are less than 7, so all outcomes are favorable:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{6 \\text{ favorable outcomes}}{6 \\text{ total outcomes}} = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nc) The numbers 1 and 4 appear, each on one face of the die:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{2 \\text{ favorable outcomes 1or4}}{6 \\text{ total outcomes}} = \\frac{1}{3} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAnswer for a): frac16 \u003Cbr />\nAnswer for b): 1 \u003Cbr />\nAnswer for c): frac13",1299,260,"determine-the-probability-that-when-throwing-a-die-it-will-land-a-number-5-b-a-number-less-than-7-c-number-1-or-4",{"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},537907,"Ivan learned 15 out of 20 questions. What is the probability that the student got a question he did not learn?","- Ivan je nauΔio 15 pitanja od 20, tako da je broj pitanja koja nije nauΔio \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 20 - 15 = 5 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Ukupan broj pitanja je 20.\u003Cbr />\n- Vjerojatnost da je Ivan dobio pitanje koje nije nauΔio iznosi \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{5}{20} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Jednostavnim deljenjem dobijamo vjerojatnost: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{5}{20} = \\frac{1}{4} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\nOdgovor je: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{4} \u003C/math-field>\u003C/math-field>.",518,104,"ivan-learned-15-out-of-20-questions-what-is-the-probability-that-the-student-got-a-question-he-did-not-learn",{"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},537906,"561-t+154=137","1. Start with the equation:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>561-t+154=137\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Distribute the negative sign:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>561-t-154=137\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Simplify the left side by combining like terms:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>407-t=137\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Subtract 407 from both sides:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-t=137-407\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplify the right side:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-t=-270\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Multiply both sides by -1:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>t=270\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>t = 270\u003C/math-field>\u003C/math-field>",1257,251,"561-t-154-137",{"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},537905,"431+Bβ29=678","First, simplify the equation:\u003Cbr />\n\u003Cbr />\n1. Start with the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>431 + Bβ29 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Distribute and simplify: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>431 + B - 29 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Combine like terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B + 402 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Isolate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B\u003C/math-field>\u003C/math-field> by subtracting 402 from both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 678 - 402\u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Calculate the right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 276\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nFinal answer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 276\u003C/math-field>\u003C/math-field>",1140,228,"431-b-29-678",{"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},537904,"Vicente counted 2,367 seashells at the beach. Then he realized he made a mistake and subtracted 400 seashells. How many seashells did he actually count?","1. Start with the original count: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2367\u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Subtract the adjustment of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>400\u003C/math-field>\u003C/math-field>: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2367 - 400 = 1967\u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. The actual number of seashells counted: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1967\u003C/math-field>\u003C/math-field>.",447,89,"vicente-counted-2-367-seashells-at-the-beach-then-he-realized-he-made-a-mistake-and-subtracted-400-seashells-how-many-seashells-did-he-actually-count",{"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},537903,"Find the critical value Za/2 needed to construct a confidence interval with the given level \n\nLevel 99.7%","1. Identify that the level of confidence is 99.7%.\u003Cbr />\n2. Calculate the area in each tail: \u003Cbr />\n - The confidence level of 99.7% means there's 0.3% in the tails combined.\u003Cbr />\n - The area in one tail is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{0.3\\%}{2} = 0.15\\% \u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. Determine the z-score for the 99.85th percentile since0.15.