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^x+1 +1 describe transformation","","Solution:\u003Cbr />\n1. Given function:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -2

$4$ ^{x+1} + 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Base function:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 4^x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Identify transformations step-by-step:\u003Cbr />\n - **Translation horizontally**: The function has \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>

$x+1$ \u003C/math-field>\u003C/math-field> as the exponent instead of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>. This indicates a horizontal shift to the left by 1 unit.\u003Cbr />\n - **Vertical stretch and reflection**: The coefficient before \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n - **Vertical stretch**: The factor \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\u003C/math-field>\u003C/math-field> indicates that the function is stretched vertically by a factor of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n - **Reflection**: The negative sign indicates a reflection across the x-axis.\u003Cbr />\n - **Vertical translation**: The \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>+1\u003C/math-field>\u003C/math-field> outside the function indicates a vertical shift upwards by 1 unit.\u003Cbr />\n\u003Cbr />\n4. Describe the complete transformation:\u003Cbr />\n - The function \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 4^x\u003C/math-field>\u003C/math-field> undergoes the following transformations: a horizontal shift to the left by 1 unit, a vertical stretch by a factor of 2, reflection across the x-axis, and finally a vertical shift upwards by 1 unit.",1255,251,"y-2-4-x-1-1-describe-transformation",{"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},538086,"Add the polynomials g

$x$ =x3-2x2+3x-1+4x2-x+2","Solution: \u003Cbr />\n1. Write down the given polynomials:\u003Cbr />\n- First polynomial: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g

$x$ = x^3 - 2x^2 + 3x - 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Second polynomial: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x^2 - x + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Align and add the polynomials term by term:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g

$x$ = x^3 - 2x^2 + 3x - 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x^2 - x + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add the corresponding like terms:\u003Cbr />\n- For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3\u003C/math-field>\u003C/math-field> terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3\u003C/math-field>\u003C/math-field>\u003Cbr />\n- For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2\u003C/math-field>\u003C/math-field> terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2x^2 + 4x^2 = 2x^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x - x = 2x\u003C/math-field>\u003C/math-field>\u003Cbr />\n- For constant terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-1 + 2 = 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. The resulting polynomial after addition is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3 + 2x^2 + 2x + 1\u003C/math-field>\u003C/math-field>",739,148,"add-the-polynomials-g-x-x3-2x2-3x-1-4x2-x-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},538085,"R=3m. Calculate the volume of the sphere. Round to the nearest tenth if necessary","1. The formula for the volume of a sphere is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi R^3 \u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>2. Substitute the given radius \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> R = 3 \\, \\text{m} \u003C/math-field>\u003C/math-field> into the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi

$3$ ^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3^3 = 27 \u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>4. Thus, the volume becomes:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi \\times 27 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify the expression:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4 \\times 27}{3} \\pi = 36 \\pi \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Use the approximation \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\pi \\approx 3.1416 \u003C/math-field>\u003C/math-field> :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 36 \\times 3.1416 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Calculate the approximate volume:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V\\approx113.0973\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>8. Round to the nearest tenth:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 113.1 \\, \\text{m}^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, the volume of the sphere is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 113.1 \\, \\text{m}^3 \u003C/math-field>\u003C/math-field> .",1203,241,"r-3m-calculate-the-volume-of-the-sphere-round-to-the-nearest-tenth-if-necessary",{"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},538084,"Width of 12 in. Calculate the volume of the sphere. Round to the nearest tenth if necessary","1. Identify the radius of the sphere. Given the width is 12 inches, the diameter is 12 inches. Therefore, the radius is half of the diameter:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = \\frac{12}{2} = 6 \\, \\text{in} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the formula for the volume of a sphere:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi r^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute the radius into the formula:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi

$6$ ^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi \\times 216 = \\frac{864}{3} \\pi = 288 \\pi \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Approximate using \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\pi \\approx 3.1416 \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 288 \\times 3.1416 = 904.8 \\, \\text{in}^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. The volume of the sphere, rounded to the nearest tenth, is approximately:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 904.8 \\, \\text{in}^3 \u003C/math-field>\u003C/math-field>",278,56,"width-of-12-in-calculate-the-volume-of-the-sphere-round-to-the-nearest-tenth-if-necessary",{"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},538083,"Calculate the volume

$to the nearest tenth of a cubic centimeter$ of a golf ball whose diameter is 4.267cm","1. The formula for the volume of a sphere is given by \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{4}{3} \\pi r^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>2. The diameter of the golf ball is given as 4.267 cm, so the radius is half of that: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{4.267}{2} = 2.1335 \\, \\text{cm}\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>3. Substitute the radius into the volume formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{4}{3} \\pi

$2.1335$ ^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>4. Calculate the cube of the radius: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>

