The most popular questions on the topic of general

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\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{dy}{dx} = -2x + 5\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Now, this gives us the slope of the curve at any point on the curve. So, if we want to find the slope at a specific point, we need to substitute the x-coordinate of that point into the derivative expression. \u003Cbr>\u003Cbr>Therefore, the slope of the tangent to the curve \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -x^2 + 5x - 6\u003C/math-field>\u003C/math-field> at any point is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{-2x + 5}\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Note: The slope of the tangent changes depending on the x-coordinate of the point on the curve, as given by the derivative of the function y.",1138,228,"find-the-slope-of-the-tangents-to-the-curve-y-x2-5x-6",{"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},535652,"Which three of the following discrete variables are binary\r\nWhich side of a coin lands uppermost when thrown \r\nWhether you have a pet\r\nRank in the armed forces\r\nWhether you wear glasses\r\nGrade of musical proficiency\r\nThe last two digits of the telephone number of a football team","Which side of a coin lands uppermost when thrown\nWhether you have a pet\nWhether you wear glasses",470,94,"which-three-of-the-following-discrete-variables-are-binary-which-side-of-a-coin-lands-uppermost-when-thrown-whether-you-have-a-pet-rank-in-the-armed-forces-whether-you-wear-glasses-grade-of-musi",{"id":51,"category":36,"text_question":52,"photo_question":38,"text_answer":53,"step_text_answer":8,"step_photo_answer":8,"views":54,"likes":55,"slug":56},535651,"A NaOH titrant solution with 2 grams of NaOH in 100mL where the Volume is 40mL, was used to determine the concentration of HCl acid

$analyte solution$ where the volume = 20mL. Calculate the concentration of HCl acid analyte solution in mol/L. Present your solution in mol/L to 1 significant figure. Enter a numeric value only without the mol/L unit.","Given:\u003Cbr>- Mass of NaOH = 2 grams\u003Cbr>- Volume of NaOH solution = 100 mL = 0.1 L\u003Cbr>- Volume of HCl solution = 20 mL = 0.02 L\u003Cbr>- Volume of NaOH titrant solution = 40 mL = 0.04 L\u003Cbr>\u003Cbr>1. Calculate moles of NaOH:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Moles of NaOH} = \\frac{2 \\, \\text{g}}{40 \\, \\text{g/mol}} = 0.05 \\, \\text{mol}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Calculate the molarity of NaOH

$\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M_1\u003C/math-field>\u003C/math-field>$ :\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M_1 = \\frac{0.05 \\, \\text{mol}}{0.1 \\, \\text{L}} = 0.5 \\, \\text{mol/L}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Use the titration formula to find the molarity of the HCl solution

$\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M_2\u003C/math-field>\u003C/math-field>$ :\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M_1V_1 = M_2V_2\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.5 \\, \\text{mol/L} \\times 0.04 \\, \\text{L} = M_2 \\times 0.02 \\, \\text{L}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>M_2 = \\frac{0.5 \\times 0.04}{0.02} = 1.0 \\, \\text{mol/L}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, the concentration of the HCl acid analyte solution is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bf{1.0}\u003C/math-field>\u003C/math-field> mol/L

$rounded to 1 significant figure$ . \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{1.0}\u003C/math-field>\u003C/math-field>",955,191,"a-naoh-titrant-solution-with-2-grams-of-naoh-in-100ml-where-the-volume-is-40ml-was-used-to-determine-the-concentration-of-hcl-acid-analyte-solution-where-the-volume-20ml-calculate-the-concentrat",{"id":58,"category":36,"text_question":59,"photo_question":38,"text_answer":60,"step_text_answer":8,"step_photo_answer":8,"views":61,"likes":62,"slug":63},535650,"An object of mass 500 g and density 0.8 g/cm³ is immersed in a liquid of\n density 1.2 g/cm³. What is the volume of the object that remains outside the liquid?","Para encontrar el volumen del objeto que queda fuera del líquido, primero debemos determinar el volumen del objeto y luego restar el volumen de la porción que está sumergida en el líquido.\n\n Denotemos:\n - m como la masa del objeto

$500 g$ \n - ho_o como densidad del objeto

$0,8 g/cm³$ \n - ho_l como densidad del líquido

$1,2 g/cm³$ \n - V_o como volumen del objeto

$por determinar$ \n - V_s como el volumen de la porción del objeto sumergida en el líquido\n\n Sabemos que la densidad ho se define como\n ho = m/v\n\n A partir de esto, podemos reorganizar la ecuación para resolver el volumen:\n V = m/ho\n\n Para el objeto:\n V_o = m/ho_o\n Vo = 500/0,8\n Vo = 625 cm ^ 3\n\n Ahora, para encontrar el volumen de la porción sumergida en el líquido, podemos utilizar el hecho de que la masa del líquido desplazado es igual a la masa del objeto sumergido:\n m_desplazamiento = m_ objeto sumergido\n ho_l *V_s = m\n\n Podemos resolver para V_s:\n V_s = m/ho_l\n V_s = 500/1,2\n V_s=416,67cm^3\n\n Finalmente, para encontrar el volumen del objeto que queda fuera del líquido, restamos el volumen sumergido al volumen total del objeto:\n Volumen fuera del líquido = V_o - V_s\n Volumen fuera del líquido = 625 - 416,67\n Volumen exterior del líquido = 208,33 cm^3\n Entonces, el volumen del objeto que queda fuera del líquido es aproximadamente 208,33 cm^3.",1036,207,"an-object-of-mass-500-g-and-density-0-8-g-cm-is-immersed-in-a-liquid-of-density-1-2-g-cm-what-is-the-volume-of-the-object-that-remains-outside-the-liquid",{"id":65,"category":36,"text_question":66,"photo_question":38,"text_answer":67,"step_text_answer":8,"step_photo_answer":8,"views":68,"likes":69,"slug":70},535649,"Prove that in every right triangle whose acute angles measure 75 and 15 degrees, the height corresponding to the hypotenuse is equal to a quarter of it.","He aquí una prueba de que en todo triángulo rectángulo con ángulos agudos de 75 y 15 grados, la altura correspondiente a la hipotenusa es igual a un cuarto de la hipotenusa:\n\n **1. Identificar elementos clave:**\n\n Denotemos el triángulo rectángulo con:\n\n * A como el ángulo recto\n * B como el vértice del ángulo de 75 grados\n * C como el vértice del ángulo de 15 grados\n * h como la altura trazada desde B hacia el lado AC

$la hipotenusa$ \n * a como la longitud del lado AB

$opuesto al ángulo de 75 grados$ \n * c como la longitud del lado AC

$la hipotenusa$ \n\n **2. Relacionar ángulos y lados usando trigonometría:**\n\n Como tenemos un triángulo rectángulo y queremos encontrar la altura

$h$ en relación con la hipotenusa

$c$ , podemos usar razones trigonométricas.\n\n * Conocemos un ángulo agudo

$B = 75 grados$ y necesitamos resolver un lado relativo a la hipotenusa.\n\n **3. Aplicar función sinusoidal:**\n\n La función seno

