implemented new rules lin residents. A key component of these rules is that residents should work no more than 80 hours per we of weekly hours worked in 2022 by a sample of residents at the Tidelands Medical Center. $Use t Distri\n84 86 84 86 79 82 87 81 84 78 74 86\n\nB. What is the point estimate of the population standard deviation?\nNote: Round your answer to 2 decimal places.\nc. What is the margin of error for a 90% confidence interval estimate?\nNote: Round your answer to 2 decimal places.\nd. Develop a 90% confidence interval for the population mean.\nNote: Round your answers to 2 decimal places.","","B. Calculate the sample standard deviation (\\(s\\$):\u003Cbr>\u003Cbr>1. List the data: \\(84, 86, 84, 86, 79, 82, 87, 81, 84, 78, 74, 86\\).\u003Cbr>\u003Cbr>2. Calculate the sample mean (\\(\\bar{x}\\)): \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bar{x} = \\frac{84 + 86 + 84 + 86 + 79 + 82 + 87 + 81 + 84 + 78 + 74 + 86}{12} = \\frac{991}{12} = 82.58\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Apply the standard deviation formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{\\frac{\\sum (x_i - \\bar{x})^2}{n - 1}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{\\frac{(84-82.58)^2 + (86-82.58)^2 + \\ldots + (86-82.58)^2}{11}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{\\frac{1.98 + 11.78 + 1.98 + 11.78 + 13.04 + 0.3364 + 20.57 + 2.48 + 1.98 + 21.02 + 73.73 + 11.78}{11}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{\\frac{40.54 + 36.84 + 2.48 + 34.82}{11}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{\\frac{151.46}{11}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s=\\sqrt{15.5379}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s\\approx3.94\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>C. Margin of Error:\u003Cbr>\u003Cbr>1. Determine the critical value for 90% confidence with \\( n = 12 \\) which results in degrees of freedom \\( df = 11 \\). Use the t-distribution table.\u003Cbr>\u003Cbr>2. Critical value (\\(t^*\\)) for 90% confidence interval with \\(df = 11\\) is approximately 1.796.\u003Cbr>\u003Cbr>3. Calculate the margin of error:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E=t^*\\times\\frac{s}{\\sqrt{n}}=1.796\\times\\frac{3.94}{\\sqrt{12}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E=1.796\\times1.137\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>E\\approx2.04\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>D. Develop a 90% Confidence Interval:\u003Cbr>\u003Cbr>1. Use the point estimate, margin of error, and sample mean:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bar{x}\\pm E=82.58\\pm2.04\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Calculate the confidence interval:\u003Cbr>\u003Cbr>Lower limit: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>82.58-2.04=80.54\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Upper limit: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>82.58+2.04=84.62\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Round each bound to 2 decimal places: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(80.54,84.62)\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Answer: 90% Confidence Interval = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(80.54,84.62)\u003C/math-field>\u003C/math-field>",422,84,"in-2003-the-accreditation-council-for-graduate-medical-education-acgme-implemented-new-rules-lin-residents-a-key-component-of-these-rules-is-that-residents-should-work-no-more-than-80-hours-per-we",{"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},538093,"FIND THE AREA UNDER THE Standard Normal Distribution: To the right of z = - 2.01","To find the area to the right of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = -2.01\u003C/math-field>\u003C/math-field> on a standard normal distribution:\u003Cbr />\n\u003Cbr />\n1. We need to find