$2.1335$ ^3 = 9.707432537375\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>5. Substitute this back into the formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V=\\frac{4}{3}\\pi\\times9.707432537375\\approx40.7\\,\\text{cm}^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>6. The volume of the golf ball is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>40.7\\,\\text{cm}^3\u003C/math-field>\u003C/math-field> .",1440,288,"calculate-the-volume-to-the-nearest-tenth-of-a-cubic-centimeter-of-a-golf-ball-whose-diameter-is-4-267cm",{"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},538082,"Find the length of each base edge

$to the nearest tenth of a meter$ of the 24m tall glass square pyramids of the Muttart Conservatory in Alberta, Canada, if each contains 5280m^3 of space","1. Volume V of a square pyramid is given by the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{1}{3} B h\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>where B is the area of the base and h is the height of the pyramid.\u003Cbr>\u003Cbr>2. Given that the height h = 24 m and the volume V = 5280 m^3.\u003Cbr>\u003Cbr>3. The base is square, so if the side length of the base is s, then:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = s^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substituting into the volume formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5280 = \\frac{1}{3} s^2 \\times 24\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify and solve for s^2:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5280 = 8 s^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s^2 = \\frac{5280}{8} = 660\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Solve for s:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{660} \\approx 25.7\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. To find the length of each base edge to the nearest tenth of a meter, compute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s \\approx 25.7 \\, \\text{m}\u003C/math-field>\u003C/math-field>",418,84,"find-the-length-of-each-base-edge-to-the-nearest-tenth-of-a-meter-of-the-24m-tall-glass-square-pyramids-of-the-muttart-conservatory-in-alberta-canada-if-each-contains-5280m-3-of-space",{"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},538081,"An observer is 150 meters away\n distance of a hot air balloon online\n straight line at ground level. From your position,\n measures an elevation angle of 40° up to\n the base of the balloon. At what height is\n find the hot air balloon?","Solution:\u003Cbr />\n1. Dado:\u003Cbr />\n- Distancia horizontal desde el observador hasta la base del globo: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>d = 150 \\ m\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Ángulo de elevación: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta = 40^{\\circ}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Usamos la función tangente para encontrar la altura \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h\u003C/math-field>\u003C/math-field> del globo aerostático. La tangente de un ángulo en un triángulo rectángulo es la razón entre la altura y la distancia horizontal:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan

$\\theta$ = \\frac{h}{d}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Sustituimos los valores conocidos en la ecuación:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan

$40^{\\circ}$ = \\frac{h}{150}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Resolvemos para \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h = 150 \\times \\tan

$40^{\\circ}$ \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculamos el valor numérico:\u003Cbr />\n* Usando una calculadora, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan

$40^{\\circ}$ \\approx 0.8391\u003C/math-field>\u003C/math-field>\u003Cbr />\n* Entonces: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h \\approx 150 \\times 0.8391 = 125.865 \\ m\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nLa altura del globo aerostático es aproximadamente \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>125.865 \\ m\u003C/math-field>\u003C/math-field>.",667,133,"an-observer-is-150-meters-away-distance-of-a-hot-air-balloon-online-straight-line-at-ground-level-from-your-position-measures-an-elevation-angle-of-40-up-to-the-base-of-the-balloon-at-what-hei",{"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},538080,"A plane ticket has gone up 18%, now costing

