The most popular questions on the topic of general

\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 2.58 +

$0.47 \\times 0.45$ \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 2.58 + 0.2115 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 2.7915 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n Thus, the highest 32% of grade point averages are above:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x > 2.7915 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. **Calculate the z-score for the 32nd percentile:**\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> z = -0.47 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. **Convert this z-score to an actual grade point average for the lowest 32%:**\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\mu +

$z \\times \\sigma$ \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 2.58 +

$-0.47 \\times 0.45$ \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 2.58 - 0.2115 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 2.3685 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n Thus, the lowest 32% of grade point averages are below:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C 2.3685 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n **Summary:**\u003Cbr />\n\u003Cbr />\n - The highest 32% of grade point averages lie above:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x > 2.7915 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n - The lowest 32% of grade point averages lie below:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C 2.3685 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n**Answer:**\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Highest 32\\%: } x > 2.7915\u003C/math-field>\u003C/math-field>\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Lowest 32\\%: } x \u003C 2.3685\u003C/math-field>\u003C/math-field>",545,109,"suppose-that-grade-point-averages-of-undergraduate-students-at-one-university-have-a-bell-shaped-distribution-with-a-mean-of-2-58-and-a-standard-deviation-of-0-45-please-do-not-round-your-answer-des",{"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},536545,"Determine the compound amount of a debt of

$1,600,000 agreed at a rate of 6.5% compounded monthly for 4 years and 6 months.","1. Identify the principal, interest rate, compounding frequency, and time.\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = 1,600,000\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{6.5}{100} = 0.065\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 12\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t = 4.5 \\text{ years}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Use the compound interest formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A = P \\left(1 + \\frac{r}{n}\\right)^{nt}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate individual components:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{r}{n} = \\frac{0.065}{12} = 0.0054167\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>nt = 12 \\times 4.5 = 54\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substitute into the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A = 1,600,000 \\left(1 + 0.0054167 \\right)^{54}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Calculate the exponent:\u003Cbr>\u003Cbr>6. Final calculation:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{A=2141944.99}\u003C/math-field>\u003C/math-field>",652,130,"determine-the-compound-amount-of-a-debt-of-1-600-000-agreed-at-a-rate-of-6-5-compounded-monthly-for-4-years-and-6-months",{"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},536544,"The manager of a furniture factory finds that it costs$ 2,200 to manufacture 100 chairs in one day and

$4,800 to produce 300 chairs in one day. In reference to this information, answer the following questions:\n -\n Assuming that the relationship between cost and the number of chairs produced is linear, find an equation that expresses this relationship.\n -. What is the slope of the line, and what does it represent? and What is the intersection point and of this line, how is it interpreted?\n -. If the number of chairs produced in one day is 220, what is the cost?","First, calculate the slope \$ m \$:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> m = \\frac{4800 - 2200}{300 - 100}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> m = \\frac{2600}{200}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> m = 13 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nNext, determine the y-intercept \$ b \$ using the point \$ (100, 2200) \$:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> b = 2200 - 13 \\times 100 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> b = 2200 - 1300 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> b = 900 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThus, the linear equation is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> C = 13x + 900 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe slope \$ m = 13 \$ represents the cost increase per additional chair produced. The intersection point (0, 900) means that the base cost when no chairs are produced is$ 900.\u003Cbr />\n\u003Cbr />\nFinally, to find the cost for producing 220 chairs, substitute \$ x = 220 \$:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> C = 13 \\times 220 + 900 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> C = 2860 + 900 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> C = 3860 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the cost to produce 220 chairs in one day is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> C = 3860 \u003C/math-field>\u003C/math-field>",435,87,"the-manager-of-a-furniture-factory-finds-that-it-costs-2-200-to-manufacture-100-chairs-in-one-day-and-4-800-to-produce-300-chairs-in-one-day-in-reference-to-this-information-answer-the-following-q",{"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},536543,"Determine the solution set of the following inequality:\n\n x3−x2≥25x−25","1. Reordenamos la inecuación:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3 - x^2 - 25x + 25 \\geq 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Factorizamos el polinomio.