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You own 24 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

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Answer to a math question You own 24 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

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Sigrid
4.5
112 Answers
1. Calculate the total number of ways to arrange 9 CDs out of 24. This is the number of permutations of 9 CDs, given by:

24P9 = \frac{24!}{(24-9)!} = \frac{24!}{15!}

2. For the arrangement to be in alphabetical order, there is exactly 1 way sinceonlyonespecificorderisalphabetical.

3. The probability that the CDs are in alphabetical order is the number of favorable outcomes 1 divided by the total number of arrangements calculated in step 1:

\frac{1}{\frac{24!}{15!}} = \frac{15!}{24!}

4. Simplify this to get the probability that the CDs are in alphabetical order:

\frac{1}{9!}

Therefore, the final answer is: \frac{1}{9!}=\frac{1}{362880}

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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 naučio 15 pitanja od 20, tako da je broj pitanja koja nije naučio \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 naučio 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+Bβˆ’29=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 + Bβˆ’29 = 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>133βˆ’1\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 \\leftfrac1βˆ’(1+r)βˆ’nrright\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 \\leftfrac1βˆ’(1+0.00625)βˆ’1800.00625right\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+12wβˆ’5 = 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,sincewidthcanβ€²tbenegative\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 + 3xβˆ’8 = 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},[218,222,226,230,234,237,241,245,249,253,257,261,265,269,273,277,281,285,289,293],{"id":219,"category":36,"text_question":220,"slug":221},532048,"CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated withjustification that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.","case-6-1-prepare-a-production-plan-what-problems-arrive-midwest-plastics-company-has-conducted-profit-planning-for-several-years-the-president-stated-with-justification-that-inventory-control-an",{"id":223,"category":36,"text_question":224,"slug":225},532082,"Calculate the 6th term of PA whose 1st term is 6.5 and the ratio 5","calculate-the-6th-term-of-pa-whose-1st-term-is-6-5-and-the-ratio-5",{"id":227,"category":36,"text_question":228,"slug":229},533919,"a bank finds that the balances in its savings accounts are normally distributed with a mean of 500andastandarddeviationoffof40. What is the probability that a randomly selected account has a balance of more than 