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A set of final grades for an Introduction to Statistics course is normally distributed with a mean of 75 and a deviation of 6. With a 10% probability that the student takes the exam, what is the highest score within this percentage? Write your answer using 2 decimal places.

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Answer to a math question A set of final grades for an Introduction to Statistics course is normally distributed with a mean of 75 and a deviation of 6. With a 10% probability that the student takes the exam, what is the highest score within this percentage? Write your answer using 2 decimal places.

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Miles
4.9
100 Answers
1. Identify known values:
\mu = 75
\sigma = 6
z = -1.28

2. Use the z-score formula rearranged for X:
X = \mu + z \times \sigma

3. Substitute the values into the formula:
X = 75 + (-1.28) \times 6

4. Calculate:
X = 75 - 7.68
X = 67.32

5. Therefore, the highest score within the bottom 10% is:
X = 67.32

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There are several students in the class and some pairs are friends thefriendshiprelationshipissymmetrical. Every student has at least one friend. The whole class came to MatFyz, where each student chooses exactly one of the lectures: either mathematics or computer science. Can you prove that ineachsuchclass the students can divide themselves into two lectures so that each studentZhad at least one friend who attended a different lecture than the student himself Z.","","1. Consider the students and friends as a graph where each student is a vertex, and an undirected edge exists between two vertices if both students are friends. \u003Cbr />\n2. The problem requires proving that this graph is bipartite. \u003Cbr />\n3. A graph is bipartite if and only if it has no odd-length cycles.\u003Cbr />\n4. Start with any vertex and perform BFS or DFS to try to color the graph using two colors, such that no two adjacent vertices share the same color. \u003Cbr />\n5. If successful, you have a bipartite graph, meaning that nodes can be divided into two groups, each corresponding to one lecture.\u003Cbr />\n6. If at any point you find a vertex with the same color during the graph traversal across an edge, there exists an odd-length cycle.\u003Cbr />\n7. The presence of such a cycle would contradict the criteria as friendship is symmetrical, ensuring each cycle detected can be colored alternately, validating bipartiteness.\u003Cbr />\n8. Since each student has at least one friend, and that ensures the graph has no isolated points, every path will connect properly into two sets.\u003Cbr />\n9. Thus, the students can always be divided into two lectures maintaining the condition.\u003Cbr />\n\u003Cbr />\nAnswer: The students can always be divided in a manner where each student has at least one friend attending a different lecture.",1006,201,"task-4-1-5-points-there-are-several-students-in-the-class-and-some-pairs-are-friends-the-friendship-relationship-is-symmetrical-every-student-has-at-least-one-friend-the-whole-class-came-to-matfy",{"id":44,"category":36,"text_question":45,"photo_question":38,"text_answer":46,"step_text_answer":8,"step_photo_answer":8,"views":47,"likes":48,"slug":49},537910,"There are 120 seats in the cinema. Eighth grades come with the same number of students. If three grades come, there will be 54 free seats left. How many seats will be left if four grades come?\n Can you solve the problem in the form of a proportion or ratio?","Ako u dvoranu dolaze tri razredna odjela i ostaje 54 slobodna mjesta, to znači da dolazi \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field> učenika, gdje je \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> broj učenika u jednom razredu.\u003Cbr />\n\u003Cbr />\nBroj zauzetih mjesta s tri razreda:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>120 - 54 = 66\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nDakle:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x = 66 \\Rightarrow x = \\frac{66}{3} = 22\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nBroj učenika u jednom razredu je \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>22\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\nAko dolaze četiri razreda to znači da dolazi \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4 \\times 22 = 88\u003C/math-field>\u003C/math-field> učenika.