\u003Cbr />\n4. Look up this value in the standard normal distribution table or using a calculator, the critical z-score is typically approximately 3.00 forastandardnormaldistribution.\u003Cbr />\n5. Conclude that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> z_{\\frac{\\alpha}{2}} = 3.00 \u003C/math-field>\u003C/math-field> for a 99.7% confidence interval.",805,161,"find-the-critical-value-za-2-needed-to-construct-a-confidence-interval-with-the-given-level-level-99-7",{"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},537902,"i need 3 addition or subtraction problems with 2 or 3 digit number that equal 5","1. Solve \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12 - 7\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cbr />\n - Calculate: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12 - 7 = 5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n - Answer: \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 />\n2. Solve \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>102 - 97\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cbr />\n - Calculate: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>102 - 97 = 5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n - Answer: \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 />\n3. Solve \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>55 - 50\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cbr />\n - Calculate: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>55 - 50 = 5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n - Answer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\u003C/math-field>\u003C/math-field>",783,157,"i-need-3-addition-or-subtraction-problems-with-2-or-3-digit-number-that-equal-5",{"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},537901,"i need 3 rounding problems that equal 9","1. Round 8.5 to the nearest integer:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8.5 \\approx 9\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n2. Round 8.7 to the nearest integer:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8.7 \\approx 9\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n3. Round 9.2 to the nearest integer:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>9.2 \\approx 9\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nAnswer: 9, 9, 9",1229,246,"i-need-3-rounding-problems-that-equal-9",{"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},537900,"72 forth graders are going on a camping trip. 9 chaperones are also going. If a van can seat 12 people how many vans are needed?","1. Calculate the total number of people: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 72 + 9 = 81 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Divide the total number of people by the number of seats per van:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{81}{12} = 6.75 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Round up to the nearest whole number, because you can't have a fraction of a van: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\lceil 6.75 \\rceil = 7 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, 7 vans are needed.",801,160,"72-forth-graders-are-going-on-a-camping-trip-9-chaperones-are-also-going-if-a-van-can-seat-12-people-how-many-vans-are-needed",{"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},537899,"81 divided by 12","1. Start with the division: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{81}{12} \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Simplify the fraction: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{81}{12} = \\frac{27}{4} \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Convert the fraction to a mixed number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{27}{4} = 6 \\frac{3}{4} \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Alternatively, divide to get the decimal: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 81 \\div 12 = 6.75 \u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Answer in decimal: 6.75",635,127,"81-divided-by-12",{"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},537898,"Factor the expression using GCF 39-13","Solution:\u003Cbr />\n1. Identify the numbers in the expression: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>39\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Determine the greatest common factor GCF of the numbers:\u003Cbr />\n- The factors of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>39\u003C/math-field>\u003C/math-field> are: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1, 3, 13, 39\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The factors of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13\u003C/math-field>\u003C/math-field> are: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1, 13\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The common factors are: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1, 13\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Therefore, the greatest common factor is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Factor the expression by dividing each term by the