dx :","Solution:\u003Cbr />\n1. Identify the function to integrate: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>fx = 5 - 2x + 3x^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Integrate each term:\u003Cbr />\n- The integral of a constant \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\u003C/math-field>\u003C/math-field> with respect to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- The integral of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2x\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-\\frac{2}{2}x^2 = -x^2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- The integral of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x^2\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{3}{3}x^3 = x^3\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Combine the integrals:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int 5−2x+3x2 \\, dx = 5x - x^2 + x^3 + C\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Evaluate the definite integral from \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Compute the antiderivative at \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field>: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F4 = 54 - 4^2 + 4^3 = 20 - 16 + 64 = 68\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Compute the antiderivative at \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F1 = 51 - 1^2 + 1^3 = 5 - 1 + 1 = 5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Find the difference \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>F4 - F1\u003C/math-field>\u003C/math-field>: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>68 - 5 = 63\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. The value of the integral is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int_1^4 5−2x+3x2 \\, dx = 63\u003C/math-field>\u003C/math-field>",1389,278,"evaluate-int-1-4-5-2x-3x-2-dx",{"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},537915,"Find the area between y = 9 - x^2 and y = x + 1 from x = -1 to x = 2","Solution:\u003Cbr />\n\u003Cbr />\n1. Given:\u003Cbr />\n- Curve 1: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 9 - x^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Curve 2: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = x + 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Interval for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Find points of intersection:\u003Cbr />\n- Set \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 9 - x^2\u003C/math-field>\u003C/math-field> equal to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = x + 1\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>9 - x^2 = x + 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Rearrange and simplify:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 + x - 8 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Factor the quadratic equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x−2x+4 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- 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 = 2 \\quad \\text{and} \\quad x = -4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Valid intersection within the given interval is at \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Calculate area between curves from \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Integral of top curve minus bottom curve:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int_{-1}^{2} (9−x2 - x+1) \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\int_{-1}^{2} 8−x2−x \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve the integral:\u003Cbr />\n- Integrate term-by-term:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\left[ 8x - \\frac{x^3}{3} - \\frac{x^2}{2} \\right]_{-1}^{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Evaluate at upper and lower limits:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\left8(2 - \\frac{2^3}{3} - \\frac{2^2}{2} \\right) - \\left8(−1 - \\frac{−1^3}{3} - \\frac{−1^2}{2} \\right)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Simplify and calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\left16−frac83−2right - \\left−8+frac13−frac12right\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 14 - \\frac{8}{3} + 8 - \\frac{1}{3} + \\frac{1}{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 22 - \\frac{9}{3} + \\frac{3}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 22 - 3 + 0.5\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 19.5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. The area between the curves from \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field> is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{19.5}\u003C/math-field>\u003C/math-field>",1091,218,"find-the-area-between-y-9-x-2-and-y-x-1-from-x-1-to-x-2",{"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},537914,"Integration by parts for \\int \\ln x dx :","Solution:\u003Cbr />\n1. Identify the components of integration by parts:\u003Cbr />\n - Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>u = \\ln x\u003C/math-field>\u003C/math-field>, then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>du = \\frac{1}{x} \\, dx\u003C/math-field>\u003C/math-field>.