The most popular questions on the topic of general

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150.\u003Cbr />\u003Cbr />\\textbf{Answer:} The simple discount is

$150.",938,188,"definition-of-simple-discount-and-examples",{"id":44,"category":36,"text_question":45,"photo_question":38,"text_answer":46,"step_text_answer":8,"step_photo_answer":8,"views":47,"likes":48,"slug":49},535201,"For each function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. y=xcubed-2","answer:\nThe points on the graph where the tangent line is horizontal are precisely the points where first derivative is 0.\nHere, we have \u003Cmath-field read-only>f(x)=x^3 - 2\u003C/math-field>\nSo, \u003Cmath-field read-only>f'(x)=3x^2\u003C/math-field>\n\u003Cmath-field read-only>f'(x)=0\u003C/math-field> implies \u003Cmath-field read-only>3x^2=0\u003C/math-field> which is possible only when \u003Cmath-field read-only>x=0\u003C/math-field>.\nTherefore, \u003Cmath-field read-only>x=0\u003C/math-field> is the only point on the graph of \u003Cmath-field read-only>f(x)=x^3 - 2\u003C/math-field> where the tangent line is horizontal.",313,63,"for-each-function-find-the-points-on-the-graph-at-which-the-tangent-line-is-horizontal-if-none-exist-state-that-fact-y-xcubed-2",{"id":51,"category":36,"text_question":52,"photo_question":38,"text_answer":53,"step_text_answer":8,"step_photo_answer":8,"views":54,"likes":55,"slug":56},535200,"Of a test with 27 questions, 90% were correct. How many questions were there in total?","Let's denote the total number of questions as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />Given that 90% of the questions were correct, we can write the equation:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 0.90x = 27 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Solving for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{27}{0.90} \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 30 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Therefore, there were a total of$ \\boxed{30}

$questions in the test.",362,72,"of-a-test-with-27-questions-90-were-correct-how-many-questions-were-there-in-total",{"id":58,"category":36,"text_question":59,"photo_question":38,"text_answer":60,"step_text_answer":8,"step_photo_answer":8,"views":61,"likes":62,"slug":63},535199,"If 1.15 fluid ounces of vinegar are needed to prepare 1.54 pints of sauce. How much vinegar is needed to make 2.55 pints of sauce?","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$ \\frac{x}{2.55}=\\frac{1.15}{1.54}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba(0, 0, 0, .3);\nbox-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$ x=1.90422…

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1084,217,"if-1-15-fluid-ounces-of-vinegar-are-needed-to-prepare-1-54-pints-of-sauce-how-much-vinegar-is-needed-to-make-2-55-pints-of-sauce",{"id":65,"category":36,"text_question":66,"photo_question":38,"text_answer":67,"step_text_answer":8,"step_photo_answer":8,"views":68,"likes":69,"slug":70},535198,"Juan bought 2 pounds of seed for .63, how many pounds can he buy for$ 5.94?","Primero necesitamos encontrar cuánto cuesta 1 libra de semilla:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{0.63}{2} = 0.315\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Entonces, Juan puede comprar 1 libra de semilla por

$0.315.\u003Cbr />\u003Cbr />Ahora, queremos saber cuántas libras puede comprar con$ 5.94:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{5.94}{0.315} \\approx 18.857\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Por lo tanto, Juan podrá comprar aproximadamente 18.857 libras de semilla por

$5.94.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{18.857}\u003C/math-field>\u003C/math-field> libras.",898,180,"juan-bought-2-pounds-of-seed-for-63-how-many-pounds-can-he-buy-for-5-94",{"id":72,"category":36,"text_question":73,"photo_question":38,"text_answer":74,"step_text_answer":8,"step_photo_answer":8,"views":75,"likes":76,"slug":77},535197,"A rectangular waterbed is 8 ft long, 6 ft wide, and 2 ft tall.\r\n\r\nHow many gallons of water are needed to fill the waterbed?\r\n\r\nAssume 1 gallon is 0.13 cu ft. Round to the nearest whole gallon.","\u003Cmath-field read-only> Volume=8\\times6\\times2=96\\:cubic\\:ft \u003C/math-field>\n\u003Cmath-field read-only> 0.13\\:cu\\:ft=1\\:gallon \u003C/math-field>\n\u003Cmath-field read-only> 1\\:cu\\:ft=\\frac{1}{0.13}\\:gallon \u003C/math-field>\n\u003Cmath-field read-only> 96\\:cu\\:ft=\\frac{96}{0.13}=738\\:gallon \u003C/math-field>\ntotal gallon = 738",1381,276,"a-rectangular-waterbed-is-8-ft-long-6-ft-wide-and-2-ft-tall-how-many-gallons-of-water-are-needed-to-fill-the-waterbed-assume-1-gallon-is-0-13-cu-ft-round-to-the-nearest-whole-gallon",{"id":79,"category":36,"text_question":80,"photo_question":38,"text_answer":81,"step_text_answer":8,"step_photo_answer":8,"views":82,"likes":83,"slug":84},535196,"Summer Co. expects to pay a dividend of$ 4.00 per share—one year from now—out of earnings of

$7.50 per share. If the required rate of return on the stock is 15 percent and its dividends are growing at a constant rate of 10 percent per year, calculate the present value of growth opportunities for the stock (PVGO).\n\n(Hint 1: b =1- Dividend/Earnings)\n\n(Hint 2: you will need to re-arrange g=ROE x b to get ROE!)\n\n \nGroup of answer choices\n$ 50\n

$80\n$ 30\n

$26","**Step 1: Calculate Retention Ratio**\u003Cbr>Given formula:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b = 1 - \\frac{D}{E}\u003C/math-field>\u003C/math-field> \u003Cbr>Given values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D = \\\u003C/math-field>\u003C/math-field> (D1)\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E = \\\u003C/math-field>\u003C/math-field> \u003Cbr>Substitute values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b = 1 - \\frac{4.00}{7.50}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b = 1 - 0.5333\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b \\approx 0.4667\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>**Step 2: Calculate Return on Equity (ROE)**\u003Cbr>Given relationship:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g = ROE \\times b\u003C/math-field>\u003C/math-field> \u003Cbr>Given growth rate:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g = 10\\%\u003C/math-field>\u003C/math-field> or 0.10\u003Cbr>Substitute retention ratio:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.10 = ROE \\times 0.4667\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>ROE = \\frac{0.10}{0.4667}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>ROE \\approx 0.214\u003C/math-field>\u003C/math-field> or \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>21.4\\%\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>**Step 3: Calculate Stock Price ( \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> )**\u003Cbr>Using Gordon Growth Model:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\frac{D_1}{r - g}\u003C/math-field>\u003C/math-field> \u003Cbr>Given values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_1 = \\\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 15\\%\u003C/math-field>\u003C/math-field> or 0.15\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g = 10\\%\u003C/math-field>\u003C/math-field> or 0.10\u003Cbr>Substitute values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\frac{4.00}{0.15 - 0.10}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\frac{4.00}{0.05}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>**Step 4: Calculate PVGO**\u003Cbr>Using PVGO formula:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PVGO = P - \\frac{E}{r}\u003C/math-field>\u003C/math-field> \u003Cbr>Given values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E = \\\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 15\\%\u003C/math-field>\u003C/math-field> or 0.15\u003Cbr>Substitute values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PVGO = 80.00 - \\frac{7.50}{0.15}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PVGO = 80.00 - 50.00\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PVGO = \\\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Answer:\u003Cbr>The present value of growth opportunities (PVGO) for the stock is approximately$ 30.",666,133,"summer-co-expects-to-pay-a-dividend-of-4-00-per-share-one-year-from-now-out-of-earnings-of-7-50-per-share-if-the-required-rate-of-return-on-the-stock-is-15-percent-and-its-dividends-are-growing-at",{"id":86,"category":36,"text_question":87,"photo_question":38,"text_answer":88,"step_text_answer":8,"step_photo_answer":8,"views":89,"likes":90,"slug":91},535195,"You have a rectangular space where you plan to create an obstacle course for an animal. The area of the rectangular space is represented by the expression 6x2 − 16x. The width of the rectangular space is represented by the expression 2x.\n\nPart A: Write an expression to represent the length of the rectangular space. Then simplify your expression. Show all your work.

