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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 = -24^{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.",null,1255,251,"y-2-4-x-1-1-describe-transformation",{"id":16,"category":7,"text_question":17,"photo_question":9,"text_answer":18,"step_text_answer":11,"step_photo_answer":11,"views":19,"likes":20,"slug":21},538086,"Add the polynomials gx=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>gx = 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>gx = 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":23,"category":7,"text_question":24,"photo_question":9,"text_answer":25,"step_text_answer":11,"step_photo_answer":11,"views":26,"likes":27,"slug":28},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":30,"category":7,"text_question":31,"photo_question":9,"text_answer":32,"step_text_answer":11,"step_photo_answer":11,"views":33,"likes":34,"slug":35},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":37,"category":7,"text_question":38,"photo_question":9,"text_answer":39,"step_text_answer":11,"step_photo_answer":11,"views":40,"likes":41,"slug":42},538083,"Calculate the volume tothenearesttenthofacubiccentimeter 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":44,"category":7,"text_question":45,"photo_question":9,"text_answer":46,"step_text_answer":11,"step_photo_answer":11,"views":47,"likes":48,"slug":49},538082,"Find the length of each base edge tothenearesttenthofameter 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":51,"category":7,"text_question":52,"photo_question":9,"text_answer":53,"step_text_answer":11,"step_photo_answer":11,"views":54,"likes":55,"slug":56},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>\\tantheta = \\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>\\tan40circ = \\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 \\tan40circ\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>\\tan40circ \\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":58,"category":7,"text_question":59,"photo_question":9,"text_answer":60,"step_text_answer":11,"step_photo_answer":11,"views":61,"likes":62,"slug":63},538080,"A plane ticket has gone up 18%, now costing 4,720.Howmuchdiditcostbeforetheincrease?","\u003Cmathfieldreadonlydefaultmode=\"inlinemath\"class=\"mathexpression\">\u003Cmathfieldreadonly>textSolution:\u003C/mathfield>\u003C/mathfield>\u003Cbr/>\n1.Definevariables:\u003Cbr/>\nLet\u003Cmathfieldreadonlydefaultmode=\"inlinemath\"class=\"mathexpression\">\u003Cmathfieldreadonly>P\u003C/mathfield>\u003C/mathfield>betheoriginalpriceoftheplaneticket.\u003Cbr/>\n\u003Cmathfieldreadonlydefaultmode=\"inlinemath\"class=\"mathexpression\">\u003Cmathfieldreadonly>P\u003C/mathfield>\u003C/mathfield>increasedby18\\frac{x}{15}=\\frac{4}{3}\u003C/mathfield>\n\u003Cbr>\n\u003C/div>\n\n\u003Cdiv>\n\n\u003Cmathfieldstyle=\"fontsize:16px;padding:8px;borderradius:8px;border:1pxsolidrgba(0,0,0,.3);boxshadow:000rgba(0,0,0,.2)\n\"readonly>x=20\u003C/math-field>\n    \u003Cbr>\n  \u003C/div>",467,93,"15-75-of",{"id":121,"category":7,"text_question":122,"photo_question":9,"text_answer":123,"step_text_answer":11,"step_photo_answer":11,"views":124,"likes":62,"slug":125},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":127,"category":7,"text_question":128,"photo_question":9,"text_answer":129,"step_text_answer":11,"step_photo_answer":11,"views":130,"likes":48,"slug":131},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":133,"category":7,"text_question":134,"photo_question":9,"text_answer":135,"step_text_answer":11,"step_photo_answer":11,"views":136,"likes":137,"slug":138},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":140,"category":7,"text_question":141,"photo_question":9,"text_answer":142,"step_text_answer":11,"step_photo_answer":11,"views":143,"likes":144,"slug":145},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":147,"last":148,"prev":11,"next":149},1,187,2,{"current_page":147,"from":147,"last_page":148,"links":151,"path":189,"per_page":190,"to":190,"total":191},[152,155,158,161,164,167,170,173,176,179,182,185,187],{"url":147,"label":153,"active":154},"1",true,{"url":149,"label":156,"active":157},"2",false,{"url":159,"label":160,"active":157},3,"3",{"url":162,"label":163,"active":157},4,"4",{"url":165,"label":166,"active":157},5,"5",{"url":168,"label":169,"active":157},6,"6",{"url":171,"label":172,"active":157},7,"7",{"url":174,"label":175,"active":157},8,"8",{"url":177,"label":178,"active":157},9,"9",{"url":180,"label":181,"active":157},10,"10",{"url":183,"label":184,"active":157},186,"186",{"url":148,"label":186,"active":157},"187",{"url":149,"label":188,"active":157},"Next »","https://api.math-master.org/api/question",20,3737,{"data":193},[194,196,198,200,202,204],{"id":147,"title":195,"slug":11},"Algebra",{"id":149,"title":197,"slug":11},"Geometry",{"id":159,"title":199,"slug":11},"Coordinate-geometry",{"id":162,"title":201,"slug":11},"Statistics",{"id":165,"title":203,"slug":11},"Calculus",{"id":168,"title":205,"slug":11},"General",{"data":207},{"id":208,"category":7,"slug":209,"text_question":210,"photo_question":11,"text_answer":211,"step_text_answer":11,"step_photo_answer":11,"views":212,"likes":213,"expert":214},537760,"a-discussion-topic-will-be-posted-here-shortly-you-must-reply-to-the-question-with-your-own-response-by-thurs-oct-31-you-must-also-reply-to-the-posts-of-2-peers-by-sunday-nov-3-please-see-the-syll","A discussion topic will be posted here shortly. You must reply to the question with your own response by Thurs Oct 31. You must also reply to the posts of 2 peers by Sunday, Nov 3. Please see the syllabus for discussion requirements. Each of your 3 posts should be a minimum of 300 words and use a properly formatted citation to support your ideas \nHere's this week's discussion: \nPart A:  Describe a remote encounter, a phone encounter, and a face-to-face encounter that you have had recently. How did you evaluate the encounter, and what were the most important factors determining your satisfaction/dissatisfaction in each case?\nPart B: Think about a service organization that retains you as a loyal customer. Has your relationship with the company evolved over time? Why are you loyal to this provider? What are the benefits to you of staying loyal and not switching to another provider? What would it take for you to switch?","**Part A:**\n\n1. **Remote Encounter**  \n   Recently, I had a remote encounter with a customer service team via email regarding an issue with an online purchase. The response was quick and well-structured, and they provided clear steps to resolve the problem. I evaluated the encounter based on response time, clarity, and the helpfulness of the solution. My satisfaction stemmed from the quick turnaround and the ease with which I could follow their guidance.\n\n2. **Phone Encounter**  \n   I had a phone conversation with my bank to resolve a transaction issue. The representative was polite, but the hold time was long, and I had to repeat my details multiple times. I evaluated the encounter based on wait time, the representative’s helpfulness, and the resolution provided. My satisfaction was somewhat mixed; while the representative was helpful, the hold time and repeated explanations made the experience less efficient.\n\n3. **Face-to-Face Encounter**  \n   Recently, I visited a local store for a product exchange. The staff was friendly and proactive in assisting me, making the process smooth and efficient. I evaluated the encounter based on their attentiveness, problem-solving ability, and the speed of service. I was very satisfied due to the friendly and proactive approach, which made the interaction feel personal and efficient.\n\n**Part B:**\n\nI am a loyal customer of Vodacom(or any service provider), a company I’ve used for several years for internet and streaming services. Over time, my relationship with them has grown as they’ve consistently met my needs by offering reliable service, competitive pricing, and regular loyalty rewards. I’m loyal because they’ve built trust by resolving any issues quickly and by providing occasional discounts or service upgrades. The benefit of staying loyal is the reliability and familiarity of the service, and I don’t need to re-establish my preferences with a new provider. However, if their service quality dropped, or if a competitor offered significantly better service at a lower price, I might consider switching.",1100,220,{"id":215,"name":216,"photo":217,"biography":218,"created_at":11,"updated_at":11,"rating":219,"total_answer":220},21,"Jon","https://api.math-master.org/img/experts/21/21.