GCF:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>39 - 13 = 13 \\times 3 - 13 \\times 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Factor out the GCF \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13\u003C/math-field>\u003C/math-field>: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>133β1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify the expression inside the parentheses:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3 - 1 = 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Therefore, the factored expression is: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13 \\times 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplified result: \u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13 \\times 2 = 26\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThus, the expression \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>39 - 13\u003C/math-field>\u003C/math-field> factors to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>132\u003C/math-field>\u003C/math-field> or simplifies to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26\u003C/math-field>\u003C/math-field>.",373,75,"factor-the-expression-using-gcf-39-13",{"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},537897,"Is 4 a factor of 1,671,349? \nHow do you know without multiplying or dividing?","1. Identify the last two digits of the number 1,671,349: 49.\u003Cbr />\n2. Check if 49 is divisible by 4:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 49 \\div 4 = 12.25 \u003C/math-field>\u003C/math-field>\u003Cbr />\n Since 12.25 is not an integer, 49 is not divisible by 4.\u003Cbr />\n3. Conclude that 1,671,349 is not divisible by 4.\u003Cbr />\n\u003Cbr />\nAnswer: 4 is not a factor of 1,671,349.",1093,219,"is-4-a-factor-of-1-671-349-how-do-you-know-without-multiplying-or-dividing",{"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},537896,"Is 3 a factor of 711?\nHow do you know without multiplying or dividing?","1. According to the divisibility rule of 3, a number is divisible by 3 if the sum of its digits is divisible by 3.\u003Cbr />\n2. The digits of 711 are 7, 1, and 1.\u003Cbr />\n3. Find the sum of these digits: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 7 + 1 + 1 = 9 \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Check if the sum is divisible by 3. Since:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 9 \\div 3 = 3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n5. The sum 9 is divisible by 3, so 711 is also divisible by 3.\u003Cbr />\n6. Therefore, 3 is a factor of 711.",329,66,"is-3-a-factor-of-711-how-do-you-know-without-multiplying-or-dividing",{"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},537894,"What is the amount of an annuity if the payments are 60attheendofeachmonthfor\n10yearsat3.5434.00 are made at the end of\n every month for 15 years at an interest rate of 7.5% per year computed monthly?","Solution:\u003Cbr>\u003Cbr>1. Given:\u003Cbr>\u003Cbr>- Monthly payment: USD 434.00\u003Cbr>\u003Cbr>- Number of years: 15\u003Cbr>\u003Cbr>- Annual interest rate: 7.5%\u003Cbr>\u003Cbr>- Number of compounding periods per year: 12\u003Cbr>\u003Cbr>2. Convert the annual interest rate to a monthly interest rate:\u003Cbr>\u003Cbr>- Monthly interest rate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{7.5\\%}{12} = \\frac{0.075}{12}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Monthly interest rate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 0.00625\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate the total number of payments:\u003Cbr>\u003Cbr>- Total number of payments \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 15 \\, \\text{years} \\times 12 \\, \\text{payments/year}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Total number of payments \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 180\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Use the present value of an annuity formula:\u003Cbr>\u003Cbr>- Present Value PV formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PV = C \\times \\leftfrac1β(1+r)βnrright\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Where:\u003Cbr>\u003Cbr>* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C = 434\u003C/math-field>\u003C/math-field> monthlypayment\u003Cbr>\u003Cbr>* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 0.00625\u003C/math-field>\u003C/math-field> monthlyinterestrate\u003Cbr>\u003Cbr>* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 180\u003C/math-field>\u003C/math-field> totalnumberofpayments\u003Cbr>\u003Cbr>5. Substitute the values into the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PV = 434 \\times \\leftfrac1β(1+0.00625)β1800.00625right\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Calculate:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PV\\approx46817.07\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>The present value of the annuity is approximately USD 46817.07.",874,175,"what-is-the-present-value-of-an-annuity-if-payments-of-434-00-are-made-at-the-end-of-every-month-for-15-years-at-an-interest-rate-of-7-5-per-year-computed-monthly",{"id":156,"category":36,"text_question":157,"photo_question":38,"text_answer":158,"step_text_answer":8,"step_photo_answer":8,"views":159,"likes":160,"slug":161},537891,"4x+5 +7 = 9 the plus sign next to the 5 is small","1. Begin by simplifying the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + 5 + 7 = 9\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Combine the constant terms on the left side: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + 12 = 9\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Subtract 12 from both sides: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = 9 - 12\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n4. Simplify the right side:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = -3\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n5. Divide both sides by 4 to solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{-3}{4}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n6. Therefore, the solution is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -0.75\u003C/math-field>\u003C/math-field>.",1045,209,"4x-5-7-9-the-plus-sign-next-to-the-5-is-small",{"id":163,"category":36,"text_question":164,"photo_question":38,"text_answer":165,"step_text_answer":8,"step_photo_answer":8,"views":166,"likes":83,"slug":167},537890,"A water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide. If the pipe is 13 feet long what are the dimensions of the garden","1. Write the equation for the Pythagorean theorem:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w^2 + w+7^2 = 13^2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Calculate the square of 13:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13^2 = 169\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Expand the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w^2 + w+7^2 = 169 \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> w^2 + w2+14w+49 = 169 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Combine like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2w^2 + 14w + 49 = 169 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplify and rearrange the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2w^2 + 14w + 49 - 169 = 0 \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> 2w^2 + 14w - 120 = 0 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Divide the entire equation by 2 to simplify:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w^2 + 7w - 60 = 0 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Factor the quadratic equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w+12wβ5 = 0 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>w\u003C/math-field>\u003C/math-field>:\u003Cbr />\n - Either \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w + 12 = 0 \u003C/math-field>\u003C/math-field> which gives \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w = -12 \u003C/math-field>\u003C/math-field> notpossibleinthiscontext,sincewidthcanβ²tbenegative\u003Cbr />\n - Or \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w - 5 = 0 \u003C/math-field>\u003C/math-field> which gives \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w = 5 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n9. Find the length:\u003Cbr />\n - Length = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> w + 7 = 5 + 7 = 12 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the width is 5 feet and the length is 12 feet.",445,"a-water-pipe-runs-diagonally-under-a-rectangular-garden-that-is-7-feet-longer-than-it-is-wide-if-the-pipe-is-13-feet-long-what-are-the-dimensions-of-the-garden",{"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},537889,"Two angels are supplementary if the sun of their angels is 180 degrees. One of the two supplementary angles is 8 degrees less than three times the other. Find the measure of each angle.","**\u003Cbr />\n\u003Cbr />\n1. Define the angles: Let the first angle be \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>. The second angle is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x - 8\u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Set up the equation for supplementary angles: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 3xβ8 = 180\u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. Simplify the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x - 8 = 180\u003C/math-field>\u003C/math-field>.\u003Cbr />\n4. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>: \u003Cbr />\n - Add 8 to both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = 188\u003C/math-field>\u003C/math-field>.\u003Cbr />\n - Divide by 4: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 47\u003C/math-field>\u003C/math-field>.\u003Cbr />\n5. Find the second angle: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x - 8 = 347 - 8 = 141 - 8 = 133\u003C/math-field>\u003C/math-field>.