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>",null,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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":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},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":86,"category":7,"text_question":87,"photo_question":9,"text_answer":88,"step_text_answer":11,"step_photo_answer":11,"views":89,"likes":13,"slug":90},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":92,"category":7,"text_question":93,"photo_question":9,"text_answer":94,"step_text_answer":11,"step_photo_answer":11,"views":95,"likes":96,"slug":97},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":99,"category":7,"text_question":100,"photo_question":9,"text_answer":101,"step_text_answer":11,"step_photo_answer":11,"views":102,"likes":103,"slug":104},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":106,"category":7,"text_question":107,"photo_question":9,"text_answer":108,"step_text_answer":11,"step_photo_answer":11,"views":109,"likes":110,"slug":111},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":113,"category":7,"text_question":114,"photo_question":9,"text_answer":115,"step_text_answer":11,"step_photo_answer":11,"views":116,"likes":117,"slug":118},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":120,"category":7,"text_question":121,"photo_question":9,"text_answer":122,"step_text_answer":11,"step_photo_answer":11,"views":123,"likes":124,"slug":125},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":127,"category":7,"text_question":128,"photo_question":9,"text_answer":129,"step_text_answer":11,"step_photo_answer":11,"views":130,"likes":131,"slug":132},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":134,"category":7,"text_question":135,"photo_question":9,"text_answer":136,"step_text_answer":11,"step_photo_answer":11,"views":137,"likes":138,"slug":139},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":141,"category":7,"text_question":142,"photo_question":9,"text_answer":143,"step_text_answer":11,"step_photo_answer":11,"views":144,"likes":145,"slug":146},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":148,"last":149,"prev":11,"next":150},1,188,2,{"current_page":148,"from":148,"last_page":149,"links":152,"path":189,"per_page":190,"to":190,"total":191},[153,156,158,161,164,167,170,173,176,179,182,185,187],{"url":148,"label":154,"active":155},"1",true,{"url":150,"label":28,"active":157},false,{"url":159,"label":160,"active":157},3,"3",{"url":162,"label":163,"active":157},4,"4",{"url":165,"label":166,"active":157},5,"5",{"url":168,"label":169,"active":157},6,"6",{"url":171,"label":172,"active":157},7,"7",{"url":174,"label":175,"active":157},8,"8",{"url":177,"label":178,"active":157},9,"9",{"url":180,"label":181,"active":157},10,"10",{"url":183,"label":184,"active":157},187,"187",{"url":149,"label":186,"active":157},"188",{"url":150,"label":188,"active":157},"Next »","https://api.math-master.org/api/question",20,3743,{"data":193},[194,196,198,200,202,204],{"id":148,"title":195,"slug":11},"Algebra",{"id":150,"title":197,"slug":11},"Geometry",{"id":159,"title":199,"slug":11},"Coordinate-geometry",{"id":162,"title":201,"slug":11},"Statistics",{"id":165,"title":203,"slug":11},"Calculus",{"id":168,"title":205,"slug":11},"General",{"data":207},[208,209,210,211,212,213],{"id":148,"title":195,"slug":11},{"id":150,"title":197,"slug":11},{"id":159,"title":199,"slug":11},{"id":162,"title":201,"slug":11},{"id":165,"title":203,"slug":11},{"id":168,"title":205,"slug":11},{"data":215},{"id":216,"category":7,"slug":217,"text_question":218,"photo_question":11,"text_answer":219,"step_text_answer":11,"step_photo_answer":11,"views":220,"likes":221,"expert":222},537971,"8-12-4-8-reduced-to-the-lowest-terms","8/12 – 4/8 reduced to the lowest terms","Solution:\u003Cbr />\n1. Simplify each fraction individually:\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{8}{12}\u003C/math-field>\u003C/math-field> can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 4:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{8 \\div 4}{12 \\div 4} = \\frac{2}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{4}{8}\u003C/math-field>\u003C/math-field> can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 4:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{4 \\div 4}{8 \\div 4} = \\frac{1}{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Subtract the simplified fractions:\u003Cbr />\n - Find a common denominator for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{2}{3}\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{2}\u003C/math-field>\u003C/math-field>, which is 6.