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.",4.6,107,{"data":222},[223,224,225,226,227,228],{"id":147,"title":195,"slug":11},{"id":149,"title":197,"slug":11},{"id":159,"title":199,"slug":11},{"id":162,"title":201,"slug":11},{"id":165,"title":203,"slug":11},{"id":168,"title":205,"slug":11},{"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":7,"text_question":234,"slug":235},532010,"A pump with average discharge of 30L/second irrigate 100m wide and 100m length field\narea crop for 12 hours. What is an average depth of irrigation in mm unIt?","a-pump-with-average-discharge-of-30l-second-irrigate-100m-wide-and-100m-length-field-area-crop-for-12-hours-what-is-an-average-depth-of-irrigation-in-mm-unit",{"id":237,"category":7,"text_question":238,"slug":239},532033,"𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)","y-x2-3-x3-2-x-1",{"id":241,"category":7,"text_question":242,"slug":243},532038,"10!\r\n-\r\n8! =","10-8",{"id":245,"category":7,"text_question":246,"slug":247},532089,"Jose bought 3/4 of oil and his sister bought 6/8, which of the two bought more oil?","jose-bought-3-4-of-oil-and-his-sister-bought-6-8-which-of-the-two-bought-more-oil",{"id":249,"category":7,"text_question":250,"slug":251},532308,"90 divided by 40","90-divided-by-40",{"id":253,"category":7,"text_question":254,"slug":255},533910,"How do you think the company has increased or decreased its income?","how-do-you-think-the-company-has-increased-or-decreased-its-income",{"id":257,"category":7,"text_question":258,"slug":259},533943,"x/20*100","x-20-100",{"id":261,"category":7,"text_question":262,"slug":263},534032,"The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below.\r\n23.0\t21.2\t23.5\t23.6\r\n20.1\t24.3\t25.2\t26.9\r\n24.6\t22.6\t26.1\t23.1\r\n25.8\t24.6\t24.3\t24.1\r\n24.8\t22.1\t22.8\t24.5\r\n(a)\r\nFind the z-scores for the largest measurement. (Round your answers to two decimal places.)\r\nz =","the-miles-per-gallon-mpg-for-each-of-20-medium-sized-cars-selected-from-a-production-line-during-the-month-of-march-are-listed-below-23-0-21-2-23-5-23-6-20-1-24-3-25-2-26-9-24-6-22-6-26-1-23-1",{"id":265,"category":7,"text_question":266,"slug":267},534086,"If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?","if-the-midpoint-of-point-a-on-the-x-3-line-and-point-b-on-the-y-2-line-is-c-2-0-what-is-the-sum-of-the-ordinate-of-point-a-and-the-abscissa-of-point-b",{"id":269,"category":7,"text_question":270,"slug":271},534204,"Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows:\n (Raúl wins) = 20%\n (Gilberto wins) = 0.05%\n (Arturo wins) = ¾%.\n\n Perform operations and order events from least to most probable.","raul-gilberto-and-arturo-are-playing-golf-the-probabilities-of-winning-for-each-one-are-as-follows-raul-wins-20-gilberto-wins-0-05-arturo-wins-perform-operations-and-order-ev",{"id":273,"category":7,"text_question":274,"slug":275},534231,"89, ÷ 10","89-10",{"id":277,"category":7,"text_question":278,"slug":279},534276,"Use the power rule for logarithms to solve the following word problem exactly. If you invest1, 000 at 5% interest compounded annually, how many years will it take before you have 2,000?","usethepowerruleforlogarithmstosolvethefollowingwordproblemexactlyifyouinvest1000at5interestcompoundedannuallyhowmanyyearswillittakebeforeyouhave2000","id":281,"category":7,"textquestion":282,"slug":283,534288,"Thepoints(5,4)and(3,6)aretheendsofthediameterofthecirclecalculatesubequation","thepoints54and36aretheendsofthediameterofthecirclecalculatesubequation","id":285,"category":7,"textquestion":286,"slug":287,534346,"Theprobabilityofgrowingaseedlingfromaseedis0.62.HowmanyseedsdoIneedtoplantsothattheprobabilityofgrowingatleastoneseedlingisgreaterthanorequalto0.87?","theprobabilityofgrowingaseedlingfromaseedis062howmanyseedsdoineedtoplantsothattheprobabilityofgrowingatleastoneseedlingisgreaterthanorequalto087","id":289,"category":7,"textquestion":290,"slug":291,534499,"Ablockslidesacrossthefloorwithaforceof20N,whichhasanangleof30°.Themassoftheblockis2kgandthecoefficientoffrictionis0.1.Calculatethevalueofalltheforcesinvolvedinthissystemandfinallythevalueoftheacceleration.","ablockslidesacrossthefloorwithaforceof20nwhichhasanangleof30themassoftheblockis2kgandthecoefficientoffrictionis01calculatethevalueofalltheforcesinvolvedint","id":293,"category":7,"textquestion":294,"slug":295,534588,"writeinsetbuildernotation1,3,9,27,81,243,...","writeinsetbuildernotation1392781243","id":297,"category":7,"textquestion":298,"slug":299,534601,"LetIbeanintervalandletf:IRbeacontinuousfunctionsuchthatf(I)Q.Show(insymbols)thatfisconstant.","letibeanintervalandletfirbeacontinuousfunctionsuchthatfiqshowinsymbolsthatfisconstant","id":301,"category":7,"textquestion":302,"slug":303,534610,"Inaschoolplayground\nWhengoingoutforrecess,80menand75womencoexist,thePatiomeasures10meters\nFor40meters(whatwillbethepopulationdensityinthe\nbreak","inaschoolplaygroundwhengoingoutforrecess80menand75womencoexistthepatiomeasures10metersfor40meterswhatwillbethepopulationdensityinthebreak","id":305,"category":7,"textquestion":306,"slug":307,534634,"646x2>0","646x20","id":309,"category":7,"textquestion":310,"slug":311,534636,"Pleaseanswertothefollowingquestions:\r\n\r\nWhatisthepriceelasticityofdemand?Canyouexplainitinyourownwords?\r\n\r\nWhatisthepriceelasticityofsupply?Canyouexplainitinyourownwords?\r\n\r\nWhatistherelationshipbetweenpriceelasticityandpositiononthedemandcurve?Forexample,asyoumoveupthedemandcurvetohigherpricesandlowerquantities,whathappenstothemeasuredelasticity?Howwouldyouexplainthat?\r\n\r\n\r\nBAssumethatthesupplyoflowskilledworkersisfairlyelastic,buttheemployersdemandforsuchworkersisfairlyinelastic.Ifthepolicygoalistoexpandemploymentforlowskilledworkers,isitbettertofocusonpolicytoolstoshiftthesupplyofunskilledlabororontoolstoshiftthedemandforunskilledlabor?\r\n\r\nWhatifthepolicygoalistoraisewagesforthisgroup?Explainyouranswerswithsupplyanddemanddiagrams.Makesuretoproperlyciteandreferenceyouracademicorpeerreviewedsources(minimum2).","pleaseanswertothefollowingquestionswhatisthepriceelasticityofdemandcanyouexplainitinyourownwordswhatisthepriceelasticityofsupplycanyouexplainitinyourownw","data":313,[314,318,322],"id":315,"question":316,"answer":317,132048,"Whatarethecharacteristicsofanellipsegivenitsequationinstandardform?","Thecharacteristicsofanellipseincludethecoordinatesofthecenter,majorandminoraxeslengths,eccentricity,foci,directrices,andtheequationofitsgraph.Additionally,itissymmetricalaboutitscenterandconsistsofallpointswhosesumofdistancestothefociisconstant.","id":319,"question":320,"answer":321,150683,"Question:Whatisthevalueofarccos(1/2)?","Answer:Thevalueofarccos(1/2)isπ/3or60degrees.Thisisbecausecos(π/3)equals1/2.Ingeneral,arccos(x)representstheanglewhosecosineisx,anditssolutionsliewithintheinterval[0,π].","id":323,"question":324,"answer":325,111401,"Whatisthevolumeofaconewitharadiusof5unitsandaheightof10units?","ThevolumeofaconeisgivenbytheformulaV=(1/3)πr²h.Plugginginthevalues,V=(1/3)π(5²)(10)=83.78cubicunits.","data":327,"questions":328,[329,333,337,341,345,349,353,357,361,365,369,373,376,380,384,388,392,396,400,404],"id":330,"category":7,"textquestion":331,"slug":332,532043,"aferrytravels1/6ofthedistancebetweentwoportsin3/7hour.Theferrytravelsataconstantrate.\nAtthisrate,whatfractionofthedistancebetweenthetwoportscantheferrytravelinonehour.","aferrytravels16ofthedistancebetweentwoportsin37hourtheferrytravelsataconstantrateatthisratewhatfractionofthedistancebetweenthetwoportscantheferrytravelinoneh","id":334,"category":7,"textquestion":335,"slug":336,533972,"FindthemeasuresofthesidesofKPLandclassifyeachtrianglebyitssidesk(2,6),p(4,0),l(3,1)","findthemeasuresofthesidesofkplandclassifyeachtrianglebyitssidesk26p40l31","id":338,"category":7,"textquestion":339,"slug":340,533983,"Anelectricalcompanymanufacturesbatteriesthathaveadurationthatisdistributedapproximatelynormally,withameanof700hoursandastandarddeviationof40hours.Findtheprobabilitythatarandomlyselectedbatteryhasanaveragelifeoflessthan810hours.","anelectricalcompanymanufacturesbatteriesthathaveadurationthatisdistributedapproximatelynormallywithameanof700hoursandastandarddeviationof40hoursfindtheprobabilitythata","id":342,"category":7,"textquestion":343,"slug":344,534051,"2.3/71.32","237132","id":346,"category":7,"textquestion":347,"slug":348,534073,"Howlongwillittakefor900 