Maths-
General
Easy
Question
Find out the simple interest on Rs. 7500 for 2 ½ years at 15 % per annum. Also find the amount
Hint:
Find the simple interest and then add it with the principal amount to get the total amount.
The correct answer is: 10437.5 Rupees
Complete step by step solution:
We calculate simple interest by the formula,
…(i)
where P is Principal amount, T is number of years and R is rate of interest
Let the sum of money P = 7500 Rs
Here, we have T = 2.5 years,
and P = 7500 Rs
On substituting the known values in (i), we get ![S I equals fraction numerator 7500 cross times 2.5 cross times 47 over 3 over denominator 100 end fraction](data:image/png;base64,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)
![not stretchy rightwards double arrow S I equals fraction numerator 7500 cross times 2.5 cross times 47 over 3 over denominator 100 end fraction equals 2937.5](data:image/png;base64,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)
We have SI = 2937.5 Rupees.
We know the formula for total amount = A = P + SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the known values in (ii), we get A = 7500 + 2937.5 = 10437.5
Hence the simple interest = 2937.5 Rupees
And total amount = A = 10437.5 Rupees.
Related Questions to study
Maths-
Find x if MN is the midsegment of △ ABC.
![](data:image/png;base64,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)
Find x if MN is the midsegment of △ ABC.
![](data:image/png;base64,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)
Maths-General
Maths-
QUESTION 12: A square has vertices (0, 0), (m, 0), and (0, m). Find the fourth
vertex.
QUESTION 12: A square has vertices (0, 0), (m, 0), and (0, m). Find the fourth
vertex.
Maths-General
Maths-
Solve each inequality and graph the solution :
x+9>15.
Note:
When we have an inequality with the symbols , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
Solve each inequality and graph the solution :
x+9>15.
Maths-General
Note:
When we have an inequality with the symbols , we use dotted lines to graph them. This is because we do not include the end point of the inequality.
Maths-
How is the solution to -4(2x-3)>36 similar to and different from the solution-4(2x-3)=36 .
Note:
The number of solutions for an inequality can be infinity. Whereas, a linear equation has only a maximum of one solution.
How is the solution to -4(2x-3)>36 similar to and different from the solution-4(2x-3)=36 .
Maths-General
Note:
The number of solutions for an inequality can be infinity. Whereas, a linear equation has only a maximum of one solution.
Maths-
Find the simple interest and the amount on Rs. 4,000 at the rate of 8% per annum for 146 days?
Find the simple interest and the amount on Rs. 4,000 at the rate of 8% per annum for 146 days?
Maths-General
Maths-
A square park has paths as shown. Use coordinates to determine whether a coffee shop at point M is the same distance from each corner.
![](data:image/png;base64,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)
A square park has paths as shown. Use coordinates to determine whether a coffee shop at point M is the same distance from each corner.
![](data:image/png;base64,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)
Maths-General
Maths-
Place a scalene triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign
coordinates to each vertex.
Place a scalene triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign
coordinates to each vertex.
Maths-General
Maths-
A gardener buys two kinds of fertilizer. Fertilizer A contains
filler materials by weight and Fertilizer B contains
filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?
A gardener buys two kinds of fertilizer. Fertilizer A contains
