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},531998,"Calculate to represent the function whose graph is a line that passes through the points 1,2 and βˆ’3,4. What is your slope?","calculate-to-represent-the-function-whose-graph-is-a-line-that-passes-through-the-points-1-2-and-3-4-what-is-your-slope",{"id":223,"category":36,"text_question":224,"slug":225},531999,"How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117","how-to-find-the-value-of-x-and-y-which-satisfy-both-equations-x-2y-24-and-8x-y-117",{"id":227,"category":36,"text_question":228,"slug":229},532005,"A=m/2-t isolate t","a-m-2-t-isolate-t",{"id":231,"category":36,"text_question":232,"slug":233},532038,"10!\r\n-\r\n8! =","10-8",{"id":235,"category":36,"text_question":236,"slug":237},532091,"the value of sin 178Β°58'","the-value-of-sin-178-58-39",{"id":239,"category":36,"text_question":240,"slug":241},534017,"2x+5^3+xβˆ’3x+3","2x-5-3-x-3-x-3",{"id":243,"category":36,"text_question":244,"slug":245},534152,"Determine the reduced equation of the straight line that is perpendicular to the straight line r: y=4x-10 and passes through the origin of the Cartesian plane","determine-the-reduced-equation-of-the-straight-line-that-is-perpendicular-to-the-straight-line-r-y-4x-10-and-passes-through-the-origin-of-the-cartesian-plane",{"id":247,"category":36,"text_question":248,"slug":249},534194,"form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?","form-a-key-for-your-lock-containing-the-numbers-2-2-5-8-how-many-different-keys-can-you-form",{"id":251,"category":36,"text_question":252,"slug":253},534217,"In the telephone exchange of a certain university, calls come in at a rate of 5 every\n 2 minutes. Assuming a Poisson distribution, the average number of calls per\n second is:\n a) 1/8\n b) 1/12\n c) 1/10\n d) 2/5\n e) 1/24","in-the-telephone-exchange-of-a-certain-university-calls-come-in-at-a-rate-of-5-every-2-minutes-assuming-a-poisson-distribution-the-average-number-of-calls-per-second-is-a-1-8-b-1-12-c-1-10",{"id":255,"category":36,"text_question":256,"slug":257},534260,"Solve the following equation for x in exact form and then find the value to the nearest hundredths makesuretoshowyourwork:\r\n\r\n5e3x – 3 = 25","solve-the-following-equation-for-x-in-exact-form-and-then-find-the-value-to-the-nearest-hundredths-make-sure-to-show-your-work-5e3x-3-25",{"id":259,"category":36,"text_question":260,"slug":261},534271,"DuocUC\n\n 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function:\n\n x+185 Cx=81300-6x+ 20000\n\n a) It is known that C90 5.344. Interpret this result.\n\n 2points\n\n b) Calculate C'x\n\n 2points\n\n 3 xΒ²+111x-0.87\n\n 20000 2000\n\n c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing.\n\n 3points\n\n d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost?\n\n ","duocucβˆ’2βˆ’theβˆ’costβˆ’cβˆ’inβˆ’pesosβˆ’forβˆ’theβˆ’productionβˆ’ofβˆ’xβˆ’metersβˆ’ofβˆ’aβˆ’certainβˆ’fabricβˆ’canβˆ’beβˆ’calculatedβˆ’throughβˆ’theβˆ’functionβˆ’xβˆ’185βˆ’cβˆ’xβˆ’81300βˆ’6xβˆ’20000βˆ’aβˆ’itβˆ’isβˆ’knownβˆ’thatβˆ’cβˆ’90βˆ’5βˆ’344βˆ’interpret","id":263,"category":36,"textquestion":264,"slug":265,534334,"Next","write-the-equation-of-the-line-that-is-parallel-to-y-4x-7-and-has-a-y-intercept-at-0-5",{"id":279,"category":36,"text_question":280,"slug":281},534510,"Consider the function fx=1/2x+1^2-3. Use the preceding/following interval method to estimate the\ninstantaneous rate of change at π‘₯ = 1.","consider-the-function-f-x-1-2-x-1-2-3-use-the-preceding-following-interval-method-to-estimate-the-instantaneous-rate-of-change-at-x-1",{"id":283,"category":36,"text_question":284,"slug":285},534513,"Given a circle π‘˜π‘†;π‘Ÿ=4π‘π‘š and a line |𝐴𝐡| = 2 π‘π‘š. Determine and construct the set of all\ncenters of circles that touch circle π‘˜ and have radius π‘Ÿ = |𝐴𝐡|","given-a-circle-k-s-r-4-cm-and-a-line-ab-2-cm-determine-and-construct-the-set-of-all-centers-of-circles-that-touch-circle-k-and-have-radius-r-ab",{"id":287,"category":36,"text_question":288,"slug":289},534527,"22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the\nchord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.","22-let-ab-be-a-chord-in-a-circle-c-and-k-a-circle-which-is-internally-tangent-to-the-circle-c-at-a-point-p-and-to-the-chord-ab-at-a-point-q-show-that-the-line-p-q-passes-through-the-midpoint-of",{"id":291,"category":36,"text_question":292,"slug":293},534559,"simplify