$4,720. How much did it cost before the increase?","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Solution:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> be the original price of the plane ticket.\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> increased by 18% means the new price is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P + 0.18P = 1.18P\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Set up the equation based on the problem statement:\u003Cbr />\n- The new price \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 4,720\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1.18P = 4,720\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Divide both sides by 1.18 to isolate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field>.\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\frac{4,720}{1.18}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P \\approx 4,000\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>\\text{Answer:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The original price of the plane ticket was approximately USD 4,000.",726,145,"a-plane-ticket-has-gone-up-18-now-costing-4-720-how-much-did-it-cost-before-the-increase",{"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},538078,"H=8mm, r=2mm. Calculate the volume of the cone round to the nearest tenth if necessary","1. Use the formula for the volume of a cone: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi r^2 H \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the given values: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> H = 8 \\, \\text{mm}, \\, r = 2 \\, \\text{mm} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (2)^2 (8) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate \$ (2)^2 \$:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (2)^2 = 4 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substitute and compute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (4)(8) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (32) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Calculate the product: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{32}{3} \\pi \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Calculate:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V\\approx33.51032\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Round to the nearest tenth:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 33.5 \\, \\text{mm}^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>This is the answer: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 33.5 \\, \\text{mm}^3 \u003C/math-field>\u003C/math-field>",631,126,"h-8mm-r-2mm-calculate-the-volume-of-the-cone-round-to-the-nearest-tenth-if-necessary",{"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},538076,"Dividing 218 or 172 by the natural number n, you get a remainder of 11. Dividing n by 11, you get a remainder equal to:","** \u003Cbr>\u003Cbr>1. Since dividing 218 by n gives a remainder of 11, 218 - 11 = 207 is divisible by n : \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>207\\equiv0\\pmod{n}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Similarly, dividing 172 by n gives a remainder of 11, so 172 - 11 = 161 is divisible by n :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>161\\equiv0\\pmod{n}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. n must be a common divisor of 207 and 161. Find the greatest common divisor of 207 and 161:\u003Cbr>\u003Cbr>- First, find the difference: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 207 - 161 = 46 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Find the prime factorization of 46:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 46 = 2 \\times 23 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Prime factorization of 161:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 161 = 7 \\times 23 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Common factor is 23.\u003Cbr>\u003Cbr>4. Therefore, the possible value of n should be 23 (since other divisions have factors that don't divide both). Now, divide n = 23 by 11:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 23 \\div 11 = 2 \\, \\text{R} \\, 1 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Thus, the remainder of dividing n by 11 is 1\u003Cbr>\u003Cbr>",1233,247,"dividing-218-or-172-by-the-natural-number-n-you-get-a-remainder-of-11-dividing-n-by-11-you-get-a-remainder-equal-to",{"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},538074,"R=24 inches\nCalculate the surface area of the sphere","1. The formula to calculate the surface area of a sphere is given by: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 4 \\pi R^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the value of the radius \$ R = 24 \$ inches into the formula: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 4 \\pi (24)^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate the square of the radius:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (24)^2 = 576 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Multiply by 4:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4 \\times 576 = 2304 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. The surface area is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A=2304\\pi=7238.23\u003C/math-field>\u003C/math-field> square inches \u003Cbr>\u003Cbr>Therefore, the surface area of the sphere is 7238.23 square inches.",923,185,"r-24-inches-calculate-the-surface-area-of-the-sphere",{"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},538073,"Andrés's age is three times Quan's.\n plus wins and both ages add up to 69 years. Nillar\n both ages.","Solution:\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> be the age of Andrés.\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field> be the age of Quan.\u003Cbr />\n\u003Cbr />\n2. Set up the equations based on the problem:\u003Cbr />\n- Andrés is three times as old as Quan: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The sum of their ages is 69: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a + q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field> into the second equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3q + q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify the equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q = \\frac{69}{4}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Compute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q = 17.25\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> using the equation \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3 \\times 17.25\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Compute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 51.75\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore:\u003Cbr />\n- Quan is approximately 17.25 years old.\u003Cbr />\n- Andrés is approximately 51.75 years old.",553,111,"andres-s-age-is-three-times-quan-s-plus-wins-and-both-ages-add-up-to-69-years-nillar-both-ages",{"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},538072,"Andrew's age is three times John's plus nine years, and their ages add up to 69 years. Find both ages.","Solution:\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> be Juan's age.\u003Cbr />\n- Andrés' age is then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Set up the equation for the total age:\u003Cbr />\n- Juan's age \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> plus Andrés' age \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9\u003C/math-field>\u003C/math-field> equals 69.\u003Cbr />\n\u003Cbr />\n3. Equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + (3x + 9) = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify and 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 + 3x + 9 = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + 9 = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = 60\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 15\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Find Andrés' age:\u003Cbr />\n- Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 15\u003C/math-field>\u003C/math-field> into Andrés' age expression:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9 = 3(15) + 9 = 45 + 9 = 54\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the ages are:\u003Cbr />\n- Juan: 15 years\u003Cbr />\n- Andrés: 54 years",531,106,"andrew-s-age-is-three-times-john-s-plus-nine-years-and-their-ages-add-up-to-69-years-find-both-ages",{"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},538071,"Solve the following linear equations:\n 1) 5x-3= 3X+7","Solution:\u003Cbr />\n1. Given Equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3 = 3x + 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field> from both sides to simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3x - 3 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Combine like terms:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - 3 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Add 3 to both sides to isolate the term with the variable:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x = 10\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Divide both sides by 2 to 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 = 5\u003C/math-field>\u003C/math-field>",1382,276,"solve-the-following-linear-equations-1-5x-3-3x-7",{"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},538070,"Solve the following linear equations:\n\n 2) 2x+4- 5x = x+8-5×","1. Start with the original equation: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x + 4 - 5x = x + 8 - 5x\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Combine like terms on both sides:\u003Cbr>\u003Cbr>- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - 5x + 4 = -3x + 4\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x - 5x + 8 = -4x + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>So the equation becomes:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-3x + 4 = -4x + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x\u003C/math-field>\u003C/math-field> to both sides to get:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 4 = 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field> from both sides:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 4\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>",674,135,"solve-the-following-linear-equations-2-2x-4-5x-x-8-5",{"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},538069,"15=75% of ?","\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>$ \\frac{x}{15}=\\frac{4}{3}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$ x=20