\u003Cbr />\n6. Conclusion: The angles are 47 degrees and 133 degrees.",1361,272,"two-angels-are-supplementary-if-the-sun-of-their-angels-is-180-degrees-one-of-the-two-supplementary-angles-is-8-degrees-less-than-three-times-the-other-find-the-measure-of-each-angle",{"first":6,"last":176,"prev":8,"next":10},180,{"current_page":6,"from":6,"last_page":176,"links":178,"path":212,"per_page":213,"to":213,"total":214},[179,182,185,187,189,191,193,196,199,202,205,208,210],{"url":6,"label":180,"active":181},"1",true,{"url":10,"label":183,"active":184},"2",false,{"url":13,"label":186,"active":184},"3",{"url":16,"label":188,"active":184},"4",{"url":19,"label":190,"active":184},"5",{"url":22,"label":192,"active":184},"6",{"url":194,"label":195,"active":184},7,"7",{"url":197,"label":198,"active":184},8,"8",{"url":200,"label":201,"active":184},9,"9",{"url":203,"label":204,"active":184},10,"10",{"url":206,"label":207,"active":184},179,"179",{"url":176,"label":209,"active":184},"180",{"url":10,"label":211,"active":184},"Next »","https://api.math-master.org/api/question",20,3586,{"data":216},{"questions":217},[218,222,226,230,234,238,242,246,250,254,258,262,266,270,274,278,282,286,290,294],{"id":219,"category":36,"text_question":220,"slug":221},532005,"A=m/2-t isolate t","a-m-2-t-isolate-t",{"id":223,"category":36,"text_question":224,"slug":225},532307,"Write 32/25 as a percent","write-32-25-as-a-percent",{"id":227,"category":36,"text_question":228,"slug":229},533937,"The ratio of tomatoes to red apples is 2:5. If there are 20 tomaoes in the garden, how many red apples are there?","the-ratio-of-tomatoes-to-red-apples-is-2-5-if-there-are-20-tomaoes-in-the-garden-how-many-red-apples-are-there",{"id":231,"category":36,"text_question":232,"slug":233},533980,"Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.","find-the-root-of-x-4-10x-5-0-using-newton-s-method-with-a-precision-of-the-smallest-positive-root",{"id":235,"category":36,"text_question":236,"slug":237},533985,"Serum cholesterol levels in men aged 18 to 24 years have a normal distribution with a mean\n 178.1mg/100 ml and standard deviation 40.7 mg/100 ml.\n The. Randomly choosing a man between 18 and 24 years old, determine the probability of\n your serum cholesterol level is less than 200.\n B. Whether a serum cholesterol level should be judged too high if it is above 7%\n higher, determine the value of the separation level of levels that are too high.\n w. Determine a 90% reference range for serum cholesterol level among men\n from 18 to 24 years old.","serum-cholesterol-levels-in-men-aged-18-to-24-years-have-a-normal-distribution-with-a-mean-178-1mg-100-ml-and-standard-deviation-40-7-mg-100-ml-the-randomly-choosing-a-man-between-18-and-24-years",{"id":239,"category":36,"text_question":240,"slug":241},534020,"The expected market return is 13,86% and the risk free rate 1%. What would then be the risk premium on the common stocks of a company which beta is 1,55? in","the-expected-market-return-is-13-86-and-the-risk-free-rate-1-what-would-then-be-the-risk-premium-on-the-common-stocks-of-a-company-which-beta-is-1-55-in-2-decimal-places",{"id":243,"category":36,"text_question":244,"slug":245},534041,"You are planning to buy a car worth 20,000.Whichofthetwodealsdescribedbelowwouldyouchoose,bothwitha48βmonthterm?(NB:estimatethemonthlypaymentofeachoffer).i)thedealerofferstotake1020,000 i.e.,nodiscount at an APR of 3%, monthly compounding.","you-are-planning-to-buy-a-car-worth-20-000-which-of-the-two-deals-described-below-would-you-choose-both-with-a-48-month-term-nb-estimate-the-monthly-payment-of-each-offer-i-the-dealer-offers",{"id":247,"category":36,"text_question":248,"slug":249},534056,"-27=-7u 5uβ3","27-7u-5-u-3",{"id":251,"category":36,"text_question":252,"slug":253},534139,"24,β7 is on the terminal arm of an angle in standard position.\nDetermine the exact values of the primary trigonometric functions.","24-7-is-on-the-terminal-arm-of-an-angle-in-standard-position-determine-the-exact-values-of-the-primary-trigonometric-functions",{"id":255,"category":36,"text_question":256,"slug":257},534176,"Three squares have a total area of 35.25 ππ2\r\n. The larger square has twice the side-length of the\r\nmiddle-sized square. The smaller square has its side length exactly 0.5 cm smaller than the\r\nmiddle-sixed square. Find the side lengths of each of the three squares.","three-squares-have-a-total-area-of-35-25-cm2-the-larger-square-has-twice-the-side-length-of-the-middle-sized-square-the-smaller-square-has-its-side-length-exactly-0-5-cm-smaller-than-the-middle",{"id":259,"category":36,"text_question":260,"slug":261},534194,"form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?","form-a-key-for-your-lock-containing-the-numbers-2-2-5-8-how-many-different-keys-can-you-form",{"id":263,"category":36,"text_question":264,"slug":265},534352,"You want to study incomes in a large city. You take a simple random sample of 5012 \r\nhouseholds and find that the distribution of household incomes is skewed right. \r\n\nIf you calculate the mean of the 5012 household incomes will the distribution of \r\nmean scores be skewed right as well? Hint: this involves the Central Limit Theorem.","you-want-to-study-incomes-in-a-large-city-you-take-a-simple-random-sample-of-5012-households-and-find-that-the-distribution-of-household-incomes-is-skewed-right-if-you-calculate-the-mean-of-the",{"id":267,"category":36,"text_question":268,"slug":269},534367,"When Sara was 15 years old, an uncle left her as inheritanceΓ a sum of 10,000 euros which he invested in a bank