\u003Cbr />\n\u003Cbr />\n3. El polinomio factorizado es:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (x^3 - x^2 - 25x + 25) = (x^2 - 25)(x - 1) = (x - 5)(x + 5)(x - 1) \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Analizamos los intervalos críticos dados por las raíces:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(-\\infty, -5), (-5, 1), (1, 5), (5, \\infty)\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n5. Encontramos los signos del polinomio en cada intervalo crítico.\u003Cbr />\n\u003Cbr />\n6. La inecuación original cumple en los siguientes intervalos:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(-\\infty, -5] \\cup [5, \\infty)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nRespuesta: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(-\\infty, -5] \\cup [5, \\infty)\u003C/math-field>\u003C/math-field>",428,86,"determine-the-solution-set-of-the-following-inequality-x3-x2-25x-25",{"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},536542,"Find a polynomial function with the zeros -2,3,5 whose graph passes through the point (6,72).","1. Given the zeros are -2, 3, 5 so the polynomial in factored form is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(x) = a(x + 2)(x - 3)(x - 5)\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Use the point (6, 72) to find a :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>72 = a(6 + 2)(6 - 3)(6 - 5)\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Simplify inside the parentheses:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>72 = a(8)(3)(1)\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Solve for a :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>72=24\\Rightarrow a=3\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Substitute a = 3 back into the polynomial:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(x) = 3(x + 2)(x - 3)(x - 5)\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Expand the polynomial:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3[(x^2 - x - 6)(x - 5)] = 3(x^3 - 6x^2 - x + 30)\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Final polynomial function is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(x) = 3x^3 - 18x^2 - 3x + 90\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>8. Answer:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{P(x) = 3x^3 - 18x^2 - 3x + 90}\u003C/math-field>\u003C/math-field>",1486,297,"find-a-polynomial-function-with-the-zeros-2-3-5-whose-graph-passes-through-the-point-6-72",{"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},536541,"5/3x-1/6=x-1/4","Step 1: Eliminate the fractions by finding a common denominator. The common denominator for 3, 6, and 4 is 12. \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12 \\left(\\frac{5}{3}x - \\frac{1}{6}\\right) = 12 \\left(x - \\frac{1}{4}\\right)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nStep 2: Distribute 12 to each term inside the parentheses.\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12 \\cdot \\frac{5}{3}x - 12 \\cdot \\frac{1}{6} = 12 \\cdot x - 12 \\cdot \\frac{1}{4}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4 \\cdot 5x - 2 = 12x - 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nStep 3: Simplify the equation.\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20x - 2 = 12x - 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nStep 4: Move the terms involving \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> to one side and constant terms to the other side.\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20x - 12x = -3 + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8x = -1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nStep 5: Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{-1}{8}\u003C/math-field>\u003C/math-field>",607,121,"5-3x-1-6-x-1-4",{"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},536540,"What is the formula for an 80% confidence interval for a population portion","1. Identify the sample proportion: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\hat{p}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Calculate the value of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z\u003C/math-field>\u003C/math-field> for an 80% confidence interval: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z_{0.10}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. Compute the standard error: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sqrt{\\frac{\\hat{p}(1 - \\hat{p})}{n}}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n4. Multiply the standard error by \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z_{0.10}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n5. Add and subtract the result from the sample proportion \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\hat{p}\u003C/math-field>\u003C/math-field> to get the interval.