$6 points$ \n\nPart B: Prove that your answer in part A is correct by multiplying the length and the width of the rectangle. Show all your work.

$4 points$ ","**Part A:**\n\nThe expression for the length of the rectangular space is:\n\n\u003Cmath-field read-only>\\frac{6x^2 - 16x}{2x}\u003C/math-field>\n\nTo simplify this expression, we can factor out 2x from the numerator and cancel it with the denominator. We get:\n\n\u003Cmath-field read-only>\\frac{2x

$3x - 8$ }{2x}\u003C/math-field>\n\n\u003Cmath-field read-only>3x - 8\u003C/math-field>\n\nTherefore, the simplified expression for the length of the rectangular space is:\n\n\u003Cmath-field read-only>3x - 8\u003C/math-field>\n\n**Part B:**\n\nTo prove that our answer in part A is correct, we need to multiply the length and the width and check if we get the same expression as the area. Using the expressions we found, we have:\n\n\u003Cmath-field read-only>

$3x - 8$

$2x$ \u003C/math-field>\n\nTo multiply these expressions, we need to use the distributive property. We get:\n\n\u003Cmath-field read-only>6x^2 - 16x - 16x + 64\u003C/math-field>\n\nTo simplify this expression, we can combine the like terms. We get:\n\n\u003Cmath-field read-only>6x^2 - 32x + 64\u003C/math-field>\n\nThis is the same expression as the area, so we have proved that our answer in part A is correct.",1184,237,"you-have-a-rectangular-space-where-you-plan-to-create-an-obstacle-course-for-an-animal-the-area-of-the-rectangular-space-is-represented-by-the-expression-6x2-16x-the-width-of-the-rectangular-space",{"id":93,"category":36,"text_question":94,"photo_question":38,"text_answer":95,"step_text_answer":8,"step_photo_answer":8,"views":96,"likes":97,"slug":98},535194,"f

$x-1$ if f

$x$ = -5x+8","Given function f

$x$ = -5x + 8.\u003Cbr />\u003Cbr />To find f

$x-1$ , we substitute

$x-1$ in place of x in the function f

$x$ .\u003Cbr />\u003Cbr />Therefore, f

$x-1$ = -5

$x-1$ + 8.\u003Cbr />\u003Cbr />Simplify the expression:\u003Cbr />\u003Cbr />f

$x-1$ = -5x + 5 + 8.\u003Cbr />\u003Cbr />Combine like terms:\u003Cbr />\u003Cbr />f

$x-1$ = -5x + 13.\u003Cbr />\u003Cbr />Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{f

$x-1$ = -5x + 13}\u003C/math-field>\u003C/math-field>.",1372,274,"f-x-1-if-f-x-5x-8",{"id":100,"category":36,"text_question":101,"photo_question":38,"text_answer":102,"step_text_answer":8,"step_photo_answer":8,"views":103,"likes":104,"slug":105},535193,"What is the equivalent fraction of 7/10 with a denominator of 20","\u003Cmath-field read-only> \\frac{7}{10}\\times\\frac{2}{2}=\\frac{14}{20} \u003C/math-field>",962,192,"what-is-the-equivalent-fraction-of-7-10-with-a-denominator-of-20",{"id":107,"category":36,"text_question":108,"photo_question":38,"text_answer":109,"step_text_answer":8,"step_photo_answer":8,"views":110,"likes":111,"slug":112},535192,"I have 20 apples and pears and my pears are 2 more than the apples how many apples and pears do I have","Let, I have x apples \nThen, i have pears

$x+2$ \nThe , x+

$x+2$ =20\ni.e. 2x+2=20\ni.e. 2x=18\ni.e. x=9\nThen, I have 9 apples\nAnd 11 pears",999,200,"i-have-20-apples-and-pears-and-my-pears-are-2-more-than-the-apples-how-many-apples-and-pears-do-i-have",{"id":114,"category":36,"text_question":115,"photo_question":38,"text_answer":116,"step_text_answer":8,"step_photo_answer":8,"views":117,"likes":118,"slug":119},535191,"How many six-digit numbers are there that are odd and have at least one zero?","Riješenje:\n\n Broj 6-znamenkastih brojeva koji su neparni i imaju barem jednu nulu jednak je broju 6-znamenkastih brojeva koji su neparni minus broj 6-znamenkastih brojeva koji su neparni i nemaju nulu.\n\n Pronalaženje broja 6-znamenkastih brojeva koji su neparni, prva znamenka mora biti neparan broj. Stoga su jedine opcije za prvu znamenku 1, 3, 5, 7 i 9. U međuvremenu, za ostalih 5 znamenki, sve mogu biti bilo što između 0 do 9. Prema tome, broj 6-znamenkastih brojeva koji su neparan je jednako\n \u003Cmath-field read-only> n\\lijevo

$neparno\\desno$ =5\\cdot10\\cdot10\\cdot10\\cdot10\\cdot10 \u003C/math-field>\n \u003Cmath-field read-only> n\\lijevo

$neparno\\desno$ =500000 \u003C/math-field>\n\n U međuvremenu, za broj šesteroznamenkastih brojeva koji su neparni i nemaju nulu, prva znamenka i dalje mora biti neparan broj. Međutim, za preostalih 5 znamenki, sve mogu biti samo između 1 i 9, jer nijedna znamenka ne može biti nula. Stoga je broj 6-znamenkastih brojeva koji su neparni i nemaju nulu jednak\n \u003Cmath-field read-only> n\\lijevo

$neparno\\:i\\:ne\\:nula\\desno$ =5\\cdot9\\cdot9\\cdot9\\cdot9\\cdot9 \u003C/math-field>\n \u003Cmath-field read-only> n\\lijevo

$neparno\\:i\\:ne\\:nula\\desno$ =295245 \u003C/math-field>\n\n Stoga je broj 6-znamenkastih brojeva koji su neparni i imaju barem jednu nulu jednak\n \u003Cmath-field read-only> n\\lijevo

$neparno\\:i\\:najmanje\\:jedan\\:nula\\desno$ =n\\lijevo

$neparno\\desno$ -n\\lijevo

$neparno\\:i\\:ne\\:nula\\ desno$ \u003C/math-field>\n \u003Cmath-field read-only> n\\lijevo

$neparno\\:i\\:najmanje\\:jedan\\:nula\\desno$ =500000-295245 \u003C/math-field>\n \u003Cmath-field read-only> n\\lijevo

$neparno\\:i\\:najmanje\\:jedan\\:nula\\desno$ =204755 \u003C/math-field>\n\n Odgovor: 204755",1191,238,"how-many-six-digit-numbers-are-there-that-are-odd-and-have-at-least-one-zero",{"id":121,"category":36,"text_question":122,"photo_question":38,"text_answer":123,"step_text_answer":8,"step_photo_answer":8,"views":124,"likes":125,"slug":126},535190,"factorize completely: 12x^2 - x -6","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba

$0, 0, 0, .3$ ;\nbox-shadow: 0 0 0 rgba

$0, 0, 0, .2$ \n\" read-only>

$12{x}^{2}+8x-9x-6$ \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba

$0, 0, 0, .3$ ;\nbox-shadow: 0 0 0 rgba

$0, 0, 0, .2$ \n\" read-only>

$4x \\times \\left( 3x+2 \\right)-9x-6$ \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba

$0, 0, 0, .3$ ;\nbox-shadow: 0 0 0 rgba

$0, 0, 0, .2$ \n\" read-only>

$4x \\times \\left( 3x+2 \\right)-3\\left( 3x+2 \\right)$ \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba

$0, 0, 0, .3$ ;\nbox-shadow: 0 0 0 rgba

$0, 0, 0, .2$ \n\" read-only>

$\\left( 3x+2 \\right) \\times \\left( 4x-3 \\right)$ \u003C/math-field>\n \u003Cbr>\n \u003C/div>",475,95,"factorize-completely-12x-2-x-6",{"id":128,"category":36,"text_question":129,"photo_question":38,"text_answer":130,"step_text_answer":8,"step_photo_answer":8,"views":131,"likes":132,"slug":133},535189,"find the values of x that satisfy the absolute inequality | 5 - X | ≤ 2","To solve the absolute inequality \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|5 - x| \\leq 2\u003C/math-field>\u003C/math-field>, we need to consider two cases, one for when the expression inside the absolute value is positive and one for when it is negative.\u003Cbr />\u003Cbr />Case 1: When \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 - x \\geq 0\u003C/math-field>\u003C/math-field>

$i.e., \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 \\geq x\u003C/math-field>\u003C/math-field>$ \u003Cbr />In this case, the absolute value expression \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|5 - x|\u003C/math-field>\u003C/math-field> simplifies to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 - x\u003C/math-field>\u003C/math-field>, so the inequality becomes:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 - x \\leq 2\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Solving for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 - x \\leq 2\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-x \\leq -3\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\geq 3\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Case 2: When \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 - x \u003C 0\u003C/math-field>\u003C/math-field>

$i.e., \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 \u003C x\u003C/math-field>\u003C/math-field>$ \u003Cbr />In this case, the absolute value expression \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|5 - x|\u003C/math-field>\u003C/math-field> simplifies to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-

$5 - x$ \u003C/math-field>\u003C/math-field> or \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-

$5 - x$ \u003C/math-field>\u003C/math-field>, so the inequality becomes:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-

$5 - x$ \\leq 2\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Solving for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-

$5 - x$ \\leq 2\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-5 + x \\leq 2\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\leq 7\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Therefore, the values of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> that satisfy the absolute inequality \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|5 - x| \\leq 2\u003C/math-field>\u003C/math-field> are \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\geq 3\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\leq 7\u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{3 \\leq x \\leq 7}\u003C/math-field>\u003C/math-field>",1459,292,"find-the-values-of-x-that-satisfy-the-absolute-inequality-5-x-2",{"id":135,"category":36,"text_question":136,"photo_question":38,"text_answer":137,"step_text_answer":8,"step_photo_answer":8,"views":138,"likes":139,"slug":140},535188,". Calculate the equations of the tangent lines drawn from the point P

$-2,7$ to the\n circumference x2 + y2 + 2x -8y +12 = 0. Graphically represent the respective\n equations.","Primero, vamos a encontrar la ecuación de la circunferencia dada:\u003Cbr>\u003Cbr>La ecuación de la circunferencia es de la forma \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 + y^2 + 2x - 8y + 12 = 0\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Completamos el cuadrado para escribir la ecuación de la circunferencia en su forma estándar:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 + 2x + 1 + y^2 - 8y + 16 = 5\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>

$x + 1$ ^2 +

$y - 4$ ^2 = 5\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Entonces, el centro de la circunferencia es \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C

$-1, 4$ \u003C/math-field>\u003C/math-field> y su radio es \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\sqrt{5}\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Para encontrar las ecuaciones de las rectas tangentes desde el punto \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P

$-2,7$ \u003C/math-field>\u003C/math-field> a la circunferencia, primero encontraremos el punto de tangencia en la circunferencia, que se encuentra en la recta que une el centro de la circunferencia con el punto \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P

$-2,7$ \u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>La pendiente de la recta que une el centro de la circunferencia con el punto \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P

$-2,7$ \u003C/math-field>\u003C/math-field> es:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>m = \\frac{7 - 4}{-2 + 1} = \\frac{3}{-1} = -3\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>El punto medo entre el centro de la circunferencia y el punto \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P

$-2,7$ \u003C/math-field>\u003C/math-field> está dado por:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M\\left

$\\frac{-1-2}{2}, \\frac{4+7}{2}\\right$ = M

$-\\frac{3}{2}, \\frac{11}{2}$ \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Hallamos la ecuación de la recta que pasa por los puntos \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P

$-2,7$ \u003C/math-field>\u003C/math-field> y \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M

$-\\frac{3}{2},\\frac{11}{2}$ \u003C/math-field>\u003C/math-field> para encontrar el punto de tangencia en la circunferencia:\u003Cbr>\u003Cbr>La ecuación de la recta es:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y - 7 = -3

$x + 2$ \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -3x -6 +7\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -3x +1\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Reemplazamos la ecuación de la recta en la ecuación de la circunferencia para encontrar el punto de tangencia:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>

$-1$ ^2 +

$1$ ^2 + 2*

$-1$ -8*1 +12 = 0\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 + 1 - 2 - 8 + 12 = 0\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2 + 6 = 0\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Esto es falso, por lo tanto, no existe punto de tangencia entre la recta y la circunferencia. Por lo tanto, las ecuaciones de las rectas tangentes trazadas desde el punto P

$-2,7$ a la circunferencia \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 + y^2 + 2x -8y +12 = 0\u003C/math-field>\u003C/math-field> no existen.\u003Cbr>\u003Cbr>\\textbf{Respuesta:} No hay rectas tangentes trazadas desde el punto P

$-2,7$ a la circunferencia \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 + y^2 + 2x -8y +12 = 0\u003C/math-field>\u003C/math-field> .",779,156,"calculate-the-equations-of-the-tangent-lines-drawn-from-the-point-p-2-7-to-the-circumference-x2-y2-2x-8y-12-0-graphically-represent-the-respective-equations",{"id":142,"category":36,"text_question":143,"photo_question":38,"text_answer":144,"step_text_answer":8,"step_photo_answer":8,"views":145,"likes":146,"slug":147},535187,"A forest ranger sights a fire to the South. A second ranger, 8 miles East of the first ranger, also sights the fire. The bearing from the second ranger to the fire is S 33

$degrees$ . How far is the first ranger from the fire?","Let's denote the position of the first ranger as point A, the position of the fire as point F, and the position of the second ranger as point B.\u003Cbr>\u003Cbr>Given:\u003Cbr>AB = 8 miles\u003Cbr>Angle FBA = 33 degrees\u003Cbr>\u003Cbr>To find the distance between the first ranger

$A$ and the fire

$F$ , denoted as AF, we can use trigonometry.\u003Cbr>\u003Cbr>We first find the length of side BF using the cosine rule:\u003Cbr>cos

$33 degrees$ = BF / AB\u003Cbr>BF = AB * cos

$33 degrees$ \u003Cbr>BF = 8 * cos

$33 degrees$ \u003Cbr>\u003Cbr>Next, we can use the sine rule to find the distance AF:\u003Cbr>sin