the cumulative distribution function (CDF) value for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = -2.01\u003C/math-field>\u003C/math-field>. \u003Cbr />\n\u003Cbr />\n2. Using the standard normal distribution table or a calculator, we find that the CDF value for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = -2.01\u003C/math-field>\u003C/math-field> is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.0222\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Since this value represents the area to the left of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = -2.01\u003C/math-field>\u003C/math-field>, the area to the right is:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 - 0.0222 = 0.9778\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the area under the standard normal distribution curve to the right of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = -2.01\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.9778\u003C/math-field>\u003C/math-field>.",878,176,"find-the-area-under-the-standard-normal-distribution-to-the-right-of-z-2-01",{"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},538092,"2²","The expression $2^2$ represents 2 raised to the power of 2, which is $2 \\times 2 = 4$. Therefore, the answer is 4.",898,180,"2",{"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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":114,"category":36,"text_question":115,"photo_question":38,"text_answer":116,"step_text_answer":8,"step_photo_answer":8,"views":117,"likes":41,"slug":118},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,"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":120,"category":36,"text_question":121,"photo_question":38,"text_answer":122,"step_text_answer":8,"step_photo_answer":8,"views":123,"likes":124,"slug":125},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":127,"category":36,"text_question":128,"photo_question":38,"text_answer":129,"step_text_answer":8,"step_photo_answer":8,"views":130,"likes":131,"slug":132},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":134,"category":36,"text_question":135,"photo_question":38,"text_answer":136,"step_text_answer":8,"step_photo_answer":8,"views":137,"likes":138,"slug":139},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":141,"category":36,"text_question":142,"photo_question":38,"text_answer":143,"step_text_answer":8,"step_photo_answer":8,"views":144,"likes":145,"slug":146},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":148,"category":36,"text_question":149,"photo_question":38,"text_answer":150,"step_text_answer":8,"step_photo_answer":8,"views":151,"likes":152,"slug":153},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":155,"category":36,"text_question":156,"photo_question":38,"text_answer":157,"step_text_answer":8,"step_photo_answer":8,"views":158,"likes":159,"slug":160},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":162,"category":36,"text_question":163,"photo_question":38,"text_answer":164,"step_text_answer":8,"step_photo_answer":8,"views":165,"likes":166,"slug":167},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":169,"category":36,"text_question":170,"photo_question":38,"text_answer":171,"step_text_answer":8,"step_photo_answer":8,"views":172,"likes":173,"slug":174},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",{"first":6,"last":176,"prev":8,"next":10},188,{"current_page":6,"from":6,"last_page":176,"links":178,"path":211,"per_page":212,"to":212,"total":213},[179,182,184,186,188,190,192,195,198,201,204,207,209],{"url":6,"label":180,"active":181},"1",true,{"url":10,"label":56,"active":183},false,{"url":13,"label":185,"active":183},"3",{"url":16,"label":187,"active":183},"4",{"url":19,"label":189,"active":183},"5",{"url":22,"label":191,"active":183},"6",{"url":193,"label":194,"active":183},7,"7",{"url":196,"label":197,"active":183},8,"8",{"url":199,"label":200,"active":183},9,"9",{"url":202,"label":203,"active":183},10,"10",{"url":205,"label":206,"active":183},187,"187",{"url":176,"label":208,"active":183},"188",{"url":10,"label":210,"active":183},"Next »","https://api.math-master.org/api/question",20,3743,{"data":215},{"id":216,"category":36,"slug":217,"text_question":218,"photo_question":8,"text_answer":219,"step_text_answer":8,"step_photo_answer":8,"views":220,"likes":221,"expert":222},537989,"5x-6y-2-6x-2y-18-solve-by-elimination","5x+6y=2\n6x+2y=18\nSolve by elimination","5x + 6y = 2 \\\\\u003Cbr>\u003Cbr>6x + 2y = 18 \\\\\u003Cbr>\u003Cbr>[SOLUTION] \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{55}{28}, \\quad y = -\\frac{16}{28} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>[STEP-BY-STEP] \u003Cbr>\u003Cbr>1. Multiply the first equation by 2:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2(5x + 6y) = 2(2) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 10x + 12y = 4 \\quad \\text{(Equation 3)} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Multiply the second equation by 6:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6(6x + 2y) = 6(18) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 36x + 12y = 108 \\quad \\text{(Equation 4)} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Subtract Equation 3 from Equation 4:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (36x + 12y) - (10x + 12y) = 108 - 4 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 26x = 104 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Solve for \\( x \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{104}{26} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{52}{13} \u003C/math-field>\u003C/math-field> \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>5. Substitute \\( x = 4 \\) back into the original first equation:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\\times4+6y=2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20+6y=2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Solve for \\( y \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6y=2-20\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6y=-18\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y=-3\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Answer:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x=4,y=-3\u003C/math-field>\u003C/math-field>",452,90,{"id":13,"name":223,"photo":224,"biography":225,"created_at":8,"updated_at":8,"rating":226,"total_answer":227},"Timmothy","https://api.math-master.org/img/experts/3/3.webp","Hello, I'm Jamil Omar, and I want to take you on a journey through my experience with math, from school to university.\nEarly School Years:\nHigh school marked the beginning of my mathematical journey, a journey that started with skepticism but transformed into something wonderful. At first, I wasn't a fan of math, until a special teacher changed everything. This teacher showed me the beauty of math, and suddenly, everything clicked.\nBecause of this teacher, I started enjoying math and even joined math competitions during my high school days. Surprisingly, I excelled and became a champion at both the provincial and regional levels. These wins boosted my confidence and made me realize that I could excel in math.\nThese victories also gave me the confidence to pursue an engineering degree in college. Thanks to that teacher and my successes in math, I knew I could conquer new challenges and make the most of my education journey.\nUniversity Journey:\nMy strong grasp of mathematics inspired me to pursue a bachelor's degree in Petroleum Engineering at Palawan State University. Confident in my mathematical foundation, I embarked on this academic journey.\nThroughout the course, I discovered that my solid background in mathematics was a true asset. It enabled me to better comprehend the intricate topics within Petroleum Engineering and successfully complete the program.