\u003Cbr />\n\u003Cbr />\nAnswer: \u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\hat{p} \\pm Z_{0.10} \\sqrt{\\frac{\\hat{p}(1 - \\hat{p})}{n}}\u003C/math-field>\u003C/math-field>",1192,238,"what-is-the-formula-for-an-80-confidence-interval-for-a-population-portion",{"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},536539,"A particularly efficient method for numerical integration of a function is the so-called Gaussian quadrature. In developing the formulas for this method it is necessary to find the roots of certain so-called Legendre polynomials. Numerically find all the roots of the sixth-order Legendre polynomial:\n P_6 (x)=1/48(693x^6-945x^4+315x^2-15)","1. Consider the polynomial given: \u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P_6(x) = \\frac{1}{48}(693x^6 - 945x^4 + 315x^2 - 15)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. To find the roots, set the polynomial equal to zero:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{48}(693x^6 - 945x^4 + 315x^2 - 15) = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Remove the fraction:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>693x^6 - 945x^4 + 315x^2 - 15 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve for \$x\$:\u003Cbr />\n \u003Cbr />\n The approximate numerical solutions are:\u003Cbr />\n \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\approx \\pm 0.23861, \\pm 0.66121, \\pm 0.93247\u003C/math-field>\u003C/math-field>",735,147,"a-particularly-efficient-method-for-numerical-integration-of-a-function-is-the-so-called-gaussian-quadrature-in-developing-the-formulas-for-this-method-it-is-necessary-to-find-the-roots-of-certain-so",{"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},536538,"Find the area under the curve Y=x+1, Y=0, X=2, X=6","First, set up the definite integral:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\int_{2}^{6} (x+1) \\, dx \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nCalculate the antiderivative:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\int (x+1) \\, dx = \\frac{x^2}{2} + x \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nEvaluate the antiderivative at the upper and lower limits of the integral:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left[ \\frac{x^2}{2} + x \\right]_{2}^{6} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSubstitute the limits:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left( \\frac{6^2}{2} + 6 \\right) - \\left( \\frac{2^2}{2} + 2 \\right) \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSimplify:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left( 18 + 6 \\right) - \\left( 2 + 2 \\right) \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 24 - 4 = 20 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSo, the area under the curve is:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 20 \u003C/math-field>\u003C/math-field>",1396,279,"find-the-area-under-the-curve-y-x-1-y-0-x-2-x-6",{"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},536537,"Amount of debt that is acquired under the following conditions: 16% interest rate compounded quarterly, payments of ¢85,000 at the end of each quarter for 2.5 years, and a final payment of ¢30,000 one quarter later.\n\n Question 11Select one:\n\n to.\n 586,500.84\n\n\n b.\n 708,913.57\n\n\n c.\n 790,695.25\n\n\n d.\n 918,956.30","1. Determinamos la tasa trimestral:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> i = \\frac{16\\%}{4} = 4\\% = 0,04 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Calculamos el número total de períodos:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n = 2,5 \\text{ años} \\times 4 \\text{ trimestres/año} + 1 \\text{ trimestre adicional} = 10 + 1 = 11 \\text{ trimestres} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculamos el valor presente de los pagos trimestrales de ¢85.000 mediante la fórmula de anualidad ordinaria:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV = R \\times \\left(1 - (1 + i)^{-n}\\right) / i \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nDonde:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> R = 85.000 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> i = 0,04 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n = 10 \u003C/math-field>\u003C/math-field> (solo los pagos trimestrales de ¢85.000)\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV = 85.000 \\times \\left(1 - (1 + 0,04)^{-10}\\right) / 0,04 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nCalculamos esto:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV = 85.000 \\times 8,110896445 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV = 689.426,20 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculamos el valor presente del pago final de ¢30.000 (que ocurre un trimestre después de los 10 trimestres):\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{final} = \\frac{30.000}{(1 + i)^{11}} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nCalculamos esto:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{final} = \\frac{30.000}{(1 + 0,04)^{11}} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{final} = \\frac{30.000}{1.558037231} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> PV_{final} = 19.257,37 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Sumamos los valores presentes calculados:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = PV + PV_{final} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = 689.426,20 + 19.257,37 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = 708.683,57 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAjustando a la opción más cercana:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = 708.913,57 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nPor lo tanto, la respuesta correcta es:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> B = 708.913,57 \u003C/math-field>\u003C/math-field>",1225,245,"amount-of-debt-that-is-acquired-under-the-following-conditions-16-interest-rate-compounded-quarterly-payments-of-85-000-at-the-end-of-each-quarter-for-2-5-years-and-a-final-payment-of-30-000-one",{"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},536536,"41 students in a university travel club. Using the venn diagram show how many traveled to Germany,France and Spain. How many students have been only to France? 