\u003Cbr />\n - Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>dv = dx\u003C/math-field>\u003C/math-field>, then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>v = x\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Apply the integration by parts formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int u \\, dv = uv - \\int v \\, du\u003C/math-field>\u003C/math-field>:\u003Cbr />\n * The formula becomes:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int \\ln x \\, dx = x \\ln x - \\int x \\leftfrac1xright \\, dx\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Simplify the remaining integral:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int x \\leftfrac1xright \\, dx = \\int 1 \\, dx = x + C\u003C/math-field>\u003C/math-field>, where \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>C\u003C/math-field>\u003C/math-field> is the integration constant.\u003Cbr />\n\u003Cbr />\n4. Substitute back to get the final result:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int \\ln x \\, dx = x \\ln x - x + C\u003C/math-field>\u003C/math-field>.\u003Cbr />",258,52,"integration-by-parts-for-int-ln-x-dx",{"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},537913,"show how to do 349-231 in a base 12 system","Solution:\u003Cbr />\n1. Convert the numbers 349 and 231 from base 12 to decimal:\u003Cbr />\n- 349 base 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3times122 + 4times121 + 9times120 = 3times144 + 4times12 + 9times1 = 432 + 48 + 9 = 489\u003C/math-field>\u003C/math-field>\u003Cbr />\n- 231 base 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2times122 + 3times121 + 1times120 = 2times144 + 3times12 + 1times1 = 288 + 36 + 1 = 325\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Subtract the converted numbers in decimal:\u003Cbr />\n- Subtraction: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>489 - 325 = 164\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Convert the result back to base 12:\u003Cbr />\n- The highest power of 12 in 164 is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12^1\u003C/math-field>\u003C/math-field> since\u003Cmath−fieldread−onlydefault−mode=\"inline−math\"class=\"math−expression\">\u003Cmath−fieldread−only>122=144\u003C/math−field>\u003C/math−field>istoolarge.\u003Cbr />\n- Divide 164 by 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>164 \\div 12 = 13 \\text{ remainder } 8\u003C/math-field>\u003C/math-field>\u003Cbr />\n- 13 in base 12 is represented as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 \\times 12 + 1\u003C/math-field>\u003C/math-field> remainder is 1.\u003Cbr />\n- Therefore, 164 in base 12 is 118.\u003Cbr />\n\u003Cbr />\n4. Therefore, 349 base 12 minus 231 base 12 equals: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>118\u003C/math-field>\u003C/math-field> base 12.",943,189,"show-how-to-do-349-231-in-a-base-12-system",{"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},537912,"show how to do 14+231 in a base 12 system","Solution:\u003Cbr />\n1. Express the numbers in their base 10 equivalent:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>14_{12} = 1 \\cdot 12^1 + 4 \\cdot 12^0 = 12 + 4 = 16\u003C/math-field>\u003C/math-field>\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>231_{12} = 2 \\cdot 12^2 + 3 \\cdot 12^1 + 1 \\cdot 12^0 = 288 + 36 + 1 = 325\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Add the numbers in base 10:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>16 + 325 = 341\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Convert the sum back to base 12:\u003Cbr />\n- To convert 341 to base 12, divide by 12 and keep track of the remainders.