Question
The front row of an auditorium has 10 seats. There are 50 rows in total. If each row has 2 more seats than the row before it, which expression gives the total number of seats in the last row?
Hint:
Hint:
If we carefully observe the seating, it is seen that the seats in the auditorium are arranged in an Arithmetic Progression. An arithmetic progression is such a sequence of numbers where the difference between consecutive terms is constant. Here, each row has 2 more seats than the row before it, so the difference between two consecutive rows is constant. We need to find the number of seats in the last row which is equivalent to finding the last term of this A.P. series
The correct answer is: ![10 plus 2 left parenthesis 50 minus 1 right parenthesis](data:image/png;base64,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)
Given,
In an auditorium, number of seats in front row = 10
Total number of rows = 50
Difference in the number of seats in consecutive rows = 2
We consider the Arithmetic Progression (A. P.) as follows:
First term of the A. P. (a) = 10
Total number of the terms (n) = 50
Common difference (d) = 2
The total number of seats in the last row is given by the last term of this series.
The last term of series is given by
![a subscript n equals a plus left parenthesis n minus 1 right parenthesis d](data:image/png;base64,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)
Putting the values of in the above formula, we get
![a subscript n equals 10 plus left parenthesis 50 minus 1 right parenthesis 2](data:image/png;base64,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)
Rewriting the above equation, we have
![a subscript n equals 10 plus 2 left parenthesis 50 minus 1 right parenthesis](data:image/png;base64,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)
Thus, the correct option is A)
Related Questions to study
Find the missing values
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAV4AAABpCAYAAAByI0u7AAAgAElEQVR4nO2dd3wVZdr+vzNzzkkjJCRUASWAQGihBkKvgQDSUQISRLBgYVdXYV/dXXF1Xd319+5ad23rK53QQktC6GAMARGMi/QivZcUklNm5vfHyTPMOQRM6GWuzwcIJ2f6M9dzP9fdJF3XdSxYsGDBwi2DfLtPwIIFCxbuN1jEa+GW49cWWdYizMK9DtvtPgEL9zY0TQO8ZCpJErquo2kasiwjSRIAqqpy5MgRFEWhatWq6LqOLMvYbNbwtHBvwhrZFm4aVFU1CFfTNIN4dV1HVVVkWebUqVNkZ2czY8YMwsPD+Z//+R+qVKmCoigW8Vq4Z2GNbAs3BZqm4fF4sNlsBulKkoQsy+i6TmFhIXv27OHLL79kxYoVnDt3josXL9KmTRuSkpJu9+lbsHBTIVlRDRZuBoRVCxiSgq7ruN1uDh06RHp6OrNmzSI3N5fu3bsTFxfHJ598gsfjYdasWdSsWRNZtlwQFu5NWBavhZsCIS8ILdfj8XDmzBnWrVvH7Nmz2bp1KzExMUycOJGBAwei6zrnz5/nrbfe4tNPP+WNN94gODj4dl+GBQs3BZbFa+GGQFVVw7IV/2qahqIo5OXlsWnTJpKTk1m3bh2RkZGMHDmS/v3788ADDxhRDOfOneO5557ju+++Y9q0aXTs2BHARydWFOX2XKAFCzcQlsVr4bqhaRqqqqIoio8DzeVyceTIEZKTk5k7dy7nz59n2LBhjBkzhvr16xtkKkg7IiKCJ554gnXr1jFt2jTq1atHpUqVjH2L71kShIW7HRbxWrhumKMWZFlGVVVOnDjB6tWrmTp1Krt27aJ9+/YkJSXRpUsXAgMD0TTtskgHTdNo374948aNY/r06XTv3p0hQ4YYDjmLcC3cK7CkBgvXDU3TcDqdBAQEcOHCBTIzM5k7dy5r166lZs2aJCYmMnjwYKpUqWIQriBRMfyEI87hcLBnzx5GjhxJ1apV+fDDD6lRo4ZxLHP8rwULdyssi9fCdUOQ4bZt25g+fToLFy7EbrczYsQIHn/8cR5++GE0TaOwsBCHwwHgQ76CdGVZxuPxUL16dZKSkvj73//O0qVLefbZZ41thN5rwcLdDMvitXBVlGSdgq8DLTc3l8zMTL766isyMjJo1KgRf/3rX4mLiyMoKIiioiIAwzEmYnsFhIwg9q8oCocPH+aFF17gzJkzzJgxw0iqsCxeC/cCLNHMwhUhZAHhAFNVFY/HY1ie+fn5bN68mXfffZfXXnuN/Px84uPjiYiIIDo6mqCgINxuN7IsG3+EA06QqMhQM/8eoEaNGowaNYrjx4/z/vvvc/HiRUMPtmDhbodFvBZKhHB4KYpiOL7Aa+mqqsrevXuZNm0af/jDH1i8eDF9+/blgw8+4L333sPhcLBkyRJcLpdBpGaLVsDfcvX/f9++fenWrRsLFixg8+bNRvabBQt3OyyN18JVIchSEGdubi4rV65k7ty5bN++nVatWvHqq6/Svn17goKCcDqdDB8+nAULFtC6dWtiYmKMfZVFJtA0jcDAQEaPHs2aNWv4+uuvadiwIdWqVbsp12nBwq2EMnny5Mm3+yQs3JkQ+q6qqhQVFbFt2zY+++wzvvrqK9xuN+PGjWPChAk0adLEcIwpikKVKlVYvXo1586do3Xr1jgcDmNfZQkJ0zSNatWqoSgKs2fPpnbt2jRq1MgKK7Nw18OyeC1cBhE5oCgKbrebw4cPk56eTnJyMhcuXCAhIYEnnniC+vXroygKHo/Hp+xjZGQkffv2ZebMmWzdupW2bdsa+y3LOWiahsPhoF+/fixdupSvvvqK2NhYHn744Zt16RYs3BJYpsN9BkFowmEmSNPj8eDxeAwnmqZpnDlzhvT0dCZPnsy//vUvqlatyvvvv8/f/vY3GjZsaBCtcJCJP3a7nfj4eCpXrsyiRYsoKiq6qsTgf05CXxaJGdWrVyc+Pp6NGzcyf/5845zN37dg4W6CZfHeZzA7ygTBAUYWGcDFixfZuXMn8+fPJz09nbCwMH7729/St29fqlatauzrakv+ChUqMHDgQD799FNycnJo3br1FeNw/c/JjLNnz/LTTz+xd+9eKlasyJw5c+jcuTOtW7c24n8Bq4aDhbsKVhzvfQb/VF3AiBZwu90cOXKEjIwMkpOTOXXqFAkJCYwePdqoraCqqpEEcTWImrtvvfUWBw8e5MMPPyQyMvKqxGsugnPx4kX27NnDkiVLyM7OplGjRjRq1Ih//vOf1KtXj48++ojIyEgKCwsJDAy0dF8LdxUsi/c+g39dBUGCZ8+eJSsri5kzZ7J582ZiY2OZOHEinTp1IigoCE3TcLvd2O32Uh8rODiYgQMH8tprr7FmzRoGDRpUouQgLG9ZlnE6nezfv5+VK1eyZs0aQkNDefLJJ+natSvh4eEcO3aMDz/8kHXr1jFgwAArttfCXQnL4r3PIEhXVPq6ePEiO3bsYOHChWRkZFCuXDmGDRvGo48+SmRkJG6326dATVkiE4Ru/M0335CZmcmbb75JVFRUiVavy+Xi8OHDrF+/nu+++46zZ8/So0cPhgwZQsWKFXG5XMiyzMGDB3nxxRdRFIW///3v1KlTB13XyzQhWLBwu2ER730AoZ+K0DBJknC5XBw/fpzFixczb9488vLySEhIIDExkUaNGgFe4hTRDWK70iYxCIedoigcOXLEsJ7Hjh2LJElGPzXhxPvuu+9IS0sjNzeXNm3a0L9/f2rXrg1c6t0mSH/58uW8+OKLPPnkkzz//PMEBQX5nJMgdivZwsKdCktquMfh7/XXNI0LFy6QnZ3N9OnT2bJlC02bNuW1116jY8eOBAUFGd8T6b1wbc4rRVHQNI0HHniATp06sX79ejp37ky9evVwuVzk5eWxfft2Fi1axJ49e2jcuDHjx4+nYcOGPjqy/7Fbt25N165dmTt3Lp06daJ169Y+3YsFSVvEa+FOhUW89zDMlp8syxQUFLB9+3bmzJlDWloaERERvPzyywwbNozw8HCjQaUgr+shLqEli1jcvn37kpWVRXp6OlWqVOGXX34hLS2NrKwsateuzYQJE2jbtq2hJwtruSRHXFhYGKNHjzY06ebNm/uEtlmLOAt3OizivYchLECXy8XRo0dZuXIlKSkpHDlyhF69evH4448TExNjyAICwnq83uW6IEKPx8ODDz7II488wpQpU5Blma1bt+JyuRg5ciQDBgwgODgYj8djaMpXOq4ISWvRogWJiYlMmzaN1NRU+vbta8gXZgeiZfVauBNhabz3MNxuNxcuXCArK4tZs2axY8cOGjduzOOPP07Hjh0JDAzE5XL5tF0HfDTda42PNXeV0DQNu93O+fPneeONNzh9+jS9e/eme/fuVK9e3eg+LOQBt9ttJGX4E6fH48HlchEYGMjhw4d5+umnKSws5D//+Q9RUVE+7YGsEDMLdyos4r0LYY6/9a+RK6zFwsJCdu3aRXJyMmlpaZQvX57hw4czYMAAqlWrZmR9ga+Gas4aux6d1NxZQpZlwwI9dOgQqqpSp04d4/fCMjbX6L1SbzW32218z+FwMG3aNN544w1efvllxo4dS0BAgHEsK6nCwp0KS2q4C2EmMzNRKoqC0+nk9OnTpKamMm/ePE6ePEl8fDyjR4+mQYMGBpmZIwv8IwL8P7sWmJ1y5iV/rVq1fI4lNFkz0V7t2OJ34vp79erFxo0bmTFjBnFxcbRo0cIgZot4LdypsIj3LoOwUgXpmq3CU6dOkZWVxaJFi8jKyqJJkyZMmDCBHj16EBAQYNRmKGkJL3CjNVH/lu9X+11pjm12FmqaRuXKlRk5ciSZmZlMnz6dWrVqERYW5jMhWbBwp8Ei3rsMQk4wh3u5XC5+/vln5syZw7JlywgLC+OVV14hISHBqF8rCsvc7bqn0KKFVauqKk2aNKFfv37MnDmTzp07M2DAAJ86DhYs3GmwNN67DObGkKK2wpo1a5g6dSrnz58nISGBESNGGEkQotqYeSl/Ny/BxbUIuUVMJjt27ODZZ5+latWqfPLJJ0RERNzV12nh3oZFvHc4/JfLYgl97tw5Nm7cSHJyMhs2bKBZs2aMGTOGbt26YbPZjN5owjI268B3s9VrzmIzZ+TJssyUKVN45513GDNmDC+99FKpivlYsHA7YBHvHQKzJimsOuCyRAKn0+lTWyEgIIDhw4czdOhQKlasCPimCIv/mwn8bibekrRtce8KCgoYP348P//8M//5z3+MtkPmkpdXipawYOFWwtJ47xCYi9eYCRguWXnHjx9n2bJlLFiwgGPHjtGnTx8SExNp2rSpz778ieVeIporXYvH46F8+fI8+eSTvPrqq8yYMYNatWpRrlw5n2ps99K9sHD3wrJ47xD4p+qKx+LxeMjNzWXz5s1MmTKFnJwcmjZtyhNPPEG7du0IDg42wrLuV4hoDXH/Pv74Y7755hveeecdQ3oBr2UsWslbsHA7YRHvHQJzgXLxf5fLxY4dO5g/fz6LFy8mLCyMpKQkBg8eTGRkpNGqR5Ik7Hb7fRs6ZW4B5HA42L17N+PHjycsLIx//OMf1KhRw8chZxGvhdsNS2q4Q2CurKVpGocPH2b16tXMmTOHw4cP07t3b5KSkmjSpAmAkep7v1u7cCm2V9y7WrVqMWrUKN566y3S09MZO3bsFdsOWbBwO2BZvLcBZssWLmWLaZpGbm4u2dnZTJs2jf/+9780btyYJ554gg4dOhAUFOQTTmbu3HC/E4qu6z71Jc6dO8eLL75odKyIjo4GLpG0hXsb4p3yT6QRXU7cbjeBgYGXVbO7Ve+TRby3GP6NHcXSV9RWmDVrFkuXLiUsLIzExEQGDRpkJEGY6xpY5PHrWLt2Lc8//zxdu3blr3/9K+XKlbvdp2ThFkEYKGaJqaioiGPHjpGVlcW+ffsYPHgwTZo0MZKLAIN0b7YcZUkNtxjmdFfwDpAjR46wfPlypk2bxtmzZ+nevTtPP/00DRo0QJIkn6wzi3RLB13XiYuLo1+/fsyfP59+/foRHx8P3Pi0aAt3FoTmL9pBiS4na9euJTk5mXXr1nHhwgUkSaJhw4bApe4stwqWxXuLYQ4XO3/+PJs2bWL27Nls2bKFhx9+mCeffJLOnTsb9WkFzGRxv2u6pYGQHbZt28bvfvc7qlSpwt/+9jdj9WDh3oWQnQBOnDjBpk2bWLx4MWvWrKFChQo0b96cdevWUb58eaZPn260mDL7TG725KxMnjx58k09ggUfSJJEUVERO3fu5Ouvv+brr78mPz+fMWPG8Jvf/IYWLVoY6cBm69isO1le+V+HKIZeqVIlbDYbs2bNIjIykpiYGOv+3ePQdZ38/HwyMzON0MKTJ08yZMgQXnnlFR599FHOnj3L2rVrCQkJoV27dgDGivJWOGEti/cGQhCk+FnMoOIzj8fDkSNHWLlyJcnJyZw6dYr4+HgSExNp0qSJTwIF4CNJmK1ca6lcOoiC6sePH+eVV17h4MGD/Pvf/6Zx48YlPh8LdzbE+3WlxquqqlJQUMCPP/7InDlzWLVqFbqu06tXL0aMGEGTJk0ICAgAYM+ePYwbN47c3Fy++eYboqOjfQpPWRrvXQLhNBNeVPOsqaoqubm5fP/990ydOpXvv/+ehg0b8tZbb9G1a1eCgoKMbcxeVvPAssi27BD3tGrVqowdO5bnnnuO5ORkHn74YZ/7akU63B0QRoj5X7vdbkQDicapCxcuRJIkOnXqxOOPP05sbCwBAQF4PB6jc3bdunV59NFH+eMf/0hqaip16tQhMDDQpxj/zYRl8d4gmOvkwiXvaGFhIdu3byclJcWIVhg+fDj9+vWjRo0ahiPgajVyLVwbhFNSyDtvv/02K1as4M9//jM9e/YEfAvCW7izIbRbEUqpqioXL15k27ZtpKWlkZaWxpkzZ+jWrRuJiYlGCKYoGAWX3ktVVfnll1+M1lGff/45TZs2NVZJN3sytoj3BkFYu3BJXzxx4gRLly4lOTmZ48ePk5CQwKhRo2jcuLGxZBLbWC//jYe/c3L37t0kJSVRrVo1Pv/8c6pUqXLFbsYW7jyY65k4nU527drF/PnzWb58OYcOHaJDhw6MGDGCTp06UaFChcsIF3xj5nVdJzk5mT/84Q+89NJLjB8/HrvdfkscbBbx3iCIQSFqK2zatInk5GSys7Np0qQJSUlJdOnSheDgYDRNM7rpihnYsnhvLPwlH7Gq+OCDD/jnP//Jm2++yciRI63ebHcRNE0jLy+PvXv3kpqaypIlSzh69CjNmjVj+PDh9OzZk0qVKhmyn5hUxTgQEMQqyzLHjx/nueee4/Dhw3z22We0bNnSsKpv5vtomVnXAP+5ylyy8eeff2bRokWkpqYiyzLjx48nMTGRyMhIH8IFjAaPVubZjYe52aZ5NTF06FB++OEHpkyZQmxsLA8//LCPU9TCrYd/81b/d0HXdS5evMiePXtYvnw5qampbN26ldDQUCZNmsSjjz5qEK7T6fSpRCccZgKimJKweCtXrsyoUaN44YUXmD9/Po0bNzasXXPBqhveEsuyeK8Mf6HdPHP6v6zHjx8nIyOD5ORkTpw4QdeuXXniiSeMko1iFjY7c8TMCpbz7GbBnDoK3iXn+vXreeaZZ3jsscd46aWXCA4O9mnO6d+xw8LNhVmLB9+ayYWFhezevZvly5eTkZHBsWPHiI2N5cEHHyQnJ4fXX3+dFi1aGOGX/iGXQvYzry7N77Esy5w5c4Znn32WvXv38tVXXxETE+PTXku86zdyPFhxvFeBf6QCXCJjc/HtrKwsPvnkE+bNm0fNmjWZMGECTz75JDVr1jT2JQaT/+CwPOo3F+aJTryE5cuX5/DhwyxcuJCmTZsaUQ5mnd5ahdwaqKpqVOYD39Xj3r17SU5O5tNPPyUzM5O6devy/PPP89RTT9GjRw927tzJ+vXriYuLM8qjmidNfyIvKZJF13WCgoKw2WykpaXhdrtp166dES0BNyeU07J4rwLziyhg9pIfOHCA5ORklixZQkhICKNGjSIhIcGIVgAr2eFOg5B6fvrpJ8aNG0fLli35xz/+QUhIyGWt7a1nd/Mhyp+KOslFRUXs27ePFStWkJaWxpEjR2jVqhWDBw+mTZs2VKlSxbBAN2zYwOuvv86ECRPo27evj4RQWp+J0IJdLhcTJkxg06ZNfPXVV7Rs2dInxvtGVwG0LN5fgZiNxYzpdrs5fvw4S5cu5R//+AfZ2dl069aN119/nYSEBCMmFyyr6U6EsLBq1KiB0+lkwYIFhISE0KxZM+NZicnVena3Dk6nkwMHDrB48WI++ugjVq5cSc2aNXnhhReYMGECjRs3Jjg4GLfbbYRgVqxYkQsXLrB27Vpat25NeHi4EdZZWpIUK9eAgABCQ0NZuHAhuq7Ttm1bH6v3RktPlsV7FfjLCnl5eUaDyaysLOrXr89TTz1F165dcTgcPg9J6EOWx/zOgliKisIpTz31FGfPnuWrr76iXr16hsVkhZjdGhQVFbF//37Wrl1Leno6+/bto0GDBgwdOpQuXbpQuXJlQ7819yKUZRmbzcauXbv4/e9/z5AhQ0hMTDQiGUpr9JjHQ15eHm+++SYrV67k888/p23btkbChTkS4kbAsniL4V+u0Sz2iwaTX3zxBV988QXnzp0jKSmJV199lZYtWxozo1mAvxVB2BbKDvFshdbrcDhYtmwZsizTsmVLqybGDYL5fTJ/JkjO6XRy8OBBFi1axKeffkpGRgaRkZE89dRTPP/887Rp04aQkBCf0C5z2ybxb0REBOfPnyczM5NGjRpRsWLFK9bU9deR/dPGg4ODKV++PCkpKaiqSlxcHAEBAT6dS27U+2yFkxVDJDOYrR2Px8OxY8dYtmwZs2bN4sSJE0aDSbE0FYK+ZSHdHTAvRTVNo0ePHmzatIk5c+bQqVMn2rVr5xNtYuHa4O+MFiu/goICjh49ytq1a0lLS2Pv3r3Url2bSZMm0aVLF6pVq+Zz7/1XjP5LfkmS6Nu3L+np6cyaNYtJkyZd8V00E6h/t2pJksjLy8PpdBIeHs7s2bN55JFH6NSp002RDC3iLYY53k+SJM6ePUtOTg7Tp083ZIUJEybQs2dPw4Mq2u9YWu7dA/NL6fF4CA8PZ/jw4axYsYKpU6dSv359IiMjb/NZ3t0wp/aKd0oUId+wYQMLFy7kv//9L1FRUfz2t7+lV69eVK5cGUVRjNCysmi0DzzwAL179yYtLY0dO3bQuHHjK35X+GzMckRBQQEHDx5k1apVZGVlUb16dQ4dOsTChQtp06YNNpvthsd6W8RbDLvdbnSr3bFjBxkZGcyaNYuQkBAmTJjAoEGDqFKlCrquG0HYYnD4SxMW7lyY4ziF1duwYUNGjBjBxx9/TLdu3Xj00Ucvi2axUDYIma2oqIjjx4/z7bffkpqaSk5ODjVq1OCll16id+/eRgSQiC4wt7Qqy/uUmJjIjh07mD17NrVr1y6x24ggUDExeDwejh8/zurVq1m3bh2qqjJ48GBiY2N59913WblyJVu2bKFNmzY3vGefRbzFcLvdnDx5klWrVjFr1iyOHTtGx44dSUpKMmrkulwu4NIyVcycFvHeXTAnr0iShMPhYNiwYSxbtowZM2bQqlUr6tate7tP866FkOlOnjzJhg0bWLx4MVu2bKFatWo899xz9OnTh6ioKACf7irmqJLSvk/Cig0LC2PAgAG8/fbbbNq0iS5dupS4vaIouN1uzpw5Q3Z2Nunp6Zw5c4ZOnTqRkJBgPPcxY8YYEpSIqLiR7/c9H9UgBHRzF1/w7UxbUFBAdnY233zzDVu2bKFBgwaMGjWKbt26Ua5cOZ/24UIjEj+L/Vua4N0Bc3igOSVUlmWWLFnCxIkTGTx4MH/605+M2q3mug/3e5SKf3qvf+id2+3m9OnTrF+/npSUFLZt20a1atXo378/ffr0oVatWsZ+/EO1/EM3S0t0LpcLRVHIzc3lvffeIz8/nz//+c9EREQY/hfwPvv8/Hw2btzIokWLOHr0KDExMQwcOJDo6GhsNpvxnttsNt58803mz5/PZ599RmxsLHDJqWfe77XgnrZ4dV03yryZs9AEeTqdTnbv3m3U8LTZbIwdO5bhw4dTtWpVYz/mIjb++dv3+4t4t6Gkl1pUserRowcdO3Zk0aJFJCQk0K5dOx/SvZK3/H6BWKKboxPE+He5XJw6dYqcnBwWLFhAVlYWFStWZOTIkTz66KMG4QqU9O6YPyvtPTY78cLDwxk0aBBvvPEGGzdupFevXsY55+fns3//flatWkVmZibVq1fnpZdeIi4uzsdoMj/fvn37kpKSwoIFC2jUqJERZSGOZ86AKyvueeI1/4FLN/bo0aOsXr2a6dOnc/jwYXr16kVSUhINGzY09F7gMg+pOe3Qwt0J/2cnrK2goCCeeuopdu7cyYwZM4iOjqZ8+fLGRFvStvcT/N8nIdmcOXOGTZs2kZaWRnZ2NuHh4YwdO5aEhATq1avn0zXiaivDa7m3gqzF82natCnt27cnNTWVJk2aEBYWxsGDB8nIyCArK4vQ0FDGjBlDly5dCAkJuSzkzex4jY6Opm/fvixdupShQ4fSunVro9SofyGdsuKeJl5JkowYW/HQc3Nz+eGHH5g1axbr1q0jOjqad955h+7duxtpo+Y26hbuD4hn3rJlSx577DE+/vhjvv32WxISErDZbDe1UtXdBPEeCZ30+++/JzU1lezsbEJCQhgyZAjDhg2jbt26BuEKp9nNgLlGL0BQUBD9+/fntddeIzk5mWrVqhk1GHr16kXv3r154IEHDGdeSc9SkHhwcDD9+/cnLS2NxYsXEx0dTWBgoI8D8Fo54p4mXhGBIAT13bt3M3fuXJYuXUpAQAATJkxg4MCBVK9eHfC+fEK7EbKEaBFt4d6FeNHEWOnVqxepqal88cUXNG7cmNq1a1s6PpdWBufOnWPDhg0sWbKE7777jvDwcEaOHEmfPn2Ijo726RDhL9PcaJijDcQxo6Oj6dixI9OnTycqKoq2bdvSr18/6tWrZ0gkgqhLIl5B5Jqm0ahRI/r168eCBQvo3r07nTp18smgu9Yws3uCeM3+QXFjxYui6zrHjh1j3bp1TJ8+nUOHDtG+fXueeeYZmjdvbujAgJHiez3ajYW7D+ageo/HQ/Xq1XniiSeYOHEiS5cuZfz48bes++zthL8kZ4aQFHJycsjIyGDt2rVIksSgQYMYMWIEDz/8sBH5Y87yMt+zm3HvzMkQ5uM89thjVKlShRYtWhATE2NETwjCNTvaS7oP4v0PCgpi0KBBLFq0iJSUFGJjYwkMDMTtdl/XRHJXRjWYNSZz4ztN0wzPpCzL5OXlsWnTJubOnUt2dja1atXimWeeoVu3bgQGBgL4hBWJfYt/73cL536BWa8UYyE3N5ff/va37Nq1i7/97W+0bdu2TM41XS9900Tv/m4PoZudzubPxHWKGgZbt25l0aJFrF+/Hl3XeeSRRxg6dCgNGzb0qeBlNnzM2jjcPH28JJ32ShKCmTOu9F3xe2HZejwe3njjDVasWMEHH3xAXFycT0betfDEXUe85lnLfOpmacDpdLJ//35SUlJYsmQJiqIwdOhQhg4dSo0aNW7XqVu4y7B582ZGjx5N27Zteffdd4mIiCj1SshLvKV7tSRJ5nYRL2DosGLFJ96x3Nxcfv75Z5YsWcLKlSsBiI+PZ/DgwTRt2tQoDHWvGShCohQTkM1m48cff+Spp56iTZs2/OUvfyE0NPSyULqy4K6VGswWqgiCFyUbRRLE4cOH6dmzJyNGjKBJkybY7XZD6L/XBouFG48WLVrw2GOPMWPGDFatWsXgwYPvuaak/rVGPB4PFy9eNCzcNWvWoCgKCQkJDBgwgIYNGxp9A6/knLoXIELlxEqocePG9OnTh7lz55KTk0P79u2v69rvOosX8OdQ4PQAACAASURBVBHHhVaTm5tLTk4Oc+bMYc2aNdSpU4cnn3ySnj17EhIS4tNexCpoY+HXIJbgBw8e5JVXXsHlcvHRRx9dFo965e3vHotXyHTnz59nx44drFq1irS0NJxOJ+3atSMpKYlWrVoZse/gqwHfaw5oc3KHWfPOyclh7NixtG/fnrfeeovQ0FDjd2XFXTd9++fZu91udu3axaJFi5g3bx52