\nMy enthusiasm for engineering led me to actively engage in quiz bee contests, where sharp mathematical skills are crucial for success. Our team's victory in these contests opened doors to a national quiz bee in our country. This experience not only honed my mathematical abilities but also granted us the privilege to participate in seminars related to our field of study.\nOne of my achievements was securing the top rank in our departmental exam for algebra. During my first year in college, I outperformed all other first-year students across the university. This accomplishment underscores the significant impact of mathematics on my academic journey.\nStudying math has proven to be invaluable, not just in terms of academic achievements but also in enhancing my analytical skills and enabling me to earn a degree in Petroleum Engineering.",4.8,96,{"data":229},{"questions":230},[231,235,239,243,247,251,255,259,263,267,271,275,279,283,287,291,295,299,303,307],{"id":232,"category":36,"text_question":233,"slug":234},532025,"given cos26=k find cos13","given-cos26-k-find-cos13",{"id":236,"category":36,"text_question":237,"slug":238},532041,"The strength of Kefexin oral suspension is 100 mg/ml.\nNora has been prescribed cefalexin at a dose of 50 mg/kg/day divided in two single doses.\nNora weighs 14 kg.\nHow many milliliters of solution for Nora should be given as a single dose?","the-strength-of-kefexin-oral-suspension-is-100-mg-ml-nora-has-been-prescribed-cefalexin-at-a-dose-of-50-mg-kg-day-divided-in-two-single-doses-nora-weighs-14-kg-how-many-milliliters-of-solution-for",{"id":240,"category":36,"text_question":241,"slug":242},533916,"math question a bookstore announces a promotion valid for the same purchase as follows: buy a book and get 10% off the total purchase! buy two books and get 20% off your total purchase! buy three or more books and get 30% off your total purchase! Marcelo wanted to buy three books that cost 20.00 each without discount but he decided to buy two books in one day and another purchase with the third book the next day. If he had bought the three books at once he would have saved the following amount.","math-question-a-bookstore-announces-a-promotion-valid-for-the-same-purchase-as-follows-buy-a-book-and-get-10-off-the-total-purchase-buy-two-books-and-get-20-off-your-total-purchase-buy-three-or-m",{"id":244,"category":36,"text_question":245,"slug":246},533948,"Derivative of x squared","derivative-of-x-squared",{"id":248,"category":36,"text_question":249,"slug":250},534026,"\"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?\"\n\n The answer is the number of response units.","if-three-wolves-catch-three-rabbits-in-three-hours-how-many-wolves-would-it-take-to-catch-a-hundred-rabbits-in-a-hundred-hours-the-answer-is-the-number-of-response-units",{"id":252,"category":36,"text_question":253,"slug":254},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":256,"category":36,"text_question":257,"slug":258},534044,"Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?","perpetual-annuities-are-a-series-of-payments-whose-duration-has-no-end-explain-how-can-we-calculate-them-if-they-have-no-end",{"id":260,"category":36,"text_question":261,"slug":262},534128,"The equation of the straight line that passes through the coordinate point (2,5) and is parallel to the straight line with equation x 2y 9 = 0 is","the-equation-of-the-straight-line-that-passes-through-the-coordinate-point-2-5-and-is-parallel-to-the-straight-line-with-equation-x-2y-9-0-is",{"id":264,"category":36,"text_question":265,"slug":266},534237,"User\n The average height of Aranka, Böske, Cili, Delinke and Lili is 172 cm. We know that Aranka and Cili are both 172 cm tall. The sum of the heights of Böské and Delinke is 336 cm.