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",467,93,"15-75-of",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":90,"slug":153},538067,"Naria Wants to build a perimeter wall fence around 400 sqm lot. The frontage of the lot is 20 meters. The wall height is 1.2 meters below the ground and 3.8 meters above the ground .\nThe cost of constructing the wall is 750 per square meter. Additionally,she plans to install a 5-meter-wide gate that costs ₱50,000.\nHow much Maria spend in total for the wall and the gate\na. Php 281,250.00\nb. Php 106,250.00\nc. Php 331,250.00\nd. Php 218,250.00","1. Determine the dimensions of the lot. Given the frontage is 20 meters, calculate the other side using the area:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Area} = 20 \\times x = 400 \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{400}{20} = 20 \\, \\text{meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Calculate the perimeter of the lot:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Perimeter} = 2 \\times (20 + 20) = 80 \\, \\text{meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate the total height of the wall:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Total height} = 1.2 + 3.8 = 5 \\, \\text{meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate the wall area excluding the gate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Wall area} = (\\text{Perimeter} - \\text{Gate width}) \\times \\text{Total height} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Wall area} = (80 - 5) \\times 5 = 75 \\times 5 = 375 \\, \\text{sqm} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate the cost of the wall:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Wall cost} = 375 \\times 750 = 281,250 \\, \\text{PHP} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Calculate total cost including the gate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Total cost} = \\text{Wall cost} + \\text{Gate cost} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Total cost} = 281,250 + 50,000 = 331,250 \\, \\text{PHP} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Therefore, the total cost is: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Php} \\, 331,250.00 \u003C/math-field>\u003C/math-field>",727,"naria-wants-to-build-a-perimeter-wall-fence-around-400-sqm-lot-the-frontage-of-the-lot-is-20-meters-the-wall-height-is-1-2-meters-below-the-ground-and-3-8-meters-above-the-ground-the-cost-of-const",{"id":155,"category":36,"text_question":156,"photo_question":38,"text_answer":157,"step_text_answer":8,"step_photo_answer":8,"views":158,"likes":76,"slug":159},538066,"2. A rectangular lot has a\n30 meters.\nallocated along the frontage. What is the gross area\nfrontage of 18 meters and a depth of\nHowever, a public right of way of 3 meters is\nReve\nof\nthe\nlot?\na. 520 sqm\nb. 540 sqm\nC. 560 sqm\nd. 580 sqm\nReV","1. Calculate the area of the rectangular lot without the right of way:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Area}_{\\text{total}} = \\text{frontage} \\times \\text{depth} = 18 \\, \\text{m} \\times 30 \\, \\text{m} = 540 \\, \\text{sqm} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. No need to subtract any area because the problem states that the right of way has already been accounted for in the dimensions provided.\u003Cbr />\n\u003Cbr />\n3. Therefore, the gross area of the lot remains:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 540 \\, \\text{sqm} \u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cbr />\nThus, the answer is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>540 \\, \\text{sqm}\u003C/math-field>\u003C/math-field>.",420,"2-a-rectangular-lot-has-a-30-meters-allocated-along-the-frontage-what-is-the-gross-area-frontage-of-18-meters-and-a-depth-of-however-a-public-right-of-way-of-3-meters-is-reve-of-the-lot-a-520-sq",{"id":161,"category":36,"text_question":162,"photo_question":38,"text_answer":163,"step_text_answer":8,"step_photo_answer":8,"views":164,"likes":165,"slug":166},538065,"A triangular lot has a base of 15 meters and heights of 10 meters . What is the total area of the lot ?","1. The formula for the area of a triangle is given by:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = \\frac{1}{2} \\times \\text{base} \\times \\text{height} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n2. Substitute the given values into the formula:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = \\frac{1}{2} \\times 15 \\times 10 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n3. Calculate the area:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = \\frac{1}{2} \\times 150 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n4. Simplify the expression:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 75 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nTherefore, the total area of the lot is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>75 \\, \\text{square meters}\u003C/math-field>\u003C/math-field>.",425,85,"a-triangular-lot-has-a-base-of-15-meters-and-heights-of-10-meters-what-is-the-total-area-of-the-lot",{"id":168,"category":36,"text_question":169,"photo_question":38,"text_answer":170,"step_text_answer":8,"step_photo_answer":8,"views":171,"likes":172,"slug":173},538064,"4x+(x-3)=2x-(3x-4)+5","Solution:\u003Cbr />\n1. Simplify both sides of the equation.\u003Cbr />\n- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + (x - 3) = 4x + x - 3 = 5x - 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - (3x - 4) + 5 = 2x - 3x + 4 + 5 = -x + 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. The equation is now: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3 = -x + 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> to both sides to eliminate the \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-x\u003C/math-field>\u003C/math-field> from the right side and simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x + x - 3 = 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6x - 3 = 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Add 3 to both sides to isolate terms with \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>6x = 9 + 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6x = 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Divide both sides by 6 to 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{12}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Simplify the fraction:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>",1332,266,"4x-x-3-2x-3x-4-5",{"first":6,"last":175,"prev":8,"next":10},187,{"current_page":6,"from":6,"last_page":175,"links":177,"path":211,"per_page":212,"to":212,"total":213},[178,181,184,186,188,190,192,195,198,201,204,207,209],{"url":6,"label":179,"active":180},"1",true,{"url":10,"label":182,"active":183},"2",false,{"url":13,"label":185,"active":183},"3",{"url":16,"label":187,"active":183},"4",{"url":19,"label":189,"active":183},"5",{"url":22,"label":191,"active":183},"6",{"url":193,"label":194,"active":183},7,"7",{"url":196,"label":197,"active":183},8,"8",{"url":199,"label":200,"active":183},9,"9",{"url":202,"label":203,"active":183},10,"10",{"url":205,"label":206,"active":183},186,"186",{"url":175,"label":208,"active":183},"187",{"url":10,"label":210,"active":183},"Next »","https://api.math-master.org/api/question",20,3737,{"data":215},{"id":216,"category":36,"slug":217,"text_question":218,"photo_question":8,"text_answer":219,"step_text_answer":8,"step_photo_answer":8,"views":220,"likes":221,"expert":222},537390,"hi-i-am-to-prove-this-e-x-int-0-infinity-1-f-x-dx-we-are-to-work-from-left-to-right-that-is-start-from-the-definition-of-the-expectation","Hi\nI am to prove this:\n\nE(X) =int_0^infinity [1 − F (x)]dx.