400?","aβˆ’bankβˆ’findsβˆ’thatβˆ’theβˆ’balancesβˆ’inβˆ’itsβˆ’savingsβˆ’accountsβˆ’areβˆ’normallyβˆ’distributedβˆ’withβˆ’aβˆ’meanβˆ’ofβˆ’500βˆ’andβˆ’aβˆ’standardβˆ’deviationβˆ’offβˆ’ofβˆ’40βˆ’whatβˆ’isβˆ’theβˆ’probabilityβˆ’thatβˆ’aβˆ’randomlyβˆ’selectedβˆ’accountβˆ’hasβˆ’a","id":231,"category":36,"textquestion":232,"slug":233,533945,"LetIβŠ‚Rbeaboundedandnonemptyinterval.Showthattherearenumbersa,b∈Rwitha≀band\nI=[a,b]orI=[a,b)orI=(a,b]orI=(a,b)","letβˆ’iβˆ’rβˆ’beβˆ’aβˆ’boundedβˆ’andβˆ’nonemptyβˆ’intervalβˆ’showβˆ’thatβˆ’thereβˆ’areβˆ’numbersβˆ’aβˆ’bβˆ’rβˆ’withβˆ’aβˆ’bβˆ’andβˆ’iβˆ’aβˆ’bβˆ’orβˆ’iβˆ’aβˆ’bβˆ’orβˆ’iβˆ’aβˆ’bβˆ’orβˆ’iβˆ’aβˆ’b","id":235,"category":36,"textquestion":236,"slug":236,533969,"7273736363βˆ’8","id":238,"category":36,"textquestion":239,"slug":240,533973,"4X225","4xβˆ’2βˆ’25","id":242,"category":36,"textquestion":243,"slug":244,534120,"If0101,whatisthebinaryrepresentationofthe4x16decoderoutput?","ifβˆ’0101βˆ’whatβˆ’isβˆ’theβˆ’binaryβˆ’representationβˆ’ofβˆ’theβˆ’4x16βˆ’decoderβˆ’output","id":246,"category":36,"textquestion":247,"slug":248,534226,"usingthemathandscienceknownaboutthejeffersonriverbridgeFindatrussinuseanddevelopaloaddiagram.Usealoadof50lboneachjointalongthebottomofthetrussforatrussthatactrsasabridgeandalongthetopjointsforatrussthatactsasaroof","usingβˆ’theβˆ’mathβˆ’andβˆ’scienceβˆ’knownβˆ’aboutβˆ’theβˆ’jeffersonβˆ’riverβˆ’bridgeβˆ’findβˆ’aβˆ’trussβˆ’inβˆ’useβˆ’andβˆ’developβˆ’aβˆ’loadβˆ’diagramβˆ’useβˆ’aβˆ’loadβˆ’ofβˆ’50βˆ’lbβˆ’onβˆ’eachβˆ’jointβˆ’alongβˆ’theβˆ’bottomβˆ’ofβˆ’theβˆ’trussβˆ’forβˆ’aβˆ’trussβˆ’thatβˆ’actrs","id":250,"category":36,"textquestion":251,"slug":252,534253,"IfX1andX2areindependentstandardnormalvariables,findP(X12+X22>2.41)","ifβˆ’x1βˆ’andβˆ’x2βˆ’areβˆ’independentβˆ’standardβˆ’normalβˆ’variablesβˆ’findβˆ’pβˆ’x1βˆ’2βˆ’x2βˆ’2βˆ’2βˆ’41","id":254,"category":36,"textquestion":255,"slug":256,534264,"Howmuchdoestheaveragecollegestudentspendonfoodpermonth?Arandomsampleof50collegestudentsshowedasamplemean670 with a standard deviation 80.Obtainthe9510250 at a rate of 1% for one month. How much interest\nis charged for 4 months?","a-contractor-gives-a-bank-note-for-10250-at-a-rate-of-1-for-one-month-how-much-interest-is-charged-for-4-months",{"id":270,"category":36,"text_question":271,"slug":272},534446,"To get to a hotel on the hill you have to travel 6 km of uphill road and every kilometer there are 6 sharp curves. Each of the sharp curves is marked by three traffic signs. How many traffic signs are there on the stretch of road that leads to the arbergi?","to-get-to-a-hotel-on-the-hill-you-have-to-travel-6-km-of-uphill-road-and-every-kilometer-there-are-6-sharp-curves-each-of-the-sharp-curves-is-marked-by-three-traffic-signs-how-many-traffic-signs-are",{"id":274,"category":36,"text_question":275,"slug":276},534491,"A salesperson earns a base salary of 600permonthplusacommissionof10100 worth of sales.