filler materials by weight and Fertilizer B contains
filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?
Maths-General
Maths-
State and prove the Midsegment Theorem.
State and prove the Midsegment Theorem.
Maths-General
Maths-
Find the midpoint and length of each side using the placement
below. What is the advantage of using 2h instead of h for the leg lengths?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUkAAADcCAYAAAD9VlPsAAAgAElEQVR4nOy9d5wlVZn//37OqRs6T+jJM8zABBgYgQEGJCsqSRBBV5Swsl9X/a5hg/paf+sG100/13Vd428VlWwAQQZBECVnGIICCkiOM8Pk6el0q855fn+cqtu3wzQDTmzPe149t7tu3bpVdW996knnOaKqSmS70dvby2OPPcaMGTOYOHEiIoK1dkfvViQS2QxmR+/AWEZVB/0APPnkk3zhC1/gnnvuwXuPMfEjiER2ZpIdvQNjHedcXQxVlauvvpqrr76alpYWDj30UDo7OxGRHb2bkUhkM0QzZhtSiJ8xBmMMTz31FFdddRUA11xzDffee2+0JCORnZx4hW5DVBXvPSKC955rr72W3/3ud1hr6erq4tJLL2Xt2rU7ejcjkcgoRJHcxogIxhhefvllrrzySrq7u+vxyRtuuIHbb799B+9hJBIZjSiS25jCmrzwwgu5//77gQE3fOXKlSxdupTe3t76et77Hbm7kUhkCDFxsw1RVYwxdHV1MWHCBD760Y/y7LPPcvXVV3PMMcewaNEiZs+ezapVq5g2bRrWWlQV51wsC4pEdhIk1kluW9I0RVUpl8sAXHnllZx22ml89atf5a/+6q/q2e/CLYdgacaMdySycxDd7W1I4UIDwx4L8YQgisW68Z4ViexcRJHchqgq1tp6drtYBpAkI0c6CssyEonsHMSY5Dak0YVudKUbn2+MPRYxzOhqRyI7D1EktyGvN7YYY5GRyM5HdLcjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJN4j3HvUKXvFZP0r/iOspigcy1XzB4EfdDvsaiUTeOMmO3oFdE8VrhqhgVMiyDdx260386Ee3sbFnHULGrKmzOOH44zjosEMoNbXiHDSXE9Q7AEwukl7BCMiOPJxIJLJZoiX5BhFjAEEMGAt333MHt9x+J5WmFsZPnMDa9Wv5wr98gY9+5KM8+shvSUo2WI11NYw2ZCSyKxAtyTdEUDrFo2rAOQzCwYccwn/913/SOaGZng29PLDsPr7w7//Kl7/8Zb705a8we+okNNqMkcguRbQk3wBKiEk65xEEMRZVBfWoehRoamri6KOO5uP/96M8+sjD/ObhRwAQYwdvLGpmJLJTE0XyDSAoIpAkdojICSqCAIm12FLC/vvuR3tbG48//gQZ4CW3QqM4RiK7BFEk3xCCMRYRASQ8SjiVkougGANZxviOdia0d5D2Z3jA51vwUkQlY2wyEtmZiSK5LTGGvt4e+np7sNZgGBDJgB/5dZFIZKchiuS2RODZZ55m44aN7DZ7NjBQJjlgQcZUTiSyMxNF8g9CCGIniILBUTIGS4KIsPbVVfzgB5cyafJU9t9v37yUoMiMK4JHVINcqoJqvfjcEexMRUGLvyKRyPZmzJQAqSpbIiQiob5xVIrNSONjELDwG3gPqCKieC1DVuX5J+/hyh/9gJaOdro29vCrG29h+ap1fPIvP8H83SdjfA2SElBBfQnvMrxaEIN4hxHFGUOGxZlwB6tohvgMTKke94xEItuPMSOS2z4BUliN4X/1YYmIAW/Ya699eOD+h7n8sstQY+mY0Mmb9j+Qvz7hZPbdZwGWflSFLlfCTtqb1a6V9ZRpsUIpq0EujiJCoo7EpQgGFUtqylhMNPsjkR2AqOqYSK+qBuf0tdgiS3LoZqRxce4OZw4jgqhHsxpZVgMRxCR4BbElknIJ74RMlZJNqdWEz17yKy67dhnzp0/gPae8hRMP2Zu5LQoYMgwlHNb3INoPpkRq2+gXSwUovb5TEolEtgJjyJLcmmxGJRt+T6wlrdVIjEFsQslajLV1V9wYS1brRVCsbaLmodvDulqCtE3j1Z6U86+6k5Vr+jnj7fsxe6KlkqYYehFSEItKCRCSfHx3JBLZ/owpkfTeIxLqFlW1/reqNtQ0KoUIDn4uEMKPecpEZFDVtyJ4VbwqiRGstSCCc4rJx3J7r7lIKkkSNpWpx2FCIiYp09u1iXccuSe2Yrj25mU8tWIjH3n3wRy2WysVb/GS4E0Zj8WSu942ARkyWicSiWxzxkyYqxBF7z2qiqqSJCW892RZRpqmpGlKlmWoKs45nHP1dQeiDop6h/MZWVbD+QznHGkaHl0WhiM65xAJQmlsglPBiw1udilktwWwtkSpVMKL4BWsOmy2iQWTS/zNB97KiUct5tFnVvDli2/k5w+vZAUtdJsmatgwxDGroVojFp1HIjuGMSOShQVZ/CxfvpzLL/8JK1Ysp1QqYYzBGIO1NgibMXVBLZ4DyQXT4VwGqhgTEjbWJhSja4wxoLBq1Sq++rWv8+Qzz6BicAg+NzwlF7UH73+Ayy9fSlqrYY3FqCPRfiouZd64Kh879RA+9K4lrNuwnq9eegs/vOs5XuhVaiiiDrEGb8ro2PmoIpFdijHjbhcus8td7FtuuZmrrvoZBx54YP25devW8pvfPMLLL7/MhAkTOOCAA5g2bVqe9AkC6DX3sAU2bdrEk089ze9//xRgWLDnQvbdd1/EGkSENWtW87WvfY0FC/dh7vx5eMJdp3DoxQhrVq/koosvZtq8OSzce/9QC+k9iVFKZMxsNpxx1DymTaxy/s/u43uX3cDKVxfz/rctYv74CqWsRiIKEoOSkciOYMyIpPceNMQUszTllltvY6+FC5k+fTrGGFauXMEXv/gl7rjjTowxpGnK/Pnz+fw//zP7vulN1HPXqnjv8N5x7rnncu1119Hb209PTw3E8hcf+zjn/NkHsYngXIaxCf1pRuYUY4tCcQCBLGXxvotoaypzz513s2DvfVGb4BHUS14f6ZlcEk7afzcmtbZw0bX3cM1N97FiTRcfetcSDphSpex7ESwDH1fhejcK50jLIpHIH8qY8eFULIglMZ7nn3+Mx556jn0OPJBSuYSr9fCDiy7ikd8+wde/9U3uvvtuLr7wPLo2vsr5F1xIV09GJoIjC+50UkVMiWOPfQff/+653HrzDVx11eUsWDCP8y++hJdWrkaNoUxK2VhsuZVmK1SBMo6aenoceFNm/ORODj5gX5546D6Wr1mDN1XU5A14VfAYjCpV9Rw6fyKfOv0ITj58Ab/7zYN8/eJrufaJVbxoW+hVgzpHlqVkrhfne/GqYTCOU9AeoLZDP4NIZCwyJkRSqY/qQzTj/vtup9rSwe577oUH+jZu4LZbbuGwI47msMMPp1qtsviAfTn+uLdy/wMPsGL1WrwoDoeqoGJJylUWH7CEeQsW0NRcYe4eczj88