that applies the interest rate of 2,5% annual. Today Sara is 18 years and wants to buy a'car, how much she can Γ² withdraw from the bank?","when-sara-was-15-years-old-an-uncle-left-her-as-inheritancea-a-sum-of-10-000-euros-which-he-invested-in-a-bank-that-applies-the-interest-rate-of-2-5-annual-today-sara-is-18-years-and-wants-to-buy",{"id":271,"category":36,"text_question":272,"slug":273},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":275,"category":36,"text_question":276,"slug":277},534428,"Two particles of electrical charges Q1=3.8Γ10-βΆC and q,=4.4Γ10-βΆC are separated in vacuum by a distance of 4.0.10-βΈ m. Since K=9.0.10βΉ N.mΒ²/CΒ², the intensity of the interaction force between them, in newtons, is?","two-particles-of-electrical-charges-q1-3-8-10-c-and-q-4-4-10-c-are-separated-in-vacuum-by-a-distance-of-4-0-10-m-since-k-9-0-10-n-m-c-the-intensity-of-the-interaction-force-between-them-in",{"id":279,"category":36,"text_question":280,"slug":281},534454,"We plan to test whether the mean mRNA expression level differs between two strains of\nyeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n\nsamples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene,\nusing an unpaired two-sample t-test for each gene theparticulartypeoftestdoesnot\nmatter.\na) What are the null hypotheses in these tests inwords? [2]\nb) If, in fact, the two strains are identical, how many of these tests do we expect to\nproduce a P-value exceeding 1/4? [2]","we-plan-to-test-whether-the-mean-mrna-expression-level-differs-between-two-strains-of-yeast-for-each-of-8-000-genes-we-will-measure-the-expression-levels-of-each-gene-in-n-samples-of-strain-1-and-m",{"id":283,"category":36,"text_question":284,"slug":285},534508,"Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DGβ₯BG. If the area of the quadrilateral AGBD is equal to s, show that ACΒ·BDβ₯2Β·s.","let-g-be-the-center-of-gravity-of-triangle-abc-we-draw-through-a-a-parallel-to-bc-on-which-we-take-a-point-d-so-that-dg-bg-if-the-area-of-the-quadrilateral-agbd-is-equal-to-s-show-that-ac-bd-2-s",{"id":287,"category":36,"text_question":288,"slug":289},534528,"If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable.\n12, 18, 21, c, 13","if-the-mean-of-the-following-numbers-is-17-find-the-c-value-produce-an-algebraic-solution-guess-and-check-is-unacceptable-12-18-21-c-13",{"id":291,"category":36,"text_question":292,"slug":293},534562,"Solve the following \n9x - 9 - 6x = 5 + 8x - 9","solve-the-following-9x-9-6x-5-8x-9",{"id":295,"category":36,"text_question":296,"slug":297},534611,"Convert 324πππ£π into base-ten","convert-324-five-into-base-ten",{"data":299},{"id":300,"category":36,"slug":301,"text_question":302,"photo_question":8,"text_answer":303,"step_text_answer":8,"step_photo_answer":8,"views":304,"likes":305,"expert":306},536047,"what-is-the-probability-that-we-choose-a-number-that-is-divisible-by-3-among-the-first-20-natural-numbers-justify-your-answer","What is the probability that we choose a number that is divisible by 3 among the first 20 natural numbers? Justify your answer","To find the probability of choosing a number that is divisible by 3 among the first 20 natural numbers, we first need to find how many numbers among the first 20 are divisible by 3.\u003Cbr />\u003Cbr />The first multiple of 3 is 3, and the last multiple of 3 that is less than or equal to 20 is 18.\u003Cbr />\u003Cbr />So, the numbers divisible by 3 among the first 20 natural numbers are 3, 6, 9, 12, 15, and 18. There are a total of 6 numbers that are divisible by 3.\u003Cbr />\u003Cbr />Now, the total number of choices is 20 from1to20. \u003Cbr />\u003Cbr />Therefore, the probability of choosing a number that is divisible by 3 among the first 20 natural numbers is given by:\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Probability} = \\frac{\\text{Number of favorable outcomes}}{\\text{Total number of outcomes}} = \\frac{6}{20} = \\frac{3}{10} = 0.3 \u003C/math-field>\u003C/math-field>\u003Cbr />\u003Cbr />\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{0.3}\u003C/math-field>\u003C/math-field> is the probability of choosing a number that is divisible by 3 among the first 20 natural numbers.",1079,216,{"id":22,"name":307,"photo":308,"biography":309,"created_at":8,"updated_at":8,"rating":310,"total_answer":311},"Jett","https://api.math-master.org/img/experts/6/6.webp","Hello,\nI am pleased to introduce myself as a Mathmaster Expert π\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 ππ",4.7,92,{"data":313},{"questions":314},[315,319,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387,391],{"id":316,"category":36,"text_question":317,"slug":318},533894,"34Γβ1-2Γ+3=7Γβ1+2","3-4-1-2-3-7-1-2",{"id":320,"category":36,"text_question":321,"slug":322},533900,"a) A tap can supply eight gallons of gasoline daily to each of its 250 customers for 60 days. By how many gallons should each customer's daily supply be reduced so that it can supply 50 more customers for twenty more days?","a-a-tap-can-supply-eight-gallons-of-gasoline-daily-to-each-of-its-250-customers-for-60-days-by-how-many-gallons-should-each-customer-39-s-daily-supply-be-reduced-so-that-it-can-supply-50-more-custo",{"id":324,"category":36,"text_question":325,"slug":326},533939,"[36,000,0000.000003^2]divided0.00000006","36-000-000-0-000003-2-divided-0-00000006",{"id":328,"category":36,"text_question":329,"slug":330},533959,"What will be the density of a fluid whose volume is 130 cubic meters\n contains 16 technical units of mass? If required Consider g=10 m/s2","what-will-be-the-density-of-a-fluid-whose-volume-is-130-cubic-meters-contains-16-technical-units-of-mass-if-required-consider-g-10-m-s2",{"id":332,"category":36,"text_question":333,"slug":334},533966,"A juice shop prepares assorted juices, for their juices they have 5 different types of\n fruit. How many types of assortments can be prepared in total, if it is considered an assortment\n to a juice made with two or more fruits?","a-juice-shop-prepares-assorted-juices-for-their-juices-they-have-5-different-types-of-fruit-how-many-types-of-assortments-can-be-prepared-in-total-if-it-is-considered-an-assortment-to-a-juice-mad",{"id":336,"category":36,"text_question":337,"slug":338},533986,"3x(2 9x 6)/5x(2-20)","3x-2-9x-6-5x-2-20",{"id":340,"category":36,"text_question":341,"slug":342},534035,"4x-3y=24 and 5x-2y=9 solve by elimination","4x-3y-24-and-5x-2y-9-solve-by-elimination",{"id":344,"category":36,"text_question":345,"slug":346},534073,"How long will it take for 900tobecome5000 at an annual rate of 11.15% compounded bimonthly?","how-long-will-it-take-for-900-to-become-5000-at-an-annual-rate-of-11-15-compounded-bimonthly",{"id":348,"category":36,"text_question":349,"slug":350},534106,"Find the equation of the line perpendicular to β5π₯β3π¦+5=0 passing through the point 0,β2","find-the-equation-of-the-line-perpendicular-to-5x-3y-5-0-passing-through-the-point-0-2",{"id":352,"category":36,"text_question":353,"slug":354},534198,"Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.","calculate-the-boiling-temperature-and-freezing-temperature-at-1-atmosphere-pressure-of-a-solution-formed-by-dissolving-123-grams-of-ferrous-oxide-in-1-890-grams-of-hcl",{"id":356,"category":36,"text_question":357,"slug":358},534206,"The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included.\r\na) What is the amount of VAT paid by the hotel for one","the-price-per-night-of-a-suite-at-the-baglioni-hotel-in-venice-is-1896-euros-vat-included-the-vat-in-italy-is-25-the-hotel-gets-a-return-of-10-out-of-the-price-vat-included-a-what-is-the-amoun",{"id":360,"category":36,"text_question":361,"slug":362},534272,"The simple average of 15\n , 30\n , 40\n , and 45\n is","the-simple-average-of-15-30-40-and-45-is",{"id":364,"category":36,"text_question":365,"slug":366},534283,"Use linear approximation to estimate the value of the sine of 31o.","use-linear-approximation-to-estimate-the-value-of-the-sine-of-31o",{"id":368,"category":36,"text_question":369,"slug":370},534385,"Sections of steel tube having an inside diameter of 9 inches, are filled with concrete to support the main floor girder in a building. If these posts are 12 feet long and there are 18 of them, how many cubic yards of concrete are required for the job?","sections-of-steel-tube-having-an-inside-diameter-of-9-inches-are-filled-with-concrete-to-support-the-main-floor-girder-in-a-building-if-these-posts-are-12-feet-long-and-there-are-18-of-them-how-man",{"id":372,"category":36,"text_question":373,"slug":374},534386,"A building lot is in the shape of a triangle with a base of 133 feet and a height of 76 feet.\nWhat is it's area in square feet?","a-building-lot-is-in-the-shape-of-a-triangle-with-a-base-of-133-feet-and-a-height-of-76-feet-what-is-it-s-area-in-square-feet",{"id":376,"category":36,"text_question":377,"slug":378},534387,"A hardware bill totals 857.63withdiscountsof5776.34 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",{"data":396},[397,401,405],{"id":398,"question":399,"answer":400},112821,"What is the result of adding the vectors v = 2i - 3j + 4k and u = -i + 5j - 2k?","The sum of the vectors is s = 2β1i + β3+5j + 4β2k = i + 2j + 2k.",{"id":402,"question":403,"answer":404},154730,"Question: What is the absolute extrema of the function fx = x^3 - 6x^2 + 9x + 2 on the interval [-2, 4]?","Answer: To find the absolute extrema, we first check the critical points within the interval. By taking the derivative of fx and setting it equal to zero, we find that the critical points are x = 1 and x = 3. Evaluating fx at these critical points and the endpoints of the interval, we get fβ2 = 2, f1 = 6, f3 = 2, and f4 = 18. Therefore, the absolute minimum is 2 at x = -2 and x = 3, while the absolute maximum is 18 at x = 4.",{"id":406,"question":407,"answer":408},111017,"Question: Convert 4.6 x 10^6 to standard notation.","Answer: In scientific notation, 4.6 x 10^6 represents 4,600,000 in standard notation.",{"$sicons":410},{"bxl:facebook-circle":411,"bxl:instagram":415,"mdi:web":417,"la:apple":419,"ph:google-logo-bold":422,"ph:google-logo":425},{"left":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":184,"hFlip":184,"body":414},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":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":184,"hFlip":184,"body":416},"\u003Cpath 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