvFMY2dEPXkzVrl07h/+GG25or776amHk5y18sixy8p63LCCLpZZayp544gnjxUNFOf7yl780VDpOWpS4KLJfeeWVjqAZPu2999724YcfFkZ2MP773/9u7du3d/h3797d3n777cLIj2UksqiQLJ566qmcV5i52S+55JKGSkd5p06dOnMFynH3q6++2hE0ZEFPN27cuBylZ37WBx980JZddlmH/6abbmqjR4+e+UIFSnDggQc26E1gkapkm2WGIVgWIouq6ETQRUQWQTDVJJPIIgLW9DBEZBEBYmQRkUUkcFUoJrKIAFFkEQFalYqILKoEZMRlRBYRoIksIkCrUhGRRZWAjLiMyCICNJFFBGhVKiKyqBKQEZcRWUSAJrKIAK1KRUQWVQIy4jIiiwjQRBYRoFWpiMiiSkBGXEZkEQGayCICtCoVEVlUCciIy4gsIkATWUSAVqUiIosqARlxGZFFBGjVIAsC6HD8+uuvDRLwmSXBP/300wznfCbyUI48Pp8/F/q/0hWcXgbkSKakXMnnSubh96TspfIlyyQ/V4MskJMjeW8+1wP7SldwZsmexD39XB675POBf/LZfZ7G/ossGkMo43ylZEFFsR/j66+/dhG3/C2IvMXyZa4/adIk16j8Of+fiubcBx98YB999JG7jj8X+r9Sspg2bZp99dVXNmXKlIZboqRffvmlk51n4FnSCsn377//3snNM06cONE10IaLBHyolCxCsJ88eXJJ7L/44ouKsK+ELMAYneGA2HxCl9CFsWPHznDO5yGyGxsGwZ36oR7yJpFFXsTMHOC77767i0uQd7k3Ff7JJ5/YMcccY4ceeqi99tprbm/GI488YlQG+wXYjci292uvvdZQThIkMWbMGDv33HPt97//vbFVm41IbC+nLMqTbpylHq1Ssrjnnntsr732srPPPtv10CgpO1l79erlZOcZDjroIHvhhRfceeSAXP75z3/annvuaZtssonLt80229g555zjlDep/KXk5vdKyMJjf/TRRzvsX3/9dYc9u4ZDsEdWsKd+PPaPPvpoLuxjyYLGTv2zeQ7dYQMdJMGuYTBFno033th23HFHu//++x3e6APlRo0aZSeccILbHo/s1E/fvn3tueeea6ifcpj7cyILj0SO/5VYFlQejahbt25O6R5//HG77rrrbLPNNrO1117bHcQNaN26ta211lp2++23u15gyJAhLvYBefi9S5cubkPVMsss4671yiuv2A8//BD0FJWSxcEHH2zIyC7EN954w/i+7rrr2jrrrGNrrLGG20LONuz99tvP9cJEFoPkIDjO8wwrrrii2z3aqVMnGzBgQPBmtkrIAuyHDx9uG2ywgZPFY0/jycL+jjvucBYShEDciWpgH0sWbPb7xz/+4XDffvvtbdiwYXbRRRcZsUl+97vfOZ1YfvnlrVWrVta1a1cXNgGChti33nprdx75V199dadb1E/v3r0dAYUStcgiqHlNn6kSsqBBE9OAkHxU3Kmnnmrrrbee7bbbbq7XpFe44YYbnFIsuuii1qNHD9cDbLHFFq5BnnzyyU4ByEfvsPjii9sSSyzhenaUIyTFkgU9FUMQlA6lRGaIAoU97bTT3HOhnMi12GKLGURAgzv//PNdmZ122sluvPFG+9vf/mbXX3+9+41IVxAPPSU9f2OpErLA9KYnZtcnpAX2kBzPcc0117geOYk9gYGeffZZ23zzzUtiD6kPHDjQ9eSNyc75WLJgiMd9qGvkOe644xxJQMg333yz3XfffTZo0CCj80BvsOywOKkb9Ou8886ze++91x1YxQsvvLAtt9xyrjMK7WREFiE1nMpTCVnQQxx77LGu0qmwjh07ugb31ltvOcuABsmQ46STTnINjuA69AxUOorGeNonhjA9e/a0hRZayPXiEyZM8KfK/o8lC3pm4i/Qg7FFnLgMNDq2ueN/oLFDJv/9739tzTXXdPIjH/lOPPFE4xm5Bol8KDAYoNwEQOa3xlIlZJGF/SGHHOLkosF47JEVsktiT69Og/UJ7KkX5N9///0tFPtYsuD6BPuhriGMlVde2ekI/gcwRXZ8WQxJCN/HeT9UxZry/iWsiGeeecYRDUR3+umnB1t1Igtf+zn+V0IWjDMZ9xL3EkUjLBzOyqRDkEZHg0ZZiXtIb/HQQw/N4BB87733rE+fPk6BiO0wfvz4oKeIJQtvCrdt29YIawdp0FvhV4HgSPzHhwG5kYdGh5ITt4GeHaUm8Z+eEMWHLF588cWgYVQlZEGDAXusGbD/4x//6GRNY3/xxRdPh/2//vWvTOx32WUXhz1+o1qTBaSARUeEMKy6o446yj777DNHsB5TLEt+B3PyYdnhl+B3P9RAt4jOBZGAPdbVt99+6+qksT8ii8YQyjgfSxZU1KeffupiRxKsld6X8bDv1fytqHyGG74hYdZTzjdIn4+eGlN5kUUWsSOPPNIptD9X7n8sWSRNYRobpi4e9qRcfMahxjgasmC49eSTT2bO2px55plOdpQfMklep5T8sWQB9jiWseQ89viB0tiTD6vOY08UdxplWjaPPURHA8WyCkkxlgUNHWcs92rZsqUxJH3ppZdmcKxCCnQa1A3xPfETQZCeKJCPz1gaEA/OeXQBsgxJIosQlFJ5YsmCnpUxMI2DQL84CDEdfc/gb4PCeosBc/Kxxx7LnOrCUbraaqs5xabSk2ayv1bW/1iyoPfEG48ydu7c2Z5++ukZZKfxEWZwlVVWcb0uz4g1xTMlE0MOlA8c6AGxTtI4JPP7z7FkAfY4BfHxcE/unYU9jQnsMeV5hlLY0+BWXXVVh/2ll14ajH0MWWDR4ZOAKLCK8AFl1TUYMtPE8+G0ZTiYxhTSQwb8FViGXBdsQpLIIgSlVJ5YsoD5mQ6lsTG0uO2221JX/r95jllIY8SU3Hbbbd3cebqxUZDgtXi1l156acNUDjUnY8mCWQ0cgvgrGKfzPZ1QbJyFDFWY8cCZmZYdBaaXZ+oU5d9hhx3cM6avlfU9lixoXMjFmL8c9hCbx57pa9Y0pOVHrljsY8gC6w0HMtHkaeRYo+mEjAz/GLqiN0cccUSmPuDfwHLys22Qnvcjpa+Z/i6ySCMS8D2WLBhKMKSggTB1ytgxnehxMTlxCtILnnHGGTP0Dr4M12IIgqmP/yK00mPIAmVkqIDskMWf//znTIckjat///5Odrz2TK2mezeu9Z///MdN8WFl5Rk3x5IF2LOuBfl9VG2Po/+fxp5hUlp2n5drQfo0XvQhFPsYsqBucRRDFjhViWieTgwlGFZBhhABnVKW7Fh+TL3iM8P6AJcsMkxfn+8iiyxUGvktliyoZBxsMD/KxnRhOtGzYRrSQ6CI9MzphBLQg9MYUX7WDaDoWcqRLsv3GLLgfkQCxxRGNqZ/s+7HbA1yoYx45rNMfUxhnhH/Ac/IdGaoKRxLFszi0ODAHpJlxWM6gT0OW54PE51ZnnTimbHgWBfjST8P9jFkgZMSHwNkwZoUfCjpBM44ZpGJ4VNWqEdIAd8KQ1vysbAuj+wiizTqAd9jyWLEiBHOxGWGAzOWXjidGHcynYVHG+uDcWc60dhYzYeDFMvisMMOS2cp+z2GLFAyelpef4CfBAVOJ8b7NEKGRYz5MXfTjkHK0AtjMeGEY4EZvpfQnjmWLJiapRGBPbMwpbDH3Ad7rI9S2GNhsSgO7A8//PA0DGW/x5AFJM1wE+yZFcsaboI7jR8ypEPCAZtOWBXMOlE/WK34PvIkkUUetH7LG0MWsDqzApiJHCx9zjL/MAtZWUfPzLQq49B0ohfG5OSNXFQ879LIk2LIguldlhLTu+FjgKzSCblYCORNYXwEWQmlZYEW+VimzLRg0mOfVcb/FkMW4IzT1WNPg8vCHj+Kx95Pq/r7+v88Iz4Dj/1VV13lTwX9z0sW4EL9Qr7MhmAhZcnOkBbnJjM9LAfnWdIJgrzlllucgx2LjgV0eZLIIg9av+WNIQtMXHo0phNx/DErkpUgBxY68U5PxvJZPSDXuuKKKxxR0MuzyCZPiiELLAmmQyELLIysNR0MQZgZwMRlhoPl1OmEGc8zYQrTC7IGI8v6SJfz32PIAryw5BhCsVo0yyri+hCixx4LoxT2f/3rXxuwZ4YlT8pLFsjAXhb0geX0WZ0H92dmimEd+nXTTTdlWh/MZrFHBF8LQ9csy6ncs4gsyqFT4lwMWcD0jJVhfsa7OP7SiV5k5MiRrhehF2TPSFaPi2cfnwfmMsvB33zzzfSlyn6PIQt8J5jCkAWfs0xhLASWH+MAxT+QZQozRmY4xowE8pdzImY9RAxZgD14MQTxTtf0tcGZ3hmLDuxZjp6FPYTIqk96eda4ZD1j+trJ73nJAnLYeeedGyxNLM90Qk58LcgOpvgrsmTnWliFTK3iT0KP8ySRRR60fssbQxaQAyRBb8piJhpWOtEAmU6ld2A2BHM5K+E/wJNND84inNAFQf5aecmCnh9LhkZEr8SzZFkDLIFGLholexeyTGEWCd11111ufUKMKRxDFswueezZy1IK+1tvvbUBe6aisxLTmAydwJ6Vm3mxz0sWLL5iuhoSYNcrPq10wvpgARa4YxmxqTArQWzsR8JKOeusszLXamSV87+JLDwSOf7HkAWLezDjWRmIwuO9TicUj6EHPQTLpemB0wkzHm843nqmHfGOhzoH/bXykgUk5h1/7GgsZQo///zzTlkhFDaM+f0I/r7857nZ2o5lwRg7rykcQxb4dzz2+FFKYX/KKac47DHRS2FPzw7JgT0NLi/2ecmCmSKGmtyTsgyp0gmZsHYgFHxB7777bjqL83NgOTHTgw7eeeedmYQ/Q8HEDyKLBBihH2PIYujQoW5JNlYFlZY1VYgfAL8GXm2mwbJ6Znp0pmBZGYmC4FDMm/KSBY2LeXvuyUuVS/WmNHyejx6XZ8xyxNEz4hQkH36ErIVd5Z4nhixCsUeeWmOflywY8vXr18/pDj6VLHLCUiKeCI2ZHahZ1gflmHXi+Zg9yyLDcrhzTmTRGEIZ52PIgkUzNDoaGrMBWQ0JIqDnwBFFr5ylGFgW/I45zLVY/5A35SULxr/Iw/1YhZo1BEEGnos8yJZFhuShrL8W5nPWM5Z7nhiyaErY5yULrDoaP7oDVtR/OvE7WII9+pNVP5SjTtAtrleqftLXTn4XWSTRCPwcQxaBl65LtrxkURehAm8SQxaBl65LtrxkURehAm8isggEKplNZJFEo76fRRb1xTt5N5FFEo3AzyKLQKBqkE1kUQNQAy8psggEKplNZJFEo76fRRb1xTt5N5FFEo3AzyKLQKBqkE1kUQNQAy8psggEKplNZJFEo76fRRb1xTt5N5FFEo3AzyKLQKBqkE1kUQNQAy8psggEKplNZJFEo76fRRb1xTt5N5FFEo3AzyKLQKBqkE1kUQNQAy8psggEKplNZJFEo76fRRb1xTt5N5FFEo3AzyKLQKBqkE1kUQNQAy8psggEKpmt6GTBJrUWLVq4gziTMftLknjU87PIop5oT38vkcX0eAR9S5IFW355CzcbfopysEPRkwWBd9mAVBTZ2ZVL7E7ighB2kB24RZEdOQllRxAh8Oet5wQ7Kor87Cb2ehPUUKqUqUWVrjNTLuPJgqhRBEHp1auXi4JFJKwiHAQC9pVORCt6jCLIjYw0MOJ9ECKP93sQK7MosiOnfz8q+POCZt7OXhT5wdvrTT0b3ixBFgBHxGWCqRItuSgHYdV8pSM7QVOKIjvkTCQxiJrwfUTYLorsyAnRIT/4E7GKQEFFkR9rzuuNyCIQAW9ZeOD0///+D+HQfHAIbCpVyVZoy6IqCOgiQkAIBCEgsgiCSZmEgBAQWUgHhIAQCEJAZBEEkzIJASEgspAOCAEhEISAyCIIJmUSAkJAZCEdEAJCIAgBkUUQTMokBISAyEI6IASEQBACIosgmJRJCAgBkYV0QAgIgSAERBZBMCmTEBACIgvpgBAQAkEIiCyCYFImISAERBbSASEgBIIQEFkEwaRMQkAI/A9nwMTleBIvWAAAAABJRU5ErkJggg==[/img]
[size=150]The area of a rectangle is 14 square units. It has side lengths [math]x[/math] and [math]y[/math]. Given each value for [math]x[/math], find [math]y[/math].[br][br][/size][math]x=2\frac{1}{3}[/math]
[math]x=4\frac{1}{5}[/math]
[math]x=\frac{7}{6}[/math]
Lin needs to save up $20 for a new game. How much money does she have if she has saved each percentage of her goal. Explain your reasoning.
25%
75%[br][br]
125%