u51x48bx2GOP8cADD/h4V/0b31mwcDV4PB6ioqJ4/PHHmThxIosXL+aZZ57B4XDc1LjeW+nE0zSN3Nxctm/fTkZGBqmpqbhcLuLj4xk2bBjNmzc3wsKED8V8jneh3VYqmK9N6N316tVjyJAhJCcns337dmJjY6/5Od3xxGsu0WcuLi4KXKxatYqZM2dy+PBh2rVrx9NPP01MTIzhZBPwj1iwYOHXIBwxHTt2pEOHDkyZMoWOHTvSrFkznxTykiZzf+ea2bEjfvaOazEWdR9HcWlb11wJZotNjHlztI+maRQUFLBr1y6WLl1Keno6eXl5dOrUicTERNq2bWuQrFnHNZ/Tve6ANqcHy7JMUFAQffr0MSIcRDabeaIsbdfwO554hY4kvIeitkJWVhZTp05l8+bNNGrUiLfffptu3boRGhrqU1vhXtPkLNwamDOiIiIiGDNmDM888wwzZsygbt26BAYGGqupkmN8JXRdu6zYdlFREbIsGz4JAJfL69gSZGsuwHSt8CcDuEQkBQUFbNu2jWXLlpGeno7T6aRjx44MHDiQFi1aGEtogSuR671qwPgbZ4JDVFWlfv36DBw4kClTphAfH0/Xrl2NVbh41qXBHc1K4kJEOTfReTQ9PZ3k5GQARo8ezciRI6levbrhjRS4l2djCzcX/lJC69ateeyxx5g/fz6tW7c2HG1XjueUfAhZkKnD4TA+v3DhAmvWrOHs2fMEBATQunVrI1njRpy/+RqEhbtz504yMzNZvHgxx48fp127dgwbNowOHToY/QKt9vaXQ9zPoKAg+vbty8yZM5k1axZt27Y1nimUnnPuaOeaOXTs6NFjrFmzmhkzZnDgwAG6d+/Oiy++SN26dQ29Fy5v62FpuhauBeasR2GtHjp0iKSkJMqVK8cnn3xCzZo1L2v5JKCqHjRNxel0IkkSAQEBBhE6nUXoOqxbt45p06bRr19//vvf/3Lq1Cn+8pe/EBYWht1uv66x61FVtOIlsuj6kJ6ezsJFCzl96jQdOnQgMTGRNm3aEBgYaJQ8NbfWsYjXF4KL3G43b7/9NvPmzePDDz+kR48ePmnRpZm07miLFzCCt2fPns369euJjm7AO+/8hZ494wkNDcWjqjhdLmRJQpEVNF1HlkXkwu0+ewt3KwShelQVpVgTrVnzQR5//HH+/re/k5qayrhx467qMzh37hxz58xB1VQeffQxKlSowMmTJ0lJSSEwKIg9u3cTFRXFyJEjycjIYPLkyZw+fZqIiIirOK10ShsBUVhYyIEDB1i+fDkrV67k4MGDxMbGMmniJDp07EBoOa+kYA4Lu4PtsNsOEVoWEBBAUlISq1evZvbs2cTGxlKuXMgVs/5Kwm0jXrMmcumha0iSV5h2ulzs27ePmTNnkpaaSlhoOV54fjyP9O9HlSpVcbs1nG43uiSh4SVdXfegajpFRd6upHaHA9lmR5Z0dFWnqLAQHa/1IdtsqDpIqMjoKLLC7QzpsXAzcGWS0vXi8oayhKp7vydLMhKgazroOkigaxqSrKCqGmg6Q4YMJScnh6lTpxIXF0fjxo29+6GYrBXFuw2gyBKrli9j06ZNNGpQn249E9i89Sfe/fs/iY+Pp17dOhw9epBjx45y6tQpKleuTLly5a5oMem6hqp6vBMBgCQjeNImvq/r3nKnu3aybPkKFi1axPlzZ4ltFcuEFyfQvn17yoeVR0PHUyx/SFxe5ete1W8vQ/H90yUdjeIQVRQkXQINKPZ/qnjQ0ZEk8Hjc1Kv3MIMHD+Trr7/h+++/p0uXLui6Vvw81F/1Ld0W4jU7vwwPb3HWpKa5OXX6HOvXf8vs2bPZuXM7nTp25KmxT1DjgWps/mET237+GacG9Rs3Jza2HZUqRqJrHvbt3sWmTRv45eBhlMAA6jaIpk3bdlQKD2PnTz+x9YcfkWyBVKvxEM1bt8AeGIRD1pB0N7LDgYRFvvcOtOI/EsbbwyVHk6aroKug66jIaLrkXSkBmqojSxKaR0NBRtd07LINj6ZRoUI4Q4cNZc26tUybMZ1Jr04kPDzcS84e1fse6zqSphIZFkq3ju3JXL2Kjd9l0q5DZzZu2ooHO517JtCsUQM++/QjpkyZSmFhIcOGDSMyMvIqNQQ0NM2NpoOGjCzb0HUZ8E4UrqJCDv3yCxs3ZDEvJYVd+/bSsEEjJrzwHPE94gmtUAE0HbfLjSpJ6FJxm3RZRrqOLKy7FvqlP7qsokrFcqUuIWmKd/jooMkamqShaypoIr1bo1evXsyfn8LcuXNp1qw5ERUq4HJ7kErBIbeceP2Dk8XsLukqFy9e5PvNPzBr1jzWrltLVFQU7777N3p074pD0fnm669YnLKY3KJ8tu3ahaQEMen1yYx7cgxnT53k3b++w+bvN1GhUkXO5+VxJq+AP7/1NnEtW/HhBx/SumVrAoPtfPrpv3nh5Qm0aRPrPbaIdb+Pxtz9Cwm9mHRlGa80hY6GhI6OpotvySiyjNPpwllUgKIoBAQGgmqjWYuWDB48mClTptCtS1f69OmDpooohOIaBZIKkk7nTu2Z06AB2Ru/5+DBw/yYk0PlKlVpGtOEenWiePXVVzh08CARERHUr1//V3p76ciyd6gqioKOjIzMxYsXOXL4MBu+Xc/8OXM4fPAXGjVryvvv/522sW2pEBaOruk4Cy7iUVUKXS4Uux1bQCA2uwTc28V/SoPLpzp/Qih2ltpk0CVUVaNevfrFjrZZbNu2jY4dOgBSqdJmlMmTJ0++QedeKphnVRGx4HK52LN7NzOmTeOjTz7m2LETJI5M5LX/eY2WLVvgsNtwu5zYFYWEhHjGPj0WHUhdmo4kK/To1oW9O7fzlz+/xaABffn3559Qv0EDZs6aS40Ho7ArCsuWLuWNP/yRxk1imLdgIZUqV6ZFi6ZoqopNpljiuL0ZRBZuJIQ5I5n+gHfO11E1FVn2hnwhSYbEJSEhS4qRNJCZ+R3LlmWwefNmdF2jUpVKBAUHUbVKFVauXMmJ4yeIi4sjpLjztGwE3mugeYiIjGTP7j2sWfstYZEVWZKaQdv27Rg08BFCggKoWCGchx56iMqVK/sUq7lSLKiuq9htDnRkiopcHDp0mCVLlvDJRx+xMCWFB2tUZ/yzz/Dciy8S07QFQUHB6KqKpkNhURHzU1LIzPyOnTt3E1wumIoRkV6L974l3uKiWMUrAO+UK3ulBl0CSUeXQJe96yZd88qh3vhtGxEREaxcuZIzZ87SNi6OkJDgywpvlYRb7rYUkQrixI4cOcL0GdOZ+OpEpk6bQod27fnw4w/53e9+R82a1XG5XLicThSbjeatWtGgcRPCK1SkZvUalAstj8NmQ1c1QkOCiIwI58Tx4+zZuZuDBw4SERlBg+hoIiMrUT48nBMnj3PkyGGCgwOoUqUSuk6x46RY07Nwz0PTNFRNw6bYjPrLziInmlsD9VK3W6fTyc5du5kydQqSLONw2Hn//73Pnr170HWdOnXr8vQzz5Cdnc306dPxqCqSVJzhVUzmKAq2oCDadmiHy+Xik08+IS8vj9jYNpQrF4zH5eFiQQEuZ5FP52pB+v6QJNB1CafTw549e5k2dRovv/wyH330MUGBgbzxxp/450f/ZOjw4QQFhZKXl0d+fj6FLhcaOllZWcyfP5+qVatw4OAB/vXpvzhz+sx9TLp4b6phDCpckqV0kDwg6UiSjK4rxXxxqX+brms0aNCAgQMHkpaWyoasLK8xWYqSBDddajCnFpozXc6dO8dPP/3E7Nmz+S4zk9pRtfjTn96g/8BBBAQEoeng8WgoNgXd47UEdI8HCY3zeXlkfvsd6BpxcW2IrBBGeHAUSaMS+fKzrzh46CWOnjpLq3ad6NKlG+EhwXTo0IGUhQspF1qB2DatadEsRiwusXnvvYX7AnqxJKqjSDInT58gLTUNWbbTv/8AFJuD9PRlqKqOrkvY7HZGJT2O6nGzaMlCjh49SsNGjQHo378/y5dlMHfuXLp3605M0xg0/ZKzSlV1bIqNRtENadQomrSVa2nbuSctWrRAUWRkDSSbDdCLHcuKz2rQHy6Xm/2/7CcrK5ulqWls27aDqKgoJkx4kUEDBlApMhJ0F9v/+1+Wpi4l/2IhNsUBkkTnzp3ZuWsn0dHRDBs2jMrr1vPOe+9x4fx5aj5Q9bJj3eu4lEmoep1iqoykKGi616oFHWQdXVfRNC/5IoGG92dvJIiOotjo168f8+bNY/78BXRo35GwsFA0zRtddSXcMOI1B2ybnQMej8donQLeGLh9+/YZtRV0XWfMk08yIvExKlX2DgC9eIkoy6BpEpIio6samqTjKipi4fwFrMxYRcsWrenbrx8BgQ7ynTqVK1ekYsUIVBUkSeHEidPs23+