Loading [MathJax]/jax/output/HTML-CSS/jax.js
14555.17 after 10 years.",660,132,"nazerhy-deposits-8-000-in-a-certificate-of-deposit-the-annual-interest-rate-is-6-and-the-interest-will-be-compounded-monthly-how-much-will-the-certificate-be-worth-in-10-years-rou",{"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},538169,"Tara deposits \n\n5,000\ninacertificateofdeposit.Theannualinterestrateis\n7\n42,500. He must place a down payment of 15,000toaffordthemonthlypayments.Hehassaved9,000 so far. What fraction of his down payment has he saved?\nA) ΒΎ1\nB) Β½\nC) β…—\nD) 116","Solution: \u003Cbr />\n1. The down payment required is USD 15,000.\u003Cbr />\n2. Darren has saved USD 9,000 so far.\u003Cbr />\n3. To find the fraction of the down payment saved, use the formula:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{fraction saved} = \\frac{\\text{amount saved}}{\\text{total down payment}}\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Substitute the given values into the formula:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{fraction saved} = \\frac{9000}{15000}\u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Simplify the fraction:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{9000}{15000} = \\frac{9}{15}\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Continue simplifying by dividing both numerator and denominator by their greatest common divisor, which is 3:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{9}{15} = \\frac{3}{5}\u003C/math-field>\u003C/math-field>\u003Cbr />\nThus, Darren has saved \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{3}{5}\u003C/math-field>\u003C/math-field> of his down payment.",1459,"fraction-64-darren-wants-to-buy-a-vehicle-for-42-500-he-must-place-a-down-payment-of-15-000-to-afford-the-monthly-payments-he-has-saved-9-000-so-far-what-fraction-of-his-down-payment-has-he-s",{"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},538156,"Find the product of the fractions in simplest form \n1/8 x 1/7","1. Multiply the numerators: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 1 \\times 1 = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Multiply the denominators: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 8 \\times 7 = 56 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Form the fraction: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{56} \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Simplify if necessary alreadyinsimplestform: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{56} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nThe answer is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{56} \u003C/math-field>\u003C/math-field>",1442,288,"find-the-product-of-the-fractions-in-simplest-form-1-8-x-1-7",{"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},538155,"Find product of fractions in simplest form\n2/9 x 12/14","1. Multiply the numerators: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2 \\times 12 = 24 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Multiply the denominators: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 9 \\times 14 = 126 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. Form the new fraction: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{24}{126} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n4. Simplify the fraction by finding the greatest common divisor GCD of 24 and 126, which is 6.\u003Cbr />\n5. Divide the numerator and the denominator by 6: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{24 \\div 6}{126 \\div 6} = \\frac{4}{21} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n6. The fraction is now in its simplest form: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{4}{21} \u003C/math-field>\u003C/math-field>.",1323,265,"find-product-of-fractions-in-simplest-form-2-9-x-12-14",{"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},538154,"WORKSHOP WEEK 5 - CRISIS MANAGEMENT AND EMERGENCY CONTROL\n\n Name: Carlos Daniel MuΓ±oz MuΓ±oz\n\n Organization: Vina Concha y Toro - Pirque Tourist Center\n\n Delivery date: June 30, 2025\n\n 1-. Emergency Scenarios.\n .\n 1st scenario: Fire in the underground cellar of the Devil's Casillero, during a guided tour, a corsocircuino in the old lighting system causes a fire in the famous cellar of the \"Devil's Casillero\". The presence of thick smoke generates panic among visitors and forces them to act quickly.\n\n Palliative Measures:\n ➒ The alarm is immediately activated to initiate evacuation.\n ➒ Trained personnel use fire extinguishers to try to contain the fire.\n ➒ Automatically close the doors of the affected sector to prevent the spread.\n ➒ The Fire Department is contacted directly from the security center.\n\n Preventive Measures:\n ➒ Monthly maintenance of the electrical system to detect faults in time.