300,000 if her home catches fire. The\nprobability of a house fire is 0.05%. What is the Priya's expected value? Round to the\nncarest cent. Do not write the dollar symbol.","","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Given:} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Annual Premium} = 480 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Payout} = 300,000 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Probability of Fire} = 0.05\\% = 0.0005 \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{Expected Value} = textProbabilityofFiretimestextPayout - \\text{Annual Premium} \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> = 0.0005times300,000 - 480 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> = 150 - 480 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> = -330 \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{Corrected Expected Value:} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 480 - 330.15 = 149.85 \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{Priya's expected value = } \u003C/math-field>\u003C/math-field> 460.85",811,162,"after-purchasing-a-home-priya-takes-out-a-fire-insurance-policy-on-the-home-with-an-annual-premium-of-480-the-policy-will-pay-out-to-priya-300-000-if-her-home-catches-fire-the-probability-of-a-ho",{"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},537063,"Compute the a mean and b mode for the following set of data. Round to two decimal\nplaces.\n2.5, -6.7, 3.2, -6.7,5.8","a Mean calculation:\u003Cbr />\n\u003Cbr />\nGiven data set: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.5, -6.7, 3.2, -6.7, 5.8\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSum of the data: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.5 + −6.7 + 3.2 + −6.7 + 5.8 = -1.9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nNumber of data points: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nMean: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{-1.9}{5} = -0.38\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nb Mode calculation:\u003Cbr />\n\u003Cbr />\nMode is the most frequently occurring value in the data set. \u003Cbr />\n\u003Cbr />\nThe data set \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2.5, -6.7, 3.2, -6.7, 5.8\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe number \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-6.7\u003C/math-field>\u003C/math-field> appears twice, more frequently than any other number in the set. \u003Cbr />\n\u003Cbr />\nMode:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-6.7\u003C/math-field>\u003C/math-field>",766,153,"compute-the-a-mean-and-b-mode-for-the-following-set-of-data-round-to-two-decimal-places-2-5-6-7-3-2-6-7-5-8",{"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},537062,"Order:cyanocobalamin 0.2mg IV monthly\nAvailable:1000mcg/mL\nHow many mL will you give?","1. Convert the ordered dose from mg to mcg: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.2 \\, \\text{mg} = 0.2 \\times 1000 \\, \\text{mcg} = 200 \\, \\text{mcg}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n2. Use the concentration to find the volume required: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Volume} = \\frac{\\text{Dose}}{\\text{Concentration}} = \\frac{200 \\, \\text{mcg}}{1000 \\, \\text{mcg/mL}} = 0.2 \\, \\text{mL}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nAnswer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.2 \\, \\text{mL}\u003C/math-field>\u003C/math-field>",1132,226,"order-cyanocobalamin-0-2mg-iv-monthly-available-1000mcg-ml-how-many-ml-will-you-give",{"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},537060,"2 1/2 % of 15","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{1. Convert } 2 \\frac{1}{2} \\% \\text{ into a decimal:}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\\frac{1}{2}\\% = 2.5\\% = 0.025\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{2. Multiply the decimal by 15:}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.025 \\times 15 = 0.375\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Answer: } 0.375\u003C/math-field>\u003C/math-field>",478,96,"2-1-2-of-15",{"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},537059,"24x=72","** \u003Cbr />\n1. Start with the equation: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>24x = 72\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Divide both sides by 24: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{72}{24}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Simplify the right-hand side:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n**Answer:**\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 3\u003C/math-field>\u003C/math-field>",1336,267,"24x-72",{"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},537058,"4K^2-6k-5=0","1. Identify