represents 2 raised to the power of 2, which is $2 \\times 2 = 4$. Therefore, the answer is 4.",898,180,"2",{"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},538090,"The ratio of Adam’s weight to John’s weight is 6:5. If Adam weighs 48 KG, find John’s weight.","Let Adam's weight be represented as \\( A \\) and John's weight as \\( J \\). \u003Cbr />\n\u003Cbr />\nGiven the ratio is 6:5, we have:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{A}{J} = \\frac{6}{5} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nWe know Adam's weight \\( A = 48 \\, \\text{KG} \\).\u003Cbr />\n\u003Cbr />\nSo substitute \\( A \\) in the ratio:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{48}{J} = \\frac{6}{5} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nBy cross-multiplying:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6J = 5 \\times 48 \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> 6J = 240 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nNow, solve for \\( J \\):\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> J = \\frac{240}{6} \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> J = 40 \\, \\text{KG} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, John's weight is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>40 \\text{ KG}\u003C/math-field>\u003C/math-field>.",591,118,"the-ratio-of-adam-s-weight-to-john-s-weight-is-6-5-if-adam-weighs-48-kg-find-john-s-weight",{"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},538089,"David cuts a rope 60 m long into two pieces in the ratio 2:3. What is the length of the shorter piece of rope?","1. Let the lengths of the two pieces of rope be represented as $2x$ and $3x$, since they are in the ratio 2:3.\u003Cbr />\n \u003Cbr />\n2. According to the problem, the sum of the lengths of the two pieces is 60 m, so:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x + 3x = 60 \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> 5x = 60 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve for $x$:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{60}{5} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 12 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. The length of the shorter piece of rope is $2x$, so:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x = 2 \\times 12 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x = 24 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the length of the shorter piece of rope is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 24 \\, \\text{m} \u003C/math-field>\u003C/math-field>",1166,233,"david-cuts-a-rope-60-m-long-into-two-pieces-in-the-ratio-2-3-what-is-the-length-of-the-shorter-piece-of-rope",{"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},538088,"Breanne made pineapple drinks by mixing pineapple syrup and water in the ratio 2:7. If she used 4 L of pineapple syrup, how much water did she use?","1. The ratio of pineapple syrup to water is 2:7. This means for every 2 parts of syrup, there are 7 parts of water.\u003Cbr />\n2. Breanne used 4 L of pineapple syrup. Set up the proportion:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{2}{7} = \\frac{4}{x} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n where \\( x \\) is the amount of water used.\u003Cbr />\n\u003Cbr />\n3. Cross-multiply to solve for \\( x \\):\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x = 7 \\cdot 4 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x = 28 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Solve for \\( x \\):\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{28}{2} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Calculate:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 14 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Therefore, Breanne used 14 L of water. \u003Cbr />\n\u003Cbr />\nAnswer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>14 \\text{ L}\u003C/math-field>\u003C/math-field>",783,157,"breanne-made-pineapple-drinks-by-mixing-pineapple-syrup-and-water-in-the-ratio-2-7-if-she-used-4-l-of-pineapple-syrup-how-much-water-did-she-use",{"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},538087,"y=-2(4)^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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":153,"slug":154},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":156,"category":36,"text_question":157,"photo_question":38,"text_answer":158,"step_text_answer":8,"step_photo_answer":8,"views":159,"likes":160,"slug":161},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":163,"category":36,"text_question":164,"photo_question":38,"text_answer":165,"step_text_answer":8,"step_photo_answer":8,"views":166,"likes":167,"slug":168},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":170,"category