\u003Cbr />\n\u003Cbr />\nBroj slobodnih mjesta s četiri razreda:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>120 - 88 = 32\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nDakle, ostat će \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>32\u003C/math-field>\u003C/math-field> slobodna mjesta.",777,155,"there-are-120-seats-in-the-cinema-eighth-grades-come-with-the-same-number-of-students-if-three-grades-come-there-will-be-54-free-seats-left-how-many-seats-will-be-left-if-four-grades-come-can-yo",{"id":51,"category":36,"text_question":52,"photo_question":38,"text_answer":53,"step_text_answer":8,"step_photo_answer":8,"views":54,"likes":55,"slug":56},537909,"There are 120 seats in the cinema. Eighth grades come with the same number of students. If three grades come, there will be 54 free seats left. How many seats will be left if four grades come?","1. Izračunaj broja mjesta zauzetih za 3 razreda: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field> \u003Cbr />\n2. Postavi jednadžbu: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>120 - 3x = 54\u003C/math-field>\u003C/math-field> \u003Cbr />\n3. Izračunaj broj učenika u jednom razredu: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x = 66\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{66}{3} = 22\u003C/math-field>\u003C/math-field> \u003Cbr />\n4. Izračunaj broj mjesta zauzetih za 4 razreda: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = 4 \\times 22 = 88\u003C/math-field>\u003C/math-field> \u003Cbr />\n5. Izračunaj broj slobodnih mjesta za 4 razreda: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>120 - 88 = 32\u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cbr />\nOdgovor: Broj učenika u jednom razredu je 22, a broj slobodnih mjesta kada dođe 4 razreda je 32.",942,188,"there-are-120-seats-in-the-cinema-eighth-grades-come-with-the-same-number-of-students-if-three-grades-come-there-will-be-54-free-seats-left-how-many-seats-will-be-left-if-four-grades-come",{"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},537908,"Determine the probability that when throwing a die, it will land:\n a) number 5\n b) a number less than 7\n c) number 1 or 4","a) The die is a cube with six faces and equal probability for each face. The number 5 appears on one face. Thus, the probability is:\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1 \\text{ favorable outcome}}{6 \\text{ total outcomes}} = \\frac{1}{6} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nb) All numbers on a standard die 1to6 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":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},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":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},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":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},537905,"431+B29=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 + B29 = 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":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},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":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},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":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},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":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},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":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},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":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},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":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},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>1331\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":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},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":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},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":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":153,"slug":154},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 \\leftfrac1(1+r)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 \\leftfrac1(1+0.00625)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":163,"category":36,"text_question":164,"photo_question":38,"text_answer":165,"step_text_answer":8,"step_photo_answer":8,"views":166,"likes":167,"slug":168},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":170,"category":36,"text_question":171,"photo_question":38,"text_answer":172,"step_text_answer":8,"step_photo_answer":8,"views":173,"likes":90,"slug":174},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+12w5 = 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,sincewidthcantbenegative\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",{"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",20,3587,{"data":216},{"id":217,"category":36,"slug":218,"text_question":219,"photo_question":8,"text_answer":220,"step_text_answer":8,"step_photo_answer":8,"views":221,"likes":222,"expert":223},537272,"a-set-of-final-grades-for-an-introduction-to-statistics-course-is-normally-distributed-with-a-mean-of-75-and-a-deviation-of-6-with-a-10-probability-that-the-student-takes-the-exam-what-is-the-hig","A set of final grades for an Introduction to Statistics course is normally distributed with a mean of 75 and a deviation of 6.\n\n With a 10% probability that the student takes the exam, what is the highest score within this percentage?