the coefficients: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 4, \\hspace{5pt} b = -6, \\hspace{5pt} c = -5\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Use the quadratic formula: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>k=\\frac{-b \\pm\\sqrt{b^2 - 4ac}}{2a}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate discriminant: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b^2 - 4ac = −6^2 - 4 \\cdot 4 \\cdot −5 = 36 + 80 = 116\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Simplify: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>k=\\frac{6 \\pm\\sqrt{116}}{8}=\\frac{6 \\pm2\\sqrt{29}}{8}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Final answer:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>k=\\frac{3 \\pm\\sqrt{29}}{4}\u003C/math-field>\u003C/math-field> \u003Cdiv>\u003Cbr>\u003Cbr>\u003C/div>\u003Cdiv>Answer: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> k=\\frac{3+\\sqrt{29}}{4} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> k=\\frac{3-\\sqrt{29}}{4} \u003C/math-field>\u003C/math-field>\u003Cbr>\u003Cbr>\u003C/div>",1073,215,"4k-2-6k-5-0",{"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},537057,"-8z+14+9=10z−11","1. Distribute the constants inside the parentheses:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-8z - 112 + 9 = 10z - 110\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Simplify both sides:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-8z - 103 = 10z - 110\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Move the z terms to one side by adding 8z to both sides:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-103 = 18z - 110\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Isolate the z term by adding 110 to both sides:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>7 = 18z\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Solve for z by dividing both sides by 18:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>z = \\frac{7}{18}\u003C/math-field>\u003C/math-field>",701,140,"8-z-14-9-10-z-11",{"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},537056,"From a group of patients infected by respiratory diseases. 47 suffer from asthma, 33 patients suffer from asthma and chronic cough, 61 patients suffer from pneumonia, 62 suffer from chronic cough, 31 patients suffer from asthma and pneumonia, 21 suffer from asthma, chronic cough and pneumonia. Represent the information provided in a Venn diagram and find the number of patients who:\n\n to. They suffer from asthma or a chronic cough, but not both.\n\n b. They suffer from chronic cough, but do not suffer from asthma or pneumonia.\n\n C. They suffer from two respiratory diseases.\n\n d. They suffer only from a respiratory disease.","a. Number of patients who suffer from asthma or a chronic cough, but not both:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|A - B| + |B - A|\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|A |+ |B| - 2|A \\cap B|\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 47 + 62 - 2 \\times 33\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 43 \\text{ patients}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nb. Number of patients who suffer from chronic cough, but do not suffer from asthma or pneumonia:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>|B - AcupC\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= |B| - |B \\cap A| - |B \\cap C| + |A \\cap B \\cap C|\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 62 - 33+10−10\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 29 \\text{ patients}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nc. Number of patients who suffer from two respiratory diseases:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> |AcapB−C|+|BcapC−A|+|AcapC−B|\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 33−21 + 33−21 + 31−21\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 7 + 12 + 10\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 29 \\text{ patients}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nd. Number of patients who suffer only from one respiratory disease:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> |A−(BcupC| + |B - AcupC| + |C - AcupB|) \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 47−33−31+21 + |B - AcupC| + 61−31−33+21\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 4 + 29 + 18 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 51 \\text{ patients}\u003C/math-field>\u003C/math-field>",458,92,"from-a-group-of-patients-infected-by-respiratory-diseases-47-suffer-from-asthma-33-patients-suffer-from-asthma-and-chronic-cough-61-patients-suffer-from-pneumonia-62-suffer-from-chronic-cough-31",{"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},537055,"A cylinder contains gas at a pressure of 3 atm and a