\n How many hours will you have to work on average each month for your income to be 2000?","aβˆ’salespersonβˆ’earnsβˆ’aβˆ’baseβˆ’salaryβˆ’ofβˆ’600βˆ’perβˆ’monthβˆ’plusβˆ’aβˆ’commissionβˆ’ofβˆ’10βˆ’ofβˆ’theβˆ’salesβˆ’sheβˆ’makesβˆ’youβˆ’discoverβˆ’thatβˆ’onβˆ’averageβˆ’itβˆ’takesβˆ’youβˆ’anβˆ’hourβˆ’andβˆ’aβˆ’halfβˆ’toβˆ’makeβˆ’100βˆ’worthβˆ’ofβˆ’salesβˆ’howβˆ’man","id":278,"category":36,"textquestion":279,"slug":280,534515,"Evaluateab+dc\nifa=56\n,b=βˆ’34\n,c=0.4\n,andd=12\n.Writeinsimplestform.","evaluateβˆ’abβˆ’dcβˆ’ifβˆ’aβˆ’56βˆ’bβˆ’34βˆ’cβˆ’0βˆ’4βˆ’andβˆ’dβˆ’12βˆ’writeβˆ’inβˆ’simplestβˆ’form","id":282,"category":36,"textquestion":283,"slug":284,534537,"2βˆ’6x=βˆ’16x+28","2βˆ’6xβˆ’16xβˆ’28","id":286,"category":36,"textquestion":287,"slug":288,534547,"2.3X0.8","2βˆ’3βˆ’xβˆ’0βˆ’8","id":290,"category":36,"textquestion":291,"slug":292,534582,"16βˆ’(xΒ²+x+2)Β²","16βˆ’xβˆ’xβˆ’2","id":294,"category":36,"textquestion":295,"slug":296,534668,"Thesupplyofagoodregistersperiodicincreases.Witheachincreaseintheoffer,thetotalreceiptsofthebiddersincrease.Indicatethecorrectstatement:a)demandiselasticb)demandisinelasticc)supplyisinelasticd)supplyhasunitelasticity.","theβˆ’supplyβˆ’ofβˆ’aβˆ’goodβˆ’registersβˆ’periodicβˆ’increasesβˆ’withβˆ’eachβˆ’increaseβˆ’inβˆ’theβˆ’offerβˆ’theβˆ’totalβˆ’receiptsβˆ’ofβˆ’theβˆ’biddersβˆ’increaseβˆ’indicateβˆ’theβˆ’correctβˆ’statementβˆ’aβˆ’demandβˆ’isβˆ’elasticβˆ’bβˆ’demandβˆ’isβˆ’inelas","data":298,"id":299,"category":36,"slug":300,"textquestion":301,"photoquestion":8,"textanswer":302,"steptextanswer":8,"stepphotoanswer":8,"views":303,"likes":304,"expert":305,537604,"youβˆ’ownβˆ’24βˆ’cdsβˆ’youβˆ’wantβˆ’toβˆ’randomlyβˆ’arrangeβˆ’9βˆ’ofβˆ’themβˆ’inβˆ’aβˆ’cdβˆ’rackβˆ’whatβˆ’isβˆ’theβˆ’probabilityβˆ’thatβˆ’theβˆ’rackβˆ’endsβˆ’upβˆ’inβˆ’alphabeticalβˆ’orderβˆ’theβˆ’probabilityβˆ’thatβˆ’theβˆ’cdsβˆ’areβˆ’inβˆ’alphabeticalβˆ’orderβˆ’is","Youown24CDs.Youwanttorandomlyarrange9oftheminaCDrack.Whatistheprobabilitythattherackendsupinalphabeticalorder?\r\n\r\nTheprobabilitythattheCDsareinalphabeticalorderis","1.Calculatethetotalnumberofwaystoarrange9CDsoutof24.Thisisthenumberofpermutationsof9CDs,givenby:\u003Cbr>\u003Cbr>\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>24P9=frac24!(24βˆ’9)!=frac24!15!\u003C/mathβˆ’field>\u003C/mathβˆ’field>\u003Cbr>\u003Cbr>2.Forthearrangementtobeinalphabeticalorder,thereisexactly1way(sinceonlyonespecificorderisalphabetical).\u003Cbr>\u003Cbr>3.TheprobabilitythattheCDsareinalphabeticalorderisthenumberoffavorableoutcomes(1)dividedbythetotalnumberofarrangementscalculatedinstep1:\u003Cbr>\u003Cbr>\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>frac1frac24!15!=frac15!24!\u003C/mathβˆ’field>\u003C/mathβˆ’field>\u003Cbr>\u003Cbr>4.SimplifythistogettheprobabilitythattheCDsareinalphabeticalorder:\u003Cbr>\u003Cbr>\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>frac19!