MNYv2kjvVkvqToSzUhU6aul/OLGO/iPf/sXfnThuby4Yjl9CplabLmFvebvzqMPLePZF17AVqp4SUK8UxVvLJiEkjFUgYVTO/jIKYdxxvFLePmFF/n6D3/JT+57jpf6PZsQnIKvKThBNMVLPyoZ6hLwMfsdiWxtxoy7LQYMAqosW7aM1uYWZkyfgaqybs1a1q7dwG6zZ1MSg6t5bNkye87urF9/DevWbmD3OVPCwEPV0EhXAbK8HAicczz3/HO0t7fT1NyGCBgDXpVLLrmC/o0r8f1ruPSl5zjk4Wf5/Oc/z4S2JiBlytROammNF19ajtiZ1F1jBVHwXjECVkBFmNTaxPtOPJwJU6ZxydKbuOTiq1n3ymGceex+zKgK7UkF4wU1/WD78VpGaEZik8pIZKszJizJAhHwtYw1q9dRqlRprraQmISuTV14n5KUgqUlRUF4EmbgSp3L44TFeBqoC5kImDL3P/Agy5bdz/HveAdTJ00g5FIsvT09dHS08dWv/TfXXPsz/vqvP8r999zN008/lyeMlI5x42htaWbFipXBUiWIukg+5tw70AzUYdSTOKVZDMcePI9PnX0CC2d2cvn1v+Grl97FU2s20WM9zipQRXwrUAbjUIlNMCKRrc2YsSQVxakjzfrp7eknGVciKVm8+jwZM5B59niMd1hbAh86jDv1JGJCN1yfC44AYlmx4hW++a1vMmu3WZzzZx+kkljEB/++qbmJk971TubOnUVZ+tln0UKaW29kw4YNxY7R0txMU1MTfb09yLiwP9YaxBiMgjFST7cYdUgu2IkkvHnhLMa3H8vF1z/Mbff9lq4N3bz/xAM4fM/JdHgoOYsYgzN9CAZLecd8AJHIGGXMiKQAiJJYi0gJ56ReizNhwgQq1RJ9vT15wiRYXN3d3ZQrJZqqTaj3OHX5FLEZqh4pl1mz6lU+//l/Zv3GTfz9P32e2bvNJHVKkvcE8gqlkkVQvKYYA6Y+rYOACGnm8N5jjEURxJh6wzQjBlMv7/F50wyPsQYnHo+w/8yJjD9tfyZ2tHH5rS/x/I8f5cPv3pOTFk5mAiniyvS7MqUkuOyRSGTrMbbcbZRSpUprWwv9vb309TlqaUpLSyudEzt44snH6entJqmUyNKUBx94gFkzZ9DZOR7vPbX+Xpxz4DyJNaxZs5r/+H+/yKO/fZwvfOFfOeTAg0KTCQEjgvcea0G9I/MewWNKoYYyn14bEDZ1ddHT083Ezs6wZFjN46CebAiCESXBUcZT0ZT54yp8+JQDOefMw1nXW+O/vnszl974KGtST1Y2ZFbwOqY+zkhkp2CMXFWK4lDvQGDu3Dn09vSwdu1arEloaWvl2GPfwe233c6FF13Mffc+yLe//W1uuukWTjzxBMZPaMMYy9KlS/nud7+L4snSlG9/+ztcd90vOPOss+mrpdx13/3cdf8DLH/pJfCKESFNM5TgPqMuxBm9y8eIh317deWrbNjYzdSpU7AiDDjXhbEbqtcVg2JRMYQ0lCAE61ZcmQk24z1LxvO5sw9m5sQ2LvrZMr511UM8uqqf1EoskYxEtgFjxt2GfKSMeo466miu+tV3ePaZ59lzxiRELe99//vooYkf//jHnPut77LXvBn85V9+khPedQqJhb5axm2330H32l4+/KFzWLN+LQ899BDr16/n++edR/qd74YyI4Gzzz6bT37so9hSQufE8SSJwfsM8mTMuPHjKZVCbFDV8exzLzJl8hR2mzGdu9Z057FODSVLQDHLIjp0cjCPAZxAzRgS389umjJpz3ZmfuQYvn3lMi676zmeWdPPh04+kINnTyAqZSSydRkzIikqZE6wpsS++x9Ee9sFPPrrB3jboYuxWDo7p/GJj/0FJ514At0bNjFlcgczZ03FaRnn4Lknn2TFKyt590nvptrUTKe1/NeX/ouNG7tJfTFsMdRidk6aRCkpMXXWHnzvgu8zcdY8LKBaYv6ei/niv+3FpM5poJ4NGzby4MMPc8SRb2XObjMpPfI7UCEjweOxmEHediGaQShN3dLMjFCiTDmFcuI4YEYbH3v/ofz4hse57bb72Lh+JX9+6ls4fO9ZtBsl8R68DbMyGlAcVhURW59VZ+gYHWmwa2MX9EgkMCZEUhAMBmtKKNDWMYU3H7QPD9x9K+tOP5VJnRPx3lO2hoUL9mx4pULmwNW48fpfMnfOXE477VQwCZVqwtx5e27uLUMZT+sEFu4zoWGJpaW1lb1b80U+5ZlnnuHpF17gL457D+Nbm2iyHtSQSYKKYvDIiFGPQrpsmMcbEJOgJUGkRrP2sWhCwl+ctIhZExKu+MUdfPHHN3L6CYdx8oF7MCMREpehEoQWMaQ+Q3AkNqnvcf1Y6u/a+FckEhkz5oJq8FXzyhxOPOEEpk6ZzOrVqxBjBgShoTWaakiiZFnKQQcdxIf//MOMGzd+i95vuIwIw06nGF555RX23HMvFi/eD58RCsjFbEYYR8YolH2wDoUUwWHJaPKemS1l3n/0vnzifcfRVhXO/8lNnH/Nw/x+g6MvcVjTReJrmExwkuCtpYiEGjwmj4QOHM/gvyKRP3bGhCUJ1FuYZVkGwP77789uu+1Ga2trvbFuIY5Ds8vlcpkjjzwSyBtlbCVUlQMPOIg3LT6IyZ2T2WgUxCMmjLCRkYR1pGPDYzWlPn+iCEbDlA4JSlNJOPWgecyZOo7v/PRufvLL+3l65Sr+73sP5YApTTQ7zVu0QdFQKDj0warNT2Axf2OeRopEIjCGRBIGBM57T6lUYsaMGXgfGuQCec/IwRTNdremONb3x3kmTuxEymU0DSVDkgtdvY5yi1AgC+ubIgMexKzkHGWvNCscvlsnHR94K9+7/m6ue/ApVl9qOfuEJbxtXjvjfT9VD+IMPgll9cG1doQ+mqErUbQiI5HBjBl3GxjoFG5CrWLRedxaO6ghbyNFI97NPf8H7Q8GY0t5l3SLGAnzbRvJY4Wy5Q3HxeKNJaNMJqXgOpuBUiHEU0ozFk5u4q//5Ag+cNwSXnplLf958c386N5nWaEJNVPGYag5JfVQc57M5YXzg3c8EonkjClLciRLscDafNz2EBHcmqI4CAWTJ0iKBLbxIT3uvYPXkSBRCfFEDVWT9eW2PnIniG/qwSrMrJT5+Nv2Y7eOZi76xb1ccMVtbFp3IKcduZCZrQlWPThHWSy28L2lwYaMuZtIpM6YEsmdH0VEB+bhCYMUt+B1gsfWtcvksUUjecNyI4DFWUOaQpOHGaWMMw6ZxdzOKv/fTx7gR0vv4fnVG/izkw9g4bhmTGIQHyRX6vHRMeZaRCJbgSiS25yi5jGIUVK2oQQxt2B1C2dmCCkVxXoNyZdi2ybMq+MRjHeUBVSCWLbbMm/Zaw9azprAeb+8n1uW/Y6u9a/yf45dwn4LZmGMxXnyDHckEhmJeG1sZ0qmhDUhBlqkTraEPF2TF+h4wIdGHXmzDgFK6qlYD4kjswmZryA1WDyng0994Aj+5Oj9+P3jz/ONH1/PDQ88TZeHzIQkkNa3GaoD/JCfQQzMyhuJjHnGjCW5zWKLfzBBfhKfJ3LUIpTQfOTLlvSkEARLXt9Y9HsbeBKTj8wRW0JRSkDJGvB5nNE55rdV+PQJi5k5vp0Lbryfr112C6s2ZZx06Dyml4VmVcT1hf0yZvCIm9zPN9q4QEP50M562iORrcSYEcmdkiJ5nYuLqS8MlYivb3RLQ/XiCC8Z6B80EOVUExJFVgS8Z3zZcvrRCxk/qZ0Lrrqd7/30Vl56dR0ffPti9hxfomQUJyVUhBI+xAKKLevAEURljPwxEUVyDCOAa3DHQenQGifuM4XJLW/jez+7m+tv+zXr1nVz5vEHsf/sDqoKZc0Is4iTCzpDAqdhjvKolZE/BqJIjmGK+Xq8+tAuwwiqUHEph+8+julnvZULf/Vrrrr7aZ7ZoHzwhP04YZ9JdBrJ58spMkQjjPKOAhn5IyEmbrY3Grpfbs8Yar3A3hicKWFsQrPrYe/xnr869RDef9KbWb62j2/+6Dauuv0JVvdk9EmJmiZkmue+FcDXowU+Jm4ifyREkdyOhKkZitIfrS/bZu+Xj2cvHkGwCFYMiEXUM6UqnHPMnnzmTw6iLcn4/hU3cMEvH+L5jTV6jKUXQ68zuKKbEB7U1bPqkchYJ7rb2xOBpJTUUzY74O1J1IEqTppRE2ouZ0iNMw+cwu7tx/Ddn93ND3+5jJdXruH0E49gwawOEu/xmdKcWASH4Ovd1KPfHRnrRJHcziQ29Ic0Ijuk3FDU5dU7lkwMVpXE1Ug05bB5E2k64+2cd83d3PTQY7zaVeNPTz6ExfOmUbEJXnxDfrvY+yiSkbFNdLe3A40yIiKoEcTkJ1+3s1Dm8+cYDeO8BcGbCs5bTJaxaHIzn/yTo3jX8Ufz3Io1fOOS67lp2ZOs73d5vluBFNTnY4AIpUKFC67aIP7RJY/s+kRLchuhQn1sdpILoc3VMEsEb4LgbPfWZJKAzcd9kw+atCWwJQxQRlk0zjLpHXuyx6QWvn/1fXzpR/fw0ppezn7LPsxs8XjXj9MyXiqU1GN8P4IjjB+v4iXMH240RaQEYrfvMUYiW5EoktuQwhkVLWasCbg8Q7xDInoy/NcimVRImXplesVy2pLd6ZzQwbk/u5Vzf34zz6/bwIdPXsLe7a1Uag4xiqhDNEO9xydlankBfT4NGsGajCIZ2XWJIhkZRk0NzkG7zThuQTsTzjyS79zwa5Y+9Cwvd3k+feJ+HDJ9PFUc4EJJkFiyfMYeIG+ZkRedRyK7MFEkI8MQAx4lUUezOg6e3knTSUcypfUxrrnxIf5tzXrOeddhHLPnJCaUSuCUUmJIDIiEKSHCOO9STO1Ednli4mY7Unev8/l2dtZOOkYyrK3hrMXRRHMGB3dU+acT3sRn33s4yzes598uv51L7n2el52lxzbhxWJdL+Wsm7Lrw6BksQlbZAwQLcntiUCpVEIAr3nH3J1QKA2eEkomYQR3Ig6TdTPRKGccOZemCe2c+4sHOfent/LKytWcccyb2HtCmcSlGGpACVUhNZW8S1EksusSRXI7I7k2GlOMwNnRezQc4xNM3vncmxrYDI8HDBV1vGvvaUxtOpTv/erXXHfjMjatepVzTjiQA2Z2UBVb7+ZmZHNzikciuw5RJLcjQRQNiOTNJhSvgt3JdESlaOqWkvgaXoTMVPEkGAztLuMte7TT+f5DuajdcMs9j7J2Yw9nnXwUhy3opN16ygLGZxhJiLZkZFcmfnt3AILB7qChiVuCx5FKLViPWkZclSSrkPgElyp9pBhT403jLR8/7Sjec+rx/OblGp+/+A4uf2g1KzJDvyqJcXn95NAjja3NI7sOUSS3OQOCEKa29hjjQcII7p3R3RYRTN4EAykhkk+565VKyZAkZTwJosKsZuFPj5zL355xNG1NCV+/9Ba+84vHeWETOBXwm8B3Q5ZBCjiPpx9HL44UPzADRSSyUxLd7W1I40yI9dkQVEFcmMJVtmyuxO2Nyf8NbYZu6zMqhjnAnVcSlzIzcbz3wClMmng4513/W35200P0r1nDh48/gN0nlSmrYl2Yp8cBzpq8uD6UGUlslhHZiYkiuZ3xKC5z9VZp6gdPJ7OrEHrxKupTjHV0WM/bFkxgUsdBXHy151d3PsCrq9dz1imHsWTuBFqtUsajBryWUAGLQ6jlJ6C8g48oEhmZKJLbGWuCxaS7eEhOvQdNMdag3pHYlDbfxeKJTXS+781Mm9LGD69/hGcvvIcPvutgTjigk6mljJKvYXwVlQTB4IxBYg48shMTv5vbEQGSkgRhER1YuAsi4rGkOIXUNpFSRVRppptZTcpZx+3HRz7wdlQqfO+K27noxl/zbE9KaizG10iyFDz0SJk+KW3/Rh+RyBYSRXI7Y0QxxpCY0PRhZ0zcbAmCYsTjjaHPlOg1VVLTghWhTfqZVVbOPHQmn33fYma0KT/4+e187efL+M3ajP6kis8ycBnqFR8TN5GdmOhu7yB23nnCt5Q8iWMsHsgICZ2yVhDtoeq6mSZlTtmnjVkdR/GVa5fx0zueYvkGwyfeeSAHT26m6mpUXC/GlJAYk4zspERLMvIGkVAehKGCUgVKCJgySDOCxWiKzTay/4w2PnfWcbznyIN48JGn+PeLfsnPHnuFdaaMkRJWd/UbRmQsE0VyB7Ir524Ug5MKxkPVeVqco+xCByA1FZxpITMt9JlmPMr8ZuX/OXERn3nPwXR1vcr//PhqLr3jd6zsTVBT2tGHE4lsluhub2tUCDMMekRMmM9aLepNvRnvLul5i6AIpjg2BfLaSi8SfjD0G0sVT8U7ZjdZzjpibzo7ylzw87s4/8pbWbUy5U9PWMTu7UmY5lsVI1k+B5Ctnz/F5e9ZNPAtajaLxr7hZIpYdtlsWGSnJIrkNkTq/yvg8lIXQdSiajAiiO6al3QoLs9jqzYZZBYXU0MoYIxg1eYzODjGGcuJ+y6gs3U85//sXq645X7WbNzAWe/Yl31mj6cJBa+IIS89B1BEFS+az5pj6+cszNsYZnDM351d84xGdlaiu709aBi1EqzGnXOkzetl4CYgA+2NGo7VACKKGg8mdDEXMsqasf/cSXz8rLfztsPncfsDv+VLF9/IHY+/zCYMjjLqEyAF6cZoCoQbikExGqbCNYNuMLKLmuSRnZ0oktsZsYAJFlbwD3f0Hm1blBSoAS7omIKkNapZxtwJZT787jfzvlMO46V1G/jShb/i0jufYA1KZkPlpPEWRVFJQ22mKhbF5kIpPg9fYFGSWG8Z2epEd3s7MjBCOW+VNuYv6dDcI0w+azHeIGqoiGB9hhGludXwp8ftx9QJ47jwqmV864p7ebVrE2cds4hZ1RJlTfDicOIpqRTTUEJ+7lSC468aHG8brcnIViaK5HYmdNiR3DOVP4I5YCRYeGpRb3M3WSgbRyIpXms0GcO7l8xh4rgWLrx2GT+89iFWrq1x9jv2Y9GUZioqWFW8F1DNhXDA2Yd84jHhj+B8RrY3USS3N3VzUsZIZHJ0hIQQT8yPVfPGw0juNoP3Spv2c9yeHew2/gj+96pfc81dz/DUmj4+/u7FvHX2OFrSlMzmXTi9r99sQijyj+FMRnYUMSYZ2YbkwYVcIOlnPioAACAASURBVLWezSmeS8CXcd5REqUly9hvQpXPfOAw3nfigfz+2dV8+fu3cv39z7MeQ68RUmPIbCgDCrluD7j8MRLZ+kSRjGxTrHqMZGAcaj0u/1GrIZ4oFmssoXFaFUjYrdXy8bct4G9P3p9S7wa+dtntnHfr71ndUyMTyBC8yWcYkyCSoQN6xq5doh/ZGYnu9jaliJAN3IusOlDFExI3RmWrBtF2NolQ0Tx9k/8TRcTgAcnn5xZvEYGaNXiFcqbsUVY+dNQcZneW+frPf8d5Vz/Cq69u4Mzj9mPPiU2IU/DgrEVFMQ1JMEdjkswXO4LKQAw4uudbD23o+7fr9yQYThTJbURoSpsBgiNBxWMRylkf+D4yEhxK4n2YOnEr4HNByNv55omhIAtFcXcx77cwIKiDnmv4vfFRhzTAVAkdzEcjiGOyWeFWASfFhaWUceGWIuARxJY4fL/ZjBs/jq8vfZBL7nyBVRs28Tcn788+08aROXAmjOwp+TANrreeLC82T1Csd6GzsVpUEjITiuDt2LuWdxjOhSbSxhi891hrMVvpO70zEEVym6L1/7UQKvVkmpGGgSVghK3V38GoBx0YpTJc/goGZ4Y39/ugx6EiqSH1MppJtqVWbSYOj8cAVjxeBYchIwE1zJvZyqfPfjPTbnqYm29/kH/csIEzTjqEIxZNZ7ymlDNQ43AmLzVCAZuLe5EgC/+bmP7eqnjv6+IoIvWfsUQUye2MJ1y4zucTZRnZaimHYiJYRnwc4I3kgocJnmypCL52wbxVMGrqIqaA9Z6qDSO1rcJ+4yvMOHZfZrd38P1fPsp/XrqMFWsW8f4ls5hWzlCXolIhFAP5IJBi8MYiWEQF0ZBNL6zpyB+OqtatyKHexlghiuQ2ZbjZYhDEJHgkWJKai5v8oV8wwUtSH+08sHSwmA0MjXx9+JEkcZQNDX5m9GMzSn2YIT5UVooqqGAwlC1Iv2dmpcIHjtqLcZ2dnH/lr/n+j5axYWUXZ75jIbuPryKZwZosF/Bgm3oJam6EMJwRTxzfvfUorMYVK1awatUqFixYQJKMLVnZ4UczUtDXD2lVXSwfasYPvXNtiZmvqq+53kh3xJHeW0Q2e/ccWH/w814ENSZ0tMlfL+KGubMDb5Q/vlaIR8mH5uXuZf72vpglYqBMMY9TDtvjgTerBytD8fZQkS2Wb25Xw77owPqhOBLIj7dh/5QQl4RcyPIi+0LLvAYFdeIxAhOscNriTia3Hcq5S+/kolt/w4t9Kecc/yb2ntxMCwmJd8HZ1tA5yOVF+wYNcWJJ8n1pOK7X+d0pPvehf4+0rS21sLbke7m57+Fov78WQ4/l9WKt5bHHHuOzn/0sxx13HO9973tZsGABLS0twMD13Lj9Xckl36Eiqao45+onrIht9Pf3Y22Y69kYU49zNH7ZRhLILflyFu5B8ZqRvuxbIpLFa4uf4R+61oVEVVETSl68KplXUi9kHjKUkimUTBuURgbv6+ZsswYttpoGq0waRSiMcR4IT2rjqxuPqL5cNYigGAvehfhjkRkuGlmoMnSaxwGRbDyHPuy9zVvDqQ5oZj4pWgq4POPtJe8uZEBEERSPQ0oZXj1lLVHycNS8hI5zDuGiGx/n1rsfY+Wq5Zz9ziUcOm867ZrQSg2jLsR8TYKXwq7Pj7+4H7xBMSk+/8Yb+kiC2bh86HZGem40Rlp36Hs17k/jd3Ok145kjBhjcG7AH2k85iLuOPT9i+v4+eef54tf/CJXXHEFxx13HKeeeioHHXQQ1Wq1vm5xPb/eY9+R7FCRLD684sQ553j22Wd55plnOOigg+jo6BjxhG7uzjf0Qx9pnca/R/rQN/fBFRfFUDEt9n8o6n1+kTd8KQBrDMYmIR6J4K3gcrFRzQ0oGezJep/7i43bL/aLgdeUyPJ6wdDjcWBUz9C0zFCRbFwnHyyp+U4YWxfousA0FNgM3UquqA07mPd3FAHRvLB8sHlbJrc8tWHeRO/B5PFJBPEmP6QUVGjRhMUT2xl/wv7s0Vbh0uvu5n9/cAcbTngzJy6ZTROQaBo2haGWQeZSKloD8eGmpUqWZWRZNsxFdM4N+n4Ugui9H/FGWmxr0PnIhaXI/g5df+h7NL63cw5r7aDl3d3ddHd3D7omrLX09fXR3d1Nf38/AEmSYK2lVqvR09NTX17gvae3t5darVZfVsQUe3t76enpoVarYYyp//T397Np06ZBAioiZFlGV1cXq1atoqenBxHhiSee4Omnn2bp0qUcddRRfOQjH2HJkiWUSqURDZOdnR3ubhdfpGeffZZrr72Wiy++mIkTJ3LBBRdgra1nz4a+Zmsw9Ev4Wtt/Pe6CWAuUAJOf5MKnLOHUgISoWV8mpKJ4Be9cEERVvIaeiqiSZp5MB98AvCpp5gZimaqoByuCc57M+Tz+6Ouy6D04nwtoA+oG3P0Bq0NwXqilHud0kLvuXRCEQe9PLhRpRi3NcOowIniT4BXSXIy8V6Rhn533+P4a6kK5lJEExJB5T5alpLUaqj53xQUvntQ5ar0elwm+BOtNgrXt/PbZGv972V08/utlVFf+jmr/BkSULl+mJwV1NRJfw6kDTDhPWUaapsMErqenh76+vmE35/7+fvr7+wfmTc8f0zSlVquRZdkgEUjTlJ6enmEWZ5Zl9PX1kWVZ/e+CNE1HvOGPRqOx0UjhkQ2l0UNrfN4YM6yEp3jeWjtM7Iv1s/rnG67XLMt44YUXePTRR3n00UfZd999KZfL9ed3FYGEHSSShQXmvef555/nxhtv5Ac/+AF33XUXtVqNI444ghdffLH+ZSzWTdO07p4XH2Lhnhf1WY3vUavVhn3ZVJU0TUnTYGU0fkmyLKNWq41ooQ69Gxdf7DRNB7tsClmWUktTsrQH55SMMsGeMTy4PqMVzx033kLy1B10tE9mkzRTy8IFmGYp3vncwgAQ+vr76c1qg2KJXj19vX11iyNTpU8t2DJ9/f309ddy4Qxdu1Uhyxy1tIavWwP5Ptdq4AdSM6oG1ITssAvLxdo8CZKv5V1uAUvdOJW8/VuaZuF9RcCU62GGPBeTN/jI7VLvyXw/XjyQIDYBSRCxZC7F+RTUhea9iUU0TPWgLsXicb5Ev1aR1vGUK1VWrlvHxRfeSvrU7TRlXaDQb0uYcjPGGsTVKCxZEaFSqVAul4eJZKlUolQaPK1EYVUlSTLMszDG0N7ePqJnUi6Xh93orbX1n8bvZrF+qVQaJkjVapWmpqZB66sq5XKZSqVCqVQadF0kSVJfPlQIy+Uy5XJ50P4Xy6vV6iAR9d5TKpVoamoaZHGrKkmS0NbWxsMPP8znPvc5XnrpJZqampgzZw7HH38855xzDgsXLqzv165YPym6HfP2jTGc9evXc91113Huuefy0EMPsWnTJmDgyzZnzpxBX8biTjXS9goXYOihFKJa0CiGI4ln4f40vqZ4Lk3TwReABgssc9mAh6nBFTU2dB031jTE7cL0Db55Ir55OkmpwpRpkxg3exEbkslkaoBgQRYYEYyEgpbM+MEJl7rXqhgT6hV97tqH86KIMdjEhkYQ+XEYzQvM8/hQcaE26l/dmR5kVSjqG9wk0SBc1mDE1BM8YgyNvY1KNsmHHTZYZFC/ARgriMkQm+brmCCquRuaJKGtXAlP4jPEh2M1EmpCBYtJyjhVTNbPrCbh0PlT6WzyJGk/1hjElpCkku9bYWGTbz8Z0UJKkoQkSYbFD4eKZEFxHkfyeoaKVBGbS5Jk0PqFSA58Jq8dChotpro9rbV77rmHM844A2stp512GqeffjoLFy4cFI9sjOVGS3IzNNZUiQjr16/nxRdfrAtkYzKku7t7ULyoWq1SqVTqX8TiDmytpVqtUi6XB92VRYTW1lbK5fKgZcVdt1i/uIN676lUKjQ1NQ2zIJIkoaOjY/Aym1CtlKmUKyTFRaCgolhjSaxFSjbEBdUjeGxS4sab7+Tz//SvvO/jn+aEPzmT9anQXy6jMrDvRiQXIEtihMRCSQb3nlSBklWSZCClY7TBlSV8Ia0xdX0SyKeLCIJmBKwYsGZQEFRyi8/mrxcZPEKHPBkkIiQ2jLsJ0yswbPRQRUx4j/orG7cjGBveZ+g1o6ogYWRMMTrGy/B4qjUD00WIV5oEWqoVms0fR2egHS02Rby1paWFT3ziExxxxBEsWrSIpqamegy3uMYKdvQ+v162q0gWJ9Q5R3t7O3/+53/O2972Ni677DKuvfZaHn74Yfr6+thzzz357ne/y9y5c+vubHGiN5c4GSmDt7kPoxDToRnKYvlI2cmh8Uv1Giw0M/oHHipZ8omqsCxf/ipoL29aMJ3jj9qLLIOyHdJ8V/O/hbygR0lk8EVfZGobl5mQJhoy3HBobEsHWaQGM0JJ0MB2tS5rg1u7KQreDRjKmu/3iO7UUAVsXJxnq4YOOzK5aet9eBAwSYLWrVQdtKGQwDLUXPhsaupDK7b6eTPBhiwEdde6TndaRIRarcbcuXNZsGABpVKpLo7AsGtrV2S7imTh1hQZwiRJmD9/Pp/5zGd4z3vew9KlS7nyyitpbW2lpaWFlpYWsiyrux4jlQAVWfHNZZlHK5so4i2N2y8Eeej6I5VLKIDLlzcaObnv6ou4m/hwiYpFNA8ZpDXKHipA1Q+xEgeJdC5TppAyrb8F9brD/HdRvDYK2cD/jVsLbnH42+VutAxZZ1A74OCbDhFyQtyyOHwxoZnFSNXsQ1zNugjXe0w6hr0w71IhRgbkWdMRS6EG4sGKweLUhydMCCtgDI2HE9l6NF4/xfUEwSAqPL5dfSTOdne3izhQIWxF4HnRokXstddenH766Tz//PO0tbXVY5BDM2KFyBbb3FwweHM1XcX6xT40CvBrfajF67339Yt4pHo0ReozDdQFocFlLomnSi5SDdYfAA2uYpHscPVDzG1IVVQFYwZPAmEYbKjpEFnxDJbNIp466FSpUAyWbHSNh2mMGSzIAuiQj0LJ3fCBzTQ+5KWbpXy89bDV6r+Fm83gZ4YSjkOxubVocpdd889K1eRF5SO9NiroG2FoHXNjPWVxLe2KyZpGtrslWX/jEYYuFZbl/PnzR62leqMnfahLPjSGORojWZl1cc1jd4PEVYrLufE9B9TIoFijGHE4GWp+DRYyQSjrYHnQYnPDPOVBJu2Q38OjNiRp6s8M2o4fvMLgNRv+GhxrHOkMBi98qDXbKJKCqEG8GWr0DsIbyGxhVw96dUO4IAh5YmxI6miebDIG9aGJRoj9KviB8cYjhWoiW8ZI1+JYO687vE5yc+xMJ7exeDjLMlatWpVHxLQ+fK5aqTBh/IRBMblg+DTG0Bo3WqzjsfpaNXFmmJBt/uzoKL8XtuVreJ551nw00Qpi7+su83CbstjPIpk0PKIafs3fR/yogUKLw3jHUIltPLeCxVPKBxXlXWmMgCnn2xggzSschoZxIluHnen6/UPZaUVyZ6OIvaxdu5bPfe5zPPf884jJ69GM5Zi3v51PfvKTdLS14+oxtzBHNIDmQudz68sXrqMmiI7+MRTu9tZoqVaXtFEFcCADLg3Lhq6jIy0fwmvqjwBSdBYvFgy9sQR70RSCupkbgRaCrAOxyMd/+1uWPXA/TiEFVIVJEyZy9NFHM66jY8QRL5FII1Ekt5AiMdTV1cWyZct450kn8fZjjyXLUlRh2vRplKvVPMZIQ+xrcNcZrdsz+VBEkby0ZfMUkvHal7I2/MDI7jYDk3JtdjOFZTbASLbb1pMWec0bBQiZyOhvqop4wRTDH71yy0038i//8UUmdE5EjSVzjnlz57Fon30YP25cPYa2q40CiWw/okiOSKMsKabo4ZU3kCgnVfbb70COe/vb66/w5GOsNc9n1E2ootwo/DXsMpTGmNrICHmLtdfc5+HlPsN/H8H1H3VbgyWxHtncYpXcAldWhcHO8Oa3Mpq+hzOZj1TKG1N2bdjEHjP34Dvnn0fnlEnUfI1yUmZce8egqogokJHNEUVyGAPjlBv9SREXRqAYg9UkjDFuwGUOERMyrMhmA9f1Yu8G0bRboDZbtoZli0RJXsvd3gK7dUs1ZStpj8hryWhYKbMGLz53zQ2JrQAJUzun0za+DbUeKwZ1DW56jElGRiGK5JYghYsarvhalnHnnXdibGg8Ua02cdghhzB16hSKxMjruey2rg2zhVt7zdW2o2W1lXZ5pHOugDUWaxPK5QSHw7sBi3ukBiqRSCNRJLcIybPWISaWpjWuueYa7rjzNtIsZfacOewxezbTp0157URFZPuiyosvvsCf/Z8/wzYZ+rJe9nvTfnzmU5+mvb19lxtHHNn+RJHcEjSfDEBCLV+1UuUvPvkJPnDW+6jVaiRJifbWVlxexRIvuZ0Hayylcpl58+ZRaauSST9zZs8GBtzs6G5HRiOK5DCKmsjGuF1eFamhy3ZiLePGjWfyxAn0po4ksYiPF9rOgjbUnaZZxtQp0/jc5/6e8VPa8plvTH34XGFJbkk3+sgfJ1Ekt4AwqMaAd3gXphEw+ZC8JLGhS42R6GrvDCj1jkx4j6hSS/vJXA3vlZQUK0m9M1EUwshrEUVyCwjXkUeMwViLyxzf+c53uPm2m/DqwXsOPOAAzj77bMZ1tO3o3f2jpbFCVPMqBbF5HyUXmv6aKIqR10kUyS0kDOLwNDc3ceaZZ/LcKy8hSd5AwSnlcilaJTuYYYVLxtLU3MqMGTNzlzoU78dcduT1MEZFssHvVRnoyOUd4PAqGJOE4m8EGVSAlxeQD9rWQLHzxM5J/O3ff3rE7IxXJXMOQ5ivxtpkoFNO1M8/iOA9K/gUYwTvPCYp5/OXO9RneQikhHgPPkWt4Z3vOZU3H3kUHeOaMGQoBtXQVi58JI0F+AMyqxqK951L805r4TugqhhrUHUIPrSZMxZVIXOeJAld2Bvvl/Gj37UZeyLZ2HMyb9IQ3LBiTpUaSoLPLN4rxoCxUEx9CqFLt6+PAw6NE0RMqJUUwmTWonijdetENUwqlSA4r4gPk3vZUnnwoJV4xbwhnPM477GqoSenU5wINQxePVbDRGLqBSQDl9HvEzpnz2LG7FmY/g35fD9NiM2bc+QjiwbGDoQPSBHUQeocmHxKD68YKaMIRj2KQ10Nq2BKFdIsDLXy+SCD0AE+32r0MHZpxqDnIYN/Ggy5MFWrITEJeEVUwyx8CkYFo5K3HpMw/k0bVS1XOsl/Btr41H8v+lxaY/IpCcxwUYzJnTdEkYyRYgoHI1x9zc+59trrAKnHGq0xYS6bJCEplahlSubDNLs3/OI6LjjvArq7expik7koDvmuIEUs2mBMQqXSRLlSolxJ8gFLirGWdevWcfmll/HE448jYl/3LIeRnZ+xZ0k2itKgEYChy0yWKr3dG2hubQuy50BM7m+LRxC8Dh0Al49lltz6qA9XHHyPMXkH7I1dGymbhEpLa33VaEv8YYjk0+d4D4nh5edf4LKfXMZb3n4c1iZkff0sX/4Sjz76JCteeJrOiR3sf8gRTN19PoggYrn5xpt46IkXOPW9pwFNFAJZf49BQ90d3jswhvXrNnLvsvt49tln6Rg3jgMOPJC5c/fAWktzczMPPPgAv/v9U3xm/p5Umirb+cxEtjVjTCTzesaiww4UTnY+ZjrhisuX0rVpI2effRbVShWDyadCHRA9Q/CoR8bnccZS0eURACchPpU6x5U/vZJxbe28892nIA1jvBvt0mhQvj7qvoEoPsu4//772bipm0MPP5ySCC+sXMl3vn0u69ZtYuOq5ax86Tlap17BZz7/Lxx58AGERiVgxNS/EzDQPb7+HhrsSu9TjBVWrHiVr3zlq/z64V/T3t7Cpu4uLr30R/zlX3+ao488kpb2dhYvXswlP7qU9evXM6V56g46Q5FtxRgRyaIA3OPzKViDy6yIOgwOMcLyl15m6dLrOPqYwylXE8Q4Nm3s5eabbuOWm26iq3st++2/L8e981R2mzUba/NtiKLqMOIRUVavWsn119/EnXffR+ZS3nzYYZx4wolM7JyITRLK5TLnn3ce+yzen90X7InmDdLsoAL1QNFILTI66hU0TMNQ6+/jhptvZNqM6UyfMQMVaG/v4OR3nsTue8yjc1yVe26/g499+h+54vKrOWi/fWnLp91FXL3JiOaNPJzmk7oVZUMoYjxiLEuXLuX22+7m81/4B956zOG88OJz/N3f/yMXXnAJB+6/mAkT2pg/bz7dPT089eTTTJs+Nd4Axxhj5vqUeiB+wH4s+libPFB/x513smr1Bo446i1glP6sl0t+eAn//h9fpFbztLd38NOf/oR//Id/YPnyV3KBJA/cO2ppyoYNG/nPL36Z886/AGsN5XKFb33rm/zPV/+H7u5urE04+OAldHV1cc+yZWQojoE5eUbq1Rgvqi1Bc5dbWbtuDY88+jCz58ymvaUZD0wcP4EjDzuCadOmUq2UOejgJSxYsCcrVqzMEzZhnnBVx+9//3vOPfdc/vkL/8IvbriJnv6UELXMy4Q0tMer9fdwyy23cvAhb+bYY99BS0srC/fah1PffQpPPPEky19ZBcD0GdOZNnUad99zz7BmdZFdnzEjkgGtd0L00DBBkSfr3cj9y+5j9rz5TJ+zG0aEhx59iEsu/QEf+vMP89VvfJX//upX+Id/+juW3X8Pt9xyc5ipL5//GhWsLXP7Hfdw/S9+xaf/5lN88xvf5Bvf+Dof+/jH+dUNv+KRRx4BlJmzdmPylCnct+xeutJeUudD0TkQh+W8MUTCvECosnz5crp7+pmzx+7h886NTMjnVkkS1qxezZo1a5k8aQqJLcIvytPPPM2///u/ct2113HbrbfxN3/zKX669GpSXzRLDj0pjVHWr1/N8hUrmDF9JuVKgvcpkDF58iTSWsbq1esBmDBxIjNnzOSuu+4iy4bPVxTZtRlTItloo9UvnnxpV9d6nnz8CWbM2p2m5mYyPL99/Lf09vdx6JGHoQJprcY+ixYyZ84sfvu7R6jV+vIZ+ARrErwT7r/3AdrbxrFkycE4lyEIS5YcTLVa5bHHH8Orp1qpsHjxYp574QVeXbMKNQPRSJExdcq3G0LeGFeV1atWUa6UmLXbbsFyq2e9BWMNrr+Xq668Eu89p77nJGySgIdSktDT08O7T3k35194PldedRWHHHY4P7/2ejb19AOhFlPzEq/e3m6cczRVmwlv44GUSrmMqpDWUiDM/tna1srq1auo1dKYpBtjjLErdiAtYvIf9RmCZ82rr9Ld18P4aZ2IETwp619dxYTx42lpH4eTYH22NDcxb/eZrFi5gv40JXMZ3odauVp/DytXvsKEydMoN7eSuRRBGd/eSlOlwvKVq0h9EOYDFr+J1a+uYs2q9VixRT0JOmx6w8iWEUIeimfd+nVkWUa5UgnWnwb7T4yi3nPLLXfy48uWcvr738+SxYvzggRLf82xaO+9OeWUU2hra6O9rYW9Fy5k+cuvkPal9SpJVMAbjFhEPWnaD5oXs2Nzt1xDwk89NkmoNjWBEVyWDuxyUS0W2aUZIyIpKBbBYFRIAOsd1tfyImPPhnXr6Cejbfp4FKXiHbqxlwoJYhIyAcRA6miTjMwpNSnhvMdrhhNPmnbR27MO0zGOrFQOV4D2UTYeRejJDP2SoKJMndhCz+p19K2tUWrMa5vC7c7/VKLlsQV4FB/qtahUm0ES0poLp1EzRPqBPm65+TY++am/520nvIsPfvBsqlYR73CSkJkqSamKMeW8prWXsnfYfkhqHusdQoa1JXxWprV5HE0VQ3fvqryzUBlPE719ICVoG9cEeLwPQpplLpQbMVBM3lBGG9lFGSMimaN5ZxdClY41hKFqqtRqNdLUIcYGOXVCxZbIanlqJU+Il4zBe6VUrqJ5x2pVxSQJ5VKZcmLp7e0Oww+NBedxmUM9lCuV4P4ZQ6mckNh8lI4yUC4UY5JviEJsVIXOzkl4p6xetToMgPKKesfdd97O//z3VzjhxJP57N/9HePa26iWbbAOjQWTkGUe5zzqPUYcpcSSmDCDkKCk/X10bezGZdDeNo5p06bx5O8fZ+3aNZSShP5axkMPPsjkSZOYPLUTgP7+ftav30hHezvlcrm+v/HmNzYYMyI57EspYYyu92HoRLnahDGWrC/EnkiaGT9pKuvWraVr43oSAwZPb28fz720gskzZmJsgrUGTxgSVyqXmDp5IhtWr6LW24s1CSRVNnRtolbrZ7fp0ygbQGHDxk2oCDYJ8978/+2daZAU5RnHf+/bPdfOzB6zyALLgiIshMMIRYxZDpUUwQVkoxEwlica4oUpquJV+ZCKSVUkH/IZrJTlhxhNTGKsIikDaIIYFVxNVcAol7CKyLJSmAT26u73zYfu6dlB3RjN4mTq+VVNzdHdU7Pb0/95nud9DhOPlhU+DUoptOuilKJpdBPWGN7pehsNJBMJDh8+zI9/tAHP91jytcX8bfdudrzwF1588SX6+noBG42PtSilcZxQGK31CYIAayxaO+zqfIX7H/ge+w4cJJGp4fL2y3ml8xU2btrEyy/v5OGHH+bJX/2apcvaGdsUjus4depfHD/ezdRpU3FdV85xlVEleZIRKoonRXVlphjsx6G+0IhCcfJYT/jLoBzGt0wgCDx2vfwi06ZORmtN56t/Ze9bb7Ps5hmkkw6+18f7x7tJ5UfRmE0yffo0nnh6K/veeJ0JC+cTBD47d73KwIBH6+TzSUQf5cjRbvL1tdTVZwlMadjXf5p5KHw0gVUYG2YajBnTxHkTJ3LwwAEGBj3SCZd3jxxl/4GDGCfDPffei+97OK4mk0nz6KOP0NraSmNjgYaGeqwN295ZG1BTk+GccwokEwoIOHDwANuefZabbrwJpR1WfP1K+gd9Hnv8l/z8sV8wYeK53H7HbVz1jatCC1U59PT08M6RI9y8ZBmOUzV2hxBRRSI5tJtgJEi2VHbW0NhEaalNeQAABxJJREFUobaOk0ePYgKL0Zo5F11M2/wFPPKzTfzjgxMklWXbM7/ny23zuGThAlwFPUePsHLVtVyz5nbuXns9l1x6KbOe3sJPf/IQe3e309vXz29++xRLly3nwhlfwLE+vjfA7r/vpWHUaOob8qUgv/CpCVO5FL7nk8vVMX/ePLb++QW6j3Uzcfw45sz9Ei917sQ3CfyA0AMwAVpr6urCWTZ33nkbFk0+W4s1AwQ2YPXqq7n6qmvI5XL09Z1i3969XHzRV5g0aQoYQz5fyy233srK1d/E8zy041KTzUaTMwEMh7u68D2fObMvrB7XTIipIpEkyiOPrEkAR6OMQxB45OsamDlrJnv2vcE/P/iAdKGW2roG7rnnuzz1u6fZ8fzzOI7DkqVXsOLKK6kfPRplDadOnuTYseMkMxkC5TKmuYWHNjzE4088yZYtW0nnall7x10sa7+cXCaJMh79vafZ/cZ+Jp4/mUKhgOOErdNwwpZaZYh2fjKi+uswKdyyYN58nnl2O3v27OHclvGk0jVkMxnQqTiTICQcu2Gx5GvzKBysCT0MrRwS+RQEaQyW1/fs5sSJE9y1bj2FQh6UQUeWYX19HXGRa7hahCJgoK+P1157jVmzZtHc3CwVVFVIlYhk0Yo0qDDlGKOiBGMLoEmk08ydO5ct23Zw+NAhGuq+iKMVLS3jWfutW7jxhusBl0wmg5tO0WcseP3s+NNWpk05j0sXfZV+A1kcWltbue++e+nr9wiUSzqXJWEV1juNSmkOHzrEsZ4TrLppDdlMGkOAo8Td/kxYsEqj0VjjMX3GdBa0tbF/735OL1xIXU0SG/hh9oDVpYPiGpjwy2DLotdhXZaxhgDD2HFNrF+/ninnXxBW3sQhkmjXOBO32DlF0d3Tw/vvn2D5sqXkclmCoCSsQnVQJSL50dio35WjXQIT0NZ2MZMnjWfbH//ABbNmoJTGWp9MOk06VYO1YdDd9z1cN8HRrkO8985b/OCH36e5ZSxYi7Uug55POpkklcwygGLAt+FKqaMwgwPs3LWLprHNXDh7TvFTxDNxZF7YZyRyu2vSab5z9zpODxrSqSTGAMbgFPt2xthSP8/i8zPQWmEsNI8NywsxOo5rf9xSm8IS+D6NhQIPPHA/+doG/CCIRg8L1UQVieSHky7Cvn8uxvpoYHRTEzdcdy3vvtfNgDeAm6pBBRoTBHGisI0qbKwxnDN6FN9et45R4yfTG7+pi3YgCCxWBfjWxdEKh7BbttffRyaVZs2aNUxobsYSoOK6H6fcExQ+MWHLubDHp9YOJgjIZXOks6ELrrBo7VIStVId/5mx6pBojjoKVNgk2feDqKpHlTQyOnulI8urs5OpFKPSWQI0vu+TSCX/13+68DlTHSIZN8ctts1XOLb0sjUOWmmssSxZekVYoaHC9WYVdd11bXjRhOWMCgdI5RvJ5+owSpO2FkU49kGp8BhrFZnoXluFSqZxE0muu3ENRoWVGeE7DulqXlRJEcv/Ch01wVVWY4nik0rjRELooEC50U7Ff+4Qt3poT08V7UsmShUD7TigUih0lI85NLQ5NEhSshS146KsE261FieVDPsF2LAuwdroSDnX/9dUh0jG18SQGNLQ72bRBVJlu0VPnPJtgEOx6a4GXDRQaqVa2r/sWlSasgsoflb+/sKnI/YTVNH6C18vH0+kzzii9Lg8hxbCs5OMDwu3J+PtH3+6SluUKnkGHxqTBOI1VAkSQBEEQRgGEUlBEIRhEJEUBEEYBhFJQRCEYRCRFARBGAYRSUEQhGEQkRQEQRiG6siTrGCMCTtXa63RWsdTE4c+VkqFPQ2tjfcTBKEyEJEcQYwxBEFQJojF+6J4Dn1NKRWNFbDhhEZBED53xGQZQay18U0Vq4Gie8/z8DyPwcHB2IIMAhlHKgiVhojkCPJR4li0ELXWpNNpEokE1trY4hy6ryAInz/ibo8gYTdtS29vL5s3b6arq4s333wTgO3btzM4OEhtbS3t7e20tLQAJetTEITKQFm5IkeMYswxCAIefPBBNmzYgOd5uK4bL9SsWrWKjRs3ks/ncRwnGlalZPFGECoEuRLPAlpr1q5dy+zZs4GSO10oFOjo6KChoSF2w+U3SxAqCxHJEaboPre0tLBixQpSqVQshG1tbSxatAgIhbNoQUpMUhAqBxHJEaYofgAdHR3MnDmTIAjI5XKsXLmSMWPGlK2Ci0gKQmUhIjmCKKXwfT9ewJk6dSodHR1Ya7nssstYvHhxWa7k0JsgCJWBrG6PIEopEolEbBkmEgmWL1/Oc889x+rVq2lqahLrURAqHFndPsv09vbS2dnJpEmTGDduHMYYXFd+qwShUhGRPItYa/F9Py5TPDPBXBCEykNikmeR4up1MReyeC8IQuUift5Z5swuP5I0LgiVzb8BhTwF7hiYJsUAAAAASUVORK5CYII=)
Find the midpoint and length of each side using the placement
below. What is the advantage of using 2h instead of h for the leg lengths?
![](data:image/png;base64,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)
Maths-General
Maths-
A sum of Rs. 4,000 is lent for 5 years at the rate of 15% per annum. Find the simple interest.?
A sum of Rs. 4,000 is lent for 5 years at the rate of 15% per annum. Find the simple interest.?
Maths-General
Maths-
Place a rectangle in a coordinate plane in a way that is
convenient for finding side lengths. Assign coordinates to each vertex.
Place a rectangle in a coordinate plane in a way that is
convenient for finding side lengths. Assign coordinates to each vertex.
Maths-General
Maths-
MN is the midsegment of △ ABC.
Find MN.
Also, find AC if CN = 35 cm
![](data:image/png;base64,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)
MN is the midsegment of △ ABC.
Find MN.
Also, find AC if CN = 35 cm
![](data:image/png;base64,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)
Maths-General
Maths-
In △ ABC, AM ≅ BM
BQ ≅ QC
Prove that MQ ∥ AC.
![](data:image/png;base64,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)
In △ ABC, AM ≅ BM
BQ ≅ QC
Prove that MQ ∥ AC.
![](data:image/png;base64,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)
Maths-General
Maths-
Write a coordinate proof.
Any right isosceles triangle can be subdivided into a pair of congruent right isosceles triangles.(Hint: Draw the segment from the right angle to the midpoint of the hypotenuse.)
Write a coordinate proof.
Any right isosceles triangle can be subdivided into a pair of congruent right isosceles triangles.(Hint: Draw the segment from the right angle to the midpoint of the hypotenuse.)
Maths-General