$33 degrees$ = AF / BF\u003Cbr>AF = BF * sin

$33 degrees$ \u003Cbr>\u003Cbr>Calculating the values:\u003Cbr>BF = 8 * cos

$33 degrees$ \u003Cbr>BF ≈ 8 * 0.8387\u003Cbr>BF ≈ 6.71 miles\u003Cbr>\u003Cbr>AF = BF * sin

$33 degrees$ \u003Cbr>AF ≈ 6.71 * 0.5446\u003Cbr>AF ≈ 3.65 miles\u003Cbr>\u003Cbr>Therefore, the first ranger is approximately 3.65 miles away from the fire.\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{AF \\approx 3.65 \\text{ miles}}\u003C/math-field>\u003C/math-field>",334,67,"a-forest-ranger-sights-a-fire-to-the-south-a-second-ranger-8-miles-east-of-the-first-ranger-also-sights-the-fire-the-bearing-from-the-second-ranger-to-the-fire-is-s-33-degrees-how-far-is-the-fir",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":153,"slug":154},535186,"Scores on a test have mean 70 and standard deviation 15. Let x denote a student’s score on this test. The professor wants to adjust the scores so that they have mean 75 and standard deviation 12. Let y denote a student’s adjusted score. y is related to x by y = a + bx, and the professor wants to find a and b so that the adjusted scores have the correct mean and standard deviation. What does a have to be?","\u003Cmath-field read-only>E

$a+bX$ =75\u003C/math-field>\n\u003Cmath-field read-only>E

$a$ +bE

$X$ =75\u003C/math-field>\n\u003Cmath-field read-only>a+70b=75\u003C/math-field>\n\u003Cmath-field read-only>70b=75-a\u003C/math-field>\nand\n\u003Cmath-field read-only>Var

$a+bX$ =12^2\u003C/math-field>\n\u003Cmath-field read-only>b^2Var

$X$ =144\u003C/math-field>\n\u003Cmath-field read-only>b^2

$15$ ^2=144\u003C/math-field>\n\u003Cmath-field read-only>b^2=\\frac{144}{225}\u003C/math-field>\n\u003Cmath-field read-only>b=\\frac{12}{15}\u003C/math-field>\n\u003Cmath-field read-only>b=\\frac{4}{5}\u003C/math-field>\nthen\n\u003Cmath-field read-only>70b=75-a\u003C/math-field>\n\u003Cmath-field read-only>56=75-a\u003C/math-field>\n\u003Cmath-field read-only>a=19\u003C/math-field>\n\ntherefore, \u003Cmath-field read-only>a=19\u003C/math-field> and \u003Cmath-field read-only>b=\\frac{4}{5}\u003C/math-field>",551,110,"scores-on-a-test-have-mean-70-and-standard-deviation-15-let-x-denote-a-student-s-score-on-this-test-the-professor-wants-to-adjust-the-scores-so-that-they-have-mean-75-and-standard-deviation-12-let",{"id":156,"category":36,"text_question":157,"photo_question":38,"text_answer":158,"step_text_answer":8,"step_photo_answer":8,"views":159,"likes":160,"slug":161},535185,"at constant temperature. What should be the volume of a sample of gas that is initially at 2 atm pressure and occupies a volume of 1L if the pressure is doubled?","To find the new volume of the gas when the pressure is doubled, we can use Boyle's Law: \u003Cbr>\u003Cbr>Boyle's Law states: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_1V_1 = P_2V_2\u003C/math-field>\u003C/math-field> where \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_1\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_1\u003C/math-field>\u003C/math-field> are the initial pressure and volume, and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_2\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_2\u003C/math-field>\u003C/math-field> are the final pressure and volume. Since the temperature is constant, we can use Boyle's Law. \u003Cbr>\u003Cbr>Given:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_1 = 2\u003C/math-field>\u003C/math-field> atm \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_1 = 1\u003C/math-field>\u003C/math-field> L\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_2 = 2 \\times P_1 = 2 \\times 2 = 4\u003C/math-field>\u003C/math-field> atm\u003Cbr>\u003Cbr>Let's substitute the values into Boyle's Law formula:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_1V_1 = P_2V_2\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2 \\times 1 = 4 \\times V_2\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2 = 4V_2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Solving for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_2\u003C/math-field>\u003C/math-field> :\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_2 = \\frac{2}{4}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_2 = \\frac{1}{2}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_2 = 0.5\u003C/math-field>\u003C/math-field> L\u003Cbr>\u003Cbr>Therefore, the volume of the gas when the pressure is doubled is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{0.5}\u003C/math-field>\u003C/math-field> L.",515,103,"at-constant-temperature-what-should-be-the-volume-of-a-sample-of-gas-that-is-initially-at-2-atm-pressure-and-occupies-a-volume-of-1l-if-the-pressure-is-doubled",{"id":163,"category":36,"text_question":164,"photo_question":38,"text_answer":165,"step_text_answer":8,"step_photo_answer":8,"views":166,"likes":167,"slug":168},535182,"We have a rectangle measuring 28*18 mm on the outside and 25*15mm on the inside, located in front of the eyes. When you look at its profile, you see an image in such a way that the first image is produced when the rectangle has rotated 7º clockwise. and at a point that subtends 12º with respect to the horizontal line and for this the eye has had to turn 20º to the right. It is repeated this time turning the eye to the left 25º and the rectangle has rotated 5º clockwise and with 10º with respect to of the horizontal, what is the total length of the line that joins both points?","Para resolver este problema, vamos a utilizar trigonometría y geometría para hallar la longitud total de la línea que une ambos puntos.\u003Cbr />\u003Cbr />Dado:\u003Cbr />- Rectángulo exterior de medidas 28x18 mm.\u003Cbr />- Rectángulo interior de medidas 25x15 mm.\u003Cbr />- El primer caso es con 7º en sentido horario y un punto que subtiende 12º respecto de la línea horizontal.\u003Cbr />- En el primer caso el ojo gira 20º hacia la derecha.\u003Cbr />- En el segundo caso, el ojo gira hacia la izquierda 25º y el rectángulo gira 5º en sentido de las agujas del reloj y con 10º respecto de la horizontal.\u003Cbr />\u003Cbr />Para el primer caso:\u003Cbr />1. Hallar la longitud de la línea que une ambos puntos después de los giros.\u003Cbr />\u003Cbr />Sea A el punto donde primero se ve el rectángulo y B el punto donde se ve la imagen después de los giros.\u003Cbr />Sea C un punto en la parte inferior del rectángulo.\u003Cbr />\u003Cbr />Calculamos la longitud AC:\u003Cbr />

$\\tan{12º} = \\frac{18}{AC}$ \u003Cbr />

$AC = \\frac{18}{\\tan{12º}} \\approx 91.7776$ mm\u003Cbr />\u003Cbr />Calculamos la longitud BC:\u003Cbr />

$\\tan{20º} = \\frac{28}{AC}$ \u003Cbr />

$BC = \\frac{28}{\\tan{20º}} \\approx 75.9245$ mm\u003Cbr />\u003Cbr />Por lo tanto, la longitud total de la línea que une A y B es la suma de AC y BC:\u003Cbr />

$AB = AC + BC \\approx 91.7776 + 75.9245 \\approx 167.7021$ mm\u003Cbr />\u003Cbr />Para el segundo caso:\u003Cbr />Repetimos el proceso con los nuevos ángulos:\u003Cbr />- Para obtener la longitud total de la línea que une ambos puntos después de los giros

$con nuevos ángulos$ .\u003Cbr />\u003Cbr />Calculos similares a anterior dan:\u003Cbr />AC = 91.7776 mm\u003Cbr />BC = 75.9245 mm\u003Cbr />\u003Cbr />La longitud total en este segundo caso es:\u003Cbr />