\n How tall is Lili?","user-the-average-height-of-aranka-boske-cili-delinke-and-lili-is-172-cm-we-know-that-aranka-and-cili-are-both-172-cm-tall-the-sum-of-the-heights-of-boske-and-delinke-is-336-cm-how-tall-is-lili",{"id":268,"category":36,"text_question":269,"slug":270},534262,"7=-4/3y -1","7-4-3y-1",{"id":272,"category":36,"text_question":273,"slug":274},534281,"Show this compound proposition to be true or false. Paris is the capital of England or Rome is the capital of Italy","show-this-compound-proposition-to-be-true-or-false-paris-is-the-capital-of-england-or-rome-is-the-capital-of-italy",{"id":276,"category":36,"text_question":277,"slug":278},534288,"The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation","the-points-5-4-and-3-6-are-the-ends-of-the-diameter-of-the-circle-calculate-subequation",{"id":280,"category":36,"text_question":281,"slug":282},534364,"List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)","list-five-numbers-that-belong-to-the-5-mod-6-numbers-alternate-phrasing-list-five-numbers-that-satisfy-equation-x-5-mod-6",{"id":284,"category":36,"text_question":285,"slug":286},534398,"effectiveness of fiscal and monetary policy under closed and open economies","effectiveness-of-fiscal-and-monetary-policy-under-closed-and-open-economies",{"id":288,"category":36,"text_question":289,"slug":290},534464,"solid obtained by rotation around the axis x = -1, the region delimited by x^2 - x + y = 0 and the abscissa axis","solid-obtained-by-rotation-around-the-axis-x-1-the-region-delimited-by-x-2-x-y-0-and-the-abscissa-axis",{"id":292,"category":36,"text_question":293,"slug":294},534526,"there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?","there-are-500-000-bacteria-at-the-end-of-a-pin-point-1000-bacteria-can-make-a-person-sick-then-bacteria-at-the-tip-of-a-pin-point-can-make-500-people-sick-also-many-people-do-not-know-that-bacteri",{"id":296,"category":36,"text_question":297,"slug":298},534573,"An election ballot asks voters to select three city judges from a group of 12 candidates. How many ways can this be done?","an-election-ballot-asks-voters-to-select-three-city-judges-from-a-group-of-12-candidates-how-many-ways-can-this-be-done",{"id":300,"category":36,"text_question":301,"slug":302},534599,"Today a father deposits $12,500 in a bank that pays 8% annual interest. Additionally, make annual contributions due of $2,000 annually for 3 years. The fund is for your son to receive an annuity and pay for his studies for 5 years. If the child starts college after 4 years, how much is the value of the annuity?\n\n solve how well it is for an exam","today-a-father-deposits-12-500-in-a-bank-that-pays-8-annual-interest-additionally-make-annual-contributions-due-of-2-000-annually-for-3-years-the-fund-is-for-your-son-to-receive-an-annuity-and-p",{"id":304,"category":36,"text_question":305,"slug":306},534631,"Beren spent 60% of the money in her piggy bank, and Ceren spent 7% of the money in her piggy bank to buy a joint gift for Deren, totaling 90 TL. In the end, it was observed that the remaining amounts in Ceren and Beren's piggy banks were equal. Therefore, what was the total amount of money that Beren and Ceren had initially?\n\nA) 120 B) 130 C) 150 D) 160 E) 180","beren-spent-60-of-the-money-in-her-piggy-bank-and-ceren-spent-7-of-the-money-in-her-piggy-bank-to-buy-a-joint-gift-for-deren-totaling-90-tl-in-the-end-it-was-observed-that-the-remaining-amounts",{"id":308,"category":36,"text_question":309,"slug":310},534693,"Find the number of liters of water needed to reduce 9 liters of lotion.