$sin$ relaciona el lado opuesto

$a$ con la hipotenusa

$c$ en un triángulo rectángulo:\n\n pecado

$B$ = a/c\n\n Sabemos que B = 75 grados y queremos encontrar h, pero esta ecuación nos ayuda a encontrar el lado a:\n\n a = c * sin

$B$ = c * sin

$75°$ **

$Ecuación 1$ **\n\n **4. Relacionar otros lados usando trigonometría:**\n\n Como el otro ángulo agudo

$C$ mide 15 grados, podemos encontrar el lado restante

$b$ usando el hecho de que la suma de los ángulos de un triángulo es 180 grados:\n\n A + B + C = 180°\n 90° + 75° + C = 180°\n C = 15°\n\n Ahora, podemos usar la función coseno

$cos$ para relacionar el lado b con la hipotenusa

$c$ :\n\n porque

$C$ = b / c\n\n Sabemos que C = 15 grados, pero no estamos resolviendo directamente b. Esta ecuación es para referencia futura.\n\n **5. Altura relativa

$h$ y lado

$a$ :**\n\n El triángulo ABC es similar a un triángulo rectángulo más pequeño formado por la altura

$h$ , la mitad de la base

$b/2$ y el ángulo recto A. Estos triángulos comparten el mismo ángulo agudo B

$75 grados$ .\n\n Como los lados correspondientes de triángulos semejantes son proporcionales:\n\n h /

$b/2$ = sin

$B$ **

$Ecuación 2$ **\n\n **6. Combinando ecuaciones y resolviendo h:**\n\n Queremos expresar h en términos de c. Ya encontramos a en la ecuación

$1$ : a = c * sin

$75°$ .\n\n Sustituya este valor de a en la ecuación

$2$ :\n\n h /

$b/2$ = pecado

$75°$ \n\n h / [

$c * cos(15°$ )/2] = c * sin

$75°$ **

$sustituyendo b/c de la relación de función cos$ **\n\n **7. Simplificando y aislando h:**\n\n * Simplifica el denominador: h / [c * cos

$15°$ /2] = 2h / c * cos

$15°$ \n * Como cos

$15°$ es un valor positivo

$ángulo agudo$ , podemos multiplicar ambos lados por c * cos

$15°$ :\n 2h = c * sen

$75°$ * cos

$15°$ \n\n * Sabemos que sin

$75°$ * cos

$15°$ se puede expresar como una identidad trigonométrica usando la fórmula de producto por suma:\n pecado

$75°$ * cos

$15°$ =

$sen(90°$ - pecado

$15°$ ) * cos

$15°$ = cos

$15°$ - pecado

$15°$ \n\n * Sustituye esta identidad y resuelve para h:\n 2h = c *

$cos(15°$ - sen

$15°$ )\n h = c *

$cos(15°$ - sen

$15°$ ) / 2\n\n **8. Conclusión:**\n\n Dado que cos

$15°$ y sen

$15°$ son valores positivos

$ángulo agudo$ , su diferencia es positiva. Por lo tanto, h = c *

$cos(15°$ - sin

$15°$ ) / 2 representa un valor positivo que es **un cuarto de la hipotenusa

$c$ **.\n\n Hemos demostrado que en todo triángulo rectángulo con ángulos agudos de 75 y 15 grados, la altura correspondiente a la hipotenusa es igual a un cuarto de la hipotenusa.",355,71,"prove-that-in-every-right-triangle-whose-acute-angles-measure-75-and-15-degrees-the-height-corresponding-to-the-hypotenuse-is-equal-to-a-quarter-of-it",{"id":72,"category":36,"text_question":73,"photo_question":38,"text_answer":74,"step_text_answer":8,"step_photo_answer":8,"views":75,"likes":76,"slug":77},535647,"find the inverse of f

$x$ =2x^

$2$ +7","Given function :\n\u003Cmath-field read-only> f

$x$ =2x^2+7 \u003C/math-field>\n\nLet the function be equal to y :\n\n\u003Cmath-field read-only> y=2x^2+7 \u003C/math-field>\n\nNow, to find the inverse of the function, find the function for x in terms of y.\n\n\u003Cmath-field read-only> y-7=2x^2 \u003C/math-field>\n\n\u003Cmath-field read-only> x^2=\\frac{y-7}{2} \u003C/math-field>\n\n\u003Cmath-field read-only> x=\\sqrt{\\frac{y-7}{2}} \u003C/math-field>\n\nHence, the inverse of the function is :\n\n\u003Cmath-field read-only> f^{-1}

$x$ =\\sqrt{\\frac{x-7}{2}} \u003C/math-field>",397,79,"find-the-inverse-of-f-x-2x-2-7",{"id":79,"category":36,"text_question":80,"photo_question":38,"text_answer":81,"step_text_answer":8,"step_photo_answer":8,"views":82,"likes":83,"slug":84},535646,"Purchases of merchandise on credit

$without signing commercial documents from the supplier$ for the amount of 350,000 plus VAT","Para encontrar el valor total a pagar por la mercancía con el Impuesto al Valor Agregado

$IVA$ , primero necesitamos identificar cuál es la tasa de IVA que se aplica. En México, la tasa de IVA general es del 16%.\u003Cbr />\u003Cbr />1. Calcular el IVA:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>IVA = 350,000 \\times 0.16 = 56,000\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />2. Calcular el total a pagar

$mercancía + IVA$ :\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Total = 350,000 + 56,000 = 406,000\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Por lo tanto, el valor total a pagar por la mercancía con el IVA incluido es de

$\\$ 406,000

$.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{Total = 406,000}\u003C/math-field>\u003C/math-field>",951,190,"purchases-of-merchandise-on-credit-without-signing-commercial-documents-from-the-supplier-for-the-amount-of-350-000-plus-vat",{"id":86,"category":36,"text_question":87,"photo_question":38,"text_answer":88,"step_text_answer":8,"step_photo_answer":8,"views":89,"likes":90,"slug":91},535644,"For a monopolist, the unit cost of manufacturing a product is$ 3 and the demand equation is p= Va. What price will give the greatest profits?","Así es como se puede determinar el precio que generará la mayor ganancia para el monopolista:\n\n **1. Comprender los conceptos**\n\n * **Beneficio:** Ingresos totales menos costo total

$Beneficio = TR - TC$ \n * **Ecuación de demanda:** En este caso, la ecuación de demanda muestra una relación inversa entre el precio

$p$ y la cantidad demandada

$implícita en 'a'$ . A medida que aumenta el precio, la cantidad demandada disminuye.\n * **Monopolista:** Un monopolista tiene el poder de fijar precios para maximizar sus ganancias.\n\n **2. Configurando las ecuaciones**\n\n * **Ingresos Totales

$TR$ :** Precio

$p$ * Cantidad

$q$ . Pero necesitamos expresar la cantidad en términos de precio usando la ecuación de la demanda. Como p = Va, podemos resolver para q: q = p/V\n * TR = p *