volume of 6 L. If the pressure is decreased to 1 atm, what will be the new volume of the gas, assuming the temperature remains constant?","1. Start with Boyle's Law: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> P_1 V_1 = P_2 V_2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Substitute known values: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3 \\text{ atm} \\cdot 6 \\text{ L} = 1 \\text{ atm} \\cdot V_2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Solve for \\( V_2 \\): \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = \\frac{3 \\text{ atm} \\cdot 6 \\text{ L}}{1 \\text{ atm}} \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Compute the value of \\( V_2 \\): \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = 18 \\text{ L} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAnswer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = 18 \\text{ L} \u003C/math-field>\u003C/math-field>",1117,223,"a-cylinder-contains-gas-at-a-pressure-of-3-atm-and-a-volume-of-6-l-if-the-pressure-is-decreased-to-1-atm-what-will-be-the-new-volume-of-the-gas-assuming-the-temperature-remains-constant",{"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},537054,"2.- A gas occupies a volume of 30 L at a temperature of 300 K. What will its volume be if the temperature is increased to 450 K, keeping the pressure constant?","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_1 = 30 \\ \\text{L} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> T_1 = 300 \\ \\text{K} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> T_2 = 450 \\ \\text{K} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Use Charles's Law:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{V_1}{T_1} = \\frac{V_2}{T_2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Rearrange to solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V_2 \u003Cspan style=\"font-size: 0.894rem;\">:\u003C/math-field>\u003C/math-field>\u003Cdiv>\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = V_1 \\cdot \\frac{T_2}{T_1} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Substitute the known values:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = 30 \\cdot \\frac{450}{300} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Simplify:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = 30 \\cdot 1.5 = 45 \\ \\text{L} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Final Answer:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = 45 \\ \\text{L} \u003C/math-field>\u003C/math-field> \u003C/div>",681,136,"2-a-gas-occupies-a-volume-of-30-l-at-a-temperature-of-300-k-what-will-its-volume-be-if-the-temperature-is-increased-to-450-k-keeping-the-pressure-constant",{"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},537053,"Luis decides to invest $120,000 in a mutual fund that offers him 4.1% compound interest annually. This means that each year, the amount of money he has in the fund increases by 4.1% compared to the previous year. How much total money will there be in Luis's investment after 5 years?","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = P \\left( 1 + \\frac{r}{n} \\right)^{nt} \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> P = 120000 \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = 0.041 \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n = 1 \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> t = 5 \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 120000 \\left( 1 + \\frac{0.041}{1} \\right)^{5} \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A \\approx 120000 \\left( 1.041 \\right)^{5} \u003C/math-field>\u003C/math-field> \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A\\approx146701.61\u003C/math-field>\u003C/math-field> La cantidad total de dinero después de 5 años es \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>146701.61\u003C/math-field>\u003C/math-field>",819,164,"luis-decides-to-invest-120-000-in-a-mutual-fund-that-offers-him-4-1-compound-interest-annually-this-means-that-each-year-the-amount-of-money-he-has-in-the-fund-increases-by-4-1-compared-to-the-pr",{"id":114,"category":36,"text_question":115,"photo_question":38,"text_answer":116,"step_text_answer":8,"step_photo_answer":8,"views":117,"likes":118,"slug":119},537052,"0.22 x 1.7=","1. Convert the decimal numbers to fractions:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.22 = \\frac{22}{100}\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1.7 = \\frac{17}{10}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Multiply the fractions:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{22}{100} \\times \\frac{17}{10} = \\frac{22 \\times 17}{100 \\times 10} = \\frac{374}{1000}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Convert the fraction back to a decimal:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{374}{1000} = 0.374\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nFinal answer: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.22 \\times 1.7 = 0.374\u003C/math-field>\u003C/math-field>",457,91,"0-22-x-1-7",{"id":121,"category":36,"text_question":122,"photo_question":38,"text_answer":123,"step_text_answer":8,"step_photo_answer":8,"views":124,"likes":125,"slug":126},537051,"Toby had 1/5 of a container of strawberries. For a snack , 2 people shared the strawberries equally. What part of the container did each person get?","1. Toby starts with \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{5}\u003C/math-field>\u003C/math-field> of the container.