\u003C/mathβˆ’field>\u003C/mathβˆ’field>\u003Cbr>\u003Cbr>Therefore,thefinalansweris:\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>frac19!=frac1362880\u003C/mathβˆ’field>\u003C/mathβˆ’field>",1389,278,"id":16,"name":306,"photo":307,"biography":308,"createdat":8,"updatedat":8,"rating":309,"totalanswer":310,"Sigrid","https://api.mathβˆ’master.org/img/experts/4/4.webp","Hi,Iβ€²mNeha,andIwanttosharemyjourneyoffallinginlovewithmaths.ItallstartedatmyhomewhenIwasacuriouskid.IcansayMathsrunsthroughmyveinsasmymotherisaMathsteacher.MathsproblemsusedtofascinatemealotsinceIwasakid.\nBackinElementarySchool,Ibeganlearningthebasicsofmathlikeadding,subtracting,andshapes.Myteacherssawmyinterestandencouragedmetoexploremore.AsImovedtoHighSchool,mathgotmoreexcitingwithstuffliketrigonometry,calculus,andfancierequations.Ijoinedmathclubs,madefriendswholovedmathandgotbetteratsolvingtoughproblems.\nThencameUniversity,wheremathturnedintoawholenewlevelofamazing.IdidmyGraduationinScience(withPhysics,Chemistry,andMathsasmajors)andthencompletedmyMasterβ€²s(PostGraduation)withMathematicsasmymajorfromGuruNanakDevUniversity.MyprofessorstaughtmeadvancedtopicslikeComplexanalysis,AbstractAlgebra,Numericalanalysis,andmanymoreandIlovedeverymomentofit.Learningbecameanadventure.\nAfterfinishinguniversity,Istartedusingmathininternshipsandjobs.IworkedinaschoolasaPGT(Postgraduateteacher)forayearandthenIgottheopportunitytotutorinternationalstudents.IreceivedanInternationalTutoringcertificateaswell.Andafterthat,Icametoknowaboutthewonderfulplatform\"MATHMASTER\"whereIβ€²mcurrentlyworking.IamgratefulthatMathmasterprovidedmewithawonderfulopportunitytoharnessandapplymyskillsinatrulyeffectivemanner.Itprovidedmeanopportunitytosharemyknowledgewithstudentsandhelpmeimprovemyproblemβˆ’solvingskills.Itβ€²sawesometoseehowmathcouldsolverealproblemsandmakeadifference.\nMyjourneywithmathshasbeenincredible.Fromthoseearlymathpuzzlestotacklingcomplextheories,Iβ€²vegrownsomuch.Mymathsjourneyhasbeenamazing.Fromcuriouskidtouniversityexplorer,Iβ€²velearnedthatmathiseverywhereandcanbesomuchfun.Iβ€²llkeepusingmymathskillstomaketheworldabetterplaceandinspireotherstoembracethemagicofnumbers.Ihopemystoryinspiresyoutoneverstopexploringbecausemathisajourneythatneverreallyends.",4.5,112,"data":312,"questions":313,[314,318,322,326,330,334,338,342,346,350,354,358,362,365,369,373,377,381,385,389],"id":315,"category":36,"textquestion":316,"slug":317,532014,"Twofirelookoutsare12.5kmapartonanorthβˆ’southline.Thenorthernfirelookoutsightsafire20Β°southofEastatthesametimeasthesouthernfirelookoutspotsitat60Β°EastofNorth.HowfaristhefirefromtheSouthernlookout?Roundyouranswertothenearesttenthofakilometer","twoβˆ’fireβˆ’lookoutsβˆ’areβˆ’12βˆ’5βˆ’kmβˆ’apartβˆ’onβˆ’aβˆ’northβˆ’southβˆ’lineβˆ’theβˆ’northernβˆ’fireβˆ’lookoutβˆ’sightsβˆ’aβˆ’fireβˆ’20βˆ’southβˆ’ofβˆ’eastβˆ’atβˆ’theβˆ’sameβˆ’timeβˆ’asβˆ’theβˆ’southernβˆ’fireβˆ’lookoutβˆ’spotsβˆ’itβˆ’atβˆ’60βˆ’eastβˆ’ofβˆ’northβˆ’howβˆ’fa","id":319,"category":36,"textquestion":320,"slug":321,532017,"HeyπŸ‘‹πŸ»\n\nTap\"CreateNewTask\"tosendyourmathproblem.