\n\nWe are to work from left to right. That is, start from the definition of the expectation.","1. Start from the definition of the expectation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E(X) = \\int_0^\\infty x f(x) \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the integration by parts formula, where \$ u = x \$ and \$ dv = f(x) \\, dx \$:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int u \\, dv = uv - \\int v \\, du\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Compute \$ du \$ and \$ v \$:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>du = dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>v = \\int f(x) \\, dx = F(x)\u003C/math-field>\u003C/math-field>\u003Cbr />\n(Where \$ F(x) \$ is the cumulative distribution function)\u003Cbr />\n\u003Cbr />\n4. Apply integration by parts:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int_0^\\infty x f(x) \\, dx = \\Big[ x F(x) \\Big]_0^\\infty - \\int_0^\\infty F(x) \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Evaluate the boundary term:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Big[ x F(x) \\Big]_0^\\infty = \\lim_{x \\to \\infty} x F(x) - 0 \\cdot F(0) = 0 \\cdot 1 - 0 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n(Since \$ F(\\infty) = 1 \$ and \$ F(0) = 0 \$)\u003Cbr />\n\u003Cbr />\n6. Hence, we have:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E(X) = 0 - \\int_0^\\infty F(x) \\, dx = -\\int_0^\\infty F(x) \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Note that \$ 1 - F(x) \$ is valid for any \$ x \$:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E(X) = \\int_0^\\infty [1 - F(x)] \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAnswer: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E(X) = \\int_0^\\infty [1 - F(x)] dx\u003C/math-field>\u003C/math-field>",951,190,{"id":223,"name":224,"photo":225,"biography":226,"created_at":8,"updated_at":8,"rating":227,"total_answer":228},11,"Lurline","https://api.math-master.org/img/experts/11/11.webp","Hello there! I am Aditi Kumari. I am from India and currently I am pursuing my masters degree in the field of economics from the Delhi School of Economics - one of the topmost institution. I have completed my bachelors in economics from Shri Ram College of Commerce which is the top ranked college in India for the study of economics.\nEconomics is a study of application of mathematics on social science. since past four years I would say I have learned in depth application of math in the field of economics. It includes using advance calculus, linear algebra, statistics, econometrics, real analysis, and optimization. I was amazed initially that we can apply so much maths to social science subject. Before coming to university life I had no idea that for the next few years all I will be practicing is maths. Calculating marginal unitity, demand behaviour, doing differentiation, integration, algebra, etc. But having said that I have never got bored of the subject, every new topic opens up new dimension of the subject and you have to start thinking afresh. I would say it is this exciting nature of the subject which made it my favourite subject in school. I always wanted to keep studying maths and keep it as my bestie. The love for the subject was there since the first grade and continues till now.\nMaths was one subject in which I mostly scored the highest, but more than that it's the nature of the subject and insightful results which made me practice it again and again and never let me confine to just a single book.",4.6,104,{"data":230},{"questions":231},[232,236,240,244,248,252,256,260,264,268,272,276,280,284,288,292,296,300,304,308],{"id":233,"category":36,"text_question":234,"slug":235},532026,"Simplify the expression sin³(x)+cos³(x), using trigonometric functions","simplify-the-expression-sin-x-cos-x-using-trigonometric-functions",{"id":237,"category":36,"text_question":238,"slug":239},533905,"If L (-2, -5) reflected across y = -4. What are the coordinates of L?","if-l-2-5-reflected-across-y-4-what-are-the-coordinates-of-l",{"id":241,"category":36,"text_question":242,"slug":243},533909,"Express the following numbers in decimal system,\n where the subscript indicates the base: 110101 (SUBINDEX=2)","express-the-following-numbers-in-decimal-system-where-the-subscript-indicates-the-base-110101-subindex-2",{"id":245,"category":36,"text_question":246,"slug":247},534015,"(5u + 6)-(3u+2)=","5u-6-3u-2",{"id":249,"category":36,"text_question":250,"slug":251},534072,"Find the sum of the first 41 terms of the progression that\r\nbegins: 32, 24, 16, …","find-the-sum-of-the-first-41-terms-of-the-progression-that-begins-32-24-16",{"id":253,"category":36,"text_question":254,"slug":255},534195,"Calculate the minimum size of a simple random sample assuming a sampling error of 5% assuming that the population size is 100 elements","calculate-the-minimum-size-of-a-simple-random-sample-assuming-a-sampling-error-of-5-assuming-that-the-population-size-is-100-elements",{"id":257,"category":36,"text_question":258,"slug":259},534272,"The simple average of 15\n , 30\n , 40\n , and 45\n is","the-simple-average-of-15-30-40-and-45-is",{"id":261,"category":36,"text_question":262,"slug":263},534294,"TEST 123123+1236ttttt","test-123123-1236ttttt",{"id":265,"category":36,"text_question":266,"slug":267},534325,"Find the center coordinates and radius of a circle for an equation written as: 3x2 + 3y2 - 6y = —12× + 24","find-the-center-coordinates-and-radius-of-a-circle-for-an-equation-written-as-3x2-3y2-6y-12-24",{"id":269,"category":36,"text_question":270,"slug":271},534382,"Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will","twenty-five-students-in-a-class-take-a-test-for-which-the-average-grade-is-75-then-a-twenty-sixth-student-enters-the-class-takes-the-same-test-and-scores-70-the-test-average-grade-calculated-with",{"id":273,"category":36,"text_question":274,"slug":275},534393,"In an orchard there are 360 trees and they are distributed in 9 rows with the same number of trees in each row.\n 2 are rows of orange trees, 4 of apple trees and the rest are of pear trees.\n What fraction of the trees in the orchard are of each type of fruit tree?\n How many trees of each type are there?","in-an-orchard-there-are-360-trees-and-they-are-distributed-in-9-rows-with-the-same-number-of-trees-in-each-row-2-are-rows-of-orange-trees-4-of-apple-trees-and-the-rest-are-of-pear-trees-what-frac",{"id":277,"category":36,"text_question":278,"slug":279},534426,"2X+2=8","2x-2-8",{"id":281,"category":36,"text_question":282,"slug":283},534439,"A company has had the following data for two consecutive years.\n Total, asset item 3,100,500 euros 3,300,550 euros.\n Net amount of business figures 4,755,250 euros /5,100 euros\n Average number of workers employed during the year 64/70\n You can present a balance sheet in an abbreviated form","a-company-has-had-the-following-data-for-two-consecutive-years-total-asset-item-3-100-500-euros-3-300-550-euros-net-amount-of-business-figures-4-755-250-euros-5-100-euros-average-number-of-work",{"id":285,"category":36,"text_question":286,"slug":287},534470,"A company dedicated to the manufacture of shirts sells the units at a price of$ 40, the cost of each shirt is