":36,"text_question":171,"photo_question":38,"text_answer":172,"step_text_answer":8,"step_photo_answer":8,"views":173,"likes":174,"slug":175},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",{"first":6,"last":177,"prev":8,"next":10},188,{"current_page":6,"from":6,"last_page":177,"links":179,"path":212,"per_page":213,"to":213,"total":214},[180,183,185,187,189,191,193,196,199,202,205,208,210],{"url":6,"label":181,"active":182},"1",true,{"url":10,"label":42,"active":184},false,{"url":13,"label":186,"active":184},"3",{"url":16,"label":188,"active":184},"4",{"url":19,"label":190,"active":184},"5",{"url":22,"label":192,"active":184},"6",{"url":194,"label":195,"active":184},7,"7",{"url":197,"label":198,"active":184},8,"8",{"url":200,"label":201,"active":184},9,"9",{"url":203,"label":204,"active":184},10,"10",{"url":206,"label":207,"active":184},187,"187",{"url":177,"label":209,"active":184},"188",{"url":10,"label":211,"active":184},"Next »","https://api.math-master.org/api/question",20,3741,{"data":216},{"id":217,"category":36,"slug":218,"text_question":219,"photo_question":8,"text_answer":220,"step_text_answer":8,"step_photo_answer":8,"views":221,"likes":222,"expert":223},536045,"formal-proof-for-proposition-3-38-equivalence-of-a-set-of-formulas-and-their-clausal-forms-a-set-of-formulas-u-is-equivalent-to-the-set-of-clauses-comprising-the-union-of-the-clausal-forms-of-the-fo","Formal proof for Proposition 3.38 (Equivalence of a set of formulas and their clausal forms)\nA set of formulas U is equivalent to the set of clauses comprising the union of the\nclausal forms of the formulas in U . Please use existing theorems to answer the formal logic problem.","To prove Proposition 3.38, we need to show that a set of formulas U is equivalent to the set of clauses comprising the union of the clausal forms of the formulas in U.\u003Cbr>\u003Cbr>Let's denote the set of formulas U as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi\u003C/math-field>\u003C/math-field> , and the set of clauses comprising the union of the clausal forms of the formulas in U as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Psi\u003C/math-field>\u003C/math-field> . We want to show that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi \\equiv \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Given a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi\u003C/math-field>\u003C/math-field> , its clausal form is denoted as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>cl(\\phi)\u003C/math-field>\u003C/math-field> . The clausal form of a set of formulas is the union of the clausal forms of each formula.\u003Cbr>\u003Cbr>We need to show two things:\u003Cbr>1. If a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> , then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>cl(\\phi) \\in \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>2. If a clause \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C \\in \\Psi\u003C/math-field>\u003C/math-field> , then there exists a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> such that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>cl(\\phi) = C\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Let's prove each part:\u003Cbr>1. Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> , then by definition of clausal form, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>cl(\\phi)\u003C/math-field>\u003C/math-field> is in the union of the clausal forms of the formulas in U. Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>cl(\\phi) \\in \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>2. Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C \\in \\Psi\u003C/math-field>\u003C/math-field> , then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C\u003C/math-field>\u003C/math-field> is a clause in the union of clausal forms of the formulas in U. By the definition of clausal form, there exists a formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\phi \\in \\Phi\u003C/math-field>\u003C/math-field> such that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>cl(\\phi) = C\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Therefore, we have shown that if \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi\u003C/math-field>\u003C/math-field> is a set of formulas, and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Psi\u003C/math-field>\u003C/math-field> is the set of clauses comprising the union of the clausal forms of the formulas in \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi\u003C/math-field>\u003C/math-field> , then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\Phi \\equiv \\Psi\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\Phi \\equiv \\Psi}\u003C/math-field>\u003C/math-field>",253,51,{"id":224,"name":225,"photo":226,"biography":227,"created_at":8,"updated_at":8,"rating":228,"total_answer":229},27,"Adonis","https://api.math-master.org/img/experts/27/27.webp","I’m a student at SRM University Andhra Pradesh in India. I’m perusing a\r\nbachelor’s degree in computer science and engineering here. My proper is from West Godavari\r\nDistrict of Andhra Pradesh in India. It is where I’ve finished my schooling till class 12. I have a\r\nsibling who is studying very parallel to me. I had very good teaching people and even some of my\r\nfriends from my childhood and spending time with those people made me a little crazy about\r\nmathematics and physics.