\n ➒ Fire drills twice a year with active participation of all staff\n ➒ Vistale and Juminosa signage in the underground corridors\n ➒ Smoke detectors connected to the monitoring center for early warnings.\n\n Scenario 2: A structure collapses during a corporate event held in the heritage gardens. Strong gusts of wind cause a poorly maintained tent to collapse. Several people are injured, causing confusion and fear.\n Palliative Measures:\n ➒ The internal team provides first aid to those affected\n ➒ The settlers are calmly evacuated to the safe zone.\n ➒ ο»ΏSAMU is called and the transfers to the local CEBEAM are coordinated.\n\n Preventive Measures:\n ➒ The assembly is supervised by a specialized and certified company\n Technical review prior to each event by the security area\n ➒ ο»ΏAvailability of shoulders with material for mild and moderate trauma.\n ➒ Clear information to the public on escape routes and safe points.\n\n 2. Prevention Plan\n At ViΓ±a Concha y Tora, where hospitality and culture are intertwined with history, the safety of our visitors is a priority. That's why our preventive plan is not only based on standards, but also on caring for people.\n\n Every team member, from guides to technical staff, receives periodic training in first aid, emergency management, and emotional support. Special attention is given to visitors with reduced mobility or in vulnerable situations, ensuring their escorted evacuation in case of emergency.\n\n Upon entry, all visitors receive a brochure with basic safety rules, including evacuation routes and meeting areas.\n\n The facilities feature clear signage, universal iconography, and communication systems publicaddresssystemsand5M5messaging to keep everyone informed in real time.\n\n Quarterly drills are conducted with different types of scenarios, allowing us to evaluate and update our protocols.\n\n The busiest areas, such as cellars and gardens, have been reinforced with non-slip floors and secure railings.\n\n Marked meeting points have also been installed where staff can guide visitors during emergencies. The ultimate goal is not just to meet a standard, but to create an environment where everyone, both employees and visitors, feel cared for and protected.\n\n 3. Actions for the Rescue of Affected Persons\n ➒ Activate internal alarms and protocols without delay.\n ➒ ο»Ώο»ΏDirect visitors to safe exit routes.\n ➒ ο»Ώο»ΏAccompany those who are in emotional shock.\n ➒ Speak words of calm in an empathetic and clear tone\n ➒ Treat minor wounds with basic first aid\n ➒ Shelter those who show symptoms of cold or stress.\n ➒ Offer water and support to decompensated people\n ➒ Prioritize the evacuation of children and the elderly.\n ➒ Use wheeled classrooms or stretchers if required.\n ➒ , Contact medical services and coordinate the L1 transfer.\n ➒ Record the viziers at the meeting points.\n ➒ Maintain eye contact to generate security.\n ➒ Prevent anyone from entering the dangerous place\n ➒ Give firm and understanding simulation instructions\n ➒ Notify family members when it is necessary to mail\n ➒ Apply basic emotional containment techniques.\n ➒ Record key facts to inform authorities\n ➒ Secure the area to avoid further accidents\n ➒ ο»Ώο»Ώο»ΏAllow return only when completely safe.\n ➒ Provide specialised assistance to those who need it.","TALLER SEMANA 5 – GESTIΓ“N DE CRISIS Y CONTROL DE EMERGENCIAS\n Nombre: Carlos Daniel MuΓ±oz MuΓ±oz\n OrganizaciΓ³n: ViΓ±a Concha y Toro – Centro TurΓ­stico Pirque\n Fecha de entrega: 30 de junio de 2025\n\n 1. Escenarios de emergencia\n Escenario 1: Incendio en la Bodega SubterrΓ‘nea – Casillero del Diablo\n DescripciΓ³n:\n Durante una visita guiada, un cortocircuito en el sistema de iluminaciΓ³n de aΓ±ejamiento provoca un incendio en la icΓ³nica bodega Casillero del Diablo. La densa humareda causa pΓ‘nico entre los visitantes, lo que requiere intervenciΓ³n inmediata.\n\n Medidas paliativas:\n\n ActivaciΓ³n inmediata del sistema de alarma contra incendios para iniciar los protocolos de evacuaciΓ³n.\n\n El personal capacitado utiliza extintores para intentar contener el incendio.\n\n Sellado automΓ‘tico de puertas de bodega para evitar la propagaciΓ³n del humo y el fuego.\n\n ComunicaciΓ³n directa con el Departamento de Bomberos local desde el centro de seguridad.\n\n Medidas preventivas:\n\n InspecciΓ³n y mantenimiento mensual del sistema elΓ©ctrico para detectar fallas de forma proactiva.\n\n Simulacros de incendio semestrales con participaciΓ³n de todo el personal.\n\n InstalaciΓ³n adecuada de seΓ±alizaciΓ³n de emergencia visible y luminosa en pasillos subterrΓ‘neos.\n\n InstalaciΓ³n de detectores de humo conectados al sistema central de monitoreo para alertas tempranas.\n\n Escenario 2: Colapso de la carpa durante un evento corporativo\n DescripciΓ³n:\n Una repentina rΓ‘faga de viento derrumba una carpa para eventos en mal estado durante una reuniΓ³n corporativa en los jardines patrimoniales. Se producen mΓΊltiples heridos y confusiΓ³n entre los asistentes.