$24, a commission is paid for the sale of a unit of shirt of$ 2 and its fixed costs are

$3500\n Determine the marginal contribution","a-company-dedicated-to-the-manufacture-of-shirts-sells-the-units-at-a-price-of-40-the-cost-of-each-shirt-is-24-a-commission-is-paid-for-the-sale-of-a-unit-of-shirt-of-2-and-its-fixed-costs-are-3",{"id":289,"category":36,"text_question":290,"slug":291},534503,"A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be \r\nNormally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and \r\nStandard deviation is measured in millimeters. \r\nWhat is the probability that an arbitrary route has a thickness less than 4.00 mm?","a-factory-produces-glass-for-windows-the-thickness-x-of-an-arbitrarily-selected-pane-of-glass-is-assumed-to-be-normally-distributed-with-expectation-u-4-10-and-standard-deviation-0-04-expect",{"id":293,"category":36,"text_question":294,"slug":295},534508,"Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DG⊥BG. If the area of the quadrilateral AGBD is equal to s, show that AC·BD≥2·s.","let-g-be-the-center-of-gravity-of-triangle-abc-we-draw-through-a-a-parallel-to-bc-on-which-we-take-a-point-d-so-that-dg-bg-if-the-area-of-the-quadrilateral-agbd-is-equal-to-s-show-that-ac-bd-2-s",{"id":297,"category":36,"text_question":298,"slug":299},534589,"Select a variable and collect at least 50 data values. For example, you may ask the students in the college how many hours they study per week or how old they are, etc.\na. Explain what your target population was.\nb. State how the sample was selected.\nc. Summarise the data by using a frequency table.\nd. Calculate all the descriptive measures for the data and describe the data\nset using the measures.\ne. Present the data in an appropriate way.\nf. Write a paragraph summarizing the data.","select-a-variable-and-collect-at-least-50-data-values-for-example-you-may-ask-the-students-in-the-college-how-many-hours-they-study-per-week-or-how-old-they-are-etc-a-explain-what-your-target-pop",{"id":301,"category":36,"text_question":302,"slug":303},534596,"calculate the product of 4 and 1/8","calculate-the-product-of-4-and-1-8",{"id":305,"category":36,"text_question":306,"slug":307},534629,"Find the orthogonal projection of a point A = (1, 2, -1) onto a line passing through the points\nPi = (0, 1, 1) and P2 = (1, 2, 3).","find-the-orthogonal-projection-of-a-point-a-1-2-1-onto-a-line-passing-through-the-points-pi-0-1-1-and-p2-1-2-3",{"id":309,"category":36,"text_question":310,"slug":311},534692,"A plant found at the bottom of a lake doubles in size every 10 days. Yeah\n It is known that in 300 days it has covered the entire lake, indicate how many days it will take to cover\n the entire lake four similar plants.","a-plant-found-at-the-bottom-of-a-lake-doubles-in-size-every-10-days-yeah-it-is-known-that-in-300-days-it-has-covered-the-entire-lake-indicate-how-many-days-it-will-take-to-cover-the-entire-lake-fo",{"data":313},{"questions":314},[315,319,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387,391],{"id":316,"category":36,"text_question":317,"slug":318},532017,"Hey👋🏻\n\nTap \"Create New Task\" to send your math problem.\n\nOne of our experts will start working on it right away!","hey-tap-create-new-task-to-send-your-math-problem-one-of-our-experts-will-start-working-on-it-right-away",{"id":320,"category":36,"text_question":321,"slug":322},532024,"2(2+2x)=12","2-2-2x-12",{"id":324,"category":36,"text_question":325,"slug":326},532298,"Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements.\nR is reflexive.\nR is symmetric.\nR is antisymmetric.\nR is transitive.\nR is a partial order.\nR is a total order.\nR is an equivalence relation.","consider-the-relation-r-defined-on-the-set-of-positive-integers-as-x-y-r-if-x-divides-y-choose-all-the-true-statements-r-is-reflexive-r-is-symmetric-r-is-antisymmetric-r-is-transitive-r-is-a",{"id":328,"category":36,"text_question":329,"slug":330},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":332,"category":36,"text_question":333,"slug":334},533983,"An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.","an-electrical-company-manufactures-batteries-that-have-a-duration-that-is-distributed-approximately-normally-with-a-mean-of-700-hours-and-a-standard-deviation-of-40-hours-find-the-probability-that-a",{"id":336,"category":36,"text_question":337,"slug":338},534056,"-27=-7u 5