$p/V$ = p²/V\n * **Costo total

$CT$ :** Costo unitario

$$3$ * Cantidad

$q$ \n * TC = 3q = 3

$p/V$ \n * **Ganancia:**\n * Beneficio = TR - TC =

$p²/V$ -

$3p/V$ \n\n **3. Encontrar el precio óptimo**\n\n Para maximizar las ganancias, un monopolista producirá donde el ingreso marginal

$MR$ sea igual al costo marginal

$MC$ . Encontremos esos:\n\n * **Ingreso Marginal

$MR$ :** La derivada de TR con respecto a p: MR =

$2p/V$ \n * **Costo Marginal

$MC$ :** La derivada de TC con respecto a p: MC =

$3 / V$ \n\n **4. Ajuste MR = MC**\n\n *

$2p/V$ =

$3/V$ \n * 2p = 3\n * p = 3/2 =

$1.50\n\n **5. Considerando la ecuación de la demanda**\n\n La ecuación de la demanda (p = Va) implica que 'V' es una constante que representa la pendiente de la curva de demanda. Necesitaremos el valor de 'V' para calcular un precio específico. Si V es muy pequeño, incluso el precio óptimo de 1,50 dólares puede no dar como resultado una ganancia positiva.\n\n **En resumen**\n\n * El precio de 1,50 dólares dará las mayores ganancias al monopolista, pero sólo si la curva de demanda permite una ganancia positiva dada la estructura de costos. Necesitará un valor para 'V' en la ecuación de demanda para obtener una respuesta más definitiva.",1494,299,"for-a-monopolist-the-unit-cost-of-manufacturing-a-product-is-3-and-the-demand-equation-is-p-va-what-price-will-give-the-greatest-profits",{"id":93,"category":36,"text_question":94,"photo_question":38,"text_answer":95,"step_text_answer":8,"step_photo_answer":8,"views":96,"likes":97,"slug":98},535643,"Trey and his friend equally share a 12 ounce jar of applesauce how much applesauce in ounces does each person receive?","To find out how much applesauce each person receives, we need to divide the total amount of applesauce by the number of people sharing it.\u003Cbr>\u003Cbr>Let's denote the total amount of applesauce in ounces as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A\u003C/math-field>\u003C/math-field> and the number of people sharing it as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>N\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>Given \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A = 12\u003C/math-field>\u003C/math-field> ounces and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>N = 2\u003C/math-field>\u003C/math-field> people, we can calculate the amount of applesauce each person receives as:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{A}{N} = \\frac{12}{2} = 6\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, each person receives \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{6}\u003C/math-field>\u003C/math-field> ounces of applesauce. \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\textbf{Answer:}\u003C/math-field>\u003C/math-field> Each person receives 6 ounces of applesauce.",335,67,"trey-and-his-friend-equally-share-a-12-ounce-jar-of-applesauce-how-much-applesauce-in-ounces-does-each-person-receive",{"id":100,"category":36,"text_question":101,"photo_question":38,"text_answer":102,"step_text_answer":8,"step_photo_answer":8,"views":103,"likes":104,"slug":105},535642,"a tortoise is walking in the desert. It walks for 9.6 meters at a speed of 6 meters per minute. For how many minutes does it walk?","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$ \\begin{matrix}6\\overline{|9.6}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{matrix}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$\\begin{matrix}\\:\\:\\:\\:1.\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\6\\overline{|9.6}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{6}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:36\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{matrix}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$\\begin{matrix}\\:\\:\\:\\:1.6\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\6\\overline{|9.6}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{6}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:36\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{36}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:0\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{matrix}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$1.6$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1414,283,"a-tortoise-is-walking-in-the-desert-it-walks-for-9-6-meters-at-a-speed-of-6-meters-per-minute-for-how-many-minutes-does-it-walk",{"id":107,"category":36,"text_question":108,"photo_question":38,"text_answer":109,"step_text_answer":8,"step_photo_answer":8,"views":110,"likes":111,"slug":112},535641,"You collect a random sample of 50 children and compute , the average height in inches. The sample standard deviation (s) equals 10. Suppose the true mean height μ equals 45 inches. For which of the following values of will a 95% confidence interval contain the true mean μ?\n\nI. = 47.5 inches \n\nII. = 50 inches \n\nIII. = 42 inches","We can use the formula for a confidence interval:\u003Cbr />\u003Cbr />Confidence Interval = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bar{x} \\pm z \\times \\frac{s}{\\sqrt{n}}\u003C/math-field>\u003C/math-field>,\u003Cbr />\u003Cbr />where:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bar{x}\u003C/math-field>\u003C/math-field> is the sample mean,\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z\u003C/math-field>\u003C/math-field> is the Z-value for the desired confidence level (95% in this case),\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s\u003C/math-field>\u003C/math-field> is the sample standard deviation,\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n\u003C/math-field>\u003C/math-field> is the sample size.\u003Cbr />\u003Cbr />Given values:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bar{x} = \\mu = 45\u003C/math-field>\u003C/math-field> inches,\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = 10\u003C/math-field>\u003C/math-field> inches,\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 50\u003C/math-field>\u003C/math-field> children,\u003Cbr />For 95% confidence level, the Z-value is 1.96 (you can refer to Z-table for this value).\u003Cbr />\u003Cbr />Plugging in these values we get:\u003Cbr />\u003Cbr />I. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>CI_{I} = 47.5 \\pm 1.96 \\times \\frac{10}{\\sqrt{50}}\u003C/math-field>\u003C/math-field>, \u003Cbr />\u003Cbr />II. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>CI_{II} = 50 \\pm 1.96 \\times \\frac{10}{\\sqrt{50}}\u003C/math-field>\u003C/math-field>, \u003Cbr />\u003Cbr />III. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>CI_{III} = 42 \\pm 1.96 \\times \\frac{10}{\\sqrt{50}}\u003C/math-field>\u003C/math-field>. \u003Cbr />\u003Cbr />Calculating these confidence intervals gives:\u003Cbr />\u003Cbr />I. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>CI_{I} = 47.5 \\pm 2.78\u003C/math-field>\u003C/math-field>, \u003Cbr />II. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>CI_{II} = 50 \\pm 2.78\u003C/math-field>\u003C/math-field>, \u003Cbr />III. \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>CI_{III} = 42 \\pm 2.78\u003C/math-field>\u003C/math-field>. \u003Cbr />\u003Cbr />Only the 95% confidence interval for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>I.\u003C/math-field>\u003C/math-field> contains the true mean height \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>45\u003C/math-field>\u003C/math-field> inches.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\text{Answer: I. } \\mu = 47.5 \\text{ inches}}\u003C/math-field>\u003C/math-field>",613,123,"you-collect-a-random-sample-of-50-children-and-compute-the-average-height-in-inches-the-sample-standard-deviation-s-equals-10-suppose-the-true-mean-height-u-equals-45-inches-for-which-of-the-f",{"id":114,"category":36,"text_question":115,"photo_question":38,"text_answer":116,"step_text_answer":8,"step_photo_answer":8,"views":117,"likes":48,"slug":118},535639,"You conduct a poll of FIU students in order to determine the percentage of students (p) who agree with the statement “Hot-dogs are one of my favorite foods”. In your poll, you find that 80 out of 100 students agree. You conduct a two-sided hypothesis test where H0: p = 0.7, where p is the proportion of students whose favorite food is hot dogs. Which of the following statements are true:\n I. You reject the null hypothesis when α = 0.05\n II. You reject the null hypothesis when α = 0.01\nIII. The test statistic (Z) equals Z = +1.5","statement I is true.