\n\n Medidas paliativas:\n\n El equipo de emergencia interna brinda primeros auxilios a los heridos.\n\n Los huΓ©spedes son guiados con calma y evacuados a la zona segura designada.\n\n Se llaman a los servicios mΓ©dicos de urgencia SAMU y se coordinan los traslados al CEBEAM.\n\n Medidas preventivas:\n\n La infraestructura del evento estΓ‘ supervisada por profesionales certificados.\n\n RevisiΓ³n tΓ©cnica de estructuras previa al evento por parte del equipo de seguridad.\n\n Disponibilidad en el sitio de botiquines mΓ©dicos para traumatismos leves a moderados.\n\n ComunicaciΓ³n clara al pΓΊblico sobre rutas de escape y zonas de seguridad.\n\n 2. Plan de prevenciΓ³n\n En ViΓ±a Concha y Toro, donde la hospitalidad, la cultura y la historia se entrelazan, la seguridad de nuestros huΓ©spedes y personal es nuestra mΓ‘xima prioridad. Nuestro plan de prevenciΓ³n se centra no solo en el cumplimiento de las normas de seguridad, sino tambiΓ©n en promover una cultura de cuidado y preparaciΓ³n.\n\n Todos los miembros del equipo, incluidos guΓ­as, tΓ©cnicos y personal administrativo, reciben capacitaciΓ³n periΓ³dica en primeros auxilios, respuesta a crisis y tΓ©cnicas de apoyo emocional.\n\n Se tiene especial cuidado en ayudar a los huΓ©spedes con movilidad limitada, garantizando asistencia de evacuaciΓ³n personalizada.\n\n A su llegada, cada visitante recibe un folleto de seguridad que detalla las rutas de evacuaciΓ³n, los contactos de emergencia y las Γ‘reas de reuniΓ³n designadas.\n\n Las instalaciones cuentan con seΓ±alizaciΓ³n clara y accesible, sΓ­mbolos universales y herramientas de comunicaciΓ³n en tiempo real porejemplo,sistemasdemegafonΓ­a,alertasSMS.\n\n Simulacros trimestrales simulan diferentes escenarios de emergencia, permitiendo la evaluaciΓ³n continua y la mejora de los protocolos.\n\n Las zonas de mucho trΓ‘fico, como las bodegas y los jardines, se han mejorado con suelos antideslizantes y barandillas reforzadas.\n\n Los puntos de reuniΓ³n de emergencia marcados estΓ‘n distribuidos por toda la propiedad para una rΓ‘pida organizaciΓ³n durante las crisis.\n\n Nuestro objetivo es ir mΓ‘s allΓ‘ de cumplir con las regulaciones: crear un entorno de confianza, seguridad y cuidado para cada visitante y empleado.\n\n 3. Acciones para el rescate de las personas afectadas\n Activar alarmas y protocolos de emergencia inmediatamente.\n\n GuΓ­e a los visitantes hacia rutas de salida seguras.\n\n Brindar apoyo emocional a quienes se encuentran en peligro o en estado de shock.\n\n Comunicarse de forma tranquila, empΓ‘tica y clara.\n\n Proporcionar primeros auxilios bΓ‘sicos para tratar lesiones menores.\n\n Refugio para personas que muestren signos de resfriado o trauma.\n\n Ofrecer agua y tranquilidad a quienes estΓ‘n desorientados.\n\n Priorizar la evacuaciΓ³n de los grupos vulnerables, especialmente niΓ±os y ancianos.\n\n Utilice sillas de ruedas o camillas para personas con problemas de movilidad.\n\n Contactar con los servicios mΓ©dicos de emergencia y coordinar el transporte a los hospitales.\n\n Registrar los nombres de los evacuados en los puntos de encuentro.\n\n Mantenga el contacto visual para proporcionar una sensaciΓ³n de seguridad.\n\n Bloquear el acceso a la zona de peligro para evitar mΓ‘s daΓ±os.\n\n Proporcionar instrucciones firmes pero de apoyo durante la evacuaciΓ³n.\n\n Informar a los miembros de la familia si es necesario, utilizando canales de comunicaciΓ³n seguros.\n\n Aplicar tΓ©cnicas bΓ‘sicas de primeros auxilios psicolΓ³gicos para gestionar las respuestas emocionales.\n\n Documentar hechos e incidentes clave para informar a las autoridades.\n\n AsegΓΊrese de que el Γ‘rea estΓ© completamente segura antes de permitir que alguien regrese.\n\n Brindar apoyo de seguimiento y asistencia especializada a quienes lo necesiten.",1188,238,"workshop-week-5-crisis-management-and-emergency-control-name-carlos-daniel-munoz-munoz-organization-vina-concha-y-toro-pirque-tourist-center-delivery-date-june-30-2025-1-emergency-sc",{"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},538153,"Find the equation of the circle that has the center 2,0 and passes through βˆ’1,βˆ’5","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- Center of the circle: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2,0\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Point on the circle: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>βˆ’1,βˆ’5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the standard equation of a circle:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’h^2 + yβˆ’k^2 = r^2\u003C/math-field>\u003C/math-field> where \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h,k\u003C/math-field>\u003C/math-field> is the center and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r\u003C/math-field>\u003C/math-field> is the radius.