w+[6+βˆ’5]","simplify-w-6-5",{"id":295,"category":36,"text_question":296,"slug":297},534696,"In a cheese factory, one pie costs 3800 denars. The fixed ones\ncosts are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter:\na) income functions. profit and costs;\nb) the break-even point and profit and loss intervals.","in-a-cheese-factory-one-pie-costs-3800-denars-the-fixed-ones-costs-are-1-200-000-denars-and-variable-costs-are-2-500-denars-per-pie-to-encounter-a-income-functions-profit-and-costs-b-the-brea",{"data":299},{"id":300,"category":36,"slug":301,"text_question":302,"photo_question":8,"text_answer":303,"step_text_answer":8,"step_photo_answer":8,"views":304,"likes":305,"expert":306},533952,"a-brass-cube-with-an-edge-of-3-cm-at-40-c-increased-its-volume-to-27-12-cm3-what-is-the-final-temperature-that-achieves-this-increase","A brass cube with an edge of 3 cm at 40 Β°C increased its volume to 27.12 cm3. What is the final temperature that achieves this increase?","40.18Β°",455,91,{"id":307,"name":308,"photo":309,"biography":310,"created_at":8,"updated_at":8,"rating":311,"total_answer":312},15,"Miles","https://api.math-master.org/img/experts/15/15.webp","My name is Ali Haider and I hold a bachelor’s degree in Electrical Engineering and I am also certified Math Expert. I have been teaching Mathematics and Physics for the past 6 years at both the high school and college level. My pass rate for Mathematics is 100%.\nIn addition to teaching, I love playing badminton and video games.\n",4.9,110,{"data":314},{"questions":315},[316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,384,388,392],{"id":317,"category":36,"text_question":318,"slug":319},532024,"22+2x=12","2-2-2x-12",{"id":321,"category":36,"text_question":322,"slug":323},533918,"5 people can complete a task in 72 hours. How many people are needed to complete the task in 60 hours.","5-people-can-complete-a-task-in-72-hours-how-many-people-are-needed-to-complete-the-task-in-60-hours",{"id":325,"category":36,"text_question":326,"slug":327},533980,"Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.","find-the-root-of-x-4-10x-5-0-using-newton-s-method-with-a-precision-of-the-smallest-positive-root",{"id":329,"category":36,"text_question":330,"slug":331},534011,"9b^2-6b-5","9b-2-6b-5",{"id":333,"category":36,"text_question":334,"slug":335},534027,"Answer the following questions regarding the expression below.\n\n \n\n0.1\n \n\n \n\na Write the number as a fraction.","answer-the-following-questions-regarding-the-expression-below-0-1-a-write-the-number-as-a-fraction",{"id":337,"category":36,"text_question":338,"slug":339},534048,"To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:","to-celebrate-the-five-year-anniversary-of-a-consultancy-specializing-in-information-technology-the-administrator-decided-to-draw-3-different-qualification-courses-among-its-10-employees-considering",{"id":341,"category":36,"text_question":342,"slug":343},534090,"If you randomly selected one person from the 900 subjects in this study, what is the probability that \nthe person exhibits the minimum BMI?","if-you-randomly-selected-one-person-from-the-900-subjects-in-this-study-what-is-the-probability-that-the-person-exhibits-the-minimum-bmi",{"id":345,"category":36,"text_question":346,"slug":347},534104,"78 percent to a decimal","78-percent-to-a-decimal",{"id":349,"category":36,"text_question":350,"slug":351},534168,"I want you to solve this problem as a grade sixth pupil in primary school:\n8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?","i-want-you-to-solve-this-problem-as-a-grade-sixth-pupil-in-primary-school-8-pigs-ate-6-bags-of-fee-in-20-days-how-long-will-it-take-10-pigs-to-eat-15-bags-of-feed-eating-at-the-same-rate",{"id":353,"category":36,"text_question":354,"slug":355},534204,"RaΓΊl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows:\n RaΓΊlwins = 20%\n Gilbertowins = 0.05%\n Arturowins = ΒΎ%.