\n\nOneofourexpertswillstartworkingonitrightaway!","heyβˆ’tapβˆ’createβˆ’newβˆ’taskβˆ’toβˆ’sendβˆ’yourβˆ’mathβˆ’problemβˆ’oneβˆ’ofβˆ’ourβˆ’expertsβˆ’willβˆ’startβˆ’workingβˆ’onβˆ’itβˆ’rightβˆ’away","id":323,"category":36,"textquestion":324,"slug":325,532300,"AhotelintheAlgarvehadtooffer1weekofvacationtooneofitsemployeesasanEastergiftinarandomchoice.Itisknownthat80peopleworkinthishotelunit,41ofwhomarePortugueseand39areforeignnationals.Thereare14Portuguesemenand23foreignwomen.Usingwhatyouknowaboutconditionalprobability,checktheprobabilitythatthegiftwasofferedtoaPortuguesecitizen,knowingthatitwasawoman.","aβˆ’hotelβˆ’inβˆ’theβˆ’algarveβˆ’hadβˆ’toβˆ’offerβˆ’1βˆ’weekβˆ’ofβˆ’vacationβˆ’toβˆ’oneβˆ’ofβˆ’itsβˆ’employeesβˆ’asβˆ’anβˆ’easterβˆ’giftβˆ’inβˆ’aβˆ’randomβˆ’choiceβˆ’itβˆ’isβˆ’knownβˆ’thatβˆ’80βˆ’peopleβˆ’workβˆ’inβˆ’thisβˆ’hotelβˆ’unitβˆ’41βˆ’ofβˆ’whomβˆ’areβˆ’portugueseβˆ’andβˆ’3","id":327,"category":36,"textquestion":328,"slug":329,533901,"Foratemperaturerangebetween177degreesCelsiusto213degreesCelsius,whatisthetemperaturerangeindegreesFahrenheit.","forβˆ’aβˆ’temperatureβˆ’rangeβˆ’betweenβˆ’177βˆ’degreesβˆ’celsiusβˆ’toβˆ’213βˆ’degreesβˆ’celsiusβˆ’whatβˆ’isβˆ’theβˆ’temperatureβˆ’rangeβˆ’inβˆ’degreesβˆ’fahrenheit","id":331,"category":36,"textquestion":332,"slug":333,533991,"Anintegeristakenatrandomfromthefirst40positiveintegers.Whatistheprobabilitythattheintegerisdivisibleby5or6?","anβˆ’integerβˆ’isβˆ’takenβˆ’atβˆ’randomβˆ’fromβˆ’theβˆ’firstβˆ’40βˆ’positiveβˆ’integersβˆ’whatβˆ’isβˆ’theβˆ’probabilityβˆ’thatβˆ’theβˆ’integerβˆ’isβˆ’divisibleβˆ’byβˆ’5βˆ’orβˆ’6","id":335,"category":36,"textquestion":336,"slug":337,534043,"Theequationofthecirclethatpassesthrough(5,3)andistangenttotheabscissaaxisatx=2is\na.(xβˆ’2)2(y3)2=9\nb.(xβˆ’2)2(yβˆ’3)2=9\nc.(xβˆ’2)2(yβˆ’3)2=4\nd.(xβˆ’2)2(y1)2=4\ne.(xβˆ’2)2(yβˆ’1)2=4","theβˆ’equationβˆ’ofβˆ’theβˆ’circleβˆ’thatβˆ’passesβˆ’throughβˆ’5βˆ’3βˆ’andβˆ’isβˆ’tangentβˆ’toβˆ’theβˆ’abscissaβˆ’axisβˆ’atβˆ’xβˆ’2βˆ’isβˆ’aβˆ’xβˆ’2βˆ’2βˆ’yβˆ’3βˆ’2βˆ’9βˆ’bβˆ’xβˆ’2βˆ’2βˆ’yβˆ’3βˆ’2βˆ’9βˆ’cβˆ’xβˆ’2βˆ’2βˆ’yβˆ’3βˆ’2βˆ’4βˆ’dβˆ’xβˆ’2βˆ’2βˆ’yβˆ’1βˆ’2βˆ’4βˆ’eβˆ’xβˆ’2","id":339,"category":36,"textquestion":340,"slug":341,534109,"4x/2+5xβˆ’3/6=7/8βˆ’1/4βˆ’x","4xβˆ’2βˆ’5xβˆ’3βˆ’6βˆ’7βˆ’8βˆ’1βˆ’4βˆ’x","id":343,"category":36,"textquestion":344,"slug":345,534150,"Primesarenumbersdivisibleonlyby1andthemselves;Thereareinfinitelymanyprimenumbersandthefirstonesare2,3,5,7,11,13,17,19,23,....Considera12βˆ’sideddie,withthefacesnumberedfrom1to12.Outof4rolls,theprobabilitythatonlythefirstthreenumbersareprimesis:","primesβˆ’areβˆ’numbersβˆ’divisibleβˆ’onlyβˆ’byβˆ’1βˆ’andβˆ’themselvesβˆ’thereβˆ’areβˆ’infinitelyβˆ’manyβˆ’primeβˆ’numbersβˆ’andβˆ’theβˆ’firstβˆ’onesβˆ’areβˆ’2βˆ’3βˆ’5βˆ’7βˆ’11βˆ’13βˆ’17βˆ’19βˆ’23βˆ’considerβˆ’aβˆ’12βˆ’sidedβˆ’dieβˆ’withβˆ’theβˆ’facesβˆ’numbe","id":347,"category":36,"textquestion":348,"slug":349,534176,"Threesquareshaveatotalareaof35.25π‘π‘š2\r\n.Thelargersquarehastwicethesideβˆ’lengthofthe\r\nmiddleβˆ’sizedsquare.Thesmallersquarehasitssidelengthexactly0.5cmsmallerthanthe\r\nmiddleβˆ’sixedsquare.Findthesidelengthsofeachofthethreesquares.","threeβˆ’squaresβˆ’haveβˆ’aβˆ’totalβˆ’areaβˆ’ofβˆ’35βˆ’25βˆ’cm2βˆ’theβˆ’largerβˆ’squareβˆ’hasβˆ’twiceβˆ’theβˆ’sideβˆ’lengthβˆ’ofβˆ’theβˆ’middleβˆ’sizedβˆ’squareβˆ’theβˆ’smallerβˆ’squareβˆ’hasβˆ’itsβˆ’sideβˆ’lengthβˆ’exactlyβˆ’0βˆ’5βˆ’cmβˆ’smallerβˆ’thanβˆ’theβˆ’middle","id":351,"category":36,"textquestion":352,"slug":353,534203,"Whatβ€²stheslopeofatangentlineatx=1forf(x)=x2.Wecanfindtheslopesofasequenceofsecantlinesthatgetcloserandclosertothetangentline.Whatweareworkingtowardsistheprocessoffindingaβ€œlimit”whichisafoundationaltopicofcalculus.","whatβˆ’sβˆ’theβˆ’slopeβˆ’ofβˆ’aβˆ’tangentβˆ’lineβˆ’atβˆ’xβˆ’1βˆ’forβˆ’fβˆ’xβˆ’x2βˆ’weβˆ’canβˆ’findβˆ’theβˆ’slopesβˆ’ofβˆ’aβˆ’sequenceβˆ’ofβˆ’secantβˆ’linesβˆ’thatβˆ’getβˆ’closerβˆ’andβˆ’closerβˆ’toβˆ’theβˆ’tangentβˆ’lineβˆ’whatβˆ’weβˆ’areβˆ’workingβˆ’towardsβˆ’isβˆ’theβˆ’process","id":355,"category":36,"textquestion":356,"slug":357,534249,"3Atreeisplantedwhenitis1.2mtall.Everyyearitsgrowthis3/8ofitspreviousyearβ€²sheight.Findhowtallthetreewillgrow.","3βˆ’aβˆ’treeβˆ’isβˆ’plantedβˆ’whenβˆ’itβˆ’isβˆ’1βˆ’2βˆ’mβˆ’tallβˆ’everyβˆ’yearβˆ’itsβˆ’growthβˆ’isβˆ’3βˆ’8βˆ’ofβˆ’itsβˆ’previousβˆ’yearβˆ’sβˆ’heightβˆ’findβˆ’howβˆ’tallβˆ’theβˆ’treeβˆ’willβˆ’grow","id":359,"category":36,"textquestion":360,"slug":361,534267,"Usethesampledataandconfidencelevelgivenbelowtocompleteparts​(a)through​(d).\nAdrugisusedtohelppreventbloodclotsincertainpatients.Inclinical​trials,among4336patientstreatedwiththe​drug,194developedtheadversereactionofnausea.Constructa​99104259 is taken out for 10 years with an annual interest rate of 9.4%, compounded quarterly. What quarterly payment is required to pay the loan off in 10 years? \n\nEnter to the nearest cent twodecimals. Do not use signsorcommasintheanswer.","17βˆ’aβˆ’loanβˆ’forβˆ’104259βˆ’isβˆ’takenβˆ’outβˆ’forβˆ’10βˆ’yearsβˆ’withβˆ’anβˆ’annualβˆ’interestβˆ’rateβˆ’ofβˆ’9βˆ’4βˆ’compoundedβˆ’quarterlyβˆ’whatβˆ’quarterlyβˆ’paymentβˆ’isβˆ’requiredβˆ’toβˆ’payβˆ’theβˆ’loanβˆ’offβˆ’inβˆ’10βˆ’yearsβˆ’enterβˆ’toβˆ’theβˆ’nearest","id":382,"category":36,"textquestion":383,"slug":384,534458,"GiventhewordWEIRD,determineafourβˆ’letteroffspringthatcanbeformedwiththelettersofthewordwrittenabove","givenβˆ’theβˆ’wordβˆ’weirdβˆ’determineβˆ’aβˆ’fourβˆ’letterβˆ’offspringβˆ’thatβˆ’canβˆ’beβˆ’formedβˆ’withβˆ’theβˆ’lettersβˆ’ofβˆ’theβˆ’wordβˆ’writtenβˆ’above","id":386,"category":36,"textquestion":387,"slug":388,534531,"Theaverageweeklyearningsintheleisureandhospitalityindustrygroupforare‐\r\ncentyearwas273. A