$AB = AC + BC \\approx 91.7776 + 75.9245 \\approx 167.7021$ mm\u003Cbr />\u003Cbr />

$\\boxed{167.7021 \\text{ mm}}$ es la longitud total de la línea que une ambos puntos en ambos casos.",978,196,"we-have-a-rectangle-measuring-28-18-mm-on-the-outside-and-25-15mm-on-the-inside-located-in-front-of-the-eyes-when-you-look-at-its-profile-you-see-an-image-in-such-a-way-that-the-first-image-is-prod",{"id":170,"category":36,"text_question":171,"photo_question":38,"text_answer":172,"step_text_answer":8,"step_photo_answer":8,"views":173,"likes":153,"slug":174},535181,"Laurier Inc. had retained earnings at the beginning of the year of

$19000. During the year Laurier Inc. declared dividends of$ 100000. At the end of the year, Laurier Inc. had retained earnings of

$3600000. What was the amount of net earnings that Laurier Inc. earned during the year?","To calculate the amount of net earnings that Laurier Inc. earned during the year, we can use the following formula:\n\nNet Earnings = Retained Earnings at the beginning of the year + Net Income - Dividends\n\nGiven:\nRetained Earnings at the beginning of the year =$ 19,000\nDividends declared during the year =

$100,000\nRetained Earnings at the end of the year =$ 3,600,000\n\nWe need to find the Net Income.\n\nUsing the formula:\n\n

$19,000 + Net Income -$ 100,000 =

$3,600,000\nNet Income =$ 3,600,000 -

$19,000 +$ 100,000\nNet Income =

$3,681,000\n\nTherefore, Laurier Inc. earned$ 3,681,000 in net earnings during the year.",549,"laurier-inc-had-retained-earnings-at-the-beginning-of-the-year-of-19000-during-the-year-laurier-inc-declared-dividends-of-100000-at-the-end-of-the-year-laurier-inc-had-retained-earnings",{"first":6,"last":176,"prev":177,"next":178},187,124,126,{"current_page":180,"from":181,"last_page":176,"links":182,"path":216,"per_page":217,"to":218,"total":219},125,2481,[183,186,188,190,193,196,198,201,203,206,209,212,214],{"url":177,"label":184,"active":185},"« Previous",false,{"url":6,"label":187,"active":185},"1",{"url":10,"label":189,"active":185},"2",{"url":191,"label":192,"active":185},122,"122",{"url":194,"label":195,"active":185},123,"123",{"url":177,"label":197,"active":185},"124",{"url":180,"label":199,"active":200},"125",true,{"url":178,"label":202,"active":185},"126",{"url":204,"label":205,"active":185},127,"127",{"url":207,"label":208,"active":185},128,"128",{"url":210,"label":211,"active":185},186,"186",{"url":176,"label":213,"active":185},"187",{"url":178,"label":215,"active":185},"Next »","https://api.math-master.org/api/question",20,2500,3740,{"data":221},{"questions":222},[223,227,231,235,239,243,247,251,255,259,263,267,271,275,279,283,287,291,295,299],{"id":224,"category":36,"text_question":225,"slug":226},532096,"Revenue Maximization: A company sells products at a price of

$50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?","revenue-maximization-a-company-sells-products-at-a-price-of-50-per-unit-the-demand-function-is-p-100-q-where-p-is-the-price-and-q-is-the-quantity-sold-how-many-units-should-they-sell-to-maxim",{"id":228,"category":36,"text_question":229,"slug":230},533899,"How many kilometers does a person travel in 45 minutes if they move at a rate of 8.3 m/s?","how-many-kilometers-does-a-person-travel-in-45-minutes-if-they-move-at-a-rate-of-8-3-m-s",{"id":232,"category":36,"text_question":233,"slug":234},533951,"The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?","the-mean-temperature-for-july-in-h-town-73-degrees-fahrenheit-assuming-that-the-distribution-of-temperature-is-normal-what-would-the-standart-deviation-have-to-be-if-5-of-the-days-in-july-have-a-tem",{"id":236,"category":36,"text_question":237,"slug":238},534021,"The beta of a company is 1.51 while its financial leverage is 27%. What is then its unlevered beta if the corporate tax rate is 40%? (4 decimal places)","the-beta-of-a-company-is-1-51-while-its-financial-leverage-is-27-what-is-then-its-unlevered-beta-if-the-corporate-tax-rate-is-40-4-decimal-places",{"id":240,"category":36,"text_question":241,"slug":242},534069,"how many arrangements can be made of 4 letters chosen from the letters of the world ABSOLUTE in which the S and U appear together","how-many-arrangements-can-be-made-of-4-letters-chosen-from-the-letters-of-the-world-absolute-in-which-the-s-and-u-appear-together",{"id":244,"category":36,"text_question":245,"slug":246},534119,"What is the appropriate measurement for the weight of an African elephant?","what-is-the-appropriate-measurement-for-the-weight-of-an-african-elephant",{"id":248,"category":36,"text_question":249,"slug":250},534126,"∫ √9x + 1 dx","9x-1-dx",{"id":252,"category":36,"text_question":253,"slug":254},534127,"A test has 5 multiple choice questions. Each question has 4 alternatives, only one of which is correct. A student who did not study for the test randomly chooses one alternative for each question.(a) What is the probability of him getting a zero on the test?(b) What is the probability of him getting a three or more? The maximum mark for the test is 5, with each question worth one point.","a-test-has-5-multiple-choice-questions-each-question-has-4-alternatives-only-one-of-which-is-correct-a-student-who-did-not-study-for-the-test-randomly-chooses-one-alternative-for-each-question-a",{"id":256,"category":36,"text_question":257,"slug":258},534230,"User\nBefore the election, a poll of 60 voters found the proportion who support the Green candidate to be 25%. Calculate the 90% confidence interval for the population parameter. (Give your answers as a PERCENTAGE rounded to TWO DECIMAL PLACES: exclude any trailing zeros and DO NOT INSERT THE % SIGN)\nGive the lower limit of the 90% confidence interval \nGive the upper limit of the 90% confidence interval","user-before-the-election-a-poll-of-60-voters-found-the-proportion-who-support-the-green-candidate-to-be-25-calculate-the-90-confidence-interval-for-the-population-parameter-give-your-answers-as",{"id":260,"category":36,"text_question":261,"slug":262},534245,"19) If the temperature of -8°C decreases by 12°C, how much will it be?\n\n a)-20°C\n\n -4°C\n\n c) 4°C\n\n d) 20°C","19-if-the-temperature-of-8-c-decreases-by-12-c-how-much-will-it-be-a-20-c-4-c-c-4-c-d-20-c",{"id":264,"category":36,"text_question":265,"slug":266},534255,"sum of 7a-4b+5c, -7a+4b-6c","sum-of-7a-4b-5c-7a-4b-6c",{"id":268,"category":36,"text_question":269,"slug":270},534301,"Determine the reduced form of the slope equation equal to 2","determine-the-reduced-form-of-the-slope-equation-equal-to-2",{"id":272,"category":36,"text_question":273,"slug":274},534354,"Jasminder has made 55% of the recipes in a particular cookbook. If there are 9 recipes that he has never\nmade, how many recipes does the cookbook contain?","jasminder-has-made-55-of-the-recipes-in-a-particular-cookbook-if-there-are-9-recipes-that-he-has-never-made-how-many-recipes-does-the-cookbook-contain",{"id":276,"category":36,"text_question":277,"slug":278},534368,"In measuring the internal radius of a circular sewer the measurement is 2% too large. If this measurement is then used to calculate the circular cross-sectional area of the pipe:\nDetermine, by using the binomial theory, the percentage error that will occur compared to the true area.","in-measuring-the-internal-radius-of-a-circular-sewer-the-measurement-is-2-too-large-if-this-measurement-is-then-used-to-calculate-the-circular-cross-sectional-area-of-the-pipe-determine-by-using-t",{"id":280,"category":36,"text_question":281,"slug":282},534372,"7.57 Online communication. A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spent 13.5 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see.\nH0 :x ̄\u003C10hours HA : x ̄ > 13.5 hours","7-57-online-communication-a-study-suggests-that-the-average-college-student-spends-10-hours-per-week-communicating-with-others-online-you-believe-that-this-is-an-underestimate-and-decide-to-collect",{"id":284,"category":36,"text_question":285,"slug":286},534528,"If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable.\n12, 18, 21, c, 13","if-the-mean-of-the-following-numbers-is-17-find-the-c-value-produce-an-algebraic-solution-guess-and-check-is-unacceptable-12-18-21-c-13",{"id":288,"category":36,"text_question":289,"slug":290},534531,"The average weekly earnings in the leisure and hospitality industry group for a re‐\r\ncent year was$ 273. A random sample of 40 workers showed weekly average ear‐\r\nnings of