\u003Cbr />\n - Convert \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{2}{3}\u003C/math-field>\u003C/math-field> to have a denominator of 6:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{2}{3} = \\frac{2 \\times 2}{3 \\times 2} = \\frac{4}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n - Convert \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{2}\u003C/math-field>\u003C/math-field> to have a denominator of 6:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{2} = \\frac{1 \\times 3}{2 \\times 3} = \\frac{3}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n - Perform the subtraction:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{4}{6} - \\frac{3}{6} = \\frac{4 - 3}{6} = \\frac{1}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. The result is already in its lowest terms.",468,94,{"id":223,"name":224,"photo":225,"biography":226,"created_at":11,"updated_at":11,"rating":227,"total_answer":228},17,"Gene","https://api.math-master.org/img/experts/17/17.webp","I embarked on my journey into the realm of mathematics with a strong foundation laid during my school years. My passion for numbers and problem-solving was evident as I completed my matriculation in the science stream with an impressive 80% marks. This early success fueled my determination to delve deeper into the world of mathematics.\n\nContinuing my academic pursuits, I pursued my intermediate studies in pre-engineering, achieving an exceptional 82% in my FSC examinations. This solidified my interest in the field and set the stage for higher education.\n\nMy thirst for knowledge and love for mathematics led me to the National University of Science and Technology (NUST), the premier engineering university in Pakistan. At NUST, I pursued a Bachelor's degree in Avionics Engineering, focusing on key subjects such as Electronics, Signal Processing, Radar, and Antennas. This immersive academic experience not only provided me with a strong theoretical foundation but also exposed me to practical applications of mathematics in the realm of avionics.\n\nDuring my time at university, I also engaged in various educational courses and classes that enriched my understanding of mathematics and its diverse applications. This multifaceted approach to learning enabled me to not only excel academically but also to develop a comprehensive grasp of mathematical concepts.\n\nFurthermore, my love for mathematics transcended the confines of the classroom. I embraced the challenge of complex problem-solving and developed a proficiency in English, which ultimately led me to a unique opportunity. For the past two years, I have been contributing as a proficient solver and reviewer for Photomath.inc, an experience that has further honed my mathematical skills and analytical thinking.\nmake it a bit more concise\n",4.5,103,{"data":230},{"questions":231},[232,236,240,244,248,252,256,260,264,268,272,276,280,284,288,292,296,300,304,308],{"id":233,"category":7,"text_question":234,"slug":235},532008,"1 + 1","1-1",{"id":237,"category":7,"text_question":238,"slug":239},533913,"Use the elimination to find the solution to each linear system.\n\nX+y=43\n2x-y=20","use-the-elimination-to-find-the-solution-to-each-linear-system-x-y-43-2x-y-20",{"id":241,"category":7,"text_question":242,"slug":243},533998,"Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places","suppose-a-large-shipment-of-cell-phones-contain-21-defective-if-the-sample-of-size-204-is-selected-what-is-the-probability-that-the-sample-proportion-will-differ-from-the-population-proportion-by-l",{"id":245,"category":7,"text_question":246,"slug":247},534080,"Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.","let-f-x-x-1-find-the-equation-of-the-tangent-line-to-the-graph-of-f-at-the-point-x0-2",{"id":249,"category":7,"text_question":250,"slug":251},534091,"A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find:\n\n to. The depreciation rate.\n\n b. The book value at the end of the sixth year.","a-company-that-manufactures-personal-hygiene-items-purchases-machinery-for-220-000-that-is-considered-to-last-7-years-it-is-estimated-that-at-the-end-of-the-period-it-will-have-a-salvage-value-of-1",{"id":253,"category":7,"text_question":254,"slug":255},534100,"Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.","reparameterize-the-curve-r-t-cos-t-i-without-t-j-t-k-by-the-arc-length",{"id":257,"category":7,"text_question":258,"slug":259},534109,"4x/2+5x-3/6=7/8-1/4-x","4x-2-5x-3-6-7-8-1-4-x",{"id":261,"category":7,"text_question":262,"slug":263},534164,"Solve : 15/16 divide 12/8 =x/y","solve-15-16-divide-12-8-x-y",{"id":265,"category":7,"text_question":266,"slug":267},534239,"The market for economics textbooks is represented by the following supply and demand equations:\r\nP = 5 + 2Qs P = 20 - Qd\r\nWhere P is the price in £s and Qs and Qd are the quantities supplied and demanded in thousands.