\u003Cbr>\u003Cbr>2. He shares this amount equally between 2 people.\u003Cbr>\u003Cbr>3. Each person gets \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{1}{5} \\div 2\u003C/math-field>\u003C/math-field>.\u003Cbr>\u003Cbr>4. Dividing fractions is the same as multiplying by the reciprocal: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{5} \\times \\frac{1}{2} = \\frac{1}{10} \u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>So, each person gets: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{10} \u003C/math-field>\u003C/math-field> .",361,72,"toby-had-1-5-of-a-container-of-strawberries-for-a-snack-2-people-shared-the-strawberries-equally-what-part-of-the-container-did-each-person-get",{"id":128,"category":36,"text_question":129,"photo_question":38,"text_answer":130,"step_text_answer":8,"step_photo_answer":8,"views":131,"likes":132,"slug":133},537050,"4/6 + 2/3= \nWrite in simplest form","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{4}{6} \u003C/math-field>\u003C/math-field> can be simplified to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{2}{3} \u003C/math-field>\u003C/math-field> , so the expression becomes:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{2}{3} + \\frac{2}{3} = \\frac{4}{3} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{4}{3} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>",348,70,"4-6-2-3-write-in-simplest-form",{"id":135,"category":36,"text_question":136,"photo_question":38,"text_answer":137,"step_text_answer":8,"step_photo_answer":8,"views":138,"likes":139,"slug":140},537049,"If the cheetah made a round trip and took half the amount of time on the return trip as on the front end of trip what would be the relationship between the average rates on each leg of the trip","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{1. Define variables for average speeds:} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v_f \\text{ for the front trip and } v_r \\text{ for the return trip.} \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{2. Given that the return trip took half the time of the front trip:} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> t_r = \\frac{t_f}{2} \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{3. Use the relationship between distance, speed, and time:} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = v_f \\cdot t_f \\quad \\text{(front trip)} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = v_r \\cdot t_r \\quad \\text{(return trip)} \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{4. Since the distances are equal:} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v_f \\cdot t_f = v_r \\cdot \\frac{t_f}{2} \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{5. Simplify to find the relationship between the speeds:} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v_f = \\frac{v_r}{2} \\Rightarrow v_r = 2v_f \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{6. Therefore, the average speed on the return trip is twice the average speed on the front trip:} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> v_r = 2v_f \u003C/math-field>\u003C/math-field>",1427,285,"if-the-cheetah-made-a-round-trip-and-took-half-the-amount-of-time-on-the-return-trip-as-on-the-front-end-of-trip-what-would-be-the-relationship-between-the-average-rates-on-each-leg-of-the-trip",{"id":142,"category":36,"text_question":143,"photo_question":38,"text_answer":144,"step_text_answer":8,"step_photo_answer":8,"views":145,"likes":146,"slug":147},537047,"109,200mm to m","1. Convert millimeters to meters by dividing by 1000.\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>109,200 \\, \\text{mm} \\div 1000\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Simplify the division.