\n shave containing 50% alcohol to a lotion containing 30% alcohol.","find-the-number-of-liters-of-water-needed-to-reduce-9-liters-of-lotion-shave-containing-50-alcohol-to-a-lotion-containing-30-alcohol",{"data":312},{"questions":313},[314,318,322,326,330,334,338,342,346,350,354,358,362,366,370,374,378,382,386,390],{"id":315,"category":36,"text_question":316,"slug":317},532024,"2(2+2x)=12","2-2-2x-12",{"id":319,"category":36,"text_question":320,"slug":321},532032,"Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)\u003Cu,w> b) <2u- 5v,3w>","let-the-vectors-be-u-1-0-2-v-0-2-3-w-2-2-3-calculate-the-following-expressions-a-u-w-b-lt-2u-5v-3w-gt",{"id":323,"category":36,"text_question":324,"slug":325},532057,"A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.","a-circular-park-has-a-diameter-of-150ft-a-circular-fence-is-to-be-placed-on-the-edge-of-this-park-calculate-the-cost-of-fencing-this-park-if-the-rate-charged-is-7-per-foot-use-3-14",{"id":327,"category":36,"text_question":328,"slug":329},532303,"How many percent is one second out a 24 hour?","how-many-percent-is-one-second-out-a-24-hour",{"id":331,"category":36,"text_question":332,"slug":333},533901,"For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.","for-a-temperature-range-between-177-degrees-celsius-to-213-degrees-celsius-what-is-the-temperature-range-in-degrees-fahrenheit",{"id":335,"category":36,"text_question":336,"slug":337},533914,"Given that y = ×(2x + 1)*, show that\r\ndy = (2x + 1)\" (Ax + B)\r\ndx\r\nwhere n, A and B are constants to be found.","given-that-y-2x-1-show-that-dy-2x-1-ax-b-dx-where-n-a-and-b-are-constants-to-be-found",{"id":339,"category":36,"text_question":340,"slug":341},533979,"A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.","a-bird-randomly-chooses-to-land-on-1-of-12-perches-available-in-its-aviary-determine-the-probability-of-it-landing-on-a-perch-numbered-8-and-then-on-a-perch-marked-with-a-prime-number-take-into-acco",{"id":343,"category":36,"text_question":344,"slug":345},534034,"(2b) to the 1/4th power. Write the expression in radical form.","2b-to-the-1-4th-power-write-the-expression-in-radical-form",{"id":347,"category":36,"text_question":348,"slug":349},534057,"Identify a pattern in the list of numbers.Then use this pattern to find the next number. 37,31,25,19,13","identify-a-pattern-in-the-list-of-numbers-then-use-this-pattern-to-find-the-next-number-37-31-25-19-13",{"id":351,"category":36,"text_question":352,"slug":353},534077,"Desarrolla (2x)(3y + 2x)5","desarrolla-2x-3y-2x-5",{"id":355,"category":36,"text_question":356,"slug":357},534087,"Find the derivatives for y=X+1/X-1","find-the-derivatives-for-y-x-1-x-1",{"id":359,"category":36,"text_question":360,"slug":361},534199,"A person decides to invest money in fixed income securities to redeem it at the end of 3 years. In this way, you make monthly deposits of R$300.00 in the 1st year, R$400.00 in the 2nd year and R$500.00 in the 3rd year. Calculate the amount, knowing that compound interest is 0.6% per month for the entire period.\n The answer is 15,828.60","a-person-decides-to-invest-money-in-fixed-income-securities-to-redeem-it-at-the-end-of-3-years-in-this-way-you-make-monthly-deposits-of-r-300-00-in-the-1st-year-r-400-00-in-the-2nd-year-and-r-500-0",{"id":363,"category":36,"text_question":364,"slug":365},534339,"X~N(2.6,1.44). find the P(X\u003C3.1)","x-n-2-6-1-44-find-the-p-x-3-1",{"id":367,"category":36,"text_question":368,"slug":369},534345,"On+January+10+2023+the+CONSTRUCTORA+DEL+ORIENTE+SAC+company+acquires+land+to+develop+a+real estate+project%2C+which+prev%C3% A9+enable+50+lots+for+commercial+use+valued+in+S%2F+50%2C000.00+each+one%2C+the+company+has+as+a+business+model+generate+ cash+flow+through%C3%A9s+of+the+rental%2C+so+47%2C+of+the+50+enabled+lots+are+planned to lease+47%2C+and+ the+rest+will be%C3%A1n+used+by+the+company+for+management%C3%B3n+and+land+control","on-january-10-2023-the-constructora-del-oriente-sac-company-acquires-land-to-develop-a-real-estate-project-2c-which-prev-c3-a9-enable-50-lots-for-commercial-use-valued-in-s-2f-50-2c000-00-each-one-2c",{"id":371,"category":36,"text_question":372,"slug":373},534382,"Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will","twenty-five-students-in-a-class-take-a-test-for-which-the-average-grade-is-75-then-a-twenty-sixth-student-enters-the-class-takes-the-same-test-and-scores-70-the-test-average-grade-calculated-with",{"id":375,"category":36,"text_question":376,"slug":377},534406,"During