\u003Cbr />\n\u003Cbr />\n3. Substitute the center into the equation:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’2^2 + yβˆ’0^2 = r^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Simplifies to: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’2^2 + y^2 = r^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Substitute point \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>βˆ’1,βˆ’5\u003C/math-field>\u003C/math-field> to find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r^2\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(βˆ’1 - 2)^2 + (βˆ’5 - 0)^2 = r^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>βˆ’3^2 + βˆ’5^2 = r^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>9 + 25 = r^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r^2 = 34\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Therefore, the equation of the circle is:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’2^2 + y^2 = 34\u003C/math-field>\u003C/math-field>",1055,211,"find-the-equation-of-the-circle-that-has-the-center-2-0-and-passes-through-1-5",{"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},538152,"4/5βˆ’2/4i + 2/3+6/9i","Solution:\u003Cbr />\n1. Add the real parts:\u003Cbr />\n- Real part of the first complex number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{4}{5}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Real part of the second complex number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{2}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Sum of the real parts: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{4}{5} + \\frac{2}{3} = \\frac{4 \\times 3 + 5 \\times 2}{5 \\times 3} = \\frac{12 + 10}{15} = \\frac{22}{15}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Add the imaginary parts:\u003Cbr />\n- Imaginary part of the first complex number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-\\frac{2}{4}i = -\\frac{1}{2}i\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Imaginary part of the second complex number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{6}{9}i = \\frac{2}{3}i\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Sum of the imaginary parts: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-\\frac{1}{2}i + \\frac{2}{3}i\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Common denominator for imaginary sum is 6: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-\\frac{1 \\times 3}{2 \\times 3}i + \\frac{2 \\times 2}{3 \\times 2}i = -\\frac{3}{6}i + \\frac{4}{6}i = \\frac{1}{6}i\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Combine the results:\u003Cbr />\n- Resulting complex number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{22}{15} + \\frac{1}{6}i\u003C/math-field>\u003C/math-field>",1048,210,"4-5-2-4i-2-3-6-9i",{"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},538151,"Find the equation of the circle in its general form if its center is the point\n C2,βˆ’2 and the line 10x - 12y + 18 = 0, is tangent to the circle","Solution:\u003Cbr>\u003Cbr>1. Determine the distance from the center of the circle \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C2,βˆ’2\u003C/math-field>\u003C/math-field> to the line \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>10x - 12y + 18 = 0\u003C/math-field>\u003C/math-field> , which is the radius of the circle:\u003Cbr>\u003Cbr>- The formula for distance from a point \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x1,y1\u003C/math-field>\u003C/math-field> to a line \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>ax + by + c = 0\u003C/math-field>\u003C/math-field> is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{|ax_1 + by_1 + c|}{\\sqrt{a^2 + b^2}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 10\u003C/math-field>\u003C/math-field> , \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b = -12\u003C/math-field>\u003C/math-field> , \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>c = 18\u003C/math-field>\u003C/math-field> , and the center \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x1,y1 = 2,βˆ’2\u003C/math-field>\u003C/math-field> :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D = \\frac{|102 - 12βˆ’2 + 18|}{\\sqrt{10^2 + βˆ’12^2}} = \\frac{|20 + 24 + 18|}{\\sqrt{100 + 144}} = \\frac{62}{\\sqrt{244}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Simplify the denominator:\u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sqrt{244} = \\sqrt{4 \\times 61} = 2\\sqrt{61}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- So, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D = \\frac{62}{2\\sqrt{61}} = \\frac{31}{\\sqrt{61}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. The radius \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{31}{\\sqrt{61}}\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>4. Write the equation of the circle in the standard form:\u003Cbr>\u003Cbr>- The equation of a circle with center \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h,k\u003C/math-field>\u003C/math-field> and radius \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r\u003C/math-field>\u003C/math-field> is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’h^2 + yβˆ’k^2 = r^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h = 2\u003C/math-field>\u003C/math-field> , \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>k = -2\u003C/math-field>\u003C/math-field> , and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{31}{\\sqrt{61}}\u003C/math-field>\u003C/math-field> :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’2^2 + y+2^2 = \\leftfrac31sqrt61right^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Calculate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r^2\u003C/math-field>\u003C/math-field> :\u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\leftfrac31sqrt61right^2 = \\frac{31^2}{61} = \\frac{961}{61}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Expand the circle equation into general form:\u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>xβˆ’2^2 + y+2^2 = \\frac{961}{61}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Expand: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 - 4x + 4 + y^2 + 4y + 4 = \\frac{961}{61}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Multiply everything by 61 to clear the fraction:\u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>61x^2 - 244x + 244 + 61y^2 + 244y + 244 = 961\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>8. Write the general form of the circle equation:\u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>61x^2+61y^2-244x+244y-473=0\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>-",1411,282,"find-the-equation-of-the-circle-in-its-general-form-if-its-center-is-the-point-c-2-2-and-the-line-10x-12y-18-0-is-tangent-to-the-circle",{"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},538150,"For a randomly selected subject, find the probability of a score greater than -2.93","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- We are working with a standard normal distribution, mean \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mu = 0\u003C/math-field>\u003C/math-field>, standard deviation \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sigma = 1\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- We want to find the probability that the score \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z\u003C/math-field>\u003C/math-field> is greater than \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2.93\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Use the standard normal distribution table Zβˆ’table to find the cumulative probability for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z = -2.93\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Cumulative probability for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z \u003C -2.93\u003C/math-field>\u003C/math-field> fromZβˆ’table is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.0017\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. To find the probability of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Z > -2.93\u003C/math-field>\u003C/math-field>, we subtract the cumulative probability from 1:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PZ>βˆ’2.93 = 1 - PZ\u003Cβˆ’2.93\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PZ>βˆ’2.93 = 1 - 0.0017 = 0.9983\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Therefore, the probability that a randomly selected subject has a score greater than \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2.93\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.9983\u003C/math-field>\u003C/math-field>.",895,179,"for-a-randomly-selected-subject-find-the-probability-of-a-score-greater-than-2-93",{"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},538149,"48 divided by 2544","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Solution:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n1. To find the result of dividing 48 by 2544, perform the division:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{48}{2544}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Simplifying the fraction:\u003Cbr />\n - Find the greatest common divisor GCD of 48 and 2544.\u003Cbr />\n - The GCD of 48 and 2544 is 48.