\n\n\nYou reject the null hypothesis when α = 0.05",472,"you-conduct-a-poll-of-fiu-students-in-order-to-determine-the-percentage-of-students-p-who-agree-with-the-statement-hot-dogs-are-one-of-my-favorite-foods-in-your-poll-you-find-that-80-out-of-100",{"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},535638,"You collect data on N = 25 student weights and find that the average student weight in your sample is 135 pounds. The sample standard deviation (s) is 5 pounds. You conduct a two-sided hypothesis test where H0: μ = 134 pounds. Which of the following statements are true:\n\n I. You reject the null hypothesis when α = 0.05\n\n II. You reject the null hypothesis when α = 0.01\n\n III. The test statistic (T) equals T = +1","test stats = \u003Cmath-field read-only> \\frac{135-134}{\\frac{5}{\\sqrt{25}}}=\\frac{1}{1}=1 \u003C/math-field>\n\nChoice III correct.",1098,220,"you-collect-data-on-n-25-student-weights-and-find-that-the-average-student-weight-in-your-sample-is-135-pounds-the-sample-standard-deviation-s-is-5-pounds-you-conduct-a-two-sided-hypothesis-t",{"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},535637,"How much must be invested today, March 1, 2024 to make equal quarterly withdrawals due for $2,500\n each during 2022, if deposits earn interest at 8% CT?","Para este problema, utilizaremos la fórmula del valor presente de una anualidad ordinaria:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP = \\dfrac{R \\times (1 - (1 + i)^{-n})}{i}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Donde:\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP\u003C/math-field>\u003C/math-field> es el valor presente total de la anualidad\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>R\u003C/math-field>\u003C/math-field> es la cantidad de cada retiro (en este caso $2,500)\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>i\u003C/math-field>\u003C/math-field> es la tasa de interés por periodo (en este caso trimestral, es decir 8%/4 = 2% o 0.02)\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n\u003C/math-field>\u003C/math-field> es el número total de periodos en la anualidad (en este caso serán 12 periodos para los cuatro retiros trimestrales de 2022)\u003Cbr>\u003Cbr>Sustituyendo los valores dados en la fórmula:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP = \\dfrac{2500 \\times (1 - (1 + 0.02)^{-12})}{0.02}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Simplificando:\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP = \\dfrac{2500 \\times (1 - 0.8194)}{0.02}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP = \\dfrac{2500 \\times 0.1806}{0.02}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP = \\dfrac{451.5}{0.02}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>VP = \\\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Por lo tanto, se deberán invertir \\ \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>22,575 hoy, marzo 1 de 2024 para poder realizar retiros trimestrales vencidos iguales por \\\u003C/math-field>\u003C/math-field> 2,500 cada uno durante 2022 y obtener un interés del 8% CT.\u003Cbr>\u003Cbr>\\textbf{Respuesta:} Se deberán invertir \\$22,575 hoy.",1317,263,"how-much-must-be-invested-today-march-1-2024-to-make-equal-quarterly-withdrawals-due-for-2-500-each-during-2022-if-deposits-earn-interest-at-8-ct",{"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},535636,"For the function f(x), the real number a where f(a)=a is called the fixed point of the function f(x). Show that when f(x) is continuous and differentiable for all real numbers x, if f’(x)≠1, then f(x) has at most one fixed point.","To show that when \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x)\u003C/math-field>\u003C/math-field> is continuous and differentiable for all real numbers \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>, if \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f'(x) \\neq 1\u003C/math-field>\u003C/math-field>, then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x)\u003C/math-field>\u003C/math-field> has at most one fixed point, we can use the Mean Value Theorem.\u003Cbr />\u003Cbr />Let's assume that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x)\u003C/math-field>\u003C/math-field> has two fixed points, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b\u003C/math-field>\u003C/math-field>, where \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a \\neq b\u003C/math-field>\u003C/math-field>. This means that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(a) = a\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(b) = b\u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />By the Mean Value Theorem, there exists a value \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>c\u003C/math-field>\u003C/math-field> between \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b\u003C/math-field>\u003C/math-field> such that:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f'(c) = \\frac{f(b) - f(a)}{b - a}\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Since \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(a) = a\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(b) = b\u003C/math-field>\u003C/math-field>, we have:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f'(c) = \\frac{b - a}{b - a} = 1\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />This contradicts the given condition that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f'(x) \\neq 1\u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />Therefore, our assumption that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x)\u003C/math-field>\u003C/math-field> has two distinct fixed points is incorrect. Hence, the function \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x)\u003C/math-field>\u003C/math-field> has at most one fixed point.\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\text{Answer}}\u003C/math-field>\u003C/math-field>: the function \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f(x)\u003C/math-field>\u003C/math-field> has at most one fixed point.",1223,245,"for-the-function-f-x-the-real-number-a-where-f-a-a-is-called-the-fixed-point-of-the-function-f-x-show-that-when-f-x-is-continuous-and-differentiable-for-all-real-numbers-x-if-f-x-1-then-f-x",{"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},535635,"Example 2:\n The head of the faculty library states that the average number of students who visit it per day is 350. To confirm or not this assumption, the number of attendees for 30 days is recorded and it is found that the average was 372.6. If the standard deviation of 52.414 and a significance level of 0.05 is considered, say whether you would support what the head of the library says.","We can use a one-sample t-test to determine if the average number of students who visit the library per day is significantly different from 350.\u003Cbr>\u003Cbr>Given data:\u003Cbr>- Null hypothesis, Ho: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mu = 350\u003C/math-field>\u003C/math-field> (average number of students per day is 350)\u003Cbr>- Alternative hypothesis, Ha: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mu \\neq 350\u003C/math-field>\u003C/math-field> (average number of students per day is not 350)\u003Cbr>- Sample mean, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\bar{x} = 372.6\u003C/math-field>\u003C/math-field> \u003Cbr>- Population standard deviation, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sigma = 52.414\u003C/math-field>\u003C/math-field> \u003Cbr>- Sample size, n = 30\u003Cbr>- Significance level, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\alpha = 0.05\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Calculate the t-score:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t = \\frac{\\bar{x} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Substitute the values:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t = \\frac{372.6 - 350}{\\frac{52.414}{\\sqrt{30}}}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t\\approx2.362\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Find the critical t-value at a significance level of 0.05 with degrees of freedom (df) = n-1 = 29 using a t-table or calculator.