a month's time, an automobile sales person receives a 6% commission on the first $5000 in sales, a 7% commission on the next $5000 sales, 8% commission on anything over $10,000. What is her commission for $36,000 in sales?","during-a-month-s-time-an-automobile-sales-person-receives-a-6-commission-on-the-first-5000-in-sales-a-7-commission-on-the-next-5000-sales-8-commission-on-anything-over-10-000-what-is-her-com",{"id":379,"category":36,"text_question":380,"slug":381},534419,"Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.","determine-the-linear-function-whose-graph-passes-through-the-points-6-2-and-has-slope-3",{"id":383,"category":36,"text_question":384,"slug":385},534456,"When taking a test with m closed answers, a student knows the correct answer with probability p, otherwise he chooses one of the possible answers at random. What is the probability that the student knows the correct answer given that he answered the question correctly.","when-taking-a-test-with-m-closed-answers-a-student-knows-the-correct-answer-with-probability-p-otherwise-he-chooses-one-of-the-possible-answers-at-random-what-is-the-probability-that-the-student-kn",{"id":387,"category":36,"text_question":388,"slug":389},534470,"A company dedicated to the manufacture of shirts sells the units at a price of $40, the cost of each shirt is $24, a commission is paid for the sale of a unit of shirt of $2 and its fixed costs are $3500\n Determine the marginal contribution","a-company-dedicated-to-the-manufacture-of-shirts-sells-the-units-at-a-price-of-40-the-cost-of-each-shirt-is-24-a-commission-is-paid-for-the-sale-of-a-unit-of-shirt-of-2-and-its-fixed-costs-are-3",{"id":391,"category":36,"text_question":392,"slug":393},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 $7 each. How much should she sell to raise money?","emile-organizes-a-community-dance-to-raise-funds-in-addition-to-paying-300-to-rent-the-room-she-must-rent-chairs-at-2-each-the-quantity-of-chairs-rented-will-be-equal-to-the-number-of-tickets-sol",{"data":395},[396,400,404],{"id":397,"question":398,"answer":399},132718,"What is the cosine value of an angle in the Trigonometric table when","its sine value is 0.866? The cosine value would be 0.5.",{"id":401,"question":402,"answer":403},160360,"Math question: Simplify the expression 4x(3x + 2) - 2(x - 5) using the distributive property.","Answer: By distributing, we have 12x^2 + 8x - 2x + 10. Simplifying further gives 12x^2 + 6x + 10.",{"id":405,"question":406,"answer":407},135819,"What is the product of \\(x^2\\) and \\(y^3\\) when \\(x = 4\\) and \\(y = 5\\)?","The product of \\(x^2\\) and \\(y^3\\) is \\(4^2 \\times 5^3 = 1600 \\times 125 = 200,000\\).",{"$sicons":409},{"bxl:facebook-circle":410,"bxl:instagram":414,"mdi:web":416,"la:apple":418,"ph:google-logo-bold":421,"ph:google-logo":424},{"left":411,"top":411,"width":412,"height":412,"rotate":411,"vFlip":183,"hFlip":183,"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":183,"hFlip":183,"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\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" d=\"M20.533 6.111A4.6 4.6 0 0 0 17.9 3.479a6.6 6.6 0 0 0-2.186-.42c-.963-.042-1.268-.054-3.71-.054s-2.755 0-3.71.054a6.6 6.6 0 0 0-2.184.42a4.6 4.6 0 0 0-2.633 2.632a6.6 6.6 0 0 0-.419 2.186c-.043.962-.056 1.267-.056 3.71s0 2.753.056 3.71c.015.748.156 1.486.419 2.187a4.6 4.6 0 0 0 2.634 2.632a6.6 6.6 0 0 0 2.185.45c.963.042 1.268.055 3.71.055s2.755 0 3.71-.055a6.6 6.6 0 0 0 2.186-.419a4.6 4.6 0 0 0 2.633-2.633c.263-.7.404-1.438.419-2.186c.043-.962.056-1.267.056-3.71s0-2.753-.056-3.71a6.6 6.6 0 0 0-.421-2.217m-1.218 9.532a5 5 0 0 1-.311 1.688a3 3 0 0 1-1.712 1.711a5 5 0 0 