14 members visited Germany,18 have been to Spain,18 have visited France,7 have visited Germany and France 8 have only been to Spain 5 have only been to Germany 5 have only been to Spain and France 3 have been to all three countries,some members have not been to any of the three","1. Start with the principle of inclusion-exclusion:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> |G \\cup F \\cup S| = |G| + |F| + |S| - |G \\cap F| - |G \\cap S| - |S \\cap F| + |G \\cap F \\cap S| \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Plug in the given values:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 41 = 14 + 18 + 18 - 7 - |G \\cap S| - 5 + 3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Combine like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 41 = 46 - |G \\cap S| - 5 - 7 + 3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 41 = 46 - |G \\cap S| - 9 \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Simplify the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> |G \\cap S| = 46 - 9 - 41 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> |G \\cap S| = 46 - 50 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> |G \\cap S| = 6 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe answer remains:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = |G \\cap S| = 6 \u003C/math-field>\u003C/math-field>",280,56,"41-students-in-a-university-travel-club-using-the-venn-diagram-show-how-many-traveled-to-germany-france-and-spain-how-many-students-have-been-only-to-france-14-members-visited-germany-18-have-been",{"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},536535,"What interest will produce $5,850 mxn for a period of 2 years and 6 months at 18% annually?","1. Determine the principal amount (P):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P=5850\\,\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Convert the time period from years and months to only years:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t = 2 + \\frac{6}{12} = 2.5 \\, \\text{years}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Use the annual interest rate (r) expressed as a decimal:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 0.18\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Calculate the simple interest (I) using the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>I = P \\cdot r \\cdot t\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>I = 5850 \\cdot 0.18 \\cdot 2.5\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>I = 5850 \\cdot 0.45\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>I=2632.50\\,\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Answer:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>I=2632.50\\,\u003C/math-field>\u003C/math-field>",565,113,"what-interest-will-produce-5-850-mxn-for-a-period-of-2-years-and-6-months-at-18-annually",{"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},536534,"Find the domain of the following function: 0,5 P F(x) = x","1. Identify the function: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F(x) = x\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. This is a linear function.\u003Cbr />\n3. A linear function is defined for all real numbers since there are no restrictions like division by zero or taking the square root of a negative number.\u003Cbr />\n\u003Cbr />\nTherefore, the answer is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Domain: } (-\\infty, \\infty)\u003C/math-field>\u003C/math-field>",927,185,"find-the-domain-of-the-following-function-0-5-p-f-x-x",{"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},536533,"ESSAY ON THE IMPORTANCE OF THE ENGLISH LANGUAGE WORLDWIDE","**La importancia del idioma inglés en el mundo**\n\n El idioma inglés desempeña un papel fundamental en la comunicación global, ya que da forma a la forma en que las personas interactúan, realizan negocios y se entienden entre sí a través de fronteras. Su importancia se extiende más allá de la mera comunicación, influyendo en la educación, la tecnología, la diplomacia y la cultura. A medida que el mundo se vuelve cada vez más interconectado, la importancia del inglés continúa creciendo, convirtiéndolo en una herramienta indispensable en el panorama global actual.\n\n **Una lengua franca para la comunicación internacional**\n\n El inglés se ha convertido en la lengua franca dominante, una lengua puente que facilita la comunicación entre hablantes de diferentes lenguas nativas. En entornos internacionales, el inglés sirve como medio común para el diálogo, asegurando que personas de diversos orígenes puedan colaborar de manera efectiva. Esto es particularmente evidente en conferencias globales, negociaciones diplomáticas y organizaciones internacionales como las Naciones Unidas y la Unión Europea, donde el inglés suele ser el principal idioma de comunicación.\n\n **El lenguaje de la economía y los negocios globales**\n\n En el ámbito de los negocios y la economía, el inglés es crucial para el comercio internacional. Las corporaciones multinacionales, las instituciones financieras y los mercados globales operan principalmente en inglés, por lo que es esencial que los profesionales dominen el idioma. El dominio del idioma inglés abre puertas a oportunidades profesionales globales, lo que permite a las personas participar en negocios internacionales, acceder a mercados globales e interactuar con clientes y socios en todo el mundo. El predominio del inglés en las negociaciones comerciales, el marketing y las comunicaciones corporativas subraya su papel como activo clave en la economía global.\n\n **Una puerta de entrada al conocimiento y la educación**\n\n El inglés es el idioma de instrucción en muchas instituciones educativas prestigiosas de todo el mundo. Las universidades e instituciones de investigación de los países de habla inglesa suelen liderar la investigación y la innovación académicas, contribuyendo significativamente al conocimiento global. El acceso a revistas académicas, libros de texto y recursos en línea en inglés permite a los estudiantes e investigadores involucrarse en desarrollos de vanguardia y participar en el intercambio global de ideas. Por lo tanto, el dominio del inglés proporciona acceso a un vasto depósito de conocimientos y mejora las oportunidades educativas a escala internacional.