\r\nI had a very good interest in mathematics from my very childhood, and I got to solve problems\r\nwith plenty of enthusiasm. It all started in class 6 where I had met my math teacher. He is\r\nextremely brilliant at teaching us. He used to attract everyone with his wonderful skills in\r\nmathematics. He used to provide us with a lot of mind cracking puzzles, and it was all fun solving\r\nthem. And that’s the start of my math journey. I passed my class 10 with very high standards, and\r\nI made everyone so proud that day. With the same motivation, I’ve cleared my class 12 and\r\nentered the field of engineering. There, I met another wonderful professor in mathematics, and\r\nhe is from the West Bengal of India. Though the level of the subject is very hard, he used to teach\r\nit with very easy techniques and my skills developed a lot with that. He made me score an\r\noutstanding grade in Calculus. And then I started missing doing that fun. So, I searched for some\r\nonline tutoring platforms where I can share my knowledge in mathematics. The result is I found\r\nmyself as an expert and solving the problems. Now, I’m feeling a lot better with doing math on\r\none side and my bachelor’s degree on another. I would like to thank the Math Expert for providing\r\nme with this beautiful opportunity. Here, there are a lot of opportunities for people like us. I will\r\ndefinitely suggest my friends to join here as an expert and enjoy the same thing I does. ",4.4,101,{"data":231},{"questions":232},[233,237,241,245,249,253,257,261,265,269,273,277,281,285,289,293,297,301,305,309],{"id":234,"category":36,"text_question":235,"slug":236},532024,"2(2+2x)=12","2-2-2x-12",{"id":238,"category":36,"text_question":239,"slug":240},533918,"5 people can complete a task in 72 hours. How many people are needed to complete the task in 60 hours.","5-people-can-complete-a-task-in-72-hours-how-many-people-are-needed-to-complete-the-task-in-60-hours",{"id":242,"category":36,"text_question":243,"slug":244},533980,"Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.","find-the-root-of-x-4-10x-5-0-using-newton-s-method-with-a-precision-of-the-smallest-positive-root",{"id":246,"category":36,"text_question":247,"slug":248},534011,"9b^2-6b-5","9b-2-6b-5",{"id":250,"category":36,"text_question":251,"slug":252},534027,"Answer the following questions regarding the expression below.\n\n \n\n0.1\n \n\n \n\n(a) Write the number as a fraction.","answer-the-following-questions-regarding-the-expression-below-0-1-a-write-the-number-as-a-fraction",{"id":254,"category":36,"text_question":255,"slug":256},534048,"To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:","to-celebrate-the-five-year-anniversary-of-a-consultancy-specializing-in-information-technology-the-administrator-decided-to-draw-3-different-qualification-courses-among-its-10-employees-considering",{"id":258,"category":36,"text_question":259,"slug":260},534090,"If you randomly selected one person from the 900 subjects in this study, what is the probability that \nthe person exhibits the minimum BMI?","if-you-randomly-selected-one-person-from-the-900-subjects-in-this-study-what-is-the-probability-that-the-person-exhibits-the-minimum-bmi",{"id":262,"category":36,"text_question":263,"slug":264},534104,"78 percent to a decimal","78-percent-to-a-decimal",{"id":266,"category":36,"text_question":267,"slug":268},534168,"I want you to solve this problem as a grade sixth pupil in primary school:\n8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?","i-want-you-to-solve-this-problem-as-a-grade-sixth-pupil-in-primary-school-8-pigs-ate-6-bags-of-fee-in-20-days-how-long-will-it-take-10-pigs-to-eat-15-bags-of-feed-eating-at-the-same-rate",{"id":270,"category":36,"text_question":271,"slug":272},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":274,"category":36,"text_question":275,"slug":276},534223,"In a order to compare the means of two populations, independent random samples of 410 observations are selected from each population, with Sample 1 the results found in the table to the right. Complete parts a through e below. X1 = 5,319 S1= 143 a. Use a 95% confidence interval to estimate the difference between the population means (H - H2) Interpret the contidence interval. The contidence interval IS (Round to one decimal place as needed.) Sample 2 X2 = 5,285 S2 = 198\n\nAa. Use a 95% confidence interval to estimate the difference between the population means (A1 - M2) Interpret the contidence interval. The contidence interval Is (Round to one decimal place as needed.)