Loading [MathJax]/jax/element/mml/optable/BasicLatin.js

^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},{"questions":216},[217,221,225,229,233,237,240,244,248,252,256,260,264,268,272,276,280,284,288,292],{"id":218,"category":36,"text_question":219,"slug":220},532002,"A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:40 a.m. Round your answer to four decimal places, if necessary.","a-particular-employee-arrives-at-work-sometime-between-8-00-a-m-and-8-50-a-m-based-on-past-experience-the-company-has-determined-that-the-employee-is-equally-likely-to-arrive-at-any-time-between-8-0",{"id":222,"category":36,"text_question":223,"slug":224},532033,"𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)","y-x2-3-x3-2-x-1",{"id":226,"category":36,"text_question":227,"slug":228},532058,"11(4x-9)= -319","11-4x-9-319",{"id":230,"category":36,"text_question":231,"slug":232},533889,"Suppose that a device has been created that launches objects at ground level and that its operation is modeled by the function h(x) = -4×² + 256x, with h being the height (in meters) and x being the distance (in meters)\nWhat is the maximum height that the object reaches?","suppose-that-a-device-has-been-created-that-launches-objects-at-ground-level-and-that-its-operation-is-modeled-by-the-function-h-x-4-256x-with-h-being-the-height-in-meters-and-x-being-the-d",{"id":234,"category":36,"text_question":235,"slug":236},533961,"2.5 / 21.85","2-5-21-85",{"id":238,"category":36,"text_question":239,"slug":239},533975,"4x567",{"id":241,"category":36,"text_question":242,"slug":243},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":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},534214,"Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tête Carrée and is made up of part of a bust that supports a cube divided into five floors.\n It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3\n Calculate, in meters, the height of the bust that supports the cube.\n Displays all the calculations you made.","nice-s-central-library-building-is-considered-one-of-the-most-original-in-the-world-as-it-is-a-mix-between-a-sculpture-and-a-work-of-habitable-architecture-it-was-called-la-tete-carree-and-is-made-u",{"id":253,"category":36,"text_question":254,"slug":255},534266,"0.1x8.2","0-1x8-2",{"id":257,"category":36,"text_question":258,"slug":259},534312,"The sick-leave time of employees in a firm in a month is normally with a mean of 100 hours and a standard deviation of 20 hours. Find the probability that the sick-leave time of an employee in a month exceeds 130 hours.","the-sick-leave-time-of-employees-in-a-firm-in-a-month-is-normally-with-a-mean-of-100-hours-and-a-standard-deviation-of-20-hours-find-the-probability-that-the-sick-leave-time-of-an-employee-in-a-month",{"id":261,"category":36,"text_question":262,"slug":263},534433,"A natural gas company has a fixed rate of 1,320 pesos plus 1,590 pesos per cubic meter of gas consumed monthly per customer.\n Indicate the cost function to determine the value in pesos of the cubic meters of gas consumed in a month per customer.\n How much did a customer who consumed 18 cubic meters of gas pay?\n If a customer paid 34,710 pesos, how many cubic meters of gas did he consume?","a-natural-gas-company-has-a-fixed-rate-of-1-320-pesos-plus-1-590-pesos-per-cubic-meter-of-gas-consumed-monthly-per-customer-indicate-the-cost-function-to-determine-the-value-in-pesos-of-the-cubic-me",{"id":265,"category":36,"text_question":266,"slug":267},534438,"1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?","1-a-jeweler-has-two-gold-bars-with-80-purity-and-the-other-with-95-purity-how-much-of-each-must-be-melted-to-obtain-a-5-kilo-ingot-with-86-purity",{"id":269,"category":36,"text_question":270,"slug":271},534460,"(6²-14)÷11•(-3)","6-14-11-3",{"id":273,"category":36,"text_question":274,"slug":275},534465,"Calculate the pH of a solution obtained by mixing 100ml of 0.2M HCl with 100ml of 0.1M NaOH","calculate-the-ph-of-a-solution-obtained-by-mixing-100ml-of-0-2m-hcl-with-100ml-of-0-1m-naoh",{"id":277,"category":36,"text_question":278,"slug":279},534546,"The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers together? Produce an algebraic solution. Guess and check is acceptable.","the-mean-of-4-numbers-is-5-and-the-mean-of-3-different-numbers-is-12-what-is-the-mean-of-the-7-numbers-together-produce-an-algebraic-solution-guess-and-check-is-acceptable",{"id":281,"category":36,"text_question":282,"slug":283},534570,"The inner radius of a spherical ball is 13 cm. How many liters of air are in it?\n Justify your answer!","the-inner-radius-of-a-spherical-ball-is-13-cm-how-many-liters-of-air-are-in-it-justify-your-answer",{"id":285,"category":36,"text_question":286,"slug":287},534623,"7-1=6\r\n6x2=12\r\n\r\nExplain that","7-1-6-6x2-12-explain-that",{"id":289,"category":36,"text_question":290,"slug":291},534644,"12[4 + (8 + 7) + 5]","12-4-8-7-5",{"id":293,"category":36,"text_question":294,"slug":295},534697,"Write a linear equation in the slope-intercept form. Slope of the line is -1 and goes through (8,4)","write-a-linear-equation-in-the-slope-intercept-form-slope-of-the-line-is-1-and-goes-through-8-4",{"data":297},{"id":298,"category":36,"slug":299,"text_question":300,"photo_question":8,"text_answer":301,"step_text_answer":8,"step_photo_answer":8,"views":68,"likes":69,"expert":302},534269,"a-researcher-is-interested-in-voting-preferences-on-change-of-the-governing-constitution-in-a-certain-country-controlled-by-two-main-parties-a-and-b-a-questionnaire-was-developed-and-sent-to-a-rand","A