\u003Cbr>\u003Cbr>Since this is a two-tailed test, we need to look for the critical t-value at \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\alpha/2 = 0.025\u003C/math-field>\u003C/math-field> for df = 29.\u003Cbr>\u003Cbr>The critical t-value is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\pm 2.045\u003C/math-field>\u003C/math-field> for df = 29.\u003Cbr>\u003Cbr>Compare the calculated t-value with the critical t-value:\u003Cbr>Since 2.366 > 2.045, we reject the null hypothesis.\u003Cbr>\u003Cbr>Therefore, we have enough evidence to reject the head of the faculty library's claim that the average number of students who visit the library per day is 350. Instead, the average number of students is significantly different from 350. \u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{ \\text{Answer: We reject the null hypothesis. The head of the faculty library claim is not supported.} }\u003C/math-field>\u003C/math-field>",474,95,"example-2-the-head-of-the-faculty-library-states-that-the-average-number-of-students-who-visit-it-per-day-is-350-to-confirm-or-not-this-assumption-the-number-of-attendees-for-30-days-is-recorded-a",{"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},535634,"three times a number increased by 44 is the same as the opposite of the number. Find The number","Let's denote the number as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>.\u003Cbr />\u003Cbr />According to the given conditions, we can write the equation:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 44 = -x\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />Now, let's solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 44 = -x\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + x = -44\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = -44\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\dfrac{-44}{4}\u003C/math-field>\u003C/math-field> \u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -11\u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{x = -11}\u003C/math-field>\u003C/math-field>",1219,244,"three-times-a-number-increased-by-44-is-the-same-as-the-opposite-of-the-number-find-the-number",{"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},535633,"Divide, if possible: 2.96/0","To divide by 0 is undefined in mathematics. Any number divided by 0 is undefined. \u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\text{Answer: Division by 0 is undefined.}}\u003C/math-field>\u003C/math-field>",316,63,"divide-if-possible-2-96-0",{"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},535632,"sean weighs 10 lb more than twice brads weight. if brad gains 10 lb, together they’ll weigh 230 lb. how much does each weigh now?","Let's denote Brad's current weight as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> lbs. \u003Cbr>\u003Cbr>According to the problem, Sean weighs 10 lbs more than twice Brad's weight, so Sean's current weight is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x + 10\u003C/math-field>\u003C/math-field> lbs.\u003Cbr>\u003Cbr>If Brad gains 10 lbs, his weight will be \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 10\u003C/math-field>\u003C/math-field> lbs.\u003Cbr>\u003Cbr>Together, Brad and Sean weigh 230 lbs, so we have the equation:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x+10+(2x+10)=230\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Solving for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> :\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x+20=230\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x=210\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x=\\frac{210}{3}\u003C/math-field>\u003C/math-field> \u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x=70\\text{ lbs}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>So, Brad's current weight is approximately 70 lbs.\u003Cbr>\u003Cbr>Plugging this back into the expression for Sean's weight:\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2(70\\overline{})+10=2\\times70\\overline{}+10=150\\text{ lbs}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, Brad currently weighs approximately 73.3 lbs and Sean currently weighs approximately 156.6 lbs.\u003Cbr>\u003Cbr> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{\\text{Brad: 70 lbs, Sean: 150 lbs}}\u003C/math-field>\u003C/math-field>",1205,241,"sean-weighs-10-lb-more-than-twice-brads-weight-if-brad-gains-10-lb-together-they-ll-weigh-230-lb-how-much-does-each-weigh-now",{"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},535631,"What is 95% of 200?","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$=200\\times \\frac{95}{100}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$=200\\times \\frac{19}{20}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$=190$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1276,255,"what-is-95-of-200",{"first":6,"last":176,"prev":177,"next":178},188,105,107,{"current_page":180,"from":181,"last_page":176,"links":182,"path":216,"per_page":217,"to":218,"total":219},106,2101,[183,186,188,190,193,196,198,201,203,206,209,212,214],{"url":177,"label":184,"active":185},"« Previous",false,{"url":6,"label":187,"active":185},"1",{"url":10,"label":189,"active":185},"2",{"url":191,"label":192,"active":185},103,"103",{"url":194,"label":195,"active":185},104,"104",{"url":177,"label":197,"active":185},"105",{"url":180,"label":199,"active":200},"106",true,{"url":178,"label":202,"active":185},"107",{"url":204,"label":205,"active":185},108,"108",{"url":207,"label":208,"active":185},109,"109",{"url":210,"label":211,"active":185},187,"187",{"url":176,"label":213,"active":185},"188",{"url":178,"label":215,"active":185},"Next »","https://api.math-master.org/api/question",20,2120,3741,{"data":221},{"questions":222},[223,227,231,235,239,243,247,251,255,259,263,267,271,275,279,283,287,291,295,299],{"id":224,"category":36,"text_question":225,"slug":226},532005,"A=m/2-t isolate t","a-m-2-t-isolate-t",{"id":228,"category":36,"text_question":229,"slug":230},532008,"1 + 1","1-1",{"id":232,"category":36,"text_question":233,"slug":234},532052,"-6n+5=-13","6n-5-13",{"id":236,"category":36,"text_question":237,"slug":238},532071,"A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?","a-normally-distributed-population-has-a-mean-of-118-with-a-standard-deviation-of-18-what-score-separates-the-lowest-72-of-the-distribution-from-the-rest-of-the-scores",{"id":240,"category":36,"text_question":241,"slug":242},532083,"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)?","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":244,"category":36,"text_question":245,"slug":246},533912,"By differentiating the function f(x)=(x³−6x)⁷ we will obtain","by-differentiating-the-function-f-x-x-6x-we-will-obtain",{"id":248,"category":36,"text_question":249,"slug":250},534004,"Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places","suppose-50-of-the-doctors-and-hospital-are-surgeons-if-a-sample-of-576-doctors-is-selected-what-is-the-probability-that-the-sample-proportion-of-surgeons-will-be-greater-than-55-round-your-answer-to",{"id":252,"category":36,"text_question":253,"slug":254},534017,"(2x+5)^3+(x-3)(x+3)","2x-5-3-x-3-x-3",{"id":256,"category":36,"text_question":257,"slug":258},534055,"7/6-(-1/9)","7-6-1-9",{"id":260,"category":36,"text_question":261,"slug":262},534147,"2x+4x=","2x-4x",{"id":264,"category":36,"text_question":265,"slug":266},534174,"find f(x) for f'(x)=3x+7","find-f-x-for-f-x-3x-7",{"id":268,"category":36,"text_question":269,"slug":270},534200,"suppose