Q9rHNefbZZ9m3Zw+KzUGtunUJCS2Hqnnnt/u5geH9Bm/2IyCpxSX/FH7cupWUeQuJiIxAsQXwp8lvEh/fm4SEPrhUlV9++QVd9RAUFERwSAiKLKEhE1EhgtGjRzNp0iSmTp1Kncl1CHA4UDWvwaBpOqpbpXqNmrSObc3KbzfQLi6OBvXroLk17DIokoyqe61wWVZ8WtkII8XtdnPy5Em+//57pk79P37ato2aD0bxu9+9Qt++fahcqSISOqpahKRrnD59ku8yszh69Bg7tu+koKiIT//1KZGVK7F9504OHz3K6dOnCQspR3Bg0O19ILcQZinH4/Fw7txZDuzfQ35uHrotiDr16lOpUiWQdJA1CgtyOXjoCEdOnKFWnbrUerA6uqbi8bjZuXMnFy7kExgYQFRUbQYOHMiMGTPZkJ1NfHx3NM0D+PZl88mGuxkXZU6dM+eJnzx5kjVr1jB//nwOHDhA69atGTduHM2bNy92TKiAV2ejeFklLBRZkfG4nKxasYqPP/4XtWrX5a233+Lhug+j6m5Wr1rLe+++z+DBA/nNy6+wLnMT41+axJdffU3DenWoWbkizVvHGufr0UGW8IYQWTLDfQNFkfF41GKNV6ZqlaoMHjSQNStW8eVnn6PYAgkJDiXx8ZHUf7gea9et4YuvviCifHm6dulM40aNUYtDsDRdo1OnTgwYMIB5c+fRt08f2rdvf6kgk80Oqge3201+QSEhISHExMQQFGhD9Wiga+h4w9QUxebzctpsNpxOJydPniQ7O5tFixaxefNmatV6iFd+N4mEPgnUKG5Z5VI9yOhIuoaqumkTF8uM2Bls2/YzTz/1DKHhYXTs1BlkiUWLFvP1119TUFDAsGFDqVKl0m18Grcebrcbm81Gfn4+U6ZMISNtCadOniTvokrXXv145eWXqFu7BidPHiF96ULS0lexcs13/P71N5jw4nhkICcnh48//ohatepw5MgRmjVrxoABA8nIWM7s2bNo3bolFSqEA75caMYNlRpKSptTFIXCwkIyMzOZPXs2GzduJDo6mj/+8Y90796d0NBQVFXF7XZityk+a35JojieUkb1uNmy+Qc++OcHKPZAXnl1Ei2aN8NVdBF7YCA7d+3iXN4F6tSuQ1jF6jSJUQkOKc/p0+fIv+hC10HzFHl53GYHqbiNtDiYFdVwX0BVvbG2cnG8pa7rxDRtTM/uXfjsi/9DlQMYN/55mjRpit1h5/kXnmfnz9sIdCg0i4khKLQcmqajyJKRQjp06FDWrFnDZ599Rv0GDahWtSoeTcPt9hDocLD/wC+sW7eWOrVr06xZE8DrW0ArLuivaWhcStPVNI0TJ04YRsrPP/9MVFQUL7/8Mj169KBWrVpoQJHbU6xXew0VCe/EosgK7kIP6UvTOHPuHM//ZgJRtaPwaDp/+NMfOHzoCJERkTRt3AT7fVTLRFRYA++qPCysPC+/8hKBAQ7e/9/PmfrNdBo3bMpvXhzDoUMHycu7QN26tVmbuRGn04Omarg8TlavXs0DD9Rg0qRJZGRkMGvWbPr168+AAQP4+ONP+PbbTPr164s5WsRc8xhuIPGKAWMu7uF0Otm3bx9paWnMmzcPl8tFUlISI0aMMBpMut1uFMW75POHJEnIioyEzsX8Ir755huyNmykVVwHNmRv5NvvtxBcLpChgwbSMrYNtWrVZnFaOodO5nLk+BkCA0Lo2q07kRUjvRlIkoQugyJJqJeKQlm4zyAheZc7gCibK2k6ISFB5BZ6UD0eLhYWUSHQQfXq1Ymq4R2rHnchHl1DojiNWJJRNa+DZdTIx3nnnXdYvXIlw0eOQEbCretoQHBwCImJI3iozsM8WLMmmgY2Y5JXkWwydsVuVNzLyclh6dKlbNiwgQoVKjB69GiGDh1K7dq10XVvOrCON6RJlry2iY7XoaepGpKuk/ntOpJnzaJzp87Ex8ej2GzomkbDho1o0rAxEuByenxi6e91aJpWXDtYN1rQ22x2NDWf+QuX48j80bsaUqFBg3q0atWQlSvWM2P2EhTFXuxkEzU37Kiqit1ux+Fw4PF46N27FwsWpLBg/gLatWtLRESEcVx/3FCpwZz9cvLkSdavX8+XX37J/v376dKlC88//zwxMTFGpXvAKIADlzu4dB2vsI2GTbETERFB+44d8GBj1aq1OJGoXDmSbl260LlLF/763nvMnDGTtWvXElGlBr+b+ArxfXtRLjgA1eNEkjTk4psH3iwln6gjC/c8ZFmUR9SQirN2tvywhZUrVtO//wC27zlARkYGfR8ZQPcenVE1cGoeJNzISCiKjKrpKJLidaTp3kLgAwYOIC0tjanTptGseXMaNW6MQ3KgqW6iatfm5YmT0JFxqcVx+ZqGIktIsh3N47Vwt27dyoIFC/juu++IjIxk3Lhx9O/fn5o1awIi8UhH03UkRcZhtxfLFTqSpBeTgofcCxf4v/+bQm5+PonDhxNWPpwiZxGK3Y7b7caDjCJJyIqErt4/lodwdimKNxPx1KnT7Ph5K7/8sp/M9d/SLi6OhIQENE0lODgYWfFQWFTonZyKuTO0XHnatGnDv//9b9LT09i5cxcNGzakSpXKlC8fypDBg/jiiy/YvHkz8fHxPtUVr1vjNc+S5pqkohPEli1bmDNnDqtXr+ahhx7irbfeonfv3oSHh19WfMSo9anrpogu3cgAEiZpUHAQf5j8ZrH2q6Ch4NZ1bDYZm6xgk2V69nqELl17ePUzuwOluDK+x61jk+1I0qU0UVmYusWxezpS8aEupUyWJW/d32q4nn5MNzJf/nqsGf9armUtmuLf6PBGXJd/TYErX5vIWBM/e6F6Pa9oKijIHD9+nLkLFmMLDuX5F3/LDz/mMHHi71mcMo+WzZtQMSICTddQZDuSpCOhICsio9ib7ebxeKhUuTLjn3uO3/zmN0ydNo3XX3+dwMAAZFlBQi4umiMjyTJ2SUZCwqPqXDhzhs0/bCUlZSHffvstYWFhjBo1iqFDh1KnTh2fe+lNSZZQJAU0rzUtSRKqroHmJXG7w8am79ezau23yIqdZRkZrF63lg6dOxMf3wubYvMStY73PSiWKe59aEYdb4+qISGxbdtPTHz1VfJz88nN99CsRScUSQdFQgVkXffeH03DLine+w7ExbXn3Lnz7N9/gKioKHr27En58uWRJOjRswcLUhYwc+YsWrVqZXCef53eayJecyM4c7TC3r17SUlJYdGiRdhsNp599lkeeeQRoqKi8Hg8RpowXHK6maMhANPS3/uDYnrZg0LKl3xCOqi6N67O7gjC7rj0ua6DTRHZJEqxFmYeaTK6dCnAvqRJpTQoqR5nWUjvZiz1/Lupms+rNDDfB+E8vRbyNe/neq/zsvFSjJL2e+kz3+/rmu7VaRWF48fPEBQcxtPPv0B04yZEVKrMCy88h6apFFw4R+WIMCTZS5iapmFTiotja6pPVTxN02jfoT29E3qTviyd7j2606VrV68koKvoqo6ieLPkdNXD2XPn2bAhi8WLF7N582aj5m+3bt1o1KjRZe10RLKRAeXSKNY9Gqomyj9KOILK06N3H9wuF4ePHUNVVZo0jUHSi7XpUiW13kvQjX91VNBBUWw0a9aEjz/5gKKCIpamrWPmzMVUjKzExP95gdBw0CQJXfJOrpLmJWtN8xbJGTp0mM8RvPHfKrVrRzF48CD+93//l+zsbBISEnC5XJdVmisz8ZYUNnb06FEyMzNJSUnh559/pl27djzxxBO0adPGOClBtP6hW1eLW7zaORjbF/+lSPLlL6QpPlcyZS9dDumyCaGs52T+vn9ER2lQWjIpC65kdV/LOZlDAktL3GZn642yeMtSxOVKx1MUGVn2aqTR0fX481t/JjAwEFmWefDBB5k8eTJOp9NYkpqP5d+63GyBi6pVOTk5TJs2jZiYGCpUqODVkCUJTdM5e/YUW7ZsIT09nfXr1xMaGsqAAQOMVungNWxKs8IQZ3WpqI6XGNq2jTM6SCiKgsvl8lmV3g967uXw8patOG46Lz8PSZJo1649oIAcSkrKcnbv3oXT6SRMCvQWS0L2Jq7gzRoUd0446sTkK8aD3W4nPj7eqNcbFxdHaGjoZbxXZuIVeoXb7SY3N5c9e/YwZcoUUlNTeeihh3j99dfp1q0bwcHBnD9//rJBWtKAEpZUWQaEMeC5NABLIpqyWkf+9XyvZ2K43vjgq1txZd+H/zX9GvzbvVzLvShpkr0elGUfJTk1hNZm7h/mcAQYzmFxzUFBQT77EGPU/5maDRFZlomJiSExMZF3332XFStWMGTIECRJIj8/n127djF37lwyMjKQJImBAweSlJRkSArm2iVlgfkchGUlSBcgICDAuOb7k3QvwZvYADt37mTdujXUrRtFgD2Q5OSlXLx4kaZNGxIaGszJU6fYv2cHOT/+l8LCQvbt28P69d8S3agelStXvownBKnruk5UVBRDhw7l888/Z9WqVQwYMADwXQFfUyF0t9vNnj17WLx4MTNmzCAnJ4caNWrQo0cP6tat6xXwTV19RQqkmYDNBZcVRblq4efSkKfwLvr/zrzMvRrEOdntdmw2mw/plGYf5oLYNpvNGPj+muTV9uG/KhD78b+W0kKSJOx2u7cMpullLssjFxOtw+Ewns+1WMxmX8D1vvzinMTPV5rMSzqO2+027q0wIPzJzhyZY5ZZxHbmF83/eLIsc/DgQX7/+9/jdrt57733cLlcLF26lBUrVuBwOOjevTsDBw4kJibGeDdKkrd+baViHls+/hJ8x60IZboWqejegLd2hqp65UhZkjjwywGmTptCenoq+XmFlA+tRK9ej/DEmCQeqFmJtWszePev7/DL/iMosgOJACIrhTNp0iv07t3beG7m1Zy434qicPToUcaNG0d4eDgffPABkZGRvobctRDvqVOnSE1NZfny5eTn5xutL8QAFXnmmqZRVFTkk1hhhjgRcyNKn9ul67jdblRVNYjcvJ0Z5hnen3jdbjdut/tXSU+cg3kCEAPXfzK50j78r0dcs9hHSTn4JV2T2I94UcR1iGVoaSC2N+uFLpfL6PV1NZjPR0wo5snyStdR0n7ECx8QEOBDXOL34vpKg8DAQOx2u8/2V3omJX0mSEicizkax0ywgsS8coMvMQqCtdlsxoQkvNfC77F582a2bNlCmzZtOHfuHDt37qRBgwb079+fVq1aERIS4tOmSuxH3CubzWZYquI67HY7drvd+L/o0ya2E+NWGCFmMihp9VXSCuZqn/3azyXtvyzHvJnQdbX4OGKcSeTlnWPv3r0UFTkJD69MVK3aBATa0TSdM2dPcODAHpxFGjabA00FWVGoXfshKlasaEx05jEknoH43Zdffsmnn37Kn/70JwYOHOgzKV4T8RYUFFBQUGAQjHjA/rvSdW9jSvGSmmWHkm/O5ds7nU5cLpdPZtyVlsslEZL/Psqy1DZbEmIf4vhX26akn1VVpbCw0Kfaf2mOL6BpmrdgUPE5lAbm+yH2Zb6OskBs7/F4M7GuXr6w5O3Fs9c0zZiExPZlJXKx/ZVWEld6zmJ74ew1j82S9gGX7qP5O+Z9CGNDvFh5eXlcuHCBoiJv8RuPx0NgYCChoaHGxCH2K17WgIAAH5IXpG6evMXqxWzdis/EtZgnA3FfZVk2jmueVGw2m89KU3wmjAbzefi3tRHbinshJgrzfRKf+a9uxeRr3pd5lWk+jpgwxIRpPlfzd8xyj3mSuSQRFUtnkpeEFVnG7rDjsAcgSTZ0DdweFVmSvN1sbHhjd0tYSZXEZ/4TitPp5ODBg0yYMIEKFSrw4YcfGoQty/K1RTWEhIQQEhJSqu9WrFjxWg5h4R6HKIYPZXNCmidgM/GWNfpE/CtQluObl5b+qyBN07hw4QIXLlwwrsvlcuF0Oo1JT5Ik3G43hYWFPpOYx+MxJmdB6mLVKL4nVk5Op9NYxYnfi88AY//miV6slswTiXC+CZgtNjPZiclOTBSCDM0TsLD8/X0c4nvmFYF4dv4EKu6hw+HA4XAY5O7xeIyJy3y8wMBAgoKCfFYuDofD0OiB4n3ZURQv8cpy8eohwIFNsSPJNhRk7HYH5YKCsNu9Re9lWcLmCCAoKAibwwYaRgEkIWsKiPMX98btdmO324mKiiI9PZ0tW7bQo0cP4/s3NF+wJIvV/PO1LC/M+7iWJYlZ1xIvS1l0rrLqqlfax43CrViW/Rr8ZYJrwbU2U7wbmpdWrlz5urb3H/NmshTEZba8S5Jr/FcQYhux8jNPWhcvXvQhf/NqwEz2ZlIVnwky9v+eOKaqeht+mrcV25lJW0xOZqlHTCbinRWrPvNkJyYefzmoYerPAAAAAk9JREFUsLDQ5154z6MIXVe9iSO6jsvtwuVW0TUJSQJddeMucqGq3mgGrbiouS6pqLoHWbs0SQiCNUsMZp+M+H9BQQFFRUUsXryYNm3aUL68NyT2uhIo/HE1Z4C/7lpanbKkQVWWF95snZiPX1r4k3VZiNh/OV5W4jc7S35NZrlVMOuG/p+Xdnvxr/layipZlPRcywrztZT2+CVdt//98N+vWWLx72tWkt5t/sy/i7F/IP6Vws7M/gEzgoODS3WddwLMFjVcbrEDPpPJlT7zkrKKy+XGW9jRm+WnqioeDUBBwoPm8aC6PWgq6JK3/q6qqjg9Rbg9TiRZRtEVY5Iwr348Ho8hBZonp4KCAhwOB6Gh3sai4rlds8VbloHqT5pl1QbNs3xZNVr/5eTVNOZf2xdcPvCvhtI4G0qzvfmeXev53yjC9n8G12r9Xuu1mJes1wJ/Pe5axqMZwhLzH+P+Roc50cL/9+bJyKxXmn9v/mO+fmHpleRrudoK1Az/52B2npY0GVxp0hPXWdJkar7H/pEcgE8yitmKNK9w/Jf3dzLEtZkjSsSk4W11diPXwWU8qbJ+91pe8uuxzsy4HtK6UXLFnSIzlEQa13puZd3e//tlvS83Qib5tf1fiXBK+r/5nK52XiWRnPnza71/V/qd/89X239J53ala7ravm7Es7nSPi59DqDhrTZbXCqA4hICxc0u0b191cw5V7rRjvjGcMFtIV4LFixYuJ9xP0ZTW7BgwcJthUW8FixYsHCLYRGvBQsWLNxiWMRrwYIFC7cY/x+BE5/3NVTX+AAAAABJRU5ErkJggg==)
Find the missing values
![](data:image/png;base64,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)
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7rGLr92i6EQLfAIgujtPrIqLzL2GKc/EMyKftsziRpmGQ4JCkBW4YjFgnh7e6hP2qdk2RtMIC/P9HlYoNQ0M9AZFRLMj37hSPcw7ZVD3DHt39Jfb+57yDrgz7qX/5v/u6aCzlv6c38ri50yncN+rsbWPvgd7n8/IVce8dK9gdSVqop2SwcMY7ufY2H73+ErYf9KA5zh0M43BSWTqW6LAdvRyu9Ax++AODMyKdiWhWT3UGOtPUSldcHhsVW4Qh0HmLT+o305VVRlqURM/lRlXC4KKqq4YLPnU2hR0XTTu39grTMfGrmL+LCmnIMQ5fXzobJNuHQfC3s2LCeg5kLua62gthA2DKdRdHjQ/BPS4iT95mk4bFHOLTj7K3bxOuHM7hh+UXk6GFiVkkGjIUBwJZkg3DodB/ay9a6o5y1bDmz8tNAUVBVB2n2GywsDYPlJzvpgXa2rXuC//rtbmY2eXld72Hvjm0cajH4xXd+zPJrb+Tq86fZYSshDZPlw4Erj3mXfpl7pvfhdLnQ+o/h8rfROgCLL7qQuRUFlgiGEIkmN4kTT5my/vM6R5rlw6GkZVJafS4lM+JDyfVAC76dL7OxycG5l32WSnNPOQBVRVEgFouine7EQxEYWhRNN1DMO0A2Jayw0fxEQsSfyxfqaWLtwz/mvifX8279Bv7jrofYdiSY6vI+Na2/h22rH+L7K59m1559PPPgv/Lky3X4NQANf+tuHnvoXu5dtZXmuhf4xY8eYON+b6rLNg3L7zlOlZ5bwmW3/oDFN92FUASK6iInLyPVZX1qijuXOUtu5cHFNwECoSi4PTl4FAAVT9F0rvnGD1nytbtREAhnGlk5ck3QobJVOBSHk+yCYqyy+J9QHGTm5JOZoL+rznTyCorJG92yLGMUDqsEQrHfqaCiKAih2HMFkBMXAMwuqXsO3TAIhwcJ9Q8Qi0WJRKy/yIAQAkUIBgb6iYTDhEIhorEY0Yg9hsSmpaUxGAoRiUZNf2MyqeFQFQW/z88zf1rLtq1vEtPssciAIhT6vF6ONB6hu7ubzZs2EY1af8MAoCoqPT09OBwOHA5zH7ULw0jeZN9IJEJrayve3l5bzaEG0GIag+FBXC4XTocTw/Tb0aEzDIPc3Fwqp05NdSlnJKnhgPgHleS3kMYgIYTpz7eSHg5JMit7HetI0jDIcEhSAjIckpSADIckJSDDIUkJyHBIUgIyHJKUgAyHJCUgwyFJCchwSFICMhySlIAMhyQl8P8FdlGU0mdbrwAAAABJRU5ErkJggg==)
The table above shows selected values for the function h . In the x y -plane, the graph of y = h(x) h is a line. What is the value of (8) ?