researcher is interested in voting preferences on change of the governing constitution in a\r\ncertain country controlled by two main parties A and B. A questionnaire was developed and sent\r\nto a random sample of voters. The cross tabs are as follows\r\nFavour Neutral Oppose\r\nMembership: Party A 70 90 85\r\nParty B 50 50 155\r\nTest at α = 0.05 whether party membership and voting preference are associated and state the\r\nconditions required for chi-square test results to be valid.","To test whether party membership and voting preference are associated, we can use a chi-square test of independence. The null hypothesis (H0) is that there is no association between party membership and voting preference, while the alternative hypothesis (H1) is that there is an association.\n\nThe observed values for the cross tabs are as follows:\n\n Favour Neutral Oppose\nParty A 70 90 85\nParty B 50 50 155\n\nTo perform the chi-square test, we need to calculate the expected values under the assumption of independence. The expected values can be obtained by assuming that party membership and voting preference are independent and calculating the expected counts based on the row and column totals.\n\nThe expected values are as follows:\n\n Favour Neutral Oppose\nParty A 58.33 58.33 128.34\nParty B 61.67 61.67 135.66\n\nNow, we can set up the chi-square test:\n\n1. Set the significance level (α) to 0.05.\n2. Calculate the degrees of freedom (df) as (number of rows - 1) * (number of columns - 1). In this case, df = (2-1) * (3-1) = 2.\n3. Calculate the chi-square test statistic using the formula:\n\n χ^2 = Σ [(O - E)^2 / E],\n\n where Σ represents the sum of the cells, O is the observed value, and E is the expected value.\n\n4. Compare the calculated chi-square test statistic with the critical chi-square value from the chi-square distribution table with the given degrees of freedom and significance level.\n5. If the calculated chi-square test statistic is greater than the critical chi-square value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.\n\nPerforming the calculations, we obtain a chi-square test statistic of approximately 22.88.\n\nLooking up the critical chi-square value with 2 degrees of freedom and a significance level of 0.05, we find a critical chi-square value of approximately 5.99.\n\nSince the calculated chi-square test statistic (22.88) is higher than the critical chi-square value (5.99), we reject the null hypothesis.\n\nTherefore, we can conclude that there is evidence to suggest an association between party membership and voting preference in this country.\n\nConditions required for the chi-square test results to be valid:\n1. Random sampling: The sample of voters should be randomly selected to ensure representativeness.\n2. Independence: The observations in the cross tabs should be independent of each other.\n3. Sufficient sample size: The expected count for each cell in the cross tabs should be at least 5. If not, the chi-square test may not be valid, and alternative methods should be considered.",{"id":303,"name":304,"photo":305,"biography":306,"created_at":8,"updated_at":8,"rating":307,"total_answer":308},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp","Hi,\nI've loved Mathematics and critical thinking for as long as I can remember. I started tutoring my fellow students in grade 6. I've studied Maths in the Faculty of Science. I started tutoring online 10 years ago. I've taken a lot of courses to help me teach the STEM curriculum better ever since.\nRegards\nRania",4.7,91,{"data":310},{"questions":311},[312,316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,384,388],{"id":313,"category":36,"text_question":314,"slug":315},532016,"Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:","let-f-x-x-6-15-x-then-f-6-f-15-is-equal-to",{"id":317,"category":36,"text_question":318,"slug":319},532065,"One contestant on a game show has 1,500 points and another contestant has -250 points. What is the difference between the scores of the contestants?","one-contestant-on-a-game-show-has-1-500-points-and-another-contestant-has-250-points-what-is-the-difference-between-the-scores-of-the-contestants",{"id":321,"category":36,"text_question":322,"slug":323},532087,"A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.","a-person-who-weighs-200-pounds-on-earth-would-weigh-about-32-pounds-on-the-moon-find-the-weight-of-a-person-on-earth-who-would-weigh-15-pounds-on-the-moon",{"id":325,"category":36,"text_question":326,"slug":327},532309,"Imagine that you are in an electronics store and you want to calculate the final price of a product after applying a discount. The product you are interested in has an original price of$ 1000 MN, but, for today, the store offers a 25% discount on all its products. Develop an algorithm that allows you to calculate the final price you will pay, but first point out the elements.","imagine-that-you-are-in-an-electronics-store-and-you-want-to-calculate-the-final-price-of-a-product-after-applying-a-discount-the-product-you-are-interested-in-has-an-original-price-of-1000-mn-but",{"id":329,"category":36,"text_question":330,"slug":331},532310,"The random variable Y is defined as the sum between two different integers selected at random between -4 and 2

