represents 2 raised to the power of 2, which is $2 \\times 2 = 4$. Therefore, the answer is 4.",null,898,180,"2",{"id":16,"category":7,"text_question":17,"photo_question":9,"text_answer":18,"step_text_answer":11,"step_photo_answer":11,"views":19,"likes":20,"slug":21},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":23,"category":7,"text_question":24,"photo_question":9,"text_answer":25,"step_text_answer":11,"step_photo_answer":11,"views":26,"likes":27,"slug":28},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":30,"category":7,"text_question":31,"photo_question":9,"text_answer":32,"step_text_answer":11,"step_photo_answer":11,"views":33,"likes":34,"slug":35},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":37,"category":7,"text_question":38,"photo_question":9,"text_answer":39,"step_text_answer":11,"step_photo_answer":11,"views":40,"likes":41,"slug":42},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":44,"category":7,"text_question":45,"photo_question":9,"text_answer":46,"step_text_answer":11,"step_photo_answer":11,"views":47,"likes":48,"slug":49},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":7,"text_question":52,"photo_question":9,"text_answer":53,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":59,"photo_question":9,"text_answer":60,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":66,"photo_question":9,"text_answer":67,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":73,"photo_question":9,"text_answer":74,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":80,"photo_question":9,"text_answer":81,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":87,"photo_question":9,"text_answer":88,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":94,"photo_question":9,"text_answer":95,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":101,"photo_question":9,"text_answer":102,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":108,"photo_question":9,"text_answer":109,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":115,"photo_question":9,"text_answer":116,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":122,"photo_question":9,"text_answer":123,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":129,"photo_question":9,"text_answer":130,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":136,"photo_question":9,"text_answer":137,"step_text_answer":11,"step_photo_answer":11,"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":7,"text_question":143,"photo_question":9,"text_answer":144,"step_text_answer":11,"step_photo_answer":11,"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",{"first":149,"last":150,"prev":11,"next":151},1,188,2,{"current_page":149,"from":149,"last_page":150,"links":153,"path":190,"per_page":191,"to":191,"total":192},[154,157,159,162,165,168,171,174,177,180,183,186,188],{"url":149,"label":155,"active":156},"1",true,{"url":151,"label":14,"active":158},false,{"url":160,"label":161,"active":158},3,"3",{"url":163,"label":164,"active":158},4,"4",{"url":166,"label":167,"active":158},5,"5",{"url":169,"label":170,"active":158},6,"6",{"url":172,"label":173,"active":158},7,"7",{"url":175,"label":176,"active":158},8,"8",{"url":178,"label":179,"active":158},9,"9",{"url":181,"label":182,"active":158},10,"10",{"url":184,"label":185,"active":158},187,"187",{"url":150,"label":187,"active":158},"188",{"url":151,"label":189,"active":158},"Next »","https://api.math-master.org/api/question",20,3741,{"data":194},[195,197,199,201,203,205],{"id":149,"title":196,"slug":11},"Algebra",{"id":151,"title":198,"slug":11},"Geometry",{"id":160,"title":200,"slug":11},"Coordinate-geometry",{"id":163,"title":202,"slug":11},"Statistics",{"id":166,"title":204,"slug":11},"Calculus",{"id":169,"title":206,"slug":11},"General",{"data":208},[209,210,211,212,213,214],{"id":149,"title":196,"slug":11},{"id":151,"title":198,"slug":11},{"id":160,"title":200,"slug":11},{"id":163,"title":202,"slug":11},{"id":166,"title":204,"slug":11},{"id":169,"title":206,"slug":11},{"data":216},{"id":217,"category":7,"slug":218,"text_question":219,"photo_question":11,"text_answer":220,"step_text_answer":11,"step_photo_answer":11,"views":221,"likes":222,"expert":223},534349,"the-volume-of-a-cube-decreases-at-a-rate-of-10-m3-s-find-the-rate-at-which-the-side-of-the-cube-changes-when-the-side-of-the-cube-is-2-m","The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.","Solution:\n\nThe