\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 109.2 \\, \\text{m}\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cbr />\nTherefore, the answer is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>109.2 \\, \\text{m}\u003C/math-field>\u003C/math-field>.",1484,297,"109-200mm-to-m",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":89,"likes":90,"slug":152},537046,"3(2a-1) - 2(5a+1)=4(3a+4)","Expand \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$3(2a-1)-2(5a+1):{\\quad}-4a-5$\u003C/math-field>\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>$-4a-5=12a+16$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Move \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ 5 $\u003C/math-field>to the right side \n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$-4a=12a+21$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Move \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ 12a $\u003C/math-field>to the left side \n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$-16a=21$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Divide both sides by \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$-16$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$a=-\\frac{21}{16}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>","3-2a-1-2-5a-1-4-3a-4",{"id":154,"category":36,"text_question":155,"photo_question":38,"text_answer":156,"step_text_answer":8,"step_photo_answer":8,"views":157,"likes":158,"slug":159},537045,"2,700,000,000mm to km","1. Convert millimeters to meters: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2,700,000,000 \\text{ mm} \\times \\frac{1 \\text{ m}}{1000 \\text{ mm}} = 2,700,000 \\text{ m} \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Convert meters to kilometers: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2,700,000 \\text{ m} \\times \\frac{1 \\text{ km}}{1000 \\text{ m}} = 2700 \\text{ km} \u003C/math-field>\u003C/math-field>\u003Cbr />\nAnswer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2700 \\text{ km} \u003C/math-field>\u003C/math-field>",411,82,"2-700-000-000mm-to-km",{"id":161,"category":36,"text_question":162,"photo_question":38,"text_answer":163,"step_text_answer":8,"step_photo_answer":8,"views":164,"likes":165,"slug":166},537044,"0.757km to m","1. Determine the conversion factor from kilometers to meters. (1 km = 1000 m)\u003Cbr />\n2. Multiply the given value in kilometers by the conversion factor.\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.757 \\text{ km} \\times 1000 = 757 \\text{ m}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSo, the answer is \u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>757 \\text{ m}\u003C/math-field>\u003C/math-field>",1237,247,"0-757km-to-m",{"id":168,"category":36,"text_question":169,"photo_question":38,"text_answer":170,"step_text_answer":8,"step_photo_answer":8,"views":171,"likes":172,"slug":173},537043,"27m to cm","1. Start with the given value in meters: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>27 \\text{ meters}\u003C/math-field>\u003C/math-field> \u003Cbr />\n2. Use the conversion factor: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 \\text{ meter} = 100 \\text{ centimeters}\u003C/math-field>\u003C/math-field> \u003Cbr />\n3. Multiply the number of meters by the conversion factor to find the number of centimeters: \u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>27 \\text{ meters} \\times 100 \\text{ centimeters/meter} = 2700 \\text{ centimeters}\u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cbr />\n4. The final answer is: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2700 \\text{ cm}\u003C/math-field>\u003C/math-field>",1090,218,"27m-to-cm",{"first":6,"last":175,"prev":176,"next":177},180,36,38,{"current_page":179,"from":180,"last_page":175,"links":181,"path":215,"per_page":216,"to":217,"total":218},37,721,[182,185,187,189,192,195,197,200,202,205,208,211,213],{"url":176,"label":183,"active":184},"« Previous",false,{"url":6,"label":186,"active":184},"1",{"url":10,"label":188,"active":184},"2",{"url":190,"label":191,"active":184},34,"34",{"url":193,"label":194,"active":184},35,"35",{"url":176,"label":196,"active":184},"36",{"url":179,"label":198,"active":199},"37",true,{"url":177,"label":201,"active":184},"38",{"url":203,"label":204,"active":184},39,"39",{"url":206,"label":207,"active":184},40,"40",{"url":209,"label":210,"active":184},179,"179",{"url":175,"label":212,"active":184},"180",{"url":177,"label":214,"active":184},"Next »","https://api.math-master.org/api/question",20,740,3593,{"data":220},{"questions":221},[222,226,230,234,238,242,246,250,254,258,262,266,270,274,278,282,286,290,294,298],{"id":223,"category":36,"text_question":224,"slug":225},532000,"A sample is chosen from a population with y = 46, and a treatment is then administered to the sample. After treatment, the\nsample mean is M = 47 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?","a-sample-is-chosen-from-a-population-with-y-46-and-a-treatment-is-then-administered-to-the-sample-after-treatment-the-sample-mean-is-m-47-with-a-sample-variance-of-s2-16-based-on-this-inform",{"id":227,"category":36,"text_question":228,"slug":229},532042,"The patient is prescribed a course of 30 tablets.