random variable x follows poisson distribution with expected value 3. what is variance of x?","suppose-random-variable-x-follows-poisson-distribution-with-expected-value-3-what-is-variance-of-x",{"id":272,"category":36,"text_question":273,"slug":274},534240,"A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall","a-storage-maker-price-is-2-50-per-square-feet-find-the-price-of-a-custom-shed-4-yards-long-and-5yards-wide-and-8-feet-tall",{"id":276,"category":36,"text_question":277,"slug":278},534320,"1. A capital of $3,831 was lent, and it has produced interest of $840 from 05-12-2022 to 1-12-2023. At what annual simple interest rate was the capital lent?","1-a-capital-of-3-831-was-lent-and-it-has-produced-interest-of-840-from-05-12-2022-to-1-12-2023-at-what-annual-simple-interest-rate-was-the-capital-lent",{"id":280,"category":36,"text_question":281,"slug":282},534333,"-1%2F2x-4%3D18","1-2f2x-4-3d18",{"id":284,"category":36,"text_question":285,"slug":286},534376,"For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?","for-what-values-of-m-is-point-p-m-1-2m-in-the-2-quadrant",{"id":288,"category":36,"text_question":289,"slug":290},534427,"Find the zero of the linear function 8x + 24 = 0","find-the-zero-of-the-linear-function-8x-24-0",{"id":292,"category":36,"text_question":293,"slug":294},534485,"X^X =49 X=?","x-x-49-x",{"id":296,"category":36,"text_question":297,"slug":298},534571,"A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?","a-group-of-17-people-spent-9-days-on-vacation-and-spent-r-776-34-on-barbecue-meat-and-the-bill-needs-to-be-divided-as-follows-6-people-stayed-for-9-days-7-people-stayed-for-4-days-and-2-people-stay",{"id":300,"category":36,"text_question":301,"slug":302},534620,"The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?","the-perimeter-of-a-rectangular-rug-is-42-feet-the-width-is-9-feet-what-is-the-length",{"data":304},[305,314,323,332,344,353,362,371,383,391,401,409,421,430,436,443,451,461,468,478],{"id":306,"name":307,"photo":308,"certificates":309,"diplomas":311,"biography":312,"rating":313,"total_answer":48},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp",[310],"https://api.math-master.org/img/experts/19/certificates/certif.webp",[],"I had very much interest from the Starting with simple addition and multiplication, my math journey led me to tackle more challenging problems. What I love most about math is how it's like a puzzle-solving adventure. It helps us understand things around us by finding patterns and connections. It's like a secret code that unveils the mysteries of the world, and I enjoy how each solution feels like a small victory. Math is like a playground for our imagination, where we can come up with creative ways to solve problems and learn new things. It's all about exploring, discovering, and having fun along the way.",4.9,{"id":315,"name":316,"photo":317,"certificates":318,"diplomas":319,"biography":321,"rating":313,"total_answer":322},18,"Nash","https://api.math-master.org/img/experts/18/18.webp",[],[320],"https://api.math-master.org/img/experts/18/diplomas/diploma.webp","My interest in mathematics boomed in my school days which led me to choose mathematics as my core subject in college and later pursue Engineering in University. I have been working at MathMaster for 10 months now and the fact that I like solving math tasks makes me interested in this field. I can work part-time at any available shift for the day and not get exhausted. Moreover solving math tasks keep my brain sharp and focused.\n\n",85,{"id":324,"name":325,"photo":326,"certificates":327,"diplomas":329,"biography":331,"rating":313,"total_answer":204},15,"Miles","https://api.math-master.org/img/experts/15/15.webp",[328],"https://api.math-master.org/img/experts/15/certificates/2fd3f3a1-34c4-417d-a85a-1459c7fc0356.webp",[330],"https://api.math-master.org/img/experts/15/diplomas/diploma.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",{"id":13,"name":333,"photo":334,"certificates":335,"diplomas":339,"biography":341,"rating":342,"total_answer":343},"Timmothy","https://api.math-master.org/img/experts/3/3.webp",[336,337,338],"https://api.math-master.org/img/experts/3/certificates/14d1b957-4891-43e9-b5bc-07fdd4d9af21.webp","https://api.math-master.org/img/experts/3/certificates/27b13919-712a-4712-b27a-e09fc16c774f.webp","https://api.math-master.org/img/experts/3/certificates/b70a3a4e-33de-47d7-b0a5-9fbefe397734.webp",[340],"https://api.math-master.org/img/experts/3/diplomas/19c9addf-312a-4437-af41-e89bc3843209 (1).webp","Hello, I'm Jamil Omar, and I want to take you on a journey through my experience with math, from school to university.\nEarly School Years:\nHigh school marked the beginning of my mathematical journey, a journey that started with skepticism but transformed into something wonderful. At first, I wasn't a fan of math, until a special teacher changed everything. This teacher showed me the beauty of math, and suddenly, everything clicked.\nBecause of this teacher, I started enjoying math and even joined math competitions during my high school days. Surprisingly, I excelled and became a champion at both the provincial and regional levels. These wins boosted my confidence and made me realize that I could excel in math.\nThese victories also gave me the confidence to pursue an engineering degree in college. Thanks to that teacher and my successes in math, I knew I could conquer new challenges and make the most of my education journey.\nUniversity Journey:\nMy strong grasp of mathematics inspired me to pursue a bachelor's degree in Petroleum Engineering at Palawan State University. Confident in my mathematical foundation, I embarked on this academic journey.\nThroughout the course, I discovered that my solid background in mathematics was a true asset. It enabled me to better comprehend the intricate topics within Petroleum Engineering and successfully complete the program.\nMy enthusiasm for engineering led me to actively engage in quiz bee contests, where sharp mathematical skills are crucial for success. Our team's victory in these contests opened doors to a national quiz bee in our country. This experience not only honed my mathematical abilities but also granted us the privilege to participate in seminars related to our field of study.\nOne of my achievements was securing the top rank in our departmental exam for algebra. During my first year in college, I outperformed all other first-year students across the university. This accomplishment underscores the significant impact of mathematics on my academic journey.\nStudying math has proven to be invaluable, not just in terms of academic achievements but also in enhancing my analytical skills and enabling me to earn a degree in Petroleum Engineering.",4.8,96,{"id":345,"name":346,"photo":347,"certificates":348,"diplomas":349,"biography":351,"rating":342,"total_answer":352},22,"Hank","https://api.math-master.org/img/experts/22/22.webp",[],[350],"https://api.math-master.org/img/experts/22/diplomas/12.webp","When I was in elementary and middle school, I did not feel the importance and beauty of mathematics, but when I joined the secondary stage, I began to feel the beauty and importance of mathematics, and I excelled in mathematics. I joined the College of Education, Department of Mathematics, and now I am a mathematics teacher.\nThen after that, I got a master's degree and a doctorate in curricula and methods of teaching mathematics.",100,{"id":354,"name":355,"photo":356,"certificates":357,"diplomas":358,"biography":360,"rating":342,"total_answer":361},35,"Hester","https://api.math-master.org/img/experts/35/35.webp",[],[359],"https://api.math-master.org/img/experts/35/diplomas/03849782-84d8-46fb-b7ed-7e3204335b13.webp","Mathematics has been my favourite subject since childhood. I studied mathematics in secondary education and secured full marks in this subject which gave me great joy and boost as i was attached to this subject. Then I opted Pre-Engineering in my higher secondary education which was mainly about the mathematics. Then I got admission in Engineering University which is ranked as Number 1 Engineering University of my country and studied different subjects of mathematics there on graduate level. I really enjoy while solving the maths questions and get too much involved in the basics and different branches of maths as it is referred as mother of sciences and I am emotionally attached to this subject.