\n\nb. Test the null hypothesis Ho versus alternative hypothesis Ha (H What is the test statistic? H2) + Give the significance level of the test, and interpret the result. Use a = 0.05. \nZ=","in-a-order-to-compare-the-means-of-two-populations-independent-random-samples-of-410-observations-are-selected-from-each-population-with-sample-1-the-results-found-in-the-table-to-the-right-complet",{"id":278,"category":36,"text_question":279,"slug":280},534286,"From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539","from-1975-through-2020-the-mean-annual-gain-of-the-dow-jones-industrial-average-was-652-a-random-sample-of-34-years-is-selected-from-this-population-what-is-the-probability-that-the-mean-gain-for-th",{"id":282,"category":36,"text_question":283,"slug":284},534363,"ind the z-score for which 72% of the distribution's area lies between -z and z.\n\n-1.7417, 1.7417\n\n-1.1538, 1.1538\n\n-1.0803, 1.0803\n\n-2.826, 2.826","ind-the-z-score-for-which-72-of-the-distribution-s-area-lies-between-z-and-z-1-7417-1-7417-1-1538-1-1538-1-0803-1-0803-2-826-2-826",{"id":286,"category":36,"text_question":287,"slug":288},534377,"The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion is greater than 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is z= 2.6. Find the P-value for this test.","the-business-college-computing-center-wants-to-determine-the-proportion-of-business-students-who-have-personal-computers-pc-s-at-home-if-the-proportion-is-greater-than-35-then-the-lab-will-modify",{"id":290,"category":36,"text_question":291,"slug":292},534488,"7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?","7-a-printing-company-found-in-its-investigations-that-there-were-an-average-of-6-errors-in-150-page-prints-based-on-this-information-what-is-the-probability-of-there-being-48-errors-in-a-1200-page",{"id":294,"category":36,"text_question":295,"slug":296},534563,"How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7","how-much-does-7-2-moles-of-ammonium-dichromate-weigh-nh4-2cr2o7",{"id":298,"category":36,"text_question":299,"slug":300},534582,"16-(x²+x+2)²","16-x-x-2",{"id":302,"category":36,"text_question":303,"slug":304},534679,"Find the rule that connects the first number to the second number of each pair.\r\nApply the rule to find the missing number in the third pair.\r\n(18 is to 22) (54 is to 26) (9 is to ?)","find-the-rule-that-connects-the-first-number-to-the-second-number-of-each-pair-apply-the-rule-to-find-the-missing-number-in-the-third-pair-18-is-to-22-54-is-to-26-9-is-to",{"id":306,"category":36,"text_question":307,"slug":308},534681,"(3b)⋅(5b^2)⋅(6b^3)","3b-5b-2-6b-3",{"id":310,"category":36,"text_question":311,"slug":312},534694,"An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?","an-invoice-for-2-880-plus-default-interest-of-48-40-was-paid-on-october-28th-interest-rate-5-5-when-was-the-bill-due",{"data":314},{"questions":315},[316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,384,388,392],{"id":317,"category":36,"text_question":318,"slug":319},532301,"A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.","a-hotel-in-the-algarve-had-to-offer-1-week-of-vacation-to-one-of-its-employees-as-an-easter-gift-in-a-random-choice-it-is-known-that-80-people-work-in-this-hotel-41-of-whom-are-portuguese-and-39-are",{"id":321,"category":36,"text_question":322,"slug":323},533993,"Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.","two-events-e-and-f-are-if-the-occurrence-of-event-e-in-a-probability-experiment-does-not-affect-the-probability-of-event-f",{"id":325,"category":36,"text_question":326,"slug":327},534073,"How long will it take for $900 to become $5000 at an annual rate of 11.15% compounded bimonthly?","how-long-will-it-take-for-900-to-become-5000-at-an-annual-rate-of-11-15-compounded-bimonthly",{"id":329,"category":36,"text_question":330,"slug":331},534119,"What is the appropriate measurement for the weight of an African elephant?","what-is-the-appropriate-measurement-for-the-weight-of-an-african-elephant",{"id":333,"category":36,"text_question":334,"slug":335},534134,"find x in the equation\n 2x-4=6","find-x-in-the-equation-2x-4-6",{"id":337,"category":36,"text_question":338,"slug":339},534141,"v\r\nIs the following statement a biconditional?