\u003Cbr />\n\u003Cbr />\n3. Divide both the numerator and the denominator by their GCD:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{48 \\div 48}{2544 \\div 48} = \\frac{1}{53}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. The simplified form of the division is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{53}\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 />\nThe simplified result of dividing 48 by 2544 is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{53}\u003C/math-field>\u003C/math-field>.",1067,213,"48-divided-by-2544",{"first":6,"last":176,"prev":8,"next":10},191,{"current_page":6,"from":6,"last_page":176,"links":178,"path":212,"per_page":213,"to":213,"total":214},[179,182,185,187,189,191,193,196,199,202,205,208,210],{"url":6,"label":180,"active":181},"1",true,{"url":10,"label":183,"active":184},"2",false,{"url":13,"label":186,"active":184},"3",{"url":16,"label":188,"active":184},"4",{"url":19,"label":190,"active":184},"5",{"url":22,"label":192,"active":184},"6",{"url":194,"label":195,"active":184},7,"7",{"url":197,"label":198,"active":184},8,"8",{"url":200,"label":201,"active":184},9,"9",{"url":203,"label":204,"active":184},10,"10",{"url":206,"label":207,"active":184},190,"190",{"url":176,"label":209,"active":184},"191",{"url":10,"label":211,"active":184},"Next »","https://api.math-master.org/api/question",20,3803,{"data":216},{"questions":217},[218,222,226,230,234,238,242,246,250,254,258,262,266,270,274,278,282,286,290,294],{"id":219,"category":36,"text_question":220,"slug":221},532056,"5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight","5-squirrels-were-found-to-have-an-average-weight-of-9-3-ounces-with-a-sample-standard-deviation-is-1-1-find-the-95-confidence-interval-of-the-true-mean-weight",{"id":223,"category":36,"text_question":224,"slug":225},532083,"Let X be a discrete random variable with range {1, 3, 5} and whose probability function is fx = PX=x. If it is known that PX=1 = 0.1 and PX=3 = 0.3. What is the value of PX=5?","let-x-be-a-discrete-random-variable-with-range-1-3-5-and-whose-probability-function-is-f-x-p-x-x-if-it-is-known-that-p-x-1-0-1-and-p-x-3-0-3-what-is-the-value-of-p-x-5",{"id":227,"category":36,"text_question":228,"slug":229},533948,"Derivative of x squared","derivative-of-x-squared",{"id":231,"category":36,"text_question":232,"slug":233},533985,"Serum cholesterol levels in men aged 18 to 24 years have a normal distribution with a mean\n 178.1mg/100 ml and standard deviation 40.7 mg/100 ml.\n The. Randomly choosing a man between 18 and 24 years old, determine the probability of\n your serum cholesterol level is less than 200.\n B. Whether a serum cholesterol level should be judged too high if it is above 7%\n higher, determine the value of the separation level of levels that are too high.\n w. Determine a 90% reference range for serum cholesterol level among men\n from 18 to 24 years old.","serum-cholesterol-levels-in-men-aged-18-to-24-years-have-a-normal-distribution-with-a-mean-178-1mg-100-ml-and-standard-deviation-40-7-mg-100-ml-the-randomly-choosing-a-man-between-18-and-24-years",{"id":235,"category":36,"text_question":236,"slug":237},534136,"Prove that it is not possible to arrange the integers 1 to 240 in a table with 15 rows and 16 columns in such a way that the sum of the numbers in each of the columns is the same.","prove-that-it-is-not-possible-to-arrange-the-integers-1-to-240-in-a-table-with-15-rows-and-16-columns-in-such-a-way-that-the-sum-of-the-numbers-in-each-of-the-columns-is-the-same",{"id":239,"category":36,"text_question":240,"slug":241},534169,"Find 2 numbers whose sum is 47 and whose subtraction is 13","find-2-numbers-whose-sum-is-47-and-whose-subtraction-is-13",{"id":243,"category":36,"text_question":244,"slug":245},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":247,"category":36,"text_question":248,"slug":249},534328,"What is 75 percent less than 60","what-is-75-percent-less-than-60",{"id":251,"category":36,"text_question":252,"slug":253},534359,"Express the trigonometric form of the complex z = -1 + i.","express-the-trigonometric-form-of-the-complex-z-1-i",{"id":255,"category":36,"text_question":256,"slug":257},534371,"Determine a general formula​ orformulas for the solution to the following equation.​ Then, determine the specific solutions​ ifany on the interval [0,2Ο€).\ncos30=0","determine-a-general-formula-or-formulas-for-the-solution-to-the-following-equation-then-determine-the-specific-solutions-if-any-on-the-interval-0-2-cos30-0",{"id":259,"category":36,"text_question":260,"slug":261},534410,"36 cars of the same model that were sold in a\n dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of\n 2, 39 days. Construct a 95% confidence interval for the population mean number of days\n that a car remains on the dealership's forecourt","36-cars-of-the-same-model-that-were-sold-in-a-dealership-and-the-number-of-days-that-each-one-remained-in-the-dealership-yard-before-being-sold-is-determined-the-sample-average-is-9-75-days-with-a",{"id":263,"category":36,"text_question":264,"slug":265},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":267,"category":36,"text_question":268,"slug":269},534492,"Find the equation of a straight line that has slope 3 and passes through the point of 1,7 .