\n\n **Influencia en medios y entretenimiento**\n\n El impacto del inglés se extiende al ámbito de los medios de comunicación y el entretenimiento, donde desempeña un papel central en la configuración de la cultura global. Las películas de Hollywood, la música popular y los programas de televisión en inglés llegan a audiencias de todo el mundo, influyendo en las tendencias culturales y fomentando el entendimiento intercultural. El atractivo global de los medios de comunicación en inglés facilita el intercambio cultural, promoviendo la diversidad y ampliando perspectivas. Además, la prevalencia del inglés en Internet y en las plataformas de redes sociales amplifica su influencia, permitiendo a las personas conectarse con comunidades globales y acceder a una gran cantidad de información y entretenimiento.\n\n **Diplomacia y Relaciones Internacionales**\n\n En diplomacia y relaciones internacionales, el inglés sirve como una herramienta crucial para la negociación y la cooperación. Como lenguaje común, permite a diplomáticos y responsables de políticas participar en debates, redactar tratados y resolver conflictos. El uso del inglés en contextos diplomáticos garantiza claridad y precisión, facilitando la resolución pacífica de problemas globales y fomentando la colaboración internacional.\n\n **Retos y oportunidades**\n\n Si bien la prominencia global del inglés ofrece numerosos beneficios, también presenta desafíos. El predominio del inglés puede contribuir a la homogeneización lingüística, amenazando la supervivencia de lenguas y culturas menos habladas. Los esfuerzos para promover el multilingüismo y preservar la diversidad lingüística son esenciales para garantizar que la influencia global del inglés no se produzca a expensas de la riqueza cultural.\n\n **Conclusión**\n\n La importancia global del idioma inglés es innegable, ya que sirve como eje en la comunicación internacional, los negocios, la educación, los medios y la diplomacia. Su uso generalizado facilita las interacciones interculturales, fomenta el crecimiento económico y permite el acceso a una gran cantidad de conocimientos y oportunidades. A medida que el mundo continúa evolucionando, es probable que persista la importancia del inglés como idioma global, dando forma a la forma en que las personas se conectan y colaboran a través de las fronteras. Equilibrar los beneficios del inglés con los esfuerzos por preservar la diversidad lingüística será crucial para mantener una comunidad global vibrante e inclusiva.",646,129,"essay-on-the-importance-of-the-english-language-worldwide",{"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},536531,"I WANT AN ESSAY ON THE IMPACT OF THE ENGLISH LANGUAGE WORLDWIDE I NEED AN INTRODUCTION A DEVELOPMENT AND A CONCLUSION\n WITH 3 BIBLIOGRAPHICAL SOURCES","El impacto del idioma inglés en todo el mundo\n\n Introducción\n\n El idioma inglés, a menudo considerado como una lengua franca global, ha dado forma significativa al mundo de innumerables maneras. Como medio de comunicación internacional, el inglés facilita las interacciones a través de fronteras y culturas, influyendo en diversos ámbitos, incluidos los negocios, la educación, los medios y la diplomacia. Su uso generalizado ha transformado las interacciones globales, convirtiéndola en una herramienta crucial para la conectividad y la colaboración en nuestro mundo cada vez más interconectado. Este ensayo explora el profundo impacto del idioma inglés en todo el mundo, destacando su papel en la comunicación global, el desarrollo económico y el intercambio cultural, al mismo tiempo que aborda los desafíos que plantea a la diversidad lingüística.\n\n Desarrollo\n\n Comunicación global y diplomacia\n\n El papel del inglés como lengua franca global es quizás su característica más definitoria. Como idioma predominante utilizado en la diplomacia internacional y las conferencias globales, el inglés permite una comunicación efectiva entre personas de diferentes orígenes lingüísticos. Organizaciones internacionales como las Naciones Unidas, la OTAN y la Organización Mundial del Comercio dependen en gran medida del inglés para llevar a cabo sus asuntos. Este lenguaje común facilita la negociación y la cooperación, permitiendo a las naciones abordar los problemas globales de manera colectiva. Según Crystal (2003), más de 1.500 millones de personas en todo el mundo utilizan el inglés, ya sea como lengua materna o como segunda lengua, lo que subraya su papel central en las interacciones globales (Crystal, D. (2003). *English as a Global Language* . Prensa de la Universidad de Cambridge).\n\n Influencia económica\n\n En el ámbito de los negocios y la economía, el inglés se ha convertido en el idioma dominante. Las corporaciones multinacionales, las instituciones financieras y los mercados globales operan principalmente en inglés, por lo que es esencial que los profesionales dominen el idioma. La capacidad de comunicarse en inglés abre puertas a oportunidades profesionales internacionales y facilita el comercio global. Un informe del British Council destaca que el dominio del inglés está vinculado a una mayor productividad económica y competitividad, demostrando su importancia en la economía global (British Council. (2013). *English and the Economy: The Impact of English on the Global Economy*) . Como el inglés sigue siendo el idioma de los negocios, influye en las políticas económicas, las estrategias de mercado y las negociaciones internacionales.