\r\nIf Shannon is watching a Tigers game, then it is on television.","v-is-the-following-statement-a-biconditional-if-shannon-is-watching-a-tigers-game-then-it-is-on-television",{"id":341,"category":36,"text_question":342,"slug":343},534176,"Three squares have a total area of 35.25 𝑐𝑚2\r\n. The larger square has twice the side-length of the\r\nmiddle-sized square. The smaller square has its side length exactly 0.5 cm smaller than the\r\nmiddle-sixed square. Find the side lengths of each of the three squares.","three-squares-have-a-total-area-of-35-25-cm2-the-larger-square-has-twice-the-side-length-of-the-middle-sized-square-the-smaller-square-has-its-side-length-exactly-0-5-cm-smaller-than-the-middle",{"id":345,"category":36,"text_question":346,"slug":347},534249,"3 A tree is planted when it is 1.2 m tall. Every year its growth is 3/8 of its previous year's height. Find how tall the tree will grow.","3-a-tree-is-planted-when-it-is-1-2-m-tall-every-year-its-growth-is-3-8-of-its-previous-year-s-height-find-how-tall-the-tree-will-grow",{"id":349,"category":36,"text_question":350,"slug":351},534253,"If X1 and X2 are independent standard normal variables, find P(X1^2 + X2^2 > 2.41)","if-x1-and-x2-are-independent-standard-normal-variables-find-p-x1-2-x2-2-2-41",{"id":353,"category":36,"text_question":354,"slug":355},534306,"Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two)\n au=a.(x,y)=(ax+a-1,ay-2a+2)\n It is known that this set with the operations defined above is a vector space.\n A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2\n\n B) show that (0,0) #0\n Suggestion find a vector W such that u+w=u\n\n C) who is the vector -u\n\n D) show that axiom A4 holds:-u+u=0","let-v-be-the-set-of-all-ordered-pairs-of-real-numbers-and-consider-the-scalar-addition-and-multiplication-operations-defined-by-u-v-x-y-s-t-x-s-1-y-t-two-au-a-x-y-ax-a-1-ay-2a-2-it-is-kn",{"id":357,"category":36,"text_question":358,"slug":359},534481,"2x-5-x+2=5x-11","2x-5-x-2-5x-11",{"id":361,"category":36,"text_question":362,"slug":363},534504,"Gender and communication : \nAnswer the question ( 1 paragraph is ok) . Please can you write about women? \n\nCompared to your other identities, how much of a role does gender play in your life? And has your own sex/gender offered you privileges or disadvantages? How so?","gender-and-communication-answer-the-question-1-paragraph-is-ok-please-can-you-write-about-women-compared-to-your-other-identities-how-much-of-a-role-does-gender-play-in-your-life-and-has",{"id":365,"category":36,"text_question":366,"slug":367},534516,"Write the inequality in the form of a\u003Cx\u003Cb.\n|x| \u003C c^2","write-the-inequality-in-the-form-of-a-x-b-x-c-2",{"id":369,"category":36,"text_question":370,"slug":371},534567,"-6 - t / 4 = -1","6-t-4-1",{"id":373,"category":36,"text_question":374,"slug":375},534569,"the product of a 2-digit number and a 3-digit number is about 50000, what are these numbers","the-product-of-a-2-digit-number-and-a-3-digit-number-is-about-50000-what-are-these-numbers",{"id":377,"category":36,"text_question":378,"slug":379},534584,"Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?","emile-organizes-a-community-dance-to-raise-funds-in-addition-to-paying-300-to-rent-the-room-she-must-rent-chairs-at-2-each-the-quantity-of-chairs-rented-will-be-equal-to-the-number-of-tickets-sol",{"id":381,"category":36,"text_question":382,"slug":383},534641,"3(x-4)=156","3-x-4-156",{"id":385,"category":36,"text_question":386,"slug":387},534642,"2p-6=8+5(p+9)","2p-6-8-5-p-9",{"id":389,"category":36,"text_question":390,"slug":391},534643,"6(k-7) -2=5","6-k-7-2-5",{"id":302,"category":36,"text_question":303,"slug":304},{"data":394},[395,399,403],{"id":396,"question":397,"answer":398},132717,"What is the value of cos(30 degrees)?","The value of cos(30 degrees) is √3/2.",{"id":400,"question":401,"answer":402},161240,"Math question: What is the slope of a line passing through the points (1,3) and (5,11)?","By using the formula (y2 - y1) / (x2 - x1), the slope can be calculated. Substituting the values, we get (11 - 3) / (5 - 1), which simplifies to 8 / 4. Therefore, the slope of the line is 2.",{"id":404,"question":405,"answer":406},110646,"Math Question: Convert the number 5,000,000,000,000,000 into scientific notation.","Answer: The number 5,000,000,000,000,000 in scientific notation is represented as 5 x 10^15. In scientific notation, the base is 5, and the exponent is 15 since we move the decimal point 15 places to the right.",{"$sicons":408},{"bxl:facebook-circle":409,"bxl:instagram":413,"mdi:web":415,"la:apple":417,"ph:google-logo-bold":420,"ph:google-logo":423},{"left":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":184,"hFlip":184,"body":412},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":184,"hFlip":184,"body":414},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle 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