formula for the volume of a cube is given by\u003Cmath-field read-only> V=s^3 \u003C/math-field>Taking the derivative of the equation with respect to t,\u003Cmath-field read-only> \\frac{\\differentialD V}{\\differentialD t}=3s^2\\frac{\\differentialD s}{\\differentialD t} \u003C/math-field>\u003Cmath-field read-only> \\frac{\\differentialD s}{\\differentialD t}=\\frac{\\frac{\\differentialD V}{\\differentialD t}}{3s^2} \u003C/math-field>Substituting values,\u003Cmath-field read-only> \\frac{\\differentialD s}{\\differentialD t}=\\frac{10}{3\\left(2\\right)^2} \u003C/math-field>\u003Cmath-field read-only> \\frac{\\differentialD s}{\\differentialD t}=\\frac{5}{6}\\operatorname{m/s} \u003C/math-field>",1208,242,{"id":224,"name":225,"photo":226,"biography":227,"created_at":11,"updated_at":11,"rating":228,"total_answer":229},32,"Velda","https://api.math-master.org/img/experts/32/32.webp","I have always been a math enthusiast since I was in my elementary years. In high school, I found math to be the easiest subject to study since I didn't need to spend a lot of time memorizing stuff. It was easy for me to remember formulas and steps in solving math problems. In college, I took Bachelor in Secondary Education major in Mathematics since it was my dream to become a teacher. Of course, it automatically followed that I had to take math as my specialization. After graduating in college, while I was job hunting, I came across Kumon Learning Center. After learning about the program, I decided to work as a Kumon Assistant Instructor. I started teaching low level mathematics; basic math up to middle high school math. After a while, I was tasked to handle the advanced level math courses where I had to deal with higher level maths such as advanced algebra, Trigonometry, and Advanced Calculus. Through my 4 years stay in Kumon, I was able to further develop my math skills. After 4 years, I decided to teach in a formal school. I was hired as a high school math teacher in one of the prestigious private university in our city and country in general. I have been teaching in the same institution for 12 years now. In my 12 years of teaching, I have experienced handling and teaching all levels in high school math. I was also able to teach for 1 semester under the math department in the college unit of the same institution. I pursued my further studies by enrolling in Master of Arts in Mathematics. As of the moment, I have completed my academic requirements and I also successfully passed the Comprehensive Exams. I am currently in my thesis writing stage in the program.\r\n\r\n",4.5,109,{"data":231},{"questions":232},[233,237,241,245,249,252,256,260,264,268,272,276,280,284,288,292,296,300,304,308],{"id":234,"category":7,"text_question":235,"slug":236},532048,"CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.","case-6-1-prepare-a-production-plan-what-problems-arrive-midwest-plastics-company-has-conducted-profit-planning-for-several-years-the-president-stated-with-justification-that-inventory-control-an",{"id":238,"category":7,"text_question":239,"slug":240},532082,"Calculate the 6th term of PA whose 1st term is 6.5 and the ratio 5","calculate-the-6th-term-of-pa-whose-1st-term-is-6-5-and-the-ratio-5",{"id":242,"category":7,"text_question":243,"slug":244},533919,"a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?","a-bank-finds-that-the-balances-in-its-savings-accounts-are-normally-distributed-with-a-mean-of-500-and-a-standard-deviation-off-of-40-what-is-the-probability-that-a-randomly-selected-account-has-a",{"id":246,"category":7,"text_question":247,"slug":248},533945,"Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and\n