\nWrite the equation of the line in general forms","find-the-equation-of-a-straight-line-that-has-slope-3-and-passes-through-the-point-of-1-7-write-the-equation-of-the-line-in-general-forms",{"id":271,"category":36,"text_question":272,"slug":273},534507,"Find the set of points formed by the expression πœ‹\u003C|π‘§βˆ’4+2𝑖|\u003C3πœ‹.","find-the-set-of-points-formed-by-the-expression-z-4-2i-3",{"id":275,"category":36,"text_question":276,"slug":277},534589,"Select a variable and collect at least 50 data values. For example, you may ask the students in the college how many hours they study per week or how old they are, etc.\na. Explain what your target population was.\nb. State how the sample was selected.\nc. Summarise the data by using a frequency table.\nd. Calculate all the descriptive measures for the data and describe the data\nset using the measures.\ne. Present the data in an appropriate way.\nf. Write a paragraph summarizing the data.","select-a-variable-and-collect-at-least-50-data-values-for-example-you-may-ask-the-students-in-the-college-how-many-hours-they-study-per-week-or-how-old-they-are-etc-a-explain-what-your-target-pop",{"id":279,"category":36,"text_question":280,"slug":281},534593,"Determine the general solution of the equation yβ€²+y=eβˆ’x\n .","determine-the-general-solution-of-the-equation-y-y-e-x",{"id":283,"category":36,"text_question":284,"slug":285},534628,"Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. \n\nPoint D lies on AB such that CB = CD\n\nPoint E lies on AC such that CE= DE\n\nDetermine angle DEC in terms of X","triangle-abc-has-ab-ac-and-angle-bac-x-with-x-being-less-than-60-degrees-point-d-lies-on-ab-such-that-cb-cd-point-e-lies-on-ac-such-that-ce-de-determine-angle-dec-in-terms-of-x",{"id":287,"category":36,"text_question":288,"slug":289},534655,"An export company grants a bonus of 100,000pesostodistributeamongthreeofitsbestemployees,sothatthefirstreceivesdoublethesecondandthelatterreceivestriplethethird.Howmuchdideachpersonreceive?","anβˆ’exportβˆ’companyβˆ’grantsβˆ’aβˆ’bonusβˆ’ofβˆ’100βˆ’000βˆ’pesosβˆ’toβˆ’distributeβˆ’amongβˆ’threeβˆ’ofβˆ’itsβˆ’bestβˆ’employeesβˆ’soβˆ’thatβˆ’theβˆ’firstβˆ’receivesβˆ’doubleβˆ’theβˆ’secondβˆ’andβˆ’theβˆ’latterβˆ’receivesβˆ’tripleβˆ’theβˆ’thirdβˆ’howβˆ’muchβˆ’did","id":291,"category":36,"textquestion":292,"slug":293,534664,"15=5(x+3)","15βˆ’5βˆ’xβˆ’3","id":295,"category":36,"textquestion":296,"slug":297,534688,"Matildeknowsthat,whendrivinghercarfromherofficetoherapartment,shespendsanormaltimeofxminutes.Inthelastweek,youhavenoticedthatwhendrivingat50mph(milesperhour),youarrivehome4minutesearlierthannormal,andwhendrivingat40mph,youarrivehome5minutesearlier\nlaterthannormal.Ifthedistancebetweenyourofficeandyourapartmentisymiles,calculatex+y.","matildeβˆ’knowsβˆ’thatβˆ’whenβˆ’drivingβˆ’herβˆ’carβˆ’fromβˆ’herβˆ’officeβˆ’toβˆ’herβˆ’apartmentβˆ’sheβˆ’spendsβˆ’aβˆ’normalβˆ’timeβˆ’ofβˆ’xβˆ’minutesβˆ’inβˆ’theβˆ’lastβˆ’weekβˆ’youβˆ’haveβˆ’noticedβˆ’thatβˆ’whenβˆ’drivingβˆ’atβˆ’50βˆ’mphβˆ’milesβˆ’perβˆ’hourβˆ’youβˆ’a","data":299,"id":267,"category":36,"slug":269,"textquestion":268,"photoquestion":8,"textanswer":300,"steptextanswer":8,"stepphotoanswer":8,"views":301,"likes":302,"expert":303,"Usepointslopeformoflinetofindtheequation.\n\u003Cmathβˆ’fieldreadβˆ’only>yβˆ’y1=m(xβˆ’x1)\u003C/mathβˆ’field>\nHere,\u003Cmathβˆ’fieldreadβˆ’only>m=3\u003C/mathβˆ’field>\u003Cmathβˆ’fieldreadβˆ’only>x1=1\u003C/mathβˆ’field>\u003Cmathβˆ’fieldreadβˆ’only>y1=7\u003C/mathβˆ’field>\nSubstitutethevaluesintheequation.\n\u003Cmathβˆ’fieldreadβˆ’only>yβˆ’7=3(xβˆ’1)\u003C/mathβˆ’field>\n\u003Cmathβˆ’fieldreadβˆ’only>yβˆ’7=3xβˆ’3\u003C/mathβˆ’field>\n\u003Cmathβˆ’fieldreadβˆ’only>y=3xβˆ’3+7\u003C/mathβˆ’field>\n\u003Cmathβˆ’fieldreadβˆ’only>y=3x+4\u003C/mathβˆ’field>",1371,274,"id":304,"name":305,"photo":306,"biography":307,"createdat":8,"updatedat":8,"rating":308,"totalanswer":309,17,"Gene","https://api.mathβˆ’master.org/img/experts/17/17.webp","Iembarkedonmyjourneyintotherealmofmathematicswithastrongfoundationlaidduringmyschoolyears.Mypassionfornumbersandproblemβˆ’solvingwasevidentasIcompletedmymatriculationinthesciencestreamwithanimpressive8050 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis.\r\n\r\nDuring a client meeting we gathered these facts. There are 2 part-time employees that each earn 1000permonth.Theutilitiesforthekennelarea(water,electricity)are200 per month. The average food cost for animals in the kennel is 800permonth.Inaddition,eachanimalthatisadoptedreceivesarabiesvaccinationthatcosts4 and is micro-chipped that costs 6.\r\n\r\nAtthecurrentcostof50, how many animals must be adopted to break-even?\r\nWhat would break-even be at a 60adoptionfee?\r\nWhatwouldbreakβˆ’evenbeifthefeewereloweredto40?