random sample of 40 workers showed weekly average ear‐\r\nnings of 285withthepopulationstandarddeviationequalto58.Atthe0.05levelof\r\nsignificancecanitbeconcludedthatthemeandiffersfrom273? Find a 95% con‐\r\nfidence interval for the weekly earnings and show that it supports the results of the\r\nhypothesis test.","the-average-weekly-earnings-in-the-leisure-and-hospitality-industry-group-for-a-re-cent-year-was-273-a-random-sample-of-40-workers-showed-weekly-average-ear-nings-of-285-with-the-population-sta",{"id":390,"category":36,"text_question":391,"slug":392},534636,"-Please answer to the following questions:\r\n\r\nWhat is the price elasticity of demand? Can you explain it in your own words? \r\n\r\nWhat is the price elasticity of supply? Can you explain it in your own words?\r\n\r\nWhat is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that?\r\n\r\n\r\nB-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? \r\n\r\nWhat if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources minimum2.","please-answer-to-the-following-questions-what-is-the-price-elasticity-of-demand-can-you-explain-it-in-your-own-words-what-is-the-price-elasticity-of-supply-can-you-explain-it-in-your-own-w",{"data":394},[395,399,403],{"id":396,"question":397,"answer":398},158084,"What is the average number of hours spent by students on homework per week? "," The answer may vary based on the data collected, but it can be found by summing the total hours spent by students and dividing by the number of students surveyed.",{"id":400,"question":401,"answer":402},149755,"Find the value of cosh2(x - sinh^2x)/tanhx when sinhx = 3.7.","The value is approximately -2.9253. Explanation: We use the identity cosh^2x - sinh^2x = 1 to substitute and simplify the expression. Then, divide by tanhx = sinhx/coshx. Given sinhx = 3.7, we can find coshx = sqrtsinh2(x + 1). Substitute these values and calculate to find the answer.",{"id":404,"question":405,"answer":406},112143,"What is the unit vector in the direction of vector v = 3,βˆ’4,12?","The unit vector is 0.2308,βˆ’0.3077,0.9231. To obtain this, divide each component of the vector v by its magnitude.",{"$sicons":408},{"bxl:facebook-circle":409,"bxl:instagram":413,"mdi:web":415,"la:apple":417,"ph:google-logo-bold":420,"ph:google-logo":423},{"left":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":184,"hFlip":184,"body":412},0,24,"\u003Cpath 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":410,"top":410,"width":411,"height":411,"rotate":410,"vFlip":184,"hFlip":184,"body":414},"\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 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" 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