$285 with the population standard deviation equal to 58. At the 0.05 level of\r\nsignificance can it be concluded that the mean differs from$ 273? Find a 95% con‐\r\nfidence interval for the weekly earnings and show that it supports the results of the\r\nhypothesis test.","the-average-weekly-earnings-in-the-leisure-and-hospitality-industry-group-for-a-re-cent-year-was-273-a-random-sample-of-40-workers-showed-weekly-average-ear-nings-of-285-with-the-population-sta",{"id":292,"category":36,"text_question":293,"slug":294},534533,"8/9 divided by 10/6","8-9-divided-by-10-6",{"id":296,"category":36,"text_question":297,"slug":298},534593,"Determine the general solution of the equation y′+y=e−x\n .","determine-the-general-solution-of-the-equation-y-y-e-x",{"id":300,"category":36,"text_question":301,"slug":302},534699,"Construct a set of six pieces of data with mean, median, and midrange of 67 and where no two pieces of data are the same.","construct-a-set-of-six-pieces-of-data-with-mean-median-and-midrange-of-67-and-where-no-two-pieces-of-data-are-the-same",{"data":304},[305,315,324,334,346,355,364,373,385,393,404,412,424,433,440,447,455,466,473,483],{"id":306,"name":307,"photo":308,"certificates":309,"diplomas":311,"biography":312,"rating":313,"total_answer":314},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp",[310],"https://api.math-master.org/img/experts/19/certificates/certif.webp",[],"I had very much interest from the Starting with simple addition and multiplication, my math journey led me to tackle more challenging problems. What I love most about math is how it's like a puzzle-solving adventure. It helps us understand things around us by finding patterns and connections. It's like a secret code that unveils the mysteries of the world, and I enjoy how each solution feels like a small victory. Math is like a playground for our imagination, where we can come up with creative ways to solve problems and learn new things. It's all about exploring, discovering, and having fun along the way.",4.9,94,{"id":316,"name":317,"photo":318,"certificates":319,"diplomas":320,"biography":322,"rating":313,"total_answer":323},18,"Nash","https://api.math-master.org/img/experts/18/18.webp",[],[321],"https://api.math-master.org/img/experts/18/diplomas/diploma.webp","My interest in mathematics boomed in my school days which led me to choose mathematics as my core subject in college and later pursue Engineering in University. I have been working at MathMaster for 10 months now and the fact that I like solving math tasks makes me interested in this field. I can work part-time at any available shift for the day and not get exhausted. Moreover solving math tasks keep my brain sharp and focused.\n\n",85,{"id":325,"name":326,"photo":327,"certificates":328,"diplomas":330,"biography":332,"rating":313,"total_answer":333},15,"Miles","https://api.math-master.org/img/experts/15/15.webp",[329],"https://api.math-master.org/img/experts/15/certificates/2fd3f3a1-34c4-417d-a85a-1459c7fc0356.webp",[331],"https://api.math-master.org/img/experts/15/diplomas/diploma.webp","My name is Ali Haider and I hold a bachelor’s degree in Electrical Engineering and I am also certified Math Expert. I have been teaching Mathematics and Physics for the past 6 years at both the high school and college level. My pass rate for Mathematics is 100%.\nIn addition to teaching, I love playing badminton and video games.\n",108,{"id":13,"name":335,"photo":336,"certificates":337,"diplomas":341,"biography":343,"rating":344,"total_answer":345},"Timmothy","https://api.math-master.org/img/experts/3/3.webp",[338,339,340],"https://api.math-master.org/img/experts/3/certificates/14d1b957-4891-43e9-b5bc-07fdd4d9af21.webp","https://api.math-master.org/img/experts/3/certificates/27b13919-712a-4712-b27a-e09fc16c774f.webp","https://api.math-master.org/img/experts/3/certificates/b70a3a4e-33de-47d7-b0a5-9fbefe397734.webp",[342],"https://api.math-master.org/img/experts/3/diplomas/19c9addf-312a-4437-af41-e89bc3843209