\n\n Write your answer using 2 decimal places.","1. Identify known values:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\mu = 75 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\sigma = 6 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> z = -1.28 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the z-score formula rearranged for \\( X \\):\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> X = \\mu + z \\times \\sigma \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute the values into the formula:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> X = 75 + (-1.28) \\times 6 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> X = 75 - 7.68 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> X = 67.32 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cbr />\n5. Therefore, the highest score within the bottom 10% is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> X = 67.32 \u003C/math-field>\u003C/math-field>",1157,231,{"id":224,"name":225,"photo":226,"biography":227,"created_at":8,"updated_at":8,"rating":228,"total_answer":229},15,"Miles","https://api.math-master.org/img/experts/15/15.webp","My name is Ali Haider and I hold a bachelor’s degree in Electrical Engineering and I am also certified Math Expert. I have been teaching Mathematics and Physics for the past 6 years at both the high school and college level. My pass rate for Mathematics is 100%.\nIn addition to teaching, I love playing badminton and video games.\n",4.9,100,{"data":231},{"questions":232},[233,237,241,245,249,253,257,261,265,269,273,277,281,285,289,293,297,301,305,309],{"id":234,"category":36,"text_question":235,"slug":236},532047,"2+2","2-2",{"id":238,"category":36,"text_question":239,"slug":240},532310,"The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?","the-random-variable-y-is-defined-as-the-sum-between-two-different-integers-selected-at-random-between-4-and-2-both-included-what-are-the-possible-values-of-the-random-variable-y-what-is-the-value",{"id":242,"category":36,"text_question":243,"slug":244},533955,"Solve the math problem \r\n400 students are asked if they live in an apartment and have a pet:\r\nApartment: 120\r\nBoth: 30\r\nPet: 90\r\n\r\nThe probability that a randomly selected student not living in an apartment has a pet is","solve-the-math-problem-400-students-are-asked-if-they-live-in-an-apartment-and-have-a-pet-apartment-120-both-30-pet-90-the-probability-that-a-randomly-selected-student-not-living-in-an-apa",{"id":246,"category":36,"text_question":247,"slug":248},534012,"Margin of error E=0.30 populations standard deviation =2.5. Population means with 95% confidence. What I the required sample size (round up to the whole number)","margin-of-error-e-0-30-populations-standard-deviation-2-5-population-means-with-95-confidence-what-i-the-required-sample-size-round-up-to-the-whole-number",{"id":250,"category":36,"text_question":251,"slug":252},534033,"Divide 22 by 5 solve it by array and an area model","divide-22-by-5-solve-it-by-array-and-an-area-model",{"id":254,"category":36,"text_question":255,"slug":256},534034,"(2b) to the 1/4th power. Write the expression in radical form.","2b-to-the-1-4th-power-write-the-expression-in-radical-form",{"id":258,"category":36,"text_question":259,"slug":260},534074,"Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?\n Draw the diagram","solve-this-mathematical-problem-if-3-5-of-a-roll-of-tape-measures-2m-how-long-is-the-complete-roll-draw-the-diagram",{"id":262,"category":36,"text_question":263,"slug":264},534096,"A construction company is working on two projects: house construction and building construction. Each house requires 4 weeks of work and produces a profit of $50,000. Each building requires 8 weeks of work and produces a profit of $100,000. The company has a total of 24 work weeks available.\n Furthermore, it is known that at least 2 houses and at least 1 building must be built to meet the demand. The company wants to maximize its profits and needs to determine how many houses and buildings it should build to meet demand and maximize profits, given time and demand constraints.","a-construction-company-is-working-on-two-projects-house-construction-and-building-construction-each-house-requires-4-weeks-of-work-and-produces-a-profit-of-50-000-each-building-requires-8-weeks-of",{"id":266,"category":36,"text_question":267,"slug":268},534107,"A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?","a-force-of-750-pounds-compresses-a-spring-3-inches-from-its-natural-length-which-is-15-inches-what-will-be-the-work-done-to-compress-it-3-inches-more",{"id":270,"category":36,"text_question":271,"slug":272},534109,"4x/2+5x-3/6=7/8-1/4-x","4x-2-5x-3-6-7-8-1-4-x",{"id":274,"category":36,"text_question":275,"slug":276},534121,"In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left.\n How many peppers and carrots were there initially?","in-a-grocery-store-when-you-take-out-3-peppers-and-4-carrots-there-are-26-peppers-and-46-carrots-left-how-many-peppers-and-carrots-were-there-initially",{"id":278,"category":36,"text_question":279,"slug":280},534204,"Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows:\n (Raúl wins) = 20%\n (Gilberto wins) = 0.05%\n (Arturo wins) = ¾%.