\r\nThe newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs 1000foraverysmalladruneverydayforamonth.IftheHumaneSocietydoesthisextraadvertising,howwillitaffectbreakeven?\r\nBasedonwhatyouhavelearnedaboutelasticity,whatpricedoyourecommendfortheadoptionfee?","theβˆ’humaneβˆ’societyβˆ’hasβˆ’askedβˆ’forβˆ’ourβˆ’helpβˆ’againβˆ’thisβˆ’weekβˆ’currentlyβˆ’theyβˆ’areβˆ’chargingβˆ’50βˆ’forβˆ’anβˆ’adoptionβˆ’feeβˆ’unfortunatelyβˆ’theyβˆ’justβˆ’pulledβˆ’thisβˆ’numberβˆ’outβˆ’ofβˆ’theβˆ’airβˆ’andβˆ’doβˆ’notβˆ’knowβˆ’whyβˆ’theyβˆ’areβˆ’c","id":354,"category":36,"textquestion":355,"slug":356,534263,"Scoresarenormallydistributedwithameanof25andstandarddeviationof5.Findtheprobabilitythatsixteenrandomlyselectedstudentshaveameanscorethatislessthan24.","scoresβˆ’areβˆ’normallyβˆ’distributedβˆ’withβˆ’aβˆ’meanβˆ’ofβˆ’25βˆ’andβˆ’standardβˆ’deviationβˆ’ofβˆ’5βˆ’findβˆ’theβˆ’probabilityβˆ’thatβˆ’sixteenβˆ’randomlyβˆ’selectedβˆ’studentsβˆ’haveβˆ’aβˆ’meanβˆ’scoreβˆ’thatβˆ’isβˆ’lessβˆ’thanβˆ’24","id":358,"category":36,"textquestion":359,"slug":360,534301,"Determinethereducedformoftheslopeequationequalto2","determineβˆ’theβˆ’reducedβˆ’formβˆ’ofβˆ’theβˆ’slopeβˆ’equationβˆ’equalβˆ’toβˆ’2","id":362,"category":36,"textquestion":363,"slug":364,534357,"MAKINGANARGUMENTYouusesyntheticdivisiontodividef(x)by(xβˆ’a)andfindthattheremainderequals15.Yourfriendconcludesthatf(15)=a.\nIsyourfriendcorrect?Explainyourreasoning.","makingβˆ’anβˆ’argumentβˆ’youβˆ’useβˆ’syntheticβˆ’divisionβˆ’toβˆ’divideβˆ’fβˆ’xβˆ’byβˆ’xβˆ’aβˆ’andβˆ’findβˆ’thatβˆ’theβˆ’remainderβˆ’equalsβˆ’15βˆ’yourβˆ’friendβˆ’concludesβˆ’thatβˆ’fβˆ’15βˆ’aβˆ’isβˆ’yourβˆ’friendβˆ’correctβˆ’explainβˆ’yourβˆ’reasoning","id":366,"category":36,"textquestion":367,"slug":368,534365,"Calculatethedifferencebetween407and27","calculateβˆ’theβˆ’differenceβˆ’betweenβˆ’407βˆ’andβˆ’27","id":370,"category":36,"textquestion":371,"slug":372,534397,"Buildatruthtableforthestatement (pvq) p","buildβˆ’aβˆ’truthβˆ’tableβˆ’forβˆ’theβˆ’statementβˆ’pvqβˆ’p","id":374,"category":36,"textquestion":375,"slug":376,534471,"Log0","log0","id":378,"category":36,"textquestion":379,"slug":380,534486,"Agiveninitialcapitalinsimpleinterestattheannualrateandfor27monthsproducedtheaccumulatedcapitalof6600umifthesamecapitalhadbeeninvestedatthesameratebutduring28monthsthesaidaccumulatedcapitalwouldbeincreasedinanamountcorrespondingto0.75250.00 per month and keeps the money in a safe in his own home. At the end of 12\n months, deposit the total saved into the savings account. Consider that, each year, deposits are\n always carried out on the same day and month; the annual yield on the savings account is 7%; and, the yield\n total is obtained by the interest compounding process. So, the amount that Paulo will have in his savings account\n after 3 years, from the moment you started saving part of your money monthly, it will be\n A) R6,644.70.\nB)R 9,210.00.\n C) R9,644.70.\nD)R 10,319.83.\n E) R13,319.83","25-paulo-saves-r-250-00-per-month-and-keeps-the-money-in-a-safe-in-his-own-home-at-the-end-of-12-months-deposit-the-total-saved-into-the-savings-account-consider-that-each-year-deposits-are-al",{"id":386,"category":36,"text_question":387,"slug":388},534569,"the product of a 2-digit number and a 3-digit number is about 50000, what are these numbers","the-product-of-a-2-digit-number-and-a-3-digit-number-is-about-50000-what-are-these-numbers",{"id":390,"category":36,"text_question":391,"slug":392},534686,"To apply a diagnostic test, in how many ways can 14 students be chosen out of 25? if the order does not matter","to-apply-a-diagnostic-test-in-how-many-ways-can-14-students-be-chosen-out-of-25-if-the-order-does-not-matter",{"data":394},[395,399,403],{"id":396,"question":397,"answer":398},161693,"What is the area of a right triangle with legs of length 5 cm and 12 cm?","The area of the right triangle is (1/2) * (5 cm) * (12 cm) = 30 cm^2.",{"id":400,"question":401,"answer":402},121809,"What is the equation of an ellipse with major axis 10 units, minor axis 6 units, centered at (0,0), and tilted 45 degrees?","The equation of the ellipse is (x^2/25) + (y^2/9) = 1, where x and y are the coordinates of any point on the ellipse.",{"id":404,"question":405,"answer":406},131319,"What are the characteristics of the hyperbola function when the transverse axis is horizontal?","When the hyperbola has a horizontal transverse axis, its equation takes the form: (x-h)^2/a^2 - (y-k)^2/b^2 = 1. The center is (h,k), the vertices are (hΒ±a,k), and the foci are (hΒ±c,k), where c^2 = a^2+b^2. The asymptotes have equations y = k Β± (b/a)(x-h), and the eccentricity is e = c/a.",{"sicons":408},{"bxl:facebook-circle":409,"bxl:instagram":413,"mdi:web":415,"la:apple":417,"ph:google-logo-bold":420,"ph:google-logo":423},{"left":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":184,"hFlip":184,"body":412},0,24,"\u003Cpath 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