I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)","let-i-r-be-a-bounded-and-nonempty-interval-show-that-there-are-numbers-a-b-r-with-a-b-and-i-a-b-or-i-a-b-or-i-a-b-or-i-a-b",{"id":250,"category":7,"text_question":251,"slug":251},533969,"7273736363-8",{"id":253,"category":7,"text_question":254,"slug":255},533973,"4X^2 25","4x-2-25",{"id":257,"category":7,"text_question":258,"slug":259},534120,"If 0101, what is the binary representation of the 4x16 decoder output?","if-0101-what-is-the-binary-representation-of-the-4x16-decoder-output",{"id":261,"category":7,"text_question":262,"slug":263},534226,"using the math and science known about the jefferson river bridge Find a truss in use and develop a load diagram. Use a load of 50 lb on each joint along the bottom of the truss for a truss that actrs as a bridge and along the top joints for a truss that acts as a roof","using-the-math-and-science-known-about-the-jefferson-river-bridge-find-a-truss-in-use-and-develop-a-load-diagram-use-a-load-of-50-lb-on-each-joint-along-the-bottom-of-the-truss-for-a-truss-that-actrs",{"id":265,"category":7,"text_question":266,"slug":267},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":269,"category":7,"text_question":270,"slug":271},534264,"How much does the average college student spend on food per month? A random sample of 50 college students showed a sample mean $670 with a standard deviation $80. Obtain the 95% confidence interval for the amount college students spend on food per month.","how-much-does-the-average-college-student-spend-on-food-per-month-a-random-sample-of-50-college-students-showed-a-sample-mean-670-with-a-standard-deviation-80-obtain-the-95-confidence-interval-fo",{"id":273,"category":7,"text_question":274,"slug":275},534354,"Jasminder has made 55% of the recipes in a particular cookbook. If there are 9 recipes that he has never\nmade, how many recipes does the cookbook contain?","jasminder-has-made-55-of-the-recipes-in-a-particular-cookbook-if-there-are-9-recipes-that-he-has-never-made-how-many-recipes-does-the-cookbook-contain",{"id":277,"category":7,"text_question":278,"slug":279},534378,"Your grandfather has run a small high street pharmacy for 40 years. After much persuasion, he has agreed to open a digital store online. List 5 potential ways to improve sales and/or margins by having a digital pharmacy through the utilisation of historic or new sales data.","your-grandfather-has-run-a-small-high-street-pharmacy-for-40-years-after-much-persuasion-he-has-agreed-to-open-a-digital-store-online-list-5-potential-ways-to-improve-sales-and-or-margins-by-having",{"id":281,"category":7,"text_question":282,"slug":283},534388,"A contractor gives a bank note for $10250 at a rate of 1% for one month. How much interest\nis charged for 4 months?","a-contractor-gives-a-bank-note-for-10250-at-a-rate-of-1-for-one-month-how-much-interest-is-charged-for-4-months",{"id":285,"category":7,"text_question":286,"slug":287},534446,"To get to a hotel on the hill you have to travel 6 km of uphill road and every kilometer there are 6 sharp curves. Each of the sharp curves is marked by three traffic signs. How many traffic signs are there on the stretch of road that leads to the arbergi?","to-get-to-a-hotel-on-the-hill-you-have-to-travel-6-km-of-uphill-road-and-every-kilometer-there-are-6-sharp-curves-each-of-the-sharp-curves-is-marked-by-three-traffic-signs-how-many-traffic-signs-are",{"id":289,"category":7,"text_question":290,"slug":291},534491,"A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales.\n How many hours will you have to work on average each month for your income to be $2000?","a-salesperson-earns-a-base-salary-of-600-per-month-plus-a-commission-of-10-of-the-sales-she-makes-you-discover-that-on-average-it-takes-you-an-hour-and-a-half-to-make-100-worth-of-sales-how-man",{"id":293,"category":7,"text_question":294,"slug":295},534515,"Evaluate ab+dc\n if a=56\n , b=−34\n , c=0.4\n , and d=12\n . Write in simplest form.","evaluate-ab-dc-if-a-56-b-34-c-0-4-and-d-12-write-in-simplest-form",{"id":297,"category":7,"text_question":298,"slug":299},534537,"2 - 6x = -16x + 28","2-6x-16x-28",{"id":301,"category":7,"text_question":302,"slug":303},534547,"2.3 X 0.8","2-3-x-0-8",{"id":305,"category":7,"text_question":306,"slug":307},534582,"16-(x²+x+2)²","16-x-x-2",{"id":309,"category":7,"text_question":310,"slug":311},534668,"The supply of a good registers periodic increases. With each increase in the offer, the total receipts of the bidders increase. Indicate the correct statement: a) demand is elastic b) demand is inelastic c) supply is inelastic d) supply has unit elasticity.","the-supply-of-a-good-registers-periodic-increases-with-each-increase-in-the-offer-the-total-receipts-of-the-bidders-increase-indicate-the-correct-statement-a-demand-is-elastic-b-demand-is-inelas",{"data":313},{"questions":314},[315,319,322,326,330,334,338,342,346,350,354,358,362,366,370,374,378,382,386,390],{"id":316,"category":7,"text_question":317,"slug":318},533925,"58+861-87","58-861-87",{"id":320,"category":7,"text_question":321,"slug":321},533975,"4x567",{"id":323,"category":7,"text_question":324,"slug":325},534015,"(5u + 6)-(3u+2)=","5u-6-3u-2",{"id":327,"category":7,"text_question":328,"slug":329},534017,"(2x+5)^3+(x-3)(x+3)","2x-5-3-x-3-x-3",{"id":331,"category":7,"text_question":332,"slug":333},534063,"A National Solidarity Bond offers A 5 year bond offering a gross return of 15%\r\n\r\nCalculate the AER for this investment. (Give your answer to two decimal places, no need for the percent or € sign in your answer)","a-national-solidarity-bond-offers-a-5-year-bond-offering-a-gross-return-of-15-calculate-the-aer-for-this-investment-give-your-answer-to-two-decimal-places-no-need-for-the-percent-or-sign-in",{"id":335,"category":7,"text_question":336,"slug":337},534094,"If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.","if-f-x-y-6xy-2-3y-3-find-3-2-f-x-y-dx",{"id":339,"category":7,"text_question":340,"slug":341},534098,"A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.","a-person-borrows-rm-1000-from-a-bank-at-an-interest-rate-of-10-after-some-time-he-pays-the-bank-rm-1900-as-full-and-final-settlement-of-the-loan-estimate-the-duration-of-his-loan",{"id":343,"category":7,"text_question":344,"slug":345},534103,"Convert 78 percent to a decimal","convert-78-percent-to-a-decimal",{"id":347,"category":7,"text_question":348,"slug":349},534261,"A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease.\n(4 Points)","a-vaccine-has-a-90-probability-of-being-effective-in-preventing-a-certain-disease-the-probability-of-getting-the-disease-if-a-person-is-not-vaccinated-is-50-in-a-certain-geographic-region-60-of",{"id":351,"category":7,"text_question":352,"slug":353},534300,"4+168×10³×d1+36×10³×d2=-12\n-10+36×10³×d1+72×10³×d2=0","4-168-10-d1-36-10-d2-12-10-36-10-d1-72-10-d2-0",{"id":355,"category":7,"text_question":356,"slug":357},534342,"Congratulations, you have saved well and are ready to begin your retirement.\nIf you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly:\nWhat is the amount of the monthly distribuion? 216.50\nHow much interest is earned in retirement?","congratulations-you-have-saved-well-and-are-ready-to-begin-your-retirement-if-you-have-1-750-000-00-saved-for-your-retirement-and-want-it-to-last-for-40-years-and-will-earn-10-8-compounded-monthl",{"id":359,"category":7,"text_question":360,"slug":361},534381,"A company made 150,000 in the first year 145,000 in the second 140,000 in the third year successively during the first decade of this company's existence it made a total of","a-company-made-150-000-in-the-first-year-145-000-in-the-second-140-000-in-the-third-year-successively-during-the-first-decade-of-this-company-s-existence-it-made-a-total-of",{"id":363,"category":7,"text_question":364,"slug":365},534424,"Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict.\nModel the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.","write-the-detailed-definition-of-a-supply-chain-logistics-related-maximization-problem-with-8-variables-and-6-constraints-each-constraint-should-have-at-least-6-variables-each-constraint-should-have",{"id":367,"category":7,"text_question":368,"slug":369},534476,"You buy a $475,000 house and put 15% down. If you take a 20 year amortization and the rate is 2.34%, what would the monthly payment be?","you-buy-a-475-000-house-and-put-15-down-if-you-take-a-20-year-amortization-and-the-rate-is-2-34-what-would-the-monthly-payment-be",{"id":371,"category":7,"text_question":372,"slug":373},534483,"A property sold for $745,000 in a co-brokered transaction. The seller has agreed to pay a 7% commission to the listing firm. The listing firm has agreed to equally split the commission with the selling firm. If the buyer’s broker will receive 8% of the selling firm’s commission, how much commission will the buyer’s broker receive? \n$14,900\n$3725\n$$37250\n$18625","a-property-sold-for-745-000-in-a-co-brokered-transaction-the-seller-has-agreed-to-pay-a-7-commission-to-the-listing-firm-the-listing-firm-has-agreed-to-equally-split-the-commission-with-the-sellin",{"id":375,"category":7,"text_question":376,"slug":377},534485,"X^X =49 X=?","x-x-49-x",{"id":379,"category":7,"text_question":380,"slug":381},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":383,"category":7,"text_question":384,"slug":385},534553,"2x-4=8","2x-4-8",{"id":387,"category":7,"text_question":388,"slug":389},534628,"Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. \n\nPoint D lies on AB such that CB = CD\n\nPoint E lies on AC such that CE= DE\n\nDetermine angle DEC in terms of X","triangle-abc-has-ab-ac-and-angle-bac-x-with-x-being-less-than-60-degrees-point-d-lies-on-ab-such-that-cb-cd-point-e-lies-on-ac-such-that-ce-de-determine-angle-dec-in-terms-of-x",{"id":391,"category":7,"text_question":392,"slug":393},534659,"Slope (7,3) and (9,5)","slope-7-3-and-9-5",{"data":395},[396,400,404],{"id":397,"question":398,"answer":399},163644,"What is the mean, mode, median, range, and average of the following set of numbers: 5, 8, 9, 12, 12, 15, 21, 22?","The mean is 13.875, mode is 12, median is 12.5, range is 17, average is 13.875. The mean represents the average of the numbers, the mode is the value that appears most frequently, the median is the middle value when the numbers are sorted, the range is the difference between the highest and lowest values, and the average is the same as the mean.",{"id":401,"question":402,"answer":403},150371,"What is the value of arccos(0) + arcsin(1) - arctan(1)?","The value is π/2 because arccos(0) = π/2, arcsin(1) = π/2, and arctan(1) = π/4, so π/2 + π/2 - π/4 = π/2.",{"id":405,"question":406,"answer":407},102269,"Question: What is the result when you divide 3/4 by 1/5 using fraction division?","Answer: To divide fractions, we invert the second fraction and multiply, so (3/4) / (1/5) = (3/4) * (5/1). Multiplying across, we get (3 * 5) / (4 * 1) = 15/4, which is equivalent to 3 3/4.",{"$sicons":409},{"bxl:facebook-circle":410,"bxl:instagram":414,"mdi:web":416,"la:apple":418,"ph:google-logo-bold":420,"ph:google-logo":423},{"left":411,"top":411,"width":412,"height":412,"rotate":411,"vFlip":158,"hFlip":158,"body":413},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":411,"top":411,"width":412,"height":412,"rotate":411,"vFlip":158,"hFlip":158,"body":415},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" 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