1-1.67.311c-.95.044-1.218.055-3.654.055c-2.438 0-2.687 0-3.655-.055a5 5 0 0 1-1.669-.311a3 3 0 0 1-1.719-1.711a5.1 5.1 0 0 1-.311-1.669c-.043-.95-.053-1.218-.053-3.654s0-2.686.053-3.655a5 5 0 0 1 .311-1.687c.305-.789.93-1.41 1.719-1.712a5 5 0 0 1 1.669-.311c.951-.043 1.218-.055 3.655-.055s2.687 0 3.654.055a5 5 0 0 1 1.67.311a3 3 0 0 1 1.712 1.712a5.1 5.1 0 0 1 .311 1.669c.043.951.054 1.218.054 3.655s0 2.698-.043 3.654z\"/>",{"left":411,"top":411,"width":412,"height":412,"rotate":411,"vFlip":183,"hFlip":183,"body":417},"\u003Cpath fill=\"currentColor\" d=\"M16.36 14c.08-.66.14-1.32.14-2s-.06-1.34-.14-2h3.38c.16.64.26 1.31.26 2s-.1 1.36-.26 2m-5.15 5.56c.6-1.11 1.06-2.31 1.38-3.56h2.95a8.03 8.03 0 0 1-4.33 3.56M14.34 14H9.66c-.1-.66-.16-1.32-.16-2s.06-1.35.16-2h4.68c.09.65.16 1.32.16 2s-.07 1.34-.16 2M12 19.96c-.83-1.2-1.5-2.53-1.91-3.96h3.82c-.41 1.43-1.08 2.76-1.91 3.96M8 8H5.08A7.92 7.92 0 0 1 9.4 4.44C8.8 5.55 8.35 6.75 8 8m-2.92 8H8c.35 1.25.8 2.45 1.4 3.56A8 8 0 0 1 5.08 16m-.82-2C4.1 13.36 4 12.69 4 12s.1-1.36.26-2h3.38c-.08.66-.14 1.32-.14 2s.06 1.34.14 2M12 4.03c.83 1.2 1.5 2.54 1.91 3.97h-3.82c.41-1.43 1.08-2.77 1.91-3.97M18.92 8h-2.95a15.7 15.7 0 0 0-1.38-3.56c1.84.63 3.37 1.9 4.33 3.56M12 2C6.47 2 2 6.5 2 12a10 10 0 0 0 10 10a10 10 0 0 0 10-10A10 10 0 0 0 12 2\"/>",{"left":411,"top":411,"width":419,"height":419,"rotate":411,"vFlip":183,"hFlip":183,"body":420},32,"\u003Cpath fill=\"currentColor\" d=\"M20.844 2c-1.64 0-3.297.852-4.407 2.156v.032c-.789.98-1.644 2.527-1.375 4.312c-.128-.05-.136-.035-.28-.094c-.692-.281-1.548-.594-2.563-.594c-3.98 0-7 3.606-7 8.344c0 3.067 1.031 5.942 2.406 8.094c.688 1.078 1.469 1.965 2.281 2.625S11.57 28 12.531 28s1.68-.324 2.219-.563c.54-.238.957-.437 1.75-.437c.715 0 1.078.195 1.625.438c.547.242 1.293.562 2.281.562c1.07 0 1.98-.523 2.719-1.188s1.36-1.519 1.875-2.343c.516-.824.922-1.633 1.219-2.282c.148-.324.258-.593.343-.812s.13-.281.188-.531l.188-.813l-.75-.343a5.3 5.3 0 0 1-1.5-1.063c-.625-.637-1.157-1.508-1.157-2.844A4.08 4.08 0 0 1 24.563 13c.265-.309.542-.563.75-.719c.105-.078.187-.117.25-.156c.062-.04.05-.027.156-.094l.843-.531l-.562-.844c-1.633-2.511-4.246-2.844-5.281-2.844c-.48 0-.82.168-1.25.25c.242-.226.554-.367.75-.624c.004-.004-.004-.028 0-.032q.018-.016.031-.031h.031a6.16 6.16 0 0 0 1.563-4.438L21.78 2zm-1.188 2.313c-.172.66-.453 1.289-.906 1.78l-.063.063c-.382.516-.972.899-1.562 1.125c.164-.652.45-1.312.844-1.812c.008-.012.023-.02.031-.032c.438-.5 1.043-.875 1.656-1.125zm-7.437 5.5c.558 0 1.172.21 1.812.468s1.239.594 2.094.594c.852 0 1.496-.336 2.25-.594s1.559-.469 2.344-.469c.523 0 1.816.333 2.906 1.344c-.191.172-.36.297-.563.531a6.2 6.2 0 0 0-1.53 4.094c0 1.906.831 3.34 1.718 4.25c.55.563.89.696 1.313.938c-.055.125-.086.222-.157.375a19 19 0 0 1-1.093 2.062c-.454.727-1.004 1.434-1.532 1.907c-.527.472-1 .687-1.375.687c-.566 0-.898-.156-1.468-.406S17.581 25 16.5 25c-1.137 0-1.977.336-2.563.594c-.585.258-.89.406-1.406.406c-.246 0-.777-.2-1.375-.688c-.597-.488-1.254-1.23-1.844-2.156c-1.183-1.851-2.093-4.394-2.093-7c0-3.941 2.199-6.343 5-6.343\"/>",{"left":411,"top":411,"width":422,"height":422,"rotate":411,"vFlip":183,"hFlip":183,"body":423},256,"\u003Cpath fill=\"currentColor\" d=\"M228 128a100 100 0 1 1-22.86-63.64a12 12 0 0 1-18.51 15.28A76 76 0 1 0 203.05 140H128a12 12 0 0 1 0-24h88a12 12 0 0 1 12 12\"/>",{"left":411,"top":411,"width":422,"height":422,"rotate":411,"vFlip":183,"hFlip":183,"body":425},"\u003Cpath fill=\"currentColor\" d=\"M224 128a96 96 0 1 1-21.95-61.09a8 8 0 1 1-12.33 10.18A80 80 0 1 0 207.6 136H128a8 8 0 0 1 0-16h88a8 8 0 0 1 8 8\"/>",{"t96FybqVTi":8,"oVhJaef6Ht":8,"5lK7LS5al0":8,"2spGeUKf3V":8,"5oSQ2a90xd":8,"2QISyIzlyM":8,"HGsO2Ckakl":8},"/general/5x-6y-2-6x-2y-18-solve-by-elimination"] AppleWebKit/537.36 $KHTML, like Gecko$ Chrome/64.0.3282.39 Safari/537.36",refreshOnResize:false}},app:{baseURL:"/",buildAssetsDir:"/_nuxt/",cdnURL:"https://gcdn.fx2.io/math-master.org/"}}