\r\n\r",115,{"id":363,"name":364,"photo":365,"certificates":366,"diplomas":368,"biography":370,"rating":342,"total_answer":204},14,"Brice","https://api.math-master.org/img/experts/14/14.webp",[367],"https://api.math-master.org/img/experts/14/certificates/a53728ab-4dc7-40ba-8d75-9938dd4881d9.webp",[369],"https://api.math-master.org/img/experts/14/diplomas/240b3c4c-3403-49ef-aab8-6caa8f694f93.webp","Muhammad Farooq here. I have done Bachelor's in Electrical Engineering and in my institute mode of studying was in English. Though I don not posses and certificate of diploma in English as it costs much here in Pakistan and I was not required to submit this certificate anywhere, though my courses in English as well mathematics are mentioned in my School as well collage certificate so you can check my record in these certificates",{"id":372,"name":373,"photo":374,"certificates":375,"diplomas":378,"biography":380,"rating":381,"total_answer":382},28,"Esmeralda","https://api.math-master.org/img/experts/28/28.webp",[376,377],"https://api.math-master.org/img/experts/28/certificates/883 C.webp","https://api.math-master.org/img/experts/28/certificates/883 CC.webp",[379],"https://api.math-master.org/img/experts/28/diplomas/883 D.webp","From an early age, I've been captivated by the enchanting world of mathematics. It all began during my childhood when the mere sight of numbers and equations ignited a spark within me. This fascination evolved into a lifelong passion, shaping my journey into becoming a dedicated math enthusiast.\r\n\r\nThroughout my formative years in both primary and secondary school, I eagerly participated in various math contests, emerging victorious and accumulating a treasure trove of accolades that celebrated my mathematical prowess. As I embarked on my college journey, I chose a bachelor's degree program that seamlessly intertwined mathematics with computational problem-solving.\r\n\r\nStepping into the realm of teaching was a natural progression for me. Armed with a deep reservoir of mathematical knowledge and an innate ability to explain complex concepts in simple terms, I found myself guiding college entrance exam reviewees through the intricacies of algebra, geometry, trigonometry, and pre-calculus. In the interstices of my journey, I also dabbled in the realm of freelance mathematics. With the luxury of time, I engaged in tackling a diverse array of mathematical problems and coursework. This not only honed my skills further but also cemented my belief that mathematics, while a field of study, is also a boundless realm of exploration and creativity.",4.7,98,{"id":384,"name":385,"photo":386,"certificates":387,"diplomas":388,"biography":389,"rating":381,"total_answer":390},12,"Madelyn","https://api.math-master.org/img/experts/12/12.webp",[],[],"i am kishan kushavaha from india. i am completed my primary education from jawahar Navodaya vidhyalaya Rath hamirpur utter pradesh India. Currently I am pursuing Btech degree in computer science and engineering. Math my favorite subject i am feel very happyness solving the math problems.",86,{"id":392,"name":393,"photo":394,"certificates":395,"diplomas":399,"biography":400,"rating":381,"total_answer":194},13,"Maude","https://api.math-master.org/img/experts/13/13.webp",[396,397,398],"https://api.math-master.org/img/experts/13/certificates/664eea5b-1c59-4243-bed8-3a2ffba05ef7.webp","https://api.math-master.org/img/experts/13/certificates/bccb93ad-6ae1-4c1f-bc57-5c2fc5c479b5.webp","https://api.math-master.org/img/experts/13/certificates/cd4c4772-1927-4836-ad8e-340300efad86.webp",[],"i always fond of math ,TILL my matriculation to graduation math is my fvrt subject\nwhen i was in 9th class i had a teacher named as Sir Saleem this is now died but he was bestest teacher ever\nHe teach us each and every question of every exercise of my book of mathematics and what i do is write all those questions in my register as it is and practiced a lot this build my basics and keep them strong i am highly obliged to my sir May God give him high place in jannah ..\nso come to story i have digested too much math in my mind that when i gave math final exams of board i was too much confident and just revise definitions included in course and did not do any question by hand because every question is remembered by heart , i just go through by my register and believe me i got 74/75 marks . this was my initiation in math field that go wide and wide in other fields of math.\nMy interest in mathematics grew as it related to algorithms and data. I moved up into the complexity of algebra and geometry from arithmetic's simplicity because I was fascinated by their complexities. Calculus revealed the language of transformation, while number theory and abstract algebra drove me farther into abstraction. My ability to do rigorous and challenging analysis was put to the test, building a link to the very core of patterns and structures.\n\nThe applications of theory were made possible by probability, statistics, and discrete mathematics, demonstrating the usefulness of mathematical techniques. I incorporated mathematical ideas into my digital self as the digital era developed, optimizing, forecasting, and innovating.\n\n\n\nMy story is a never-ending quest that is inextricably linked to the beauty and logic of mathematics.",{"id":402,"name":403,"photo":404,"certificates":405,"diplomas":406,"biography":407,"rating":381,"total_answer":408},7,"Cristian","https://api.math-master.org/img/experts/7/7.webp",[],[],"I embarked on my academic journey as a sports enthusiast, prior to enrolling in my undergraduate studies. My enthusiasm for mathematics had always been muted, largely owing to the seemingly endless and purposeless calculations it often involved. However, a transformative experience awaited me during my time in college. It was there that I encountered a teacher who, in our very first class, presented a simple yet profound exercise: to complete the sentence \"Mathematics is _______\" with a single word that encapsulated our immediate perception of the subject.\nI hesitated briefly before filling the blank space with the word \"boring.\" To my surprise, my teacher chose the word \"beautiful.\" This striking contrast sparked my curiosity and set the stage for a remarkable journey of discovery. Guided by her teaching and insights, it took me a span of two to three months to truly grasp the hidden allure of mathematics. What I once considered mere calculations revealed themselves to be the building blocks of exquisite mathematical and geometric forms.\nThis revelation marked the turning point in my relationship with mathematics. I came to realize that nothing in the realm of mathematics is devoid of purpose or significance. Behind every calculation lies a tapestry of captivating patterns and shapes. As I delved deeper into the core concepts, my appreciation for the elegance and depth of mathematics grew exponentially.\nThis newfound passion became the bedrock of my academic pursuits. It paved the way for my entrance into the world of mathematical exploration, ultimately leading me to pursue a PhD in mathematics. The journey has brought me under the mentorship of an esteemed 80-year-old supervisor, a venerable professor renowned for his wisdom, at Jacobs University in Germany.