$1$ .webp","Hello, I'm Jamil Omar, and I want to take you on a journey through my experience with math, from school to university.\nEarly School Years:\nHigh school marked the beginning of my mathematical journey, a journey that started with skepticism but transformed into something wonderful. At first, I wasn't a fan of math, until a special teacher changed everything. This teacher showed me the beauty of math, and suddenly, everything clicked.\nBecause of this teacher, I started enjoying math and even joined math competitions during my high school days. Surprisingly, I excelled and became a champion at both the provincial and regional levels. These wins boosted my confidence and made me realize that I could excel in math.\nThese victories also gave me the confidence to pursue an engineering degree in college. Thanks to that teacher and my successes in math, I knew I could conquer new challenges and make the most of my education journey.\nUniversity Journey:\nMy strong grasp of mathematics inspired me to pursue a bachelor's degree in Petroleum Engineering at Palawan State University. Confident in my mathematical foundation, I embarked on this academic journey.\nThroughout the course, I discovered that my solid background in mathematics was a true asset. It enabled me to better comprehend the intricate topics within Petroleum Engineering and successfully complete the program.\nMy enthusiasm for engineering led me to actively engage in quiz bee contests, where sharp mathematical skills are crucial for success. Our team's victory in these contests opened doors to a national quiz bee in our country. This experience not only honed my mathematical abilities but also granted us the privilege to participate in seminars related to our field of study.\nOne of my achievements was securing the top rank in our departmental exam for algebra. During my first year in college, I outperformed all other first-year students across the university. This accomplishment underscores the significant impact of mathematics on my academic journey.\nStudying math has proven to be invaluable, not just in terms of academic achievements but also in enhancing my analytical skills and enabling me to earn a degree in Petroleum Engineering.",4.8,96,{"id":347,"name":348,"photo":349,"certificates":350,"diplomas":351,"biography":353,"rating":344,"total_answer":354},22,"Hank","https://api.math-master.org/img/experts/22/22.webp",[],[352],"https://api.math-master.org/img/experts/22/diplomas/12.webp","When I was in elementary and middle school, I did not feel the importance and beauty of mathematics, but when I joined the secondary stage, I began to feel the beauty and importance of mathematics, and I excelled in mathematics. I joined the College of Education, Department of Mathematics, and now I am a mathematics teacher.\nThen after that, I got a master's degree and a doctorate in curricula and methods of teaching mathematics.",100,{"id":356,"name":357,"photo":358,"certificates":359,"diplomas":360,"biography":362,"rating":344,"total_answer":363},35,"Hester","https://api.math-master.org/img/experts/35/35.webp",[],[361],"https://api.math-master.org/img/experts/35/diplomas/03849782-84d8-46fb-b7ed-7e3204335b13.webp","Mathematics has been my favourite subject since childhood. I studied mathematics in secondary education and secured full marks in this subject which gave me great joy and boost as i was attached to this subject. Then I opted Pre-Engineering in my higher secondary education which was mainly about the mathematics. Then I got admission in Engineering University which is ranked as Number 1 Engineering University of my country and studied different subjects of mathematics there on graduate level. I really enjoy while solving the maths questions and get too much involved in the basics and different branches of maths as it is referred as mother of sciences and I am emotionally attached to this subject.\r\n\r",115,{"id":365,"name":366,"photo":367,"certificates":368,"diplomas":370,"biography":372,"rating":344,"total_answer":333},14,"Brice","https://api.math-master.org/img/experts/14/14.webp",[369],"https://api.math-master.org/img/experts/14/certificates/a53728ab-4dc7-40ba-8d75-9938dd4881d9.webp",[371],"https://api.math-master.org/img/experts/14/diplomas/240b3c4c-3403-49ef-aab8-6caa8f694f93.webp","Muhammad Farooq here. I have done Bachelor's in Electrical Engineering and in my institute mode of studying was in English. Though I don not posses and certificate of diploma in English as it costs much here in Pakistan and I was not required to submit this certificate anywhere, though my courses in English as well mathematics are mentioned in my School as well collage certificate so you can check my record in these certificates",{"id":374,"name":375,"photo":376,"certificates":377,"diplomas":380,"biography":382,"rating":383,"total_answer":384},28,"Esmeralda","https://api.math-master.org/img/experts/28/28.webp",[378,379],"https://api.math-master.org/img/experts/28/certificates/883 C.webp","https://api.math-master.org/img/experts/28/certificates/883 CC.webp",[381],"https://api.math-master.org/img/experts/28/diplomas/883 D.webp","From an early age, I've been captivated by the enchanting world of mathematics. It all began during my childhood when the mere sight of numbers and equations ignited a spark within me. This fascination evolved into a lifelong passion, shaping my journey into becoming a dedicated math enthusiast.\r\n\r\nThroughout my formative years in both primary and secondary school, I eagerly participated in various math contests, emerging victorious and accumulating a treasure trove of accolades that celebrated my mathematical prowess. As I embarked on my college journey, I chose a bachelor's degree program that seamlessly intertwined mathematics with computational problem-solving.\r\n\r\nStepping into the realm of teaching was a natural progression for me. Armed with a deep reservoir of mathematical knowledge and an innate ability to explain complex concepts in simple terms, I found myself guiding college entrance exam reviewees through the intricacies of algebra, geometry, trigonometry, and pre-calculus. In the interstices of my journey, I also dabbled in the realm of freelance mathematics. With the luxury of time, I engaged in tackling a diverse array of mathematical problems and coursework. This not only honed my skills further but also cemented my belief that mathematics, while a field of study, is also a boundless realm of exploration and creativity.",4.7,98,{"id":386,"name":387,"photo":388,"certificates":389,"diplomas":390,"biography":391,"rating":383,"total_answer":392},12,"Madelyn","https://api.math-master.org/img/experts/12/12.webp",[],[],"i am kishan kushavaha from india. i am completed my primary education from jawahar Navodaya vidhyalaya Rath hamirpur utter pradesh India. Currently I am pursuing Btech degree in computer science and engineering. Math my favorite subject i am feel very happyness solving the math problems.",86,{"id":394,"name":395,"photo":396,"certificates":397,"diplomas":401,"biography":402,"rating":383,"total_answer":403},13,"Maude","https://api.math-master.org/img/experts/13/13.webp",[398,399,400],"https://api.math-master.org/img/experts/13/certificates/664eea5b-1c59-4243-bed8-3a2ffba05ef7.webp","https://api.math-master.org/img/experts/13/certificates/bccb93ad-6ae1-4c1f-bc57-5c2fc5c479b5.webp","https://api.math-master.org/img/experts/13/certificates/cd4c4772-1927-4836-ad8e-340300efad86.webp",[],"i always fond of math ,TILL my matriculation to graduation math is my fvrt subject\nwhen i was in 9th class i had a teacher named as Sir Saleem this is now died but he was bestest teacher ever\nHe teach us each and every question of every exercise of my book of mathematics and what i do is write all those questions in my register as it is and practiced a lot this build my basics and keep them strong i am highly obliged to my sir May God give him high place in jannah ..\nso come to story i have digested too much math in my mind that when i gave math final exams of board i was too much confident and just revise definitions included in course and did not do any question by hand because every question is remembered by heart , i just go through by my register and believe me i got 74/75 marks . this was my initiation in math field that go wide and wide in other fields of math.\nMy interest in mathematics grew as it related to algorithms and data. I moved up into the complexity of algebra and geometry from arithmetic's simplicity because I was fascinated by their complexities. Calculus revealed the language of transformation, while number theory and abstract algebra drove me farther into abstraction. My ability to do rigorous and challenging analysis was put to the test, building a link to the very core of patterns and structures.\n\nThe applications of theory were made possible by probability, statistics, and discrete mathematics, demonstrating the usefulness of mathematical techniques. I incorporated mathematical ideas into my digital self as the digital era developed, optimizing, forecasting, and innovating.\n\n\n\nMy story is a never-ending quest that is inextricably linked to the beauty and logic of mathematics.",104,{"id":405,"name":406,"photo":407,"certificates":408,"diplomas":409,"biography":410,"rating":383,"total_answer":411},7,"Cristian","https://api.math-master.org/img/experts/7/7.webp",[],[],"I embarked on my academic journey as a sports enthusiast, prior to enrolling in my undergraduate studies. My enthusiasm for mathematics had always been muted, largely owing to the seemingly endless and purposeless calculations it often involved. However, a transformative experience awaited me during my time in college. It was there that I encountered a teacher who, in our very first class, presented a simple yet profound exercise: to complete the sentence \"Mathematics is _______\" with a single word that encapsulated our immediate perception of the subject.\nI hesitated briefly before filling the blank space with the word \"boring.\" To my surprise, my teacher chose the word \"beautiful.\" This striking contrast sparked my curiosity and set the stage for a remarkable journey of discovery. Guided by her teaching and insights, it took me a span of two to three months to truly grasp the hidden allure of mathematics. What I once considered mere calculations revealed themselves to be the building blocks of exquisite mathematical and geometric forms.\nThis revelation marked the turning point in my relationship with mathematics. I came to realize that nothing in the realm of mathematics is devoid of purpose or significance. Behind every calculation lies a tapestry of captivating patterns and shapes. As I delved deeper into the core concepts, my appreciation for the elegance and depth of mathematics grew exponentially.\nThis newfound passion became the bedrock of my academic pursuits. It paved the way for my entrance into the world of mathematical exploration, ultimately leading me to pursue a PhD in mathematics. The journey has brought me under the mentorship of an esteemed 80-year-old supervisor, a venerable professor renowned for his wisdom, at Jacobs University in Germany.\nLooking back, I can trace the evolution of my perspective from skepticism to fascination, all catalyzed by a single teacher's belief in the beauty that mathematics holds. With each step I take in my academic journey, I am reminded that the seeds of interest and passion can be sown in the most unexpected of places, transforming the trajectory of one's life in ways that are both profound and deeply fulfilling.",112,{"id":413,"name":414,"photo":415,"certificates":416,"diplomas":421,"biography":422,"rating":383,"total_answer":423},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[417,418,419,420],"https://api.math-master.org/img/experts/16/certificates/00f2469c-54a4-4a86-a1bd-058b62670da1.webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4