Note:
After finding the equation y = 2x + 3 , we can verify it by putting the third point in the equation and check if it lies on the line, that is, the third point which is lies on
So, the equation is the graph of
.
![](data:image/png;base64,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)
The table above shows selected values for the function h . In the x y -plane, the graph of y = h(x) h is a line. What is the value of (8) ?
Note:
After finding the equation y = 2x + 3 , we can verify it by putting the third point in the equation and check if it lies on the line, that is, the third point which is lies on
So, the equation is the graph of
.
A man reaches a spot from his home in 6 hrs by walking, but he can reach the same spot from his home within 2 hrs by cycle. If the given average cycling speed is 7km/hr faster than his average walking speed, then find the average cycling and walking speeds.
A man reaches a spot from his home in 6 hrs by walking, but he can reach the same spot from his home within 2 hrs by cycle. If the given average cycling speed is 7km/hr faster than his average walking speed, then find the average cycling and walking speeds.
Find the area of the following figure:
![](data:image/png;base64,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)
Find the area of the following figure:
![](data:image/png;base64,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)
Given a rectangular room whose width is 4/7 of its length y and perimeter z. Write down an equation connecting y and z. Calculate the length of the rectangular room when the given perimeter is 4400 cm.
Given a rectangular room whose width is 4/7 of its length y and perimeter z. Write down an equation connecting y and z. Calculate the length of the rectangular room when the given perimeter is 4400 cm.
A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm and 5.1 cm respectively. What is the volume of the clay required for the tile?
A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm and 5.1 cm respectively. What is the volume of the clay required for the tile?
Find the area of the given figure.
![](data:image/png;base64,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)
Find the area of the given figure.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAACACAYAAABA+ljwAAARIElEQVR4nO3de3BM9//H8edect9ImmRl3FL3bCWMUXEJipZSgoy61KWdqktp2khd41ahCCkyKWWK0ZRi3NpmVGmHqUqVQdDSusU1bsnI5rIJK9nd8/0jP/uTpt+vW3bP7snnMWNmZw/O+/Dy8dnPfi4qSZIkBEEB1HIXIAjVRYRZUAwRZkExRJgFxRBhFhRDhFlQDBFmQTFEmAXFEGEWFEOEWVAMEWYXVlpaitlslrsMt6GVuwChqvv377N06VIuXrxIYGAgU6ZMISwsTO6yXJ4IswvasmULxcXFLFy4EEmSCAkJqXS9qKiI48ePo9friYiIwGg0YrVaOX/+PK1atQLg1KlTtGrViuDgYDkeQRYqMWvOtZSVlTFs2DCGDx9OcHAw4eHh1KlTx37dZDIxefJkvLy8KCsrIy4ujvXr11NUVISPjw95eXmEh4dz+/Zt1Go1aWlp+Pn5yfhEziP6zC7m/v373Lx5k/3795OZmcmIESM4deqU/frevXuxWCysWLGClStX0qxZM27evEmvXr34/PPPyc/Pp0OHDqxatYobN25w48YNGZ/GuUQ3wwX5+/szceJEwsPDyc/P5+TJk7Ru3RqA69ev21tqDw8P+4+6deui0WjQ6/XUqVMHrVaLTqfDYrHI+ShOJVpmF6PT6dDr9Zw8edLeSr/wwgv26+Hh4Zw7d47i4mJOnz7N1atXsVgsWCwWJEniwYMHlV7bbDYZn8a5RJhdjEajISEhgV27dvHhhx/SvHlzXn31Vfv1nj17YjAYmDhxImvXrqW8vJyOHTtSu3ZtVCoVHTt2JDg4GJVKRadOnQgICJDxaZxLfAB0USUlJRQXF1O3bt1/vX7r1i1CQkLw9PR0cmWuS4RZUAzFfQA0m83k5eVhs9l48OABGo3G/iEpNDQUjUYjd4mCgyguzMePH2f48OGYzWbKy8tRq9VoNBoMBgM7d+5Er9fLXaLgIIoLc1BQED169MBoNJKRkUG9evXo1q0b9erVe+r+ZVZWFpcvX0atFp+Tn4XNZiMsLIz27ds75X6K7TPfvHmTxo0bExMTw86dO5/619tsNoYOHcqOHTvw8PCoUUNc1UWSJJo3b86uXbto2rSpw++nuJb5IavVClT8gT6rh38Bo0ePpmvXrvbfU3g8tVpNcnIyFy9eJC8vT4T5eTzvfzhqtZrp06eTkZFBVlYWqampeHt7V1N1yvfbb79x/vx54uLiiI6Odso9RWfwfwgMDCQhIYFjx46Rnp4udzluo7S0lJkzZ6LX64mLi3PafUWYH2PEiBG0b9+eJUuWkJOTI3c5bmH79u1kZmYybdo0mjRp4rT7ijA/hp+fH4mJiVy9epX169fLXY7Ly8/PJyUlhcjISN5++22n3luE+QkMGDCAPn36kJqayvnz5+Uux6UtW7aMs2fPsmDBgkoTpJxBhPkJqFQqpk+fTllZGStXrhTDdP9FdnY2X375JX369KFPnz5Ov78I8xN65ZVXGDZsGKtXr+bw4cNyl+NyJEli7ty5FBUVMXv2bDw8PJxegwjzU5g6dSq1atUiNTWV8vJyuctxKb/++is7duwgLi6Ojh07ylKDCPNTMBgMvPfee3z33Xf8+OOPcpfjMsrLy5k3bx7+/v7Ex8fLVocI81OaPn06DRo0YMmSJWJPi//zzTffcODAAWbNmuXUobh/EmF+Snq9nvj4eA4fPsyWLVvkLkd2+fn5LF68mMjISEaOHClrLSLMz2Ds2LG0bduWRYsWkZubK3c5slqxYgUXLlzgk08+kX16rQjzM/D392fy5MlkZ2fz1VdfyV2ObLKzs1m5ciW9evUiJiZG7nJEmJ9VbGwsr732Gl988QUXL16UuxxZJCcnU1RUxNy5c/Hx8ZG7HBHmZ+Xt7U1iYiJ37txh9erVcpfjdEeOHGHjxo2MHTuWDh06yF0OIML8XHr06MGQIUNYs2YNJ06ckLscp3nw4AGzZs1Cp9MxadIkVCqV3CUBIszPLSEhAbVaTWpqao2ZvL9r1y5++eUXpk6d6pRJ909KhPk5RUVFMXr0aDZt2sS+ffvkLsfhTCYTc+bMoWHDhowbN07ucioRYa4G8fHxhIaGsnz5csrKyuQux2EkSWL16tVcvHiRhQsXutx2uSLM1aBRo0Z89NFH/Pzzz2zfvl3uchwmJyeHlJQUoqOjiY2NlbucKkSYq8nYsWOJjIxkyZIlmEwmucupdjabjUWLFlFQUMDChQtdYijun0SYq4ler+fjjz/m9OnTilyRcvz4cdLT0xk5cqTTFqg+LRHmajRkyBA6depEamqqojb5Li8vJykpCa1Wy6xZs1x2izMR5mqk0+mYOXMm165dY+XKlXKXU2127drFnj17mDZtGs2bN5e7nP9KhLmavfHGG8TGxrJ27VrOnj0rdznPraCggKSkJBo1asSECRPkLud/EmGuZiqViilTpnD//n2Sk5OfezMauX399decPn2aOXPmyD4r7nFEmB0gOjqaUaNGsXXrVjIzM+Uu55ldvXqVJUuW0KlTJ4YOHSp3OY8lwuwAKpWKuLg4fHx8SElJkbucZ5aWlkZ+fj7z58/H19dX7nIeS7F7zcmtRYsWTJ48maSkJObNm0dkZKTbLIJVq9Xk5uayatUqBg0aRPfu3eUu6YmIMDvQ6NGj2bZtm31YS6VSuUUfWq1WU1ZWRkBAAImJiS4zK+5xRJgdqG7dunTp0oWcnBzWrVuHt7e3W4RZq9WybNkyLly4UOWoY1cmwuxgVquVkJAQBg4c6FY78O/evZtz58651e5N7vOn68YeHhbkTtxxbrbDW2az2czhw4dp0aIFoaGhAJw5c4ZDhw7h7e1N79697e8LwvNwaMt89+5dZs6cyahRo8jKygLg9u3bJCYm4ufnx5kzZ5g7d26V852Li4u5c+cONpsNm82GJEkUFxdTVFQEQGFhIcXFxY4sXXBDDm2ZzWYzgwYN4vbt2/bA7tu3j0aNGjFy5EhiYmIYMmQI165ds++Ek5WVxdKlSykpKSEuLo6QkBB27NhBYWEhRqORmJgYDh48iNFoJDk5mfDwcEc+guBGHNoy169fn+jo6EqzrC5fvkzt2rUB8PT0xMvLi9LSUqBioeRnn31G3759WbNmDe3atePatWscOHCAmTNnEhERQXp6OvPmzaNZs2Zs3rzZkeULbsbpoxn/HGtVqVT2cczi4mKMRiOdO3emTp06QMVSnaioKMLCwmjSpAlFRUXUq1ePJk2aiI2/hUqcMpohSZJ9WMpgMJCdnQ1U9J9tNpu9pfby8gIq+tpQ0VJLkmTvolitVvtri8XiFmO2gvM4tGW+fv06ixcv5q+//iItLY3CwkL69evHxo0biY+P5/r168TExNhHM/z9/enevTvz58+nUaNGdOnSBX9/fwICAgDw8fGhVq1aQMXc4YevBQEcHOaQkBDGjRvH+++/b//yICAggHXr1nH06FH0en2lo2gfHrdw6NAh7t27R4cOHdBoNLRu3RqAXr160bVrVwD69++v6JXQwtNzaJh9fX3tQXxUaGgo/fr1+9dfo1ar6dKlS6X3dDodAAEBAfZWOjAwsJqrFdyd+AZQUAwRZkExRJgFxRBhFhRDhFlQjBo9n9lsNrN582aOHDlCy5YtGTdunP2LG8H91OiWOS8vD5vNRu/evdm2bRt79uz515/3z1l9j05Yd8d5v0pVo1vmsLAwxowZA0BGRkaVc/2OHj3KqlWrsNls9OvXjwYNGrB582ZUKhWFhYVERUVx5swZTCYT8+fPl/UMPGcxm82o1Wo8PT3lLqWKGt0yA6xdu5bhw4dTUlJCz5497e+XlZWxdOlSunfvzurVq2nXrh2XLl3i3LlzzJo1C71ez/79+5k/fz5BQUH89NNPMj6F41mtVtLS0hg7diwjRoxg//79cpdURY0Pc8eOHRk8eDA6nY709HT7+/fu3aOgoICoqCj8/Px48cUXsVgsdO7cmdq1axMWFka7du2oXbs29evXr9IVURqLxUJERIR9im5KSkqV6QS3bt1i8+bNnDp1CoA7d+5w5coVvv32W0wmEzk5Ofa56Y5Qo7sZJSUltGjRgsjISIxGI9u3b2fy5MlAxVxrjUZDXl4eLVq0oKSkBLVabQ+tJEn2/rIkSW6zHP9ZeXl50aNHDwoKCjCbzbz00ktotf8fnytXrpCYmEidOnX4448/8Pf3Z8GCBfj4+GA2m9myZQsRERGcOXOGo0ePOmRznBod5uPHj7NhwwYCAgI4depUpUPMfX19GTp0KCkpKWzdupXOnTvj4+Njn8qq0WjsAX50TraSnTt3jmXLlrFnzx7S0tIqrTbPyMjAYDAwb948AEpLS7l58yazZ88mOjqa7t27M2PGDCZMmMC0adMcUl+NDnN0dDS1atXixo0bjB8/vsoSrHfffZeWLVtiNBrp0KEDWq2WHj16APDOO+/YRzXGjx9fI8LcvHlzFi1axODBg/n0009p164dDRo0ACpGhh7d7lar1aLT6QgMDESr1VK/fn2Cg4Px9vZ22K77NTrMnp6etGnThjZt2vzrdZVKRdu2bSu993DPtUfnUj+cyadkRUVFXLp0iWbNmhEYGIjJZKr0OaFp06ZkZmYyYMAAsrOzCQkJwWKxYLVakSQJs9lsf+2obcpqdJiFJ2e1Wtm2bRu5ubmUlpaSkJBAw4YN7ddjY2P5888/iY+Pp379+sTFxdGtWzeCgoIA6Nq1KzqdDk9Pz0pz2KuTCLPwRIKCgli0aBG5ubn4+vpW+d8oKCiI5cuXk5ubi16vR6vVMmnSJPv1hIQE+2tHnR8owiw8MbVabV9o/CzXHa3GjzMLyiHCLCiGCLOgGCLMgmKIMAuKIcIsKIYIs6AYIsyCYogwC4ohwiwohgizoBgizMK/cse9r0WYhX/ljosNRJgFxRBhFhRDhNkJVCqV22379egJYe5CsZPzH64clrvv93D3o927d+Pj4+MWZ1F7eXm55UleigtzeXk5JpOJu3fv2hdSFhQUABULT519GLtGo8FoNNK/f3+n3rc6uNt2YyrJHcdg/oeDBw/y5ptvUlpayv3794GKM1EMBgO7d++2H9PmLH///TdXrlxx+j+i5yVJEn5+frRv3x5vb2+5y3kiigvzrVu32L17N1arFa1Waz9HMDg4mH79+jlszwZBfooLs1BzKa7PrCR5eXmcPn0anU5HmzZt8PDwkLsklybC7KJMJhNpaWlIkkRmZiaDBw+utBeeUJXoZrgoq9XKvXv38Pf3Z9OmTXz//fds27bNPtQoSRLp6ekcPnyYiIgIxowZw4EDB7hz5w4nT55k5MiRnD17lqysLEaNGsXLL78s8xM5nnt9xK5BNBoNJSUlbN++nR07djBw4MBKY+YZGRn88MMP9OnTB19fX0wmk31HoQYNGvDBBx9gMpkICgpi6dKlit8/GkQ3w6XduHGDkydP4unpSWFhIRaLxb4n8t69e+nbty+xsbFAxcaGISEh9nPKf//9d8aPH8/169eZNGkSZrPZfmyzUokwu7CoqCiioqK4evUqQ4YMoVevXjRu3BioOCTonz1EtVqN1WqlvLwcT09PLBYLFovF7ca4n5UIs4syGo2kp6fTuHFjTpw4Yd/f+KHXX3+dDRs24O/vT05ODm+99ValcD/82lySJLf4Cr06aJKSkpLkLkKoSq1Wc+HCBY4dO4aXlxczZswgNDTUft1gMFBWVsaxY8do1aoVrVu3xs/PD4PBgJeXFwEBAYSHh+Ph4UFQUBAGg8EtJw89DTGaIShGzehMCTWCCLOgGCLMgmKIMAuKIcIsKIYIs6AYIsyCYogwC4ohwiwohgizoBgizIJiiDALiiHCLCjGfwCsUhl0Ha8l9QAAAABJRU5ErkJggg==)
Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.
Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.
A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.
A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.
The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where
.
![M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50](data:image/png;base64,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)
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?
Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e ., on the left side
and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.
The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where
.
![M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50](data:image/png;base64,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)
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?
Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e ., on the left side
and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.