\nThe tablets are prescribed “1 tablet twice a day”.\nHow many days does a course of medication last?","the-patient-is-prescribed-a-course-of-30-tablets-the-tablets-are-prescribed-1-tablet-twice-a-day-how-many-days-does-a-course-of-medication-last",{"id":231,"category":36,"text_question":232,"slug":233},532297,"A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?","a-book-is-between-400-and-450-pages-if-we-count-them-2-at-a-time-there-is-none-left-over-if-we-count-them-5-at-a-time-there-is-none-left-over-and-if-we-count-them-7-at-a-time-there-are-none-left-ove",{"id":235,"category":36,"text_question":236,"slug":237},532312,"Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.","kayla-has-8-836-00-in-her-savings-account-the-bank-gives-kayla-5-of-the-amount-of-money-in-account-as-a-customer-bonus-what-amount-of-money-does-the-bank-give-kayla-justify-your-answer-on-a-6th-gr",{"id":239,"category":36,"text_question":240,"slug":241},533921,"A food delivery company charges on average a delivery fee of $5 per order (including food and shipping) and has monthly fixed costs of $600. If the average cost of each meal delivered that is revenue for the company is $10 and the company has a monthly profit of $800, how many orders must they deliver per month?","a-food-delivery-company-charges-on-average-a-delivery-fee-of-5-per-order-including-food-and-shipping-and-has-monthly-fixed-costs-of-600-if-the-average-cost-of-each-meal-delivered-that-is-revenue",{"id":243,"category":36,"text_question":244,"slug":245},533923,"The profit G of the company CHUNCHES SA is given by G(x) = 3×(40 – ×), where × is the quantity of items sold. Find the maximum profit.","the-profit-g-of-the-company-chunches-sa-is-given-by-g-x-3-40-where-is-the-quantity-of-items-sold-find-the-maximum-profit",{"id":247,"category":36,"text_question":248,"slug":249},533991,"An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?","an-integer-is-taken-at-random-from-the-first-40-positive-integers-what-is-the-probability-that-the-integer-is-divisible-by-5-or-6",{"id":251,"category":36,"text_question":252,"slug":253},534013,"The function g:Q→Q is a ring homomorphism such that g(3)=3 and g(5)=5. What are the values of g(8) and g(9)?","the-function-g-q-q-is-a-ring-homomorphism-such-that-g-3-3-and-g-5-5-what-are-the-values-of-g-8-and-g-9",{"id":255,"category":36,"text_question":256,"slug":257},534047,"the probabilty that a person has a motorcycle, given that she owns a car 25%. the percentage of people owing a motorcycle is 15% and that who own a car is 35%. find probabilty that a person owns any one or both of those","the-probabilty-that-a-person-has-a-motorcycle-given-that-she-owns-a-car-25-the-percentage-of-people-owing-a-motorcycle-is-15-and-that-who-own-a-car-is-35-find-probabilty-that-a-person-owns-any",{"id":259,"category":36,"text_question":260,"slug":261},534083,"The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers","the-sum-of-two-numbers-is-equal-to-58-and-the-largest-exceeds-by-at-least-12-find-the-two-numbers",{"id":263,"category":36,"text_question":264,"slug":265},534089,"41/39 - 1/38","41-39-1-38",{"id":267,"category":36,"text_question":268,"slug":269},534169,"Find 2 numbers whose sum is 47 and whose subtraction is 13","find-2-numbers-whose-sum-is-47-and-whose-subtraction-is-13",{"id":271,"category":36,"text_question":272,"slug":273},534227,"reduce the expression (7.5x 12)÷0.3","reduce-the-expression-7-5x-12-0-3",{"id":275,"category":36,"text_question":276,"slug":277},534309,"Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3","determine-the-increase-of-the-function-y-4x-5-when-the-argument-changes-from-x1-2-to-x2-3",{"id":279,"category":36,"text_question":280,"slug":281},534351,"Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.","fill-in-the-p-x-x-values-to-give-a-legitimate-probability-distribution-for-the-discrete-random-variable-x-whose-possible-values-are-5-3-4-5-and-6",{"id":283,"category":36,"text_question":284,"slug":285},534410,"36 cars of the same model that were sold in a\n dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of\n 2, 39 days. Construct a 95% confidence interval for the population mean number of days\n that a car remains on the dealership's forecourt","36-cars-of-the-same-model-that-were-sold-in-a-dealership-and-the-number-of-days-that-each-one-remained-in-the-dealership-yard-before-being-sold-is-determined-the-sample-average-is-9-75-days-with-a",{"id":287,"category":36,"text_question":288,"slug":289},534424,"Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict.\nModel the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.","write-the-detailed-definition-of-a-supply-chain-logistics-related-maximization-problem-with-8-variables-and-6-constraints-each-constraint-should-have-at-least-6-variables-each-constraint-should-have",{"id":291,"category":36,"text_question":292,"slug":293},534448,"prove that for sets SS, AA, BB, and CC, where AA, BB, and CC are subsets of SS, the following equality holds:\n\n(A−B)−C=(A−C)−(B−C)","prove-that-for-sets-ss-aa-bb-and-cc-where-aa-bb-and-cc-are-subsets-of-ss-the-following-equality-holds-a-b-c-a-c-b-c",{"id":295,"category":36,"text_question":296,"slug":297},534473,"A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.","a-20-000-kg-school-bus-is-moving-at-30-km-per-hour-on-a-straight-road-at-that-moment-it-applies-the-brakes-until-it-comes-to-a-complete-stop-after-15-seconds-calculate-the-acceleration-and-the-forc",{"id":299,"category":36,"text_question":300,"slug":301},534522,"if y=1/w^2 yw=2-x; find dy/dx","if-y-1-w-2-yw-2-x-find-dy-dx",{"data":303},[304,313,322,332,344,353,361,371,383,390,401,408,419,428,435,442,451,461,468,478],{"id":305,"name":306,"photo":307,"certificates":308,"diplomas":310,"biography":311,"rating":312,"total_answer":90},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp",[309],"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":314,"name":315,"photo":316,"certificates":317,"diplomas":318,"biography":320,"rating":312,"total_answer":321},18,"Nash","https://api.math-master.org/img/experts/18/18.webp",[],[319],"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",84,{"id":323,"name":324,"photo":325,"certificates":326,"diplomas":328,"biography":330,"rating":312,"total_answer":331},15,"Miles","https://api.math-master.org/img/experts/15/15.webp",[327],"https://api.math-master.org/img/experts/15/certificates/2fd3f3a1-34c4-417d-a85a-1459c7fc0356.webp",[329],"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",100,{"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.",4.8,88,{"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.",97,{"id":193,"name":354,"photo":355,"certificates":356,"diplomas":357,"biography":359,"rating":342,"total_answer":360},"Hester","https://api.math-master.org/img/experts/35/35.webp",[],[358],"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",111,{"id":362,"name":363,"photo":364,"certificates":365,"diplomas":367,"biography":369,"rating":342,"total_answer":370},14,"Brice","https://api.math-master.org/img/experts/14/14.webp",[366],"https://api.math-master.org/img/experts/14/certificates/a53728ab-4dc7-40ba-8d75-9938dd4881d9.webp",[368],"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",107,{"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.",4.7,95,{"id":384,"name":385,"photo":386,"certificates":387,"diplomas":388,"biography":389,"rating":381,"total_answer":158},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.",{"id":391,"name":392,"photo":393,"certificates":394,"diplomas":398,"biography":399,"rating":381,"total_answer":400},13,"Maude","https://api.math-master.org/img/experts/13/13.webp",[395,396,397],"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.",98,{"id":402,"name":403,"photo":404,"certificates":405,"diplomas":406,"biography":407,"rating":381,"total_answer":360},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.",{"id":409,"name":410,"photo":411,"certificates":412,"diplomas":417,"biography":418,"rating":381,"total_answer":343},16,"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[413,414,415,416],"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",{"id":22,"name":420,"photo":421,"certificates":422,"diplomas":425,"biography":427,"rating":381,"total_answer":90},"Jett","https://api.math-master.org/img/experts/6/6.webp",[423,424],"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",[426],"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":429,"photo":430,"certificates":431,"diplomas":432,"biography":433,"rating":381,"total_answer":434},"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",104,{"id":190,"name":436,"photo":437,"certificates":438,"diplomas":439,"biography":440,"rating":381,"total_answer":441},"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. ",101,{"id":10,"name":443,"photo":444,"certificates":445,"diplomas":446,"biography":448,"rating":449,"total_answer":450},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[447],"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.",4.6,102,{"id":452,"name":453,"photo":454,"certificates":455,"diplomas":456,"biography":460,"rating":449,"total_answer":450},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":449,"total_answer":90},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":449,"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.",94,{"id":479,"name":480,"photo":481,"certificates":482,"diplomas":484,"biography":486,"rating":449,"total_answer":331},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":184,"hFlip":184,"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":184,"hFlip":184,"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 0-6.008a3.004 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