\n\n Perform operations and order events from least to most probable.","raul-gilberto-and-arturo-are-playing-golf-the-probabilities-of-winning-for-each-one-are-as-follows-raul-wins-20-gilberto-wins-0-05-arturo-wins-perform-operations-and-order-ev",{"id":282,"category":36,"text_question":283,"slug":284},534282,"There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?","there-are-3-orchards-a-b-and-c-orchard-a-has-60-fewer-trees-than-orchard-b-orchard-c-has-3-times-as-many-trees-as-orchard-b-if-the-three-orchards-have-430-trees-altogether-how-many-trees-does-or",{"id":286,"category":36,"text_question":287,"slug":288},534304,"2)A tourist has 15 pairs of pants in his hotel room closet. Suppose 5 are blue and the rest are black. The tourist leaves his room twice a day. He takes a pair of pants and puts them on, the tourist leaves the first pair of pants in the closet again and takes another one and puts them on. What is the probability that the two pants chosen are black?","2-a-tourist-has-15-pairs-of-pants-in-his-hotel-room-closet-suppose-5-are-blue-and-the-rest-are-black-the-tourist-leaves-his-room-twice-a-day-he-takes-a-pair-of-pants-and-puts-them-on-the-tourist-l",{"id":290,"category":36,"text_question":291,"slug":292},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":294,"category":36,"text_question":295,"slug":296},534423,"find missing measure for triangle \narea = 48 m square\nbase = 10m\nheaighy = ? m","find-missing-measure-for-triangle-area-48-m-square-base-10m-heaighy-m",{"id":298,"category":36,"text_question":299,"slug":300},534517,"solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0","solve-r-the-following-equation-4-x-squared-35-9-over-x-squared-is-equal-to-0",{"id":302,"category":36,"text_question":303,"slug":304},534569,"the product of a 2-digit number and a 3-digit number is about 50000, what are these numbers","the-product-of-a-2-digit-number-and-a-3-digit-number-is-about-50000-what-are-these-numbers",{"id":306,"category":36,"text_question":307,"slug":308},534579,"What js the greatest 4-digit even number that can be formed by 3,6,1,4?","what-js-the-greatest-4-digit-even-number-that-can-be-formed-by-3-6-1-4",{"id":310,"category":36,"text_question":311,"slug":312},534650,"A rectangular swimming pool has a length of 14 feet, a width of 26 feet and a depth of 5 feet. Round answers to the nearest hundredth as needed.\n\n\n(a) How many cubic feet of water can the pool hold?\n cubic feet\n(b) The manufacturer suggests filling the pool to 95% capacity. How many cubic feet of water is this?\n cubic feet","a-rectangular-swimming-pool-has-a-length-of-14-feet-a-width-of-26-feet-and-a-depth-of-5-feet-round-answers-to-the-nearest-hundredth-as-needed-a-how-many-cubic-feet-of-water-can-the-pool-hold",{"data":314},{"questions":315},[316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,384,388,392],{"id":317,"category":36,"text_question":318,"slug":319},533921,"A food delivery company charges on average a delivery fee of $5 per order (including food and shipping) and has monthly fixed costs of $600. If the average cost of each meal delivered that is revenue for the company is $10 and the company has a monthly profit of $800, how many orders must they deliver per month?","a-food-delivery-company-charges-on-average-a-delivery-fee-of-5-per-order-including-food-and-shipping-and-has-monthly-fixed-costs-of-600-if-the-average-cost-of-each-meal-delivered-that-is-revenue",{"id":321,"category":36,"text_question":322,"slug":323},533927,"The graph of the equation x²= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F(_,_) and a directrix y=_____","the-graph-of-the-equation-x-4py-is-a-parabola-with-focus-f-and-directrix-y-therefore-the-graph-of-x-12y-is-a-parabola-with-focus-f-and-a-directrix-y",{"id":325,"category":36,"text_question":326,"slug":327},534015,"(5u + 6)-(3u+2)=","5u-6-3u-2",{"id":329,"category":36,"text_question":330,"slug":331},534043,"The equation of the circle that passes through (5,3) and is tangent to the abscissa axis at x=2 is\n a.(x-2)^2 (y 3)^2 = 9\n b.(x-2)^2 (y-3)^2 = 9\n c.(x-2)^2 (y-3)^2 = 4\n d.(x-2)^2 (y 1)^2 = 4\n e.(x-2)^2 (y-1)^2 = 4","the-equation-of-the-circle-that-passes-through-5-3-and-is-tangent-to-the-abscissa-axis-at-x-2-is-a-x-2-2-y-3-2-9-b-x-2-2-y-3-2-9-c-x-2-2-y-3-2-4-d-x-2-2-y-1-2-4-e-x-2",{"id":333,"category":36,"text_question":334,"slug":335},534097,"Pedro had 80% of the amount needed to buy a game. Of this amount, you spent 15% on a watch and therefore, you will need to add another R$640.00 to purchase this game. Is the value of the game?","pedro-had-80-of-the-amount-needed-to-buy-a-game-of-this-amount-you-spent-15-on-a-watch-and-therefore-you-will-need-to-add-another-r-640-00-to-purchase-this-game-is-the-value-of-the-game",{"id":337,"category":36,"text_question":338,"slug":339},534103,"Convert 78 percent to a decimal","convert-78-percent-to-a-decimal",{"id":341,"category":36,"text_question":342,"slug":343},534117,"According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card","according-to-a-survey-in-a-country-27-of-adults-do-not-own-a-credit-card-suppose-a-simple-random-sample-of-800-adults-is-obtained-describe-the-sampling-distribution-of-p-hat-the-sample-proportion",{"id":345,"category":36,"text_question":346,"slug":347},534177,"The sum of two numbers is 144. Double the first number minus thrice the second number is equal to 63. Determine the first