$both included$ . What are the possible values of the random variable Y? What is the value of P

$Y=-3$ ? And whether it is less than or equal to -5?","the-random-variable-y-is-defined-as-the-sum-between-two-different-integers-selected-at-random-between-4-and-2-both-included-what-are-the-possible-values-of-the-random-variable-y-what-is-the-value",{"id":333,"category":36,"text_question":334,"slug":335},533902,"For a temperature range between -3 degrees Celsius to 5 degrees Celsius, what is the temperature range in degrees Farenheight","for-a-temperature-range-between-3-degrees-celsius-to-5-degrees-celsius-what-is-the-temperature-range-in-degrees-farenheight",{"id":337,"category":36,"text_question":338,"slug":339},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":341,"category":36,"text_question":342,"slug":343},534024,"Analyze the following situation\n\n Juan is starting a new business, he indicates that the price of his product corresponds to p=6000−4x\n , where x\n represent the number of tons produced and sold and p\n It is given in dollars.\n\n According to the previous information, what is the maximum income that Juan can obtain with his new product?","analyze-the-following-situation-juan-is-starting-a-new-business-he-indicates-that-the-price-of-his-product-corresponds-to-p-6000-4x-where-x-represent-the-number-of-tons-produced-and-sold-and-p",{"id":345,"category":36,"text_question":346,"slug":347},534212,"A mutual fund manager has a

$350 million portfolio with a beta of 1.10. The risk-free\nrate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an\nadditional$ 150 million which she plans to invest in several different stocks. After\ninvesting the additional funds, she wants to reduce the portfolio’s risk level so that once\nthe additional funds are invested the portfolio’s required return will be 9.20%. What\nmust the average beta of the new stocks added to the portfolio be

$not the new\nportfolio’s beta$ to achieve the desired required rate of return?","a-mutual-fund-manager-has-a-350-million-portfolio-with-a-beta-of-1-10-the-risk-free-rate-is-3-5-and-the-market-risk-premium-is-6-00-the-manager-expects-to-receive-an-additional-150-million-whic",{"id":349,"category":36,"text_question":350,"slug":351},534219,"The Humane Society has asked for our help again this week. Currently they are charging

$50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis.\r\n\r\nDuring a client meeting we gathered these facts. There are 2 part-time employees that each earn$ 1000 per month. The utilities for the kennel area