\r\nWhat is the equilibrium price?","the-market-for-economics-textbooks-is-represented-by-the-following-supply-and-demand-equations-p-5-2qs-p-20-qd-where-p-is-the-price-in-s-and-qs-and-qd-are-the-quantities-supplied-and-deman",{"id":269,"category":7,"text_question":270,"slug":271},534258,"Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block.\nA. What is the acceleration of the blocks?\nB. What is the force of the 4.3-kg block on the 5.4 -kg block?\nC. What is the force of the 5.4 -kg block on the 4.3 -kg block?","shows-two-blocks-masses-4-3-kg-and-5-4-kg-being-pushed-across-a-frictionless-surface-by-a-22-5-n-horizontal-force-applied-to-the-4-3-kg-block-a-what-is-the-acceleration-of-the-blocks-b-what-is-t",{"id":273,"category":7,"text_question":274,"slug":275},534316,"X³-27","x-27",{"id":277,"category":7,"text_question":278,"slug":279},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":281,"category":7,"text_question":282,"slug":283},534372,"7.57 Online communication. A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spent 13.5 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see.\nH0 :x ̄\u003C10hours HA : x ̄ > 13.5 hours","7-57-online-communication-a-study-suggests-that-the-average-college-student-spends-10-hours-per-week-communicating-with-others-online-you-believe-that-this-is-an-underestimate-and-decide-to-collect",{"id":285,"category":7,"text_question":286,"slug":287},534453,"A person runs 175 yards per minute write a variable that represents the relationship between time and distance","a-person-runs-175-yards-per-minute-write-a-variable-that-represents-the-relationship-between-time-and-distance",{"id":289,"category":7,"text_question":290,"slug":291},534478,"Let N be the total number of ways to choose at least one ride, out of a total of 7 different ones, existing in an amusement park. Can it be said that N is a natural number equal to?","let-n-be-the-total-number-of-ways-to-choose-at-least-one-ride-out-of-a-total-of-7-different-ones-existing-in-an-amusement-park-can-it-be-said-that-n-is-a-natural-number-equal-to",{"id":293,"category":7,"text_question":294,"slug":295},534502,"a) 6x − 5 > x + 20","a-6x-5-x-20",{"id":297,"category":7,"text_question":298,"slug":299},534559,"simplify w+[6+(-5)]","simplify-w-6-5",{"id":301,"category":7,"text_question":302,"slug":303},534563,"How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7","how-much-does-7-2-moles-of-ammonium-dichromate-weigh-nh4-2cr2o7",{"id":305,"category":7,"text_question":306,"slug":307},534596,"calculate the product of 4 and 1/8","calculate-the-product-of-4-and-1-8",{"id":309,"category":7,"text_question":310,"slug":311},534660,"The length of a rectangle is five more than its width. if the perimeter is 120, find both the length and the width.","the-length-of-a-rectangle-is-five-more-than-its-width-if-the-perimeter-is-120-find-both-the-length-and-the-width",{"data":313},{"questions":314},[315,319,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387,391],{"id":316,"category":7,"text_question":317,"slug":318},532030,"Find two natural numbers whose sum is 230 and their difference is 10. Set up the system and solve it.","find-two-natural-numbers-whose-sum-is-230-and-their-difference-is-10-set-up-the-system-and-solve-it",{"id":320,"category":7,"text_question":321,"slug":322},532042,"The patient is prescribed a course of 30 tablets.\nThe tablets are prescribed “1 tablet twice a day”.\nHow many days does a course of medication last?","the-patient-is-prescribed-a-course-of-30-tablets-the-tablets-are-prescribed-1-tablet-twice-a-day-how-many-days-does-a-course-of-medication-last",{"id":324,"category":7,"text_question":325,"slug":326},532076,"(x^2+3x)/(x^2-9)=","x-2-3x-x-2-9",{"id":328,"category":7,"text_question":329,"slug":330},532090,"String x = 5\r\nInt y=2\r\nSystem.out.println(x+y)","string-x-5-int-y-2-system-out-println-x-y",{"id":332,"category":7,"text_question":333,"slug":334},532297,"A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?","a-book-is-between-400-and-450-pages-if-we-count-them-2-at-a-time-there-is-none-left-over-if-we-count-them-5-at-a-time-there-is-none-left-over-and-if-we-count-them-7-at-a-time-there-are-none-left-ove",{"id":336,"category":7,"text_question":337,"slug":338},533904,"If O(3,-2) is reflected across x = 2. What are the coordinates of O","if-o-3-2-is-reflected-across-x-2-what-are-the-coordinates-of-o",{"id":340,"category":7,"text_question":341,"slug":342},534012,"Margin of error E=0.30 populations standard deviation =2.5. Population means with 95% confidence. What I the required sample size (round up to the whole number)","margin-of-error-e-0-30-populations-standard-deviation-2-5-population-means-with-95-confidence-what-i-the-required-sample-size-round-up-to-the-whole-number",{"id":344,"category":7,"text_question":345,"slug":346},534115,"How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword?\r\nBy subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.","how-many-anagrams-of-the-word-sromec-there-that-do-not-contain-strom-most-moc-or-cest-as-a-subword-by-subword-is-meant-anything-that-is-created-by-omitting-some-letters-for-example-the-word-emr",{"id":348,"category":7,"text_question":349,"slug":350},534146,"I need to know what 20% or £3292.75","i-need-to-know-what-20-or-3292-75",{"id":352,"category":7,"text_question":353,"slug":354},534220,"A triangular window has a base of 6 ft. and a height of 7 ft. What is its area?","a-triangular-window-has-a-base-of-6-ft-and-a-height-of-7-ft-what-is-its-area",{"id":356,"category":7,"text_question":357,"slug":358},534245,"19) If the temperature of -8°C decreases by 12°C, how much will it be?\n\n a)-20°C\n\n -4°C\n\n c) 4°C\n\n d) 20°C","19-if-the-temperature-of-8-c-decreases-by-12-c-how-much-will-it-be-a-20-c-4-c-c-4-c-d-20-c",{"id":360,"category":7,"text_question":361,"slug":362},534265,"If a two-branch parallel current divider network, if the resistance of one branch is doubled while keeping all other factors constant, what happens to the current flow through that branch and the other branch?\n\nSelect one:\n\na. The current through the doubled resistance branch remains unchanged, and the current through the other branch decreases.\n\nb. The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged.\n\nc. The current through the doubled resistance branch increases, and the current through the other branch remains unchanged.\n\nd. The current through both branches remain unchanged.","if-a-two-branch-parallel-current-divider-network-if-the-resistance-of-one-branch-is-doubled-while-keeping-all-other-factors-constant-what-happens-to-the-current-flow-through-that-branch-and-the-othe",{"id":364,"category":7,"text_question":365,"slug":366},534324,"Solve equations by equalization method\n X-8=-2y\n 2x+y=7","solve-equations-by-equalization-method-x-8-2y-2x-y-7",{"id":368,"category":7,"text_question":369,"slug":370},534325,"Find the center coordinates and radius of a circle for an equation written as: 3x2 + 3y2 - 6y = —12× + 24","find-the-center-coordinates-and-radius-of-a-circle-for-an-equation-written-as-3x2-3y2-6y-12-24",{"id":372,"category":7,"text_question":373,"slug":374},534334,"Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.","next-c3-b3n-2c-we-are-given-a-series-of-tri-c3-a1angles-right-c3-a1angles-3cbr-2f-3ey-in-each-one-of-them-are-known-2-28two-29-measurements-of-sides-3cbr-2f-3elet-s-determine-all-trigonom-c3-a9tri",{"id":376,"category":7,"text_question":377,"slug":378},534384,"A,B,C and D are the corners of a rectangular building. Find the lengths the diagonals if AB measures 38' - 9\" and AD measures 56' - 3\"","a-b-c-and-d-are-the-corners-of-a-rectangular-building-find-the-lengths-the-diagonals-if-ab-measures-38-9-and-ad-measures-56-3",{"id":380,"category":7,"text_question":381,"slug":382},534387,"A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?","a-hardware-bill-totals-857-63-with-discounts-of-5-and-3-what-is-the-net-cost-of-the-material",{"id":384,"category":7,"text_question":385,"slug":386},534533,"8/9 divided by 10/6","8-9-divided-by-10-6",{"id":388,"category":7,"text_question":389,"slug":390},534635,"the length of the fenced in area is to be 5 ft greater than the width and the total amount of fencing to be used is 89 ft find the width and length","the-length-of-the-fenced-in-area-is-to-be-5-ft-greater-than-the-width-and-the-total-amount-of-fencing-to-be-used-is-89-ft-find-the-width-and-length",{"id":392,"category":7,"text_question":393,"slug":394},534648,"Paola went on vacation for 15 days if it rained 20% of the days. How many days did it rain?","paola-went-on-vacation-for-15-days-if-it-rained-20-of-the-days-how-many-days-did-it-rain",{"data":396},[397,401,405],{"id":398,"question":399,"answer":400},113402,"What is the result of subtracting vector A (-3, 5) from vector B (7, -2)?","The subtraction of vector A from vector B results in the vector (-10, -7).",{"id":402,"question":403,"answer":404},124916,"What is the graph of the logarithmic function f(x) = log(base 2) x + 3?","The graph of the logarithmic function f(x) = log(base 2) x + 3 is a curve that passes through the point (1, 1) and approaches y = 3 as x approaches positive infinity. It has a vertical asymptote at x = 0 and is always increasing.",{"id":406,"question":407,"answer":408},112248,"What is the unit vector of a vector v = 2i + 3j - 4k?","The unit vector of v is (2/29)i + (3/29)j - (4/29)k. 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