\n\n Perform operations and order events from least to most probable.","raul-gilberto-and-arturo-are-playing-golf-the-probabilities-of-winning-for-each-one-are-as-follows-raul-wins-20-gilberto-wins-0-05-arturo-wins-perform-operations-and-order-ev",{"id":357,"category":36,"text_question":358,"slug":359},534223,"In a order to compare the means of two populations, independent random samples of 410 observations are selected from each population, with Sample 1 the results found in the table to the right. Complete parts a through e below. X1 = 5,319 S1= 143 a. Use a 95% confidence interval to estimate the difference between the population means Hβˆ’H2 Interpret the contidence interval. The contidence interval IS Roundtoonedecimalplaceasneeded. Sample 2 X2 = 5,285 S2 = 198\n\nAa. Use a 95% confidence interval to estimate the difference between the population means A1βˆ’M2 Interpret the contidence interval. The contidence interval Is Roundtoonedecimalplaceasneeded.\n\nb. Test the null hypothesis Ho versus alternative hypothesis Ha HWhatistheteststatistic?H2 + Give the significance level of the test, and interpret the result. Use a = 0.05. \nZ=","in-a-order-to-compare-the-means-of-two-populations-independent-random-samples-of-410-observations-are-selected-from-each-population-with-sample-1-the-results-found-in-the-table-to-the-right-complet",{"id":361,"category":36,"text_question":362,"slug":363},534286,"From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539","from-1975-through-2020-the-mean-annual-gain-of-the-dow-jones-industrial-average-was-652-a-random-sample-of-34-years-is-selected-from-this-population-what-is-the-probability-that-the-mean-gain-for-th",{"id":365,"category":36,"text_question":366,"slug":367},534363,"ind the z-score for which 72% of the distribution's area lies between -z and z.\n\n-1.7417, 1.7417\n\n-1.1538, 1.1538\n\n-1.0803, 1.0803\n\n-2.826, 2.826","ind-the-z-score-for-which-72-of-the-distribution-s-area-lies-between-z-and-z-1-7417-1-7417-1-1538-1-1538-1-0803-1-0803-2-826-2-826",{"id":369,"category":36,"text_question":370,"slug":371},534377,"The business college computing center wants to determine the proportion of business students who have personal computers PCβ€²s at home. If the proportion is greater than 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is z= 2.6. Find the P-value for this test.","the-business-college-computing-center-wants-to-determine-the-proportion-of-business-students-who-have-personal-computers-pc-s-at-home-if-the-proportion-is-greater-than-35-then-the-lab-will-modify",{"id":373,"category":36,"text_question":374,"slug":375},534488,"7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?","7-a-printing-company-found-in-its-investigations-that-there-were-an-average-of-6-errors-in-150-page-prints-based-on-this-information-what-is-the-probability-of-there-being-48-errors-in-a-1200-page",{"id":377,"category":36,"text_question":378,"slug":379},534563,"How much does 7.2 moles of ammonium dichromate weigh? NH42Cr2O7","how-much-does-7-2-moles-of-ammonium-dichromate-weigh-nh4-2cr2o7",{"id":381,"category":36,"text_question":382,"slug":383},534582,"16-xΒ²+x+2Β²","16-x-x-2",{"id":385,"category":36,"text_question":386,"slug":387},534679,"Find the rule that connects the first number to the second number of each pair.\r\nApply the rule to find the missing number in the third pair.\r\n18isto22 54isto26 9isto?","find-the-rule-that-connects-the-first-number-to-the-second-number-of-each-pair-apply-the-rule-to-find-the-missing-number-in-the-third-pair-18-is-to-22-54-is-to-26-9-is-to",{"id":389,"category":36,"text_question":390,"slug":391},534681,"3bβ‹…5b2β‹…6b3","3b-5b-2-6b-3",{"id":393,"category":36,"text_question":394,"slug":395},534694,"An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?","an-invoice-for-2-880-plus-default-interest-of-48-40-was-paid-on-october-28th-interest-rate-5-5-when-was-the-bill-due",{"data":397},[398,402,406],{"id":399,"question":400,"answer":401},127400,"What is the value of sqrt9 - sqrt4?","The value is 3 - 2 = 1. The square root of 9 is 3 and the square root of 4 is 2. Subtracting them gives 1 as the result.",{"id":403,"question":404,"answer":405},118846,"What is the formula for finding the total number of diagonals in a polygon with n sides?","The formula is n*nβˆ’3/2, where n represents the number of sides.",{"id":407,"question":408,"answer":409},130605,"What is the radius of a circle with the equation x^2 + y^2 = 49?","The radius of the circle is 7 units because the equation implies r^2 = 49, so r = √49 = 7. 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