$water, electricity$ are

$200 per month. The average food cost for animals in the kennel is$ 800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs

$4 and is micro-chipped that costs$ 6. \r\n\r\nAt the current cost of

$50, how many animals must be adopted to break-even?\r\nWhat would break-even be at a$ 60 adoption fee? \r\nWhat would break-even be if the fee were lowered to

$40?\r\nThe newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs$ 1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven?\r\nBased on what you have learned about elasticity, what price do you recommend for the adoption fee?","the-humane-society-has-asked-for-our-help-again-this-week-currently-they-are-charging-50-for-an-adoption-fee-unfortunately-they-just-pulled-this-number-out-of-the-air-and-do-not-know-why-they-are-c",{"id":353,"category":36,"text_question":354,"slug":355},534271,"DuocUC\n\n 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function:\n\n

$x+185$ C

$x$ =81300-6x+ 20000\n\n a) It is known that C

$90$ 5.344. Interpret this result.\n\n

$2 points$ \n\n b) Calculate C'

$x$ \n\n

$2 points$ \n\n 3 x²+111x-0.87\n\n 20000 2000\n\n c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing.\n\n

$3 points$ \n\n d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost?\n\n

$","duocuc-2-the-cost-c-in-pesos-for-the-production-of-x-meters-of-a-certain-fabric-can-be-calculated-through-the-function-x-185-c-x-81300-6x-20000-a-it-is-known-that-c-90-5-344-interpret",{"id":357,"category":36,"text_question":358,"slug":359},534409,"9/14 x 7/27 carry out indicated operation","9-14-x-7-27-carry-out-indicated-operation",{"id":361,"category":36,"text_question":362,"slug":363},534463,"Calculate the area of the parallelogram with adjacent vertices (1,4, −2$ ,

$−3,1,6$ 𝑦

$1, −2,3$ ","calculate-the-area-of-the-parallelogram-with-adjacent-vertices-1-4-2-3-1-6-y-1-2-3",{"id":365,"category":36,"text_question":366,"slug":367},534538,"A 20-year old hopes to retire by age 65. To help with future expenses, they invest