to become 5000atanannualrateof11.153,831 was lent, and it has produced interest of 840from05122022to1122023.Atwhatannualsimpleinterestratewasthecapitallent?","1acapitalof3831waslentandithasproducedinterestof840from05122022to1122023atwhatannualsimpleinterestratewasthecapitallent","id":366,"category":7,"textquestion":367,"slug":368,534343,"Showworkon4108dividedby4","showworkon4108dividedby4","id":370,"category":7,"textquestion":371,"slug":372,534388,"Acontractorgivesabanknotefor10250 at a rate of 1% for one month. How much interest\nis charged for 4 months?","a-contractor-gives-a-bank-note-for-10250-at-a-rate-of-1-for-one-month-how-much-interest-is-charged-for-4-months",{"id":374,"category":7,"text_question":375,"slug":375},534401,"2x2",{"id":377,"category":7,"text_question":378,"slug":379},534419,"Determine the Linear function whose graph passes through the points 6,2 and has slope 3.","determine-the-linear-function-whose-graph-passes-through-the-points-6-2-and-has-slope-3",{"id":381,"category":7,"text_question":382,"slug":383},534445,"Find the area of a triangle ABC when m\u003CC = 14 degrees, a = 5.7 miles, and b = 9.3 miles.","find-the-area-of-a-triangle-abc-when-m-c-14-degrees-a-5-7-miles-and-b-9-3-miles",{"id":385,"category":7,"text_question":386,"slug":387},534592,"A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.","a-candy-manufacturer-must-monitor-deviations-in-the-amount-of-sugar-in-their-products-they-want-their-products-to-meet-standards-they-selected-a-random-sample-of-20-candies-and-found-that-the-sandard",{"id":389,"category":7,"text_question":390,"slug":391},534596,"calculate the product of 4 and 1/8","calculate-the-product-of-4-and-1-8",{"id":393,"category":7,"text_question":394,"slug":395},534626,"Let A denote the set of all people who were alive in 2010. Let B denote the set of all\nreal numbers. Let f assign, to each person in A, their weight during the year 2010.\nIs f a function? Explain in complete sentences.","let-a-denote-the-set-of-all-people-who-were-alive-in-2010-let-b-denote-the-set-of-all-real-numbers-let-f-assign-to-each-person-in-a-their-weight-during-the-year-2010-is-f-a-function-explain-in-c",{"id":397,"category":7,"text_question":398,"slug":399},534657,"If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. \n\nRound answer to 2 decimal places and enter the units.","if-the-area-of-a-circle-is-75-7ft2-what-is-the-radius-give-the-answer-in-metres-round-answer-to-2-decimal-places-and-enter-the-units",{"id":401,"category":7,"text_question":402,"slug":403},534677,"In an experiment to assess the effect of listening to audiobooks while driving, participants were asked to drive down a straight road in a driving simulator. The accompanying data on time inmilliseconds to react when a pedestrian walked into the street for 10 drivers listening to an audiobook are consistent with summary statistics and graphs that appeared in the paper \"Good Distractions: Testing the Effect of Listening to an Audiobook on Driving Performance in Simple and Complex Road Environments.\"† Roundyouranswerstofourdecimalplaces.\r\n1,018 1,007 1,054 988 937 1,030 1,065 1,011 860 1,106\r\nA button hyperlink to the SALT program that reads: Use SALT.\r\nCalculate the variance for this data set.\r\n7437.7333\r\n \r\nIncorrect: Your answer is incorrect.\r\nCalculate the standard deviation for this data set.\r\n86.2022\r\n \r\nIncorrect: Your answer is incorrect.","in-an-experiment-to-assess-the-effect-of-listening-to-audiobooks-while-driving-participants-were-asked-to-drive-down-a-straight-road-in-a-driving-simulator-the-accompanying-data-on-time-in-millisec",{"id":405,"category":7,"text_question":406,"slug":407},534698,"Question 3\r\nA square has a perimeter given by the algebraic expression 24x – 16. 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