\nLooking back, I can trace the evolution of my perspective from skepticism to fascination, all catalyzed by a single teacher's belief in the beauty that mathematics holds. With each step I take in my academic journey, I am reminded that the seeds of interest and passion can be sown in the most unexpected of places, transforming the trajectory of one's life in ways that are both profound and deeply fulfilling.",112,{"id":410,"name":411,"photo":412,"certificates":413,"diplomas":418,"biography":419,"rating":381,"total_answer":420},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[414,415,416,417],"https://api.math-master.org/img/experts/16/certificates/00f2469c-54a4-4a86-a1bd-058b62670da1.webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4 (1).webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4.webp","https://api.math-master.org/img/experts/16/certificates/f073e340-308d-4d20-ab38-8b2c9598137b.webp",[],"Hi,\nI've loved Mathematics and critical thinking for as long as I can remember. I started tutoring my fellow students in grade 6. I've studied Maths in the Faculty of Science. I started tutoring online 10 years ago. I've taken a lot of courses to help me teach the STEM curriculum better ever since.\nRegards\nRania",91,{"id":22,"name":422,"photo":423,"certificates":424,"diplomas":427,"biography":429,"rating":381,"total_answer":48},"Jett","https://api.math-master.org/img/experts/6/6.webp",[425,426],"https://api.math-master.org/img/experts/6/certificates/a05d6f13-1579-47ba-9f4d-1379fd868a32.webp","https://api.math-master.org/img/experts/6/certificates/fcc9c87f-66d3-4474-adfd-13fee92c6090.webp",[428],"https://api.math-master.org/img/experts/6/diplomas/ff175d15-b3af-4041-89fc-d9ac937be8d4.webp","Hello,\nI am pleased to introduce myself as a Mathmaster Expert 😊\nI am Engr. Paul Eejay Dy, a Registered Civil Engineer in the Philippines and Mathematics has always been my favorite subject.\nStudying Mathematics is a really difficult but fun experience for me and with the help of really great teachers and professors that helped me on this journey, I overcame all the obstacles that came my way until I achieved my dream profession.\nSo for all Mathmaster users, it is a great pleasure to be part of your journey into this rough but fulfilling journey of studying Mathematics. Study hard, and keep fighting for your dreams 😇🙏",{"id":19,"name":431,"photo":432,"certificates":433,"diplomas":434,"biography":435,"rating":381,"total_answer":177},"Rasheed","https://api.math-master.org/img/experts/5/5.webp",[],[],"Born with an insatiable curiosity, I began my journey with mathematics during my school years. From solving basic arithmetic problems to unraveling complex algebraic equations, I developed a deep passion for the subject. Upon entering university, my learnings diving into advanced topics like abstract algebra, numerical analysis and differential equations.\nIn retrospect, my journey through the realm of mathematics has been an exhilarating adventure of discovery, learning, and growth.\n",{"id":437,"name":438,"photo":439,"certificates":440,"diplomas":441,"biography":442,"rating":381,"total_answer":204},34,"Dexter","https://api.math-master.org/img/experts/34/34.webp",[],[],"I had done my schooling in SPHS, one of premier academic institutions in the city which covered all courses upto K-12. Mathematics had always been my forte, love & passion which earned me a good amount of reputation and accreditation at various phases of my career. My penchant in Maths was observed by my professors in school who did not hesitate to shower me the honour of one of the best mathematics students taught by them. I had a straight A in Mathematics and related sciences right from school to university level. After crossing the barrier of high school with elan, I did not hesitate to continue my graduation in Mathematics major from JU which enlists within the top 5 universities in the country. I stood first in my faculty in the final year of graduation with 85% score amounting to GPA 4.0. During the 3 year graduation, I silently earned the recognition of the top Mathematics student of the class in the eyes of my professors and my fellow students who used to crowd around me when they got stuck in any topic of maths. Overall my journey as a student of Mathematics was challenging, rewarding, enriching and a superbly enjoyable phase of my career. ",{"id":10,"name":444,"photo":445,"certificates":446,"diplomas":447,"biography":449,"rating":450,"total_answer":191},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[448],"https://api.math-master.org/img/experts/2/diplomas/1ea09f59-7559-4ce7-8bad-50bcc43ea9ed.webp","My names is James Agustin Molina, I am from Philippines. Back when I in high school, I was not the best in Math in my class; but, If I were to compare my math skills to my other subjects, I think Math is my best subject. I always find solving and learning math techniques fun. Because I think my Math is the my best subject and I always fascinated in how things work, I took engineering in my college. In college, I really enjoyed math and thinking of pursuing a teaching career. I also took and passed my licensure exam right after graduation. Currently, I am taking my Masters Degree in Mathematics.",4.6,{"id":452,"name":453,"photo":454,"certificates":455,"diplomas":456,"biography":460,"rating":450,"total_answer":180},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp",[],[457,458,459],"https://api.math-master.org/img/experts/29/diplomas/458 2.webp","https://api.math-master.org/img/experts/29/diplomas/458 d.webp","https://api.math-master.org/img/experts/29/diplomas/458 dd.webp","In my school days I was not good in Mathematics but there was something which always attracted me towards Mathematics as playing with numbers and doing round of questions of different exercises of workbook was fun for me and as a hobby I inclined to Math's. I never thought of teaching mathematics and making a career out of it but somethings bound to happen.",{"id":462,"name":463,"photo":464,"certificates":465,"diplomas":466,"biography":467,"rating":450,"total_answer":145},30,"Bud","https://api.math-master.org/img/experts/30/30.webp",[],[],"I started my mathematics journey when i was in school and i went for a lot of competitions in mathematics back then and after worth, i proceeded into the university to study Electronics and Electrical Engineering and the course of studying it, i came across a lot of mathematics course which grounded me alot in mathematics.",{"id":469,"name":470,"photo":471,"certificates":472,"diplomas":473,"biography":476,"rating":450,"total_answer":477},31,"Frederik","https://api.math-master.org/img/experts/31/31.webp",[],[474,475],"https://api.math-master.org/img/experts/31/diplomas/344.webp","https://api.math-master.org/img/experts/31/diplomas/344D.webp","Hi, my name is Nitin,\r\nI started taking an interest in maths, because of my grandfather, who was a maths professor at HNBGU University, initially, I was not that good at maths, but with practice, I improved a lot, and I became pretty good at it when I got excellent marks in class 10th maths, I chose maths as my primary subject I completed my college and graduation, currently I am pursuing my master, I loved teaching maths, I also teach maths in a local school, and I want to become a professor in maths just like my grandfather.",97,{"id":479,"name":480,"photo":481,"certificates":482,"diplomas":484,"biography":486,"rating":450,"total_answer":204},21,"Jon","https://api.math-master.org/img/experts/21/21.webp",[483],"https://api.math-master.org/img/experts/21/certificates/41e2a05c-d94f-4bcc-9258-f2a7fe4c3c02.webp",[485],"https://api.math-master.org/img/experts/21/diplomas/9258cda6-9255-4b34-8806-23628b0a8153.webp","I passed my matric from Govt.City Muslim school Faisalabad and got first division in school by getting 981/1000 marks.\nAfter matric i got admission in Shiblee Colege Faisalabad and got 883/1100 marks in degree of inter with Math.\nNow currently i'm student of BS Math and running my last semester.",{"$sicons":488},{"bxl:facebook-circle":489,"bxl:instagram":493,"mdi:web":495,"la:apple":497,"ph:google-logo-bold":500,"ph:google-logo":503},{"left":490,"top":490,"width":491,"height":491,"rotate":490,"vFlip":185,"hFlip":185,"body":492},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":490,"top":490,"width":491,"height":491,"rotate":490,"vFlip":185,"hFlip":185,"body":494},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 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