two numbers.","the-sum-of-two-numbers-is-144-double-the-first-number-minus-thrice-the-second-number-is-equal-to-63-determine-the-first-two-numbers",{"id":349,"category":36,"text_question":350,"slug":351},534312,"The sick-leave time of employees in a firm in a month is normally with a mean of 100 hours and a standard deviation of 20 hours. Find the probability that the sick-leave time of an employee in a month exceeds 130 hours.","the-sick-leave-time-of-employees-in-a-firm-in-a-month-is-normally-with-a-mean-of-100-hours-and-a-standard-deviation-of-20-hours-find-the-probability-that-the-sick-leave-time-of-an-employee-in-a-month",{"id":353,"category":36,"text_question":354,"slug":355},534324,"Solve equations by equalization method\n X-8=-2y\n 2x+y=7","solve-equations-by-equalization-method-x-8-2y-2x-y-7",{"id":357,"category":36,"text_question":358,"slug":359},534337,"If the regression equation is given by 4x –y + 5 = 0, then the slope of regression line of y on x is","if-the-regression-equation-is-given-by-4x-y-5-0-then-the-slope-of-regression-line-of-y-on-x-is",{"id":361,"category":36,"text_question":362,"slug":363},534407,"How to convert 45 kg into grams","how-to-convert-45-kg-into-grams",{"id":365,"category":36,"text_question":366,"slug":367},534415,"In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). \r\n\r\nCalculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1)\r\n )\r\n\r\n\r\n\r\n\r\n\r\nGive your answers to 4 decimal places and in a range between 0 and 1","in-a-24-hours-period-the-average-number-of-boats-arriving-at-a-port-is-10-assuming-that-boats-arrive-at-a-random-rate-that-is-the-same-for-all-subintervals-of-equal-length-i-e-the-probability-of-a",{"id":369,"category":36,"text_question":370,"slug":371},534450,"In poker, a full house consists of five cards, where two of the cards have the\nsame number (or letter) and the remaining three also have the same number (or\nletter) as each other (but not as the previous two cards). Use a search engine or\nWikipedia to understand the concept better if necessary.\nIn how many different ways can one obtain a full house?","in-poker-a-full-house-consists-of-five-cards-where-two-of-the-cards-have-the-same-number-or-letter-and-the-remaining-three-also-have-the-same-number-or-letter-as-each-other-but-not-as-the-previ",{"id":373,"category":36,"text_question":374,"slug":375},534457,"At the end of a lively discussion within your study group, your class neighbor, for the relevance of your points of view, asks your opinion on the subject of their debate which is the following question Am I the slave of my unconscious?\n Solve the problem posed by this subject in an argumentative production.","at-the-end-of-a-lively-discussion-within-your-study-group-your-class-neighbor-for-the-relevance-of-your-points-of-view-asks-your-opinion-on-the-subject-of-their-debate-which-is-the-following-questi",{"id":377,"category":36,"text_question":378,"slug":379},534479,"Solve for B write your answer as a fraction or as a whole number. B-1/7=4","solve-for-b-write-your-answer-as-a-fraction-or-as-a-whole-number-b-1-7-4",{"id":381,"category":36,"text_question":382,"slug":383},534510,"Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the\ninstantaneous rate of change at 𝑥 = 1.","consider-the-function-f-x-1-2-x-1-2-3-use-the-preceding-following-interval-method-to-estimate-the-instantaneous-rate-of-change-at-x-1",{"id":385,"category":36,"text_question":386,"slug":387},534522,"if y=1/w^2 yw=2-x; find dy/dx","if-y-1-w-2-yw-2-x-find-dy-dx",{"id":389,"category":36,"text_question":390,"slug":391},534585,"Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?","marc-jean-and-michelle-have-traveled-a-lot-marc-drove-twice-as-much-as-jean-but-it-was-michelle-who-drove-the-most-with-100km-more-than-marc-they-respected-their-objective-of-not-exceeding-1350km",{"id":393,"category":36,"text_question":394,"slug":395},534595,"The slope of the tangent line to the curve f(x)=4tan x at the point (π/4,4)","the-slope-of-the-tangent-line-to-the-curve-f-x-4tan-x-at-the-point-4-4",{"data":397},[398,402,406],{"id":399,"question":400,"answer":401},163389,"What is the mode of the following data set: {5, 7, 7, 9, 9, 9}?","The mode of the given data set is 9, which appears most frequently (3 times).",{"id":403,"question":404,"answer":405},159935,"Question: Factor the expression 4x^2 + 12x - 3 using the distributive property.","Answer: Applying the distributive property, we can factor the expression as (2x - 1)(2x + 3).",{"id":407,"question":408,"answer":409},103398,"Q: Simplify √(108 + √(425 + √(63)))","A: The simplified radical expression is √(6 + √7)",{"$sicons":411},{"bxl:facebook-circle":412,"bxl:instagram":416,"mdi:web":418,"la:apple":420,"ph:google-logo-bold":423,"ph:google-logo":426},{"left":413,"top":413,"width":414,"height":414,"rotate":413,"vFlip":184,"hFlip":184,"body":415},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":413,"top":413,"width":414,"height":414,"rotate":413,"vFlip":184,"hFlip":184,"body":417},"\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\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" 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