\n\n Intercambio cultural y medios\n\n El inglés también juega un papel fundamental en el intercambio cultural y los medios de comunicación. El dominio global de los medios de comunicación en inglés, incluidas las películas de Hollywood, la música popular y el contenido en línea, influye en las tendencias culturales y fomenta el entendimiento intercultural. Los medios en inglés llegan a audiencias de todo el mundo, moldeando percepciones y promoviendo la diversidad cultural. Según un análisis de The Economist, los medios en idioma inglés tienen un impacto significativo en la cultura global, convirtiéndolos en una poderosa herramienta tanto para el entretenimiento como para la difusión de información (The Economist. (2014). *The English Language: How English Became the World's Language *). Esta influencia cultural se extiende a Internet, donde el inglés es el idioma más utilizado, lo que facilita la comunicación global y el acceso a la información.\n\n Desafíos a la diversidad lingüística\n\n Si bien la prevalencia global del inglés ofrece numerosos beneficios, también plantea desafíos. El predominio del inglés puede llevar a la marginación de lenguas y culturas menos habladas. Los lingüistas advierten que la difusión del inglés puede contribuir a la homogeneización lingüística, amenazando la supervivencia de las lenguas minoritarias. Los esfuerzos para promover el multilingüismo y preservar la diversidad lingüística son esenciales para garantizar que la influencia global del inglés no se produzca a expensas de la riqueza cultural.\n\n Conclusión\n\n El impacto del idioma inglés en todo el mundo es profundo y multifacético. Como lengua franca global, el inglés facilita la comunicación internacional, impulsa el crecimiento económico e influye en el intercambio cultural. Su uso generalizado en la diplomacia, los negocios y los medios de comunicación subraya su importancia en el mundo moderno. Sin embargo, el predominio del inglés también presenta desafíos, particularmente en lo que respecta a la diversidad lingüística. Equilibrar los beneficios del inglés con los esfuerzos por preservar y promover otros idiomas será crucial para mantener una comunidad global diversa e inclusiva. El idioma inglés continúa dando forma a las interacciones globales, lo que refleja su papel central a la hora de conectar a las personas y fomentar la colaboración a través de las fronteras.\n\n Bibliografía\n\n 1. Cristal, D. (2003). El inglés como idioma global. Prensa de la Universidad de Cambridge.\n 2. Consejo Británico. (2013). El inglés y la economía: el impacto del inglés en la economía global.\n 3. El economista. (2014). El idioma inglés: cómo el inglés se convirtió en el idioma del mundo.",745,149,"i-want-an-essay-on-the-impact-of-the-english-language-worldwide-i-need-an-introduction-a-development-and-a-conclusion-with-3-bibliographical-sources",{"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},536530,"How do you get from 683486441 to 745694223","To find the difference between the two numbers, subtract the smaller number from the larger number:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>745694223 - 683486441 = 62107882\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nTherefore, the answer is \u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>62107882.\u003C/math-field>\u003C/math-field>",877,175,"how-do-you-get-from-683486441-to-745694223",{"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},536529,"15x-20=6x-(x+2)+(-x+3)","Remove parentheses \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$(-a)=-a$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$15x-20=6x-(x+2)-x+3$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Group like terms \n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$15x-20=6x-x-(x+2)+3$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Add similar elements: \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ 6x-x=5x$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$15x-20=5x-(x+2)+3$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Expand \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$5x-(x+2)+3:{\\quad}4x+1$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$15x-20=4x+1$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Move \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ 20 $\u003C/math-field>to the right side \n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$15x=4x+21$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Move \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ 4x $\u003C/math-field>to the left side \n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$11x=21$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Divide both sides by \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$11$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$x=\\frac{21}{11}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1438,288,"15x-20-6x-x-2-x-3",{"id":156,"category":36,"text_question":157,"photo_question":38,"text_answer":158,"step_text_answer":8,"step_photo_answer":8,"views":159,"likes":146,"slug":160},536528,"30w-(-w+6)+(-5w+4)=-(5w+6)+(-8+3w)","1. Distribute the negative signs:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>30w + w - 6 - 5w + 4 = -5w - 6 - 8 + 3w\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Combine like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26w - 2 = -2w - 14\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Move all terms involving \$ w \$ to one side and constants to the other:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26w + 2w = -14 + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>28w = -12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve for \$ w \$:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>w = \\frac{-12}{28} = \\frac{-6}{14} = \\frac{-3}{7}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Correcting the calculation:\u003Cbr />\nReturning