$u-3$ ","27-7u-5-u-3",{"id":340,"category":36,"text_question":341,"slug":342},534094,"If f

$x,y$ =6xy^2+3y^3 find

$∫3,-2$ f

$x,y$ dx.","if-f-x-y-6xy-2-3y-3-find-3-2-f-x-y-dx",{"id":344,"category":36,"text_question":345,"slug":346},534110,"-3

$-4x+5$ =-6

$7x-8$ +9-10x","3-4x-5-6-7x-8-9-10x",{"id":348,"category":36,"text_question":349,"slug":350},534115,"How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword?\r\nBy subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.","how-many-anagrams-of-the-word-sromec-there-that-do-not-contain-strom-most-moc-or-cest-as-a-subword-by-subword-is-meant-anything-that-is-created-by-omitting-some-letters-for-example-the-word-emr",{"id":352,"category":36,"text_question":353,"slug":354},534135,"What is 28 marks out of 56 as a percentage","what-is-28-marks-out-of-56-as-a-percentage",{"id":356,"category":36,"text_question":357,"slug":358},534249,"3 A tree is planted when it is 1.2 m tall. Every year its growth is 3/8 of its previous year's height. Find how tall the tree will grow.","3-a-tree-is-planted-when-it-is-1-2-m-tall-every-year-its-growth-is-3-8-of-its-previous-year-s-height-find-how-tall-the-tree-will-grow",{"id":360,"category":36,"text_question":361,"slug":362},534254,"Convert 9/13 to a percent","convert-9-13-to-a-percent",{"id":364,"category":36,"text_question":365,"slug":366},534280,"A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?","a-machine-produces-255-bolts-in-24-minutes-at-the-same-rate-how-many-bolts-would-be-produced-in-40-minutes",{"id":368,"category":36,"text_question":369,"slug":370},534324,"Solve equations by equalization method\n X-8=-2y\n 2x+y=7","solve-equations-by-equalization-method-x-8-2y-2x-y-7",{"id":372,"category":36,"text_question":373,"slug":374},534364,"List five numbers that belong to the 5

$mod 6$ numbers. Alternate phrasing, list five numbers that satisfy equation x = 5