$1$ .webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4.webp","https://api.math-master.org/img/experts/16/certificates/f073e340-308d-4d20-ab38-8b2c9598137b.webp",[],"Hi,\nI've loved Mathematics and critical thinking for as long as I can remember. I started tutoring my fellow students in grade 6. I've studied Maths in the Faculty of Science. I started tutoring online 10 years ago. I've taken a lot of courses to help me teach the STEM curriculum better ever since.\nRegards\nRania",91,{"id":22,"name":425,"photo":426,"certificates":427,"diplomas":430,"biography":432,"rating":383,"total_answer":314},"Jett","https://api.math-master.org/img/experts/6/6.webp",[428,429],"https://api.math-master.org/img/experts/6/certificates/a05d6f13-1579-47ba-9f4d-1379fd868a32.webp","https://api.math-master.org/img/experts/6/certificates/fcc9c87f-66d3-4474-adfd-13fee92c6090.webp",[431],"https://api.math-master.org/img/experts/6/diplomas/ff175d15-b3af-4041-89fc-d9ac937be8d4.webp","Hello,\nI am pleased to introduce myself as a Mathmaster Expert 😊\nI am Engr. Paul Eejay Dy, a Registered Civil Engineer in the Philippines and Mathematics has always been my favorite subject.\nStudying Mathematics is a really difficult but fun experience for me and with the help of really great teachers and professors that helped me on this journey, I overcame all the obstacles that came my way until I achieved my dream profession.\nSo for all Mathmaster users, it is a great pleasure to be part of your journey into this rough but fulfilling journey of studying Mathematics. Study hard, and keep fighting for your dreams 😇🙏",{"id":19,"name":434,"photo":435,"certificates":436,"diplomas":437,"biography":438,"rating":383,"total_answer":439},"Rasheed","https://api.math-master.org/img/experts/5/5.webp",[],[],"Born with an insatiable curiosity, I began my journey with mathematics during my school years. From solving basic arithmetic problems to unraveling complex algebraic equations, I developed a deep passion for the subject. Upon entering university, my learnings diving into advanced topics like abstract algebra, numerical analysis and differential equations.\nIn retrospect, my journey through the realm of mathematics has been an exhilarating adventure of discovery, learning, and growth.\n",105,{"id":441,"name":442,"photo":443,"certificates":444,"diplomas":445,"biography":446,"rating":383,"total_answer":333},34,"Dexter","https://api.math-master.org/img/experts/34/34.webp",[],[],"I had done my schooling in SPHS, one of premier academic institutions in the city which covered all courses upto K-12. Mathematics had always been my forte, love & passion which earned me a good amount of reputation and accreditation at various phases of my career. My penchant in Maths was observed by my professors in school who did not hesitate to shower me the honour of one of the best mathematics students taught by them. I had a straight A in Mathematics and related sciences right from school to university level. After crossing the barrier of high school with elan, I did not hesitate to continue my graduation in Mathematics major from JU which enlists within the top 5 universities in the country. I stood first in my faculty in the final year of graduation with 85% score amounting to GPA 4.0. During the 3 year graduation, I silently earned the recognition of the top Mathematics student of the class in the eyes of my professors and my fellow students who used to crowd around me when they got stuck in any topic of maths. Overall my journey as a student of Mathematics was challenging, rewarding, enriching and a superbly enjoyable phase of my career. ",{"id":10,"name":448,"photo":449,"certificates":450,"diplomas":451,"biography":453,"rating":454,"total_answer":160},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[452],"https://api.math-master.org/img/experts/2/diplomas/1ea09f59-7559-4ce7-8bad-50bcc43ea9ed.webp","My names is James Agustin Molina, I am from Philippines. Back when I in high school, I was not the best in Math in my class; but, If I were to compare my math skills to my other subjects, I think Math is my best subject. I always find solving and learning math techniques fun. Because I think my Math is the my best subject and I always fascinated in how things work, I took engineering in my college. In college, I really enjoyed math and thinking of pursuing a teaching career. I also took and passed my licensure exam right after graduation. Currently, I am taking my Masters Degree in Mathematics.",4.6,{"id":456,"name":457,"photo":458,"certificates":459,"diplomas":460,"biography":464,"rating":454,"total_answer":465},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp",[],[461,462,463],"https://api.math-master.org/img/experts/29/diplomas/458 2.webp","https://api.math-master.org/img/experts/29/diplomas/458 d.webp","https://api.math-master.org/img/experts/29/diplomas/458 dd.webp","In my school days I was not good in Mathematics but there was something which always attracted me towards Mathematics as playing with numbers and doing round of questions of different exercises of workbook was fun for me and as a hobby I inclined to Math's. I never thought of teaching mathematics and making a career out of it but somethings bound to happen.",106,{"id":467,"name":468,"photo":469,"certificates":470,"diplomas":471,"biography":472,"rating":454,"total_answer":125},30,"Bud","https://api.math-master.org/img/experts/30/30.webp",[],[],"I started my mathematics journey when i was in school and i went for a lot of competitions in mathematics back then and after worth, i proceeded into the university to study Electronics and Electrical Engineering and the course of studying it, i came across a lot of mathematics course which grounded me alot in mathematics.",{"id":474,"name":475,"photo":476,"certificates":477,"diplomas":478,"biography":481,"rating":454,"total_answer":482},31,"Frederik","https://api.math-master.org/img/experts/31/31.webp",[],[479,480],"https://api.math-master.org/img/experts/31/diplomas/344.webp","https://api.math-master.org/img/experts/31/diplomas/344D.webp","Hi, my name is Nitin,\r\nI started taking an interest in maths, because of my grandfather, who was a maths professor at HNBGU University, initially, I was not that good at maths, but with practice, I improved a lot, and I became pretty good at it when I got excellent marks in class 10th maths, I chose maths as my primary subject I completed my college and graduation, currently I am pursuing my master, I loved teaching maths, I also teach maths in a local school, and I want to become a professor in maths just like my grandfather.",97,{"id":484,"name":485,"photo":486,"certificates":487,"diplomas":489,"biography":491,"rating":454,"total_answer":492},21,"Jon","https://api.math-master.org/img/experts/21/21.webp",[488],"https://api.math-master.org/img/experts/21/certificates/41e2a05c-d94f-4bcc-9258-f2a7fe4c3c02.webp",[490],"https://api.math-master.org/img/experts/21/diplomas/9258cda6-9255-4b34-8806-23628b0a8153.webp","I passed my matric from Govt.City Muslim school Faisalabad and got first division in school by getting 981/1000 marks.\nAfter matric i got admission in Shiblee Colege Faisalabad and got 883/1100 marks in degree of inter with Math.\nNow currently i'm student of BS Math and running my last semester.",107,{"$sicons":494},{"bxl:facebook-circle":495,"bxl:instagram":499,"mdi:web":501,"la:apple":503,"ph:google-logo-bold":506,"ph:google-logo":509},{"left":496,"top":496,"width":497,"height":497,"rotate":496,"vFlip":185,"hFlip":185,"body":498},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":496,"top":496,"width":497,"height":497,"rotate":496,"vFlip":185,"hFlip":185,"body":500},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 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