$6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?","a-20-year-old-hopes-to-retire-by-age-65-to-help-with-future-expenses-they-invest-6-500-today-at-an-interest-rate-of-6-4-compounded-annually-at-age-65-what-is-the-difference-between-the-exact-acc",{"id":369,"category":36,"text_question":370,"slug":371},534553,"2x-4=8","2x-4-8",{"id":373,"category":36,"text_question":374,"slug":375},534562,"Solve the following \n9x - 9 - 6x = 5 + 8x - 9","solve-the-following-9x-9-6x-5-8x-9",{"id":377,"category":36,"text_question":378,"slug":379},534591,"Sodium\r\n38.15\r\n38.78\r\n38.5\r\n38.65\r\n38.79\r\n38.89\r\n38.57\r\n38.59\r\n38.59\r\n38.8\r\n38.63\r\n38.43\r\n38.56\r\n38.46\r\n38.79\r\n38.42\r\n38.74\r\n39.12\r\n38.5\r\n38.42\r\n38.57\r\n38.37\r\n38.71\r\n38.71\r\n38.4\r\n38.56\r\n38.39\r\n38.34\r\n39.04\r\n38.8\r\nA supplier of bottled mineral water claims that his supply of water has an average sodium content of 36.6 mg/L.\r\nThe boxplot below is of the sodium contents levels taken from a random sample of 30 bottles.\r\nWith this data investigate the claim using SPSS to apply the appropriate test.\r\n\r\nDownload the data and transfer it into SPSS.\r\nCheck that your data transfer has been successful by obtaining the Std. Error of the mean for your data which should appear in SPSS output as 0.03900..\r\nIf you do not have this exact value, then you may have not transferred your data from the Excel file to SPSS correctly. Do not continue with the test until your value agrees as otherwise you may not have correct answers.\r\nUnless otherwise directed you should report all numeric values to the accuracy displayed in the SPSS output that is supplied when your data has been transferred correctly.\r\n\r\nIn the following questions, all statistical tests should be carried out at the 0.05 significance level.\r\n\r\nSample mean and median\r\n\r\nComplete the following concerning the mean and median of the data.\r\nmean = mg/L\r\n\r\n95% CI: to mg/L\r\n\r\nBased upon the 95% confidence interval, is it plausible that the average sodium content is 36.9 mg/L?\r\n \r\n\r\nmedian: mg/L\r\n\r\nThe median value is 36.9 mg/L.\r\n\r\n\t\r\nSkewness\r\n\r\nComplete the following concerning the skewness of the data.\r\n\r\nSkewness statistic = Std. Error = \r\n\r\nThe absolute value of the skewness statistic less than 2 x Std. Error\r\n\r\nTherefore the data can be considered to come from a population that is .\r\n\r\n\r\n\r\n\r\nNormality test\r\n\r\nComplete the following summary concerning the formal testing of the normality of the data.\r\nH0: The data come from a population that normal\r\n\r\nH1: The data come from a population that normal\r\n\r\nApplication of the Shapiro-Wilk test indicated that the normality assumption reasonable for sodium content (S-W( )= , p= ).\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\nMain test\r\n\r\nUsing the guidelines you have been taught that consider sample size, skewness and normality, choose and report the appropriate main test from the following ( Appropriate ONE ) \r\n\r\n\r\nYou have selected that you wish to report the one-sample t-test.\r\nH0: The mean sodium content equal to 36.9 mg/L\r\n\r\nH1: The mean sodium content equal to 36.9 mg/L\r\n\r\nApplication of the one-sample t-test indicated that the mean is 36.9 mg/L\r\n\r\n(t( ) = , p = ).\r\n\r\n\r\n\r\n\r\nYou have selected that you wish to report the Wilcoxon signed rank test.\r\n\r\nH0: The median sodium content equal to 36.9 mg/L\r\n\r\nH1: The median sodium content equal to 36.9 mg/L\r\n\r\nApplication of the Wilcoxon signed rank test indicated that the median is 36.9 mg/L \r\n\r\n(z = , N = , p = ).","sodium-38-15-38-78-38-5-38-65-38-79-38-89-38-57-38-59-38-59-38-8-38-63-38-43-38-56-38-46-38-79-38-42-38-74-39-12-38-5-38-42-38-57-38-37-38-71-38-71-38-4-38-56-38-39-38-34",{"id":381,"category":36,"text_question":382,"slug":383},534601,"Let I be an interval and let f : I → R be a continuous function such that f(I) ⊂ Q. Show (in symbols) that f is constant.","let-i-be-an-interval-and-let-f-i-r-be-a-continuous-function-such-that-f-i-q-show-in-symbols-that-f-is-constant",{"id":385,"category":36,"text_question":386,"slug":387},534643,"6(k-7) -2=5","6-k-7-2-5",{"id":389,"category":36,"text_question":390,"slug":391},534674,"Solve the system of equations by the addition method.\n\n0.01x-0.08y=-0.1\n0.2x+0.6y=0.2","solve-the-system-of-equations-by-the-addition-method-0-01x-0-08y-0-1-0-2x-0-6y-0-2",{"data":393},[394,398,402],{"id":395,"question":396,"answer":397},141298,"What is the period of the characteristic graph of the cotangent function f(x) = cot(x)?","The cotangent function has a period of π radians or 180 degrees. This means that the graph of f(x) = cot(x) repeats itself every π radians or 180 degrees.",{"id":399,"question":400,"answer":401},113095,"What is the resultant vector when adding vector A (magnitude 3, direction 30°) and vector B (magnitude 4, direction 120°)?","The resultant vector is 2i + 7.928i^ + 3.464j^. It has a magnitude of 8 and a direction of 65.13° relative to the positive x-axis.",{"id":403,"question":404,"answer":405},133110,"Math question: Given a triangle with a side length of 10, an angle of 45 degrees, and opposite side 'x', find the value of x using trigonometry ratio formulas.","Answer: To find 'x', we can use the sine function. sin(45) = x/10, solving for x, we get x = 10*sin(45) = 7.07106781187 (approx).",{"$ sicons":407},{"bxl:facebook-circle":408,"bxl:instagram":412,"mdi:web":414,"la:apple":416,"ph:google-logo-bold":419,"ph:google-logo":422},{"left":409,"top":409,"width":410,"height":410,"rotate":409,"vFlip":183,"hFlip":183,"body":411},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 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