$mod 6$ ","list-five-numbers-that-belong-to-the-5-mod-6-numbers-alternate-phrasing-list-five-numbers-that-satisfy-equation-x-5-mod-6",{"id":376,"category":36,"text_question":377,"slug":378},534455,"Total Users with an active Wise account = Total Active Users + Total Users who haven’t transacted\r\nTotal Active Users = Total MCA Users + Total Send Users = Total New Users + Retained Users\r\nTotal New Users = New Send Users + New MCA Users\r\nTotal MCA Users = New MCA Users + Retained Users who transacted this month via MCA\r\nTotal Send Users = New Send Users + Retained Users who transacted this month via Send\r\n\r\nSend CR = Total Send Users / Total Users with an active Wise account\r\nMCA CR = Total MCA Users / Total Users with an active Wise account\r\n\r\nNew Send CR = New Send Users / New Profiles Created in Month\r\nNew MCA CR = New MCA Users / New Profiles Created in Month\r\n\r\nWe have recently witnessed a drop in MCA conversion, but send user conversion is\r\nstable, can you help explain why?","total-users-with-an-active-wise-account-total-active-users-total-users-who-haven-t-transacted-total-active-users-total-mca-users-total-send-users-total-new-users-retained-users-total-new",{"id":380,"category":36,"text_question":381,"slug":382},534491,"A salesperson earns a base salary of

$600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make$ 100 worth of sales.\n How many hours will you have to work on average each month for your income to be

$2000?","a-salesperson-earns-a-base-salary-of-600-per-month-plus-a-commission-of-10-of-the-sales-she-makes-you-discover-that-on-average-it-takes-you-an-hour-and-a-half-to-make-100-worth-of-sales-how-man",{"id":384,"category":36,"text_question":385,"slug":386},534504,"Gender and communication : \nAnswer the question ( 1 paragraph is ok) . Please can you write about women? \n\nCompared to your other identities, how much of a role does gender play in your life? And has your own sex/gender offered you privileges or disadvantages? How so?","gender-and-communication-answer-the-question-1-paragraph-is-ok-please-can-you-write-about-women-compared-to-your-other-identities-how-much-of-a-role-does-gender-play-in-your-life-and-has",{"id":388,"category":36,"text_question":389,"slug":390},534531,"The average weekly earnings in the leisure and hospitality industry group for a re‐\r\ncent year was$ 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":392,"category":36,"text_question":393,"slug":394},534672,"I have a complex function I would like to integrate over. I can use two approaches and they should give the same solution. If I want to find the contour integral ∫𝛾𝑧¯𝑑𝑧\r\n for where 𝛾\r\n is the circle |𝑧−𝑖|=3\r\n oriented counterclockwise I get the following:\r\n\r\n∫2𝜋0𝑖+3𝑒𝑖𝑡⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯𝑑

$𝑖+3𝑒𝑖𝑡$ =∫2𝜋03𝑖

$−𝑖+3𝑒−𝑖𝑡$ 𝑒𝑖𝑡𝑑𝑡=18𝜋𝑖\r\n\r\nIf I directly apply the Residue Theorem, I would get\r\n\r\n∫𝛾𝑧¯𝑑𝑧=2𝜋𝑖Res

$𝑓,𝑧=0$ =2𝜋𝑖","i-have-a-complex-function-i-would-like-to-integrate-over-i-can-use-two-approaches-and-they-should-give-the-same-solution-if-i-want-to-find-the-contour-integral-z-dz-for-where-is-the-circle",{"data":396},[397,401,405],{"id":398,"question":399,"answer":400},162314,"What is the surface area of a cylinder with a radius of 3 units and height of 8 units?","The surface area of the cylinder is 150 units squared. The formula for surface area of a cylinder is 2πr

$r+h$ , where r is the radius and h is the height. Substituting the given values, we get 2π

$3$

$3+8$ = 150 units squared.",{"id":402,"question":403,"answer":404},156841,"What is the integral of x^3 + 2x^2 - 5x + 4 with respect to x?","The integral of x^3 + 2x^2 - 5x + 4 dx is

$1/4$ x^4 +

$2/3$ x^3 -

$5/2$ x^2 + 4x + C, where C is the constant of integration.",{"id":406,"question":407,"answer":408},152730,"Math Question: What is the absolute maximum and minimum values of the function f

$x$ = x^3 + 6x^2 - 9x - 7 over the interval [-3, 2]?","Answer: To find the extrema, we first take the derivative of f

$x$ and set it equal to 0. By analyzing the critical points and endpoints within the given interval, we determine that the absolute maximum value is f

$2$ = 3, and the absolute minimum value is f

$-3$ = -38.",{"$sicons":410},{"bxl:facebook-circle":411,"bxl:instagram":415,"mdi:web":417,"la:apple":419,"ph:google-logo-bold":422,"ph:google-logo":425},{"left":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":183,"hFlip":183,"body":414},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":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":183,"hFlip":183,"body":416},"\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 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" d=\"M20.533 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