to simplifying the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26w - 2 = -2w - 14\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Add \$ 2w \$ to both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26w + 2w - 2 = -14\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>28w - 2 = -14\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Add \$ 2 \$ to both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>28w = -12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Divide by 28:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>w = \\frac{-12}{28} = -\\frac{3}{7}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nRechecking the steps from start to ensure correction:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>30w + w - 6 - 5w + 4 = -5w - 6 - 8 + 3w\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nCombine like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26w - 2 = -2w - 14\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nRechecking this:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26w + 2w = -14 + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nNow getting correctly:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>28w = -12\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>w = \\frac{-12}{28} = -\\frac{3}{7}\u003C/math-field>\u003C/math-field>",875,"30w-w-6-5w-4-5w-6-8-3w",{"id":162,"category":36,"text_question":163,"photo_question":38,"text_answer":164,"step_text_answer":8,"step_photo_answer":8,"views":165,"likes":166,"slug":167},536527,"Determine the largest and smallest value in the range 1 ≤ x ≤ 3 for the function f(x)= x^2 -x + 1","Evaluate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x) = x^2 - x + 1\u003C/math-field>\u003C/math-field> at the endpoints:\u003Cbr />\n\u003Cbr />\n1. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(1) = 1^2 - 1 + 1 = 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(3) = 3^2 - 3 + 1 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSince there are no critical points within the interval \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 \\leq x \\leq 3\u003C/math-field>\u003C/math-field>, the smallest value is 1 and the largest value is 7.",491,98,"determine-the-largest-and-smallest-value-in-the-range-1-x-3-for-the-function-f-x-x-2-x-1",{"id":169,"category":36,"text_question":170,"photo_question":38,"text_answer":171,"step_text_answer":8,"step_photo_answer":8,"views":172,"likes":173,"slug":174},536523,"calculated using 31x12 algorithm","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>31 \\times 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n1. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>31 \\times 2 = 62\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>31 \\times 10 = 310\u003C/math-field>\u003C/math-field>\u003Cbr />\n3. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>62 + 310 = 372\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nResposta: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>372\u003C/math-field>\u003C/math-field>",371,74,"calculated-using-31x12-algorithm",{"first":6,"last":176,"prev":177,"next":178},188,66,68,{"current_page":180,"from":181,"last_page":176,"links":182,"path":216,"per_page":217,"to":218,"total":219},67,1321,[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},64,"64",{"url":194,"label":195,"active":185},65,"65",{"url":177,"label":197,"active":185},"66",{"url":180,"label":199,"active":200},"67",true,{"url":178,"label":202,"active":185},"68",{"url":204,"label":205,"active":185},69,"69",{"url":207,"label":208,"active":185},70,"70",{"url":210,"label":211,"active":185},187,"187",{"url":176,"label":213,"active":185},"188",{"url":178,"label":215,"active":185},"Next »","https://api.math-master.org/api/question",20,1340,3741,{"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},532052,"-6n+5=-13","6n-5-13",{"id":228,"category":36,"text_question":229,"slug":230},532061,"A car tire can rotate at a frequency of 3000 revolutions per minute. Given that a typical tire radius is 0.5 m, what is the centripetal acceleration of the tire?","a-car-tire-can-rotate-at-a-frequency-of-3000-revolutions-per-minute-given-that-a-typical-tire-radius-is-0-5-m-what-is-the-centripetal-acceleration-of-the-tire",{"id":232,"category":36,"text_question":233,"slug":234},532304,"what is 9% of 307","what-is-9-of-307",{"id":236,"category":36,"text_question":237,"slug":238},533896,"What payment 7 months from now would be equivalent in value to a $3,300 payment due 23 months from now? The value of money is 2.7% simple interest. Round your answer to 2 decimal places.\nShow all work and how you arrive at the answer..","what-payment-7-months-from-now-would-be-equivalent-in-value-to-a-3-300-payment-due-23-months-from-now-the-value-of-money-is-2-7-simple-interest-round-your-answer-to-2-decimal-places-show-all-work",{"id":240,"category":36,"text_question":241,"slug":242},533971,"The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly","the-sum-of-two-numbers-is-6-and-the-sum-of-their-squares-is-28-find-these-numbers-exactly",{"id":244,"category":36,"text_question":245,"slug":246},533979,"A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.","a-bird-randomly-chooses-to-land-on-1-of-12-perches-available-in-its-aviary-determine-the-probability-of-it-landing-on-a-perch-numbered-8-and-then-on-a-perch-marked-with-a-prime-number-take-into-acco",{"id":248,"category":36,"text_question":249,"slug":250},534008,"Supposed 60% of the register voters in a country or democrat. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64% round your answer to four decimal places","supposed-60-of-the-register-voters-in-a-country-or-democrat-if-a-sample-of-793-voters-is-selected-what-is-the-probability-that-the-sample-proportion-of-democrats-will-be-greater-than-64-round-your",{"id":252,"category":36,"text_question":253,"slug":254},534030,"The actual length of an object is 1.3 m\n . If the blueprint uses a scale of 1 : 12\n , what is the length of the line on the drawing?","the-actual-length-of-an-object-is-1-3-m-if-the-blueprint-uses-a-scale-of-1-12-what-is-the-length-of-the-line-on-the-drawing",{"id":256,"category":36,"text_question":257,"slug":258},534088,"Log(45)","log-45",{"id":260,"category":36,"text_question":261,"slug":262},534098,"A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.","a-person-borrows-rm-1000-from-a-bank-at-an-interest-rate-of-10-after-some-time-he-pays-the-bank-rm-1900-as-full-and-final-settlement-of-the-loan-estimate-the-duration-of-his-loan",{"id":264,"category":36,"text_question":265,"slug":266},534100,"Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.","reparameterize-the-curve-r-t-cos-t-i-without-t-j-t-k-by-the-arc-length",{"id":268,"category":36,"text_question":269,"slug":270},534222,"A circular window has a rubber molding around the edge. If the window has a radius of 250 mm, how long is the piece of molding that is required ? (To the nearest mm)","a-circular-window-has-a-rubber-molding-around-the-edge-if-the-window-has-a-radius-of-250-mm-how-long-is-the-piece-of-molding-that-is-required-to-the-nearest-mm",{"id":272,"category":36,"text_question":273,"slug":274},534282,"There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?","there-are-3-orchards-a-b-and-c-orchard-a-has-60-fewer-trees-than-orchard-b-orchard-c-has-3-times-as-many-trees-as-orchard-b-if-the-three-orchards-have-430-trees-altogether-how-many-trees-does-or",{"id":276,"category":36,"text_question":277,"slug":278},534469,"Determine the kinetic energy of a baseball whose mass is 100 grams and has a speed of 30 m/s.","determine-the-kinetic-energy-of-a-baseball-whose-mass-is-100-grams-and-has-a-speed-of-30-m-s",{"id":280,"category":36,"text_question":281,"slug":282},534492,"Find the equation of a straight line that has slope 3 and passes through the point of (1, 7) .\nWrite the equation of the line in general forms","find-the-equation-of-a-straight-line-that-has-slope-3-and-passes-through-the-point-of-1-7-write-the-equation-of-the-line-in-general-forms",{"id":284,"category":36,"text_question":285,"slug":286},534507,"Find the set of points formed by the expression 𝜋\u003C|𝑧−4+2𝑖|\u003C3𝜋.","find-the-set-of-points-formed-by-the-expression-z-4-2i-3",{"id":288,"category":36,"text_question":289,"slug":290},534549,"Square root of 169 with steps","square-root-of-169-with-steps",{"id":292,"category":36,"text_question":293,"slug":294},534613,"How many digits are there in Hindu-Arabic form of numeral 26 × 1011","how-many-digits-are-there-in-hindu-arabic-form-of-numeral-26-1011",{"id":296,"category":36,"text_question":297,"slug":298},534637,"g(x)=3(x+8). What is the value of g(12)","g-x-3-x-8-what-is-the-value-of-g-12",{"id":300,"category":36,"text_question":301,"slug":302},534641,"3(x-4)=156","3-x-4-156",{"data":304},[305,315,324,334,346,355,364,373,384,391,402,410,422,431,438,445,454,465,473,483],{"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":166},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,{"id":385,"name":386,"photo":387,"certificates":388,"diplomas":389,"biography":390,"rating":383,"total_answer":62},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.",{"id":392,"name":393,"photo":394,"certificates":395,"diplomas":399,"biography":400,"rating":383,"total_answer":401},13,"Maude","https://api.math-master.org/img/experts/13/13.webp",[396,397,398],"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":403,"name":404,"photo":405,"certificates":406,"diplomas":407,"biography":408,"rating":383,"total_answer":409},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":411,"name":412,"photo":413,"certificates":414,"diplomas":419,"biography":420,"rating":383,"total_answer":421},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[415,416,417,418],"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":423,"photo":424,"certificates":425,"diplomas":428,"biography":430,"rating":383,"total_answer":314},"Jett","https://api.math-master.org/img/experts/6/6.webp",[426,427],"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",[429],"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":432,"photo":433,"certificates":434,"diplomas":435,"biography":436,"rating":383,"total_answer":437},"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":439,"name":440,"photo":441,"certificates":442,"diplomas":443,"biography":444,"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":446,"photo":447,"certificates":448,"diplomas":449,"biography":451,"rating":452,"total_answer":453},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[450],"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.",4.6,103,{"id":455,"name":456,"photo":457,"certificates":458,"diplomas":459,"biography":463,"rating":452,"total_answer":464},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp",[],[460,461,462],"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":466,"name":467,"photo":468,"certificates":469,"diplomas":470,"biography":471,"rating":452,"total_answer":472},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.",95,{"id":474,"name":475,"photo":476,"certificates":477,"diplomas":478,"biography":481,"rating":452,"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":452,"total_answer":333},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.",{"$sicons":493},{"bxl:facebook-circle":494,"bxl:instagram":498,"mdi:web":500,"la:apple":502,"ph:google-logo-bold":505,"ph:google-logo":508},{"left":495,"top":495,"width":496,"height":496,"rotate":495,"vFlip":185,"hFlip":185,"body":497},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":495,"top":495,"width":496,"height":496,"rotate":495,"vFlip":185,"hFlip":185,"body":499},"\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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