\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>341 \\div 12 = 28\u003C/math-field>\u003C/math-field> with remainder \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\u003C/math-field>\u003C/math-field> therightmostdigit\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>28 \\div 12 = 2\u003C/math-field>\u003C/math-field> with remainder \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field>\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2 \\div 12 = 0\u003C/math-field>\u003C/math-field> with remainder \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Read the remainders from last to first to get \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>245_{12}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\nThus, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>14_{12} + 231_{12} = 245_{12}\u003C/math-field>\u003C/math-field>.",1182,236,"show-how-to-do-14-231-in-a-base-12-system",{"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},537911,"Task 4.1.5pointsThere 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":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},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":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},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":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},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":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},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":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},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":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},537905,"431+B−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 + B−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":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},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":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},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":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},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":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},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":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},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":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},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":170,"category":36,"text_question":171,"photo_question":38,"text_answer":172,"step_text_answer":8,"step_photo_answer":8,"views":173,"likes":174,"slug":175},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>133−1\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",{"first":6,"last":177,"prev":8,"next":10},180,{"current_page":6,"from":6,"last_page":177,"links":179,"path":213,"per_page":214,"to":214,"total":215},[180,183,186,188,190,192,194,197,200,203,206,209,211],{"url":6,"label":181,"active":182},"1",true,{"url":10,"label":184,"active":185},"2",false,{"url":13,"label":187,"active":185},"3",{"url":16,"label":189,"active":185},"4",{"url":19,"label":191,"active":185},"5",{"url":22,"label":193,"active":185},"6",{"url":195,"label":196,"active":185},7,"7",{"url":198,"label":199,"active":185},8,"8",{"url":201,"label":202,"active":185},9,"9",{"url":204,"label":205,"active":185},10,"10",{"url":207,"label":208,"active":185},179,"179",{"url":177,"label":210,"active":185},"180",{"url":10,"label":212,"active":185},"Next »","https://api.math-master.org/api/question",20,3593,{"data":217},{"questions":218},[219,223,227,231,235,239,242,246,250,254,258,262,266,270,274,278,282,286,290,294],{"id":220,"category":36,"text_question":221,"slug":222},532009,"How much volume of water in MegaLiters ML is required to irrigate 30 Hectare crop\narea with depth of 20mm?","how-much-volume-of-water-in-megaliters-ml-is-required-to-irrigate-30-hectare-crop-area-with-depth-of-20mm",{"id":224,"category":36,"text_question":225,"slug":226},533892,"I) Find the directional derivative of 𝑓𝑥,𝑦 = 𝑥 sin 𝑦 at 1,0 in the direction of the unit vector that make an angle of 𝜋/4 with positive 𝑥-axis.","i-find-the-directional-derivative-of-f-x-y-x-sin-y-at-1-0-in-the-direction-of-the-unit-vector-that-make-an-angle-of-4-with-positive-x-axis",{"id":228,"category":36,"text_question":229,"slug":230},533912,"By differentiating the function fx=x³−6x⁷ we will obtain","by-differentiating-the-function-f-x-x-6x-we-will-obtain",{"id":232,"category":36,"text_question":233,"slug":234},533915,"3x+5y=11\r\n2x-3y=1","3x-5y-11-2x-3y-1",{"id":236,"category":36,"text_question":237,"slug":238},533944,"A, B, C and D are numbers;\n\n If ABCD = 23,\n\n What is the result of ABCD BCDA CDAB DABC operation?","a-b-c-and-d-are-numbers-if-abcd-23-what-is-the-result-of-abcd-bcda-cdab-dabc-operation",{"id":240,"category":36,"text_question":241,"slug":241},533969,"7273736363-8",{"id":243,"category":36,"text_question":244,"slug":245},534005,"Determine the momentum of a 20 kg body traveling at 20 m/s.","determine-the-momentum-of-a-20-kg-body-traveling-at-20-m-s",{"id":247,"category":36,"text_question":248,"slug":249},534008,"Supposed 60% of the register voters in a country or democrat. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64% round your answer to four decimal places","supposed-60-of-the-register-voters-in-a-country-or-democrat-if-a-sample-of-793-voters-is-selected-what-is-the-probability-that-the-sample-proportion-of-democrats-will-be-greater-than-64-round-your",{"id":251,"category":36,"text_question":252,"slug":253},534020,"The expected market return is 13,86% and the risk free rate 1%. What would then be the risk premium on the common stocks of a company which beta is 1,55? in","the-expected-market-return-is-13-86-and-the-risk-free-rate-1-what-would-then-be-the-risk-premium-on-the-common-stocks-of-a-company-which-beta-is-1-55-in-2-decimal-places",{"id":255,"category":36,"text_question":256,"slug":257},534093,"2x2 and how much?","2x2-and-how-much",{"id":259,"category":36,"text_question":260,"slug":261},534110,"-3−4x+5=-67x−8+9-10x","3-4x-5-6-7x-8-9-10x",{"id":263,"category":36,"text_question":264,"slug":265},534294,"TEST 123123+1236ttttt","test-123123-1236ttttt",{"id":267,"category":36,"text_question":268,"slug":269},534424,"Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict.\nModel the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.","write-the-detailed-definition-of-a-supply-chain-logistics-related-maximization-problem-with-8-variables-and-6-constraints-each-constraint-should-have-at-least-6-variables-each-constraint-should-have",{"id":271,"category":36,"text_question":272,"slug":273},534438,"1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?","1-a-jeweler-has-two-gold-bars-with-80-purity-and-the-other-with-95-purity-how-much-of-each-must-be-melted-to-obtain-a-5-kilo-ingot-with-86-purity",{"id":275,"category":36,"text_question":276,"slug":277},534520,"Salut👋🏻\r\n\r\nAppuie sur \"Créer une nouvelle tâche\" pour envoyer ton problème de mathématiques.\r\n\r\nUn de nos experts commencera à travailler dessus immédiatement !","salut-appuie-sur-creer-une-nouvelle-tache-pour-envoyer-ton-probleme-de-mathematiques-un-de-nos-experts-commencera-a-travailler-dessus-immediatement",{"id":279,"category":36,"text_question":280,"slug":281},534617,"Consider a sample space S, and two events A and B such that\nPA∩B = 0.2, PA∪B = 0.6, PB∪̄A = 0.8\na [0.5 points] Calculate P A.\nb [0.5 points] Calculation P B","consider-a-sample-space-s-and-two-events-a-and-b-such-that-p-a-b-0-2-p-a-b-0-6-p-b-a-0-8-a-0-5-points-calculate-p-a-b-0-5-points-calculation-p-b",{"id":283,"category":36,"text_question":284,"slug":285},534662,"t+72/t=-17","t-72-t-17",{"id":287,"category":36,"text_question":288,"slug":289},534666,"fr = 1/r+9 find fx2 + 1","f-r-1-r-9-find-f-x-2-1",{"id":291,"category":36,"text_question":292,"slug":293},534677,"In an experiment to assess the effect of listening to audiobooks while driving, participants were asked to drive down a straight road in a driving simulator. The accompanying data on time inmilliseconds to react when a pedestrian walked into the street for 10 drivers listening to an audiobook are consistent with summary statistics and graphs that appeared in the paper \"Good Distractions: Testing the Effect of Listening to an Audiobook on Driving Performance in Simple and Complex Road Environments.\"† Roundyouranswerstofourdecimalplaces.\r\n1,018 1,007 1,054 988 937 1,030 1,065 1,011 860 1,106\r\nA button hyperlink to the SALT program that reads: Use SALT.\r\nCalculate the variance for this data set.\r\n7437.7333\r\n \r\nIncorrect: Your answer is incorrect.\r\nCalculate the standard deviation for this data set.\r\n86.2022\r\n \r\nIncorrect: Your answer is incorrect.","in-an-experiment-to-assess-the-effect-of-listening-to-audiobooks-while-driving-participants-were-asked-to-drive-down-a-straight-road-in-a-driving-simulator-the-accompanying-data-on-time-in-millisec",{"id":295,"category":36,"text_question":296,"slug":297},534687,"Suppose a car license plate consists of 2 letters and two digits of which the first cannot be zero. How many different plates can be engraved? consider only 26 letters and 10 digits draw an example of this.","suppose-a-car-license-plate-consists-of-2-letters-and-two-digits-of-which-the-first-cannot-be-zero-how-many-different-plates-can-be-engraved-consider-only-26-letters-and-10-digits-draw-an-example-of",{"data":299},{"id":300,"category":36,"slug":301,"text_question":302,"photo_question":8,"text_answer":303,"step_text_answer":8,"step_photo_answer":8,"views":304,"likes":305,"expert":306},534972,"what-is-the-sum-of-1-8-plus-3-8","What is the sum of 1/8 plus 3/8","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba0,0,0,.3;\nbox-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>=frac8+924\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;\npadding: 8px;\nborder-radius: 8px;\nborder: 1px solid rgba0,0,0,.3;\nbox-shadow: 0 0 0 rgba0,0,0,.2\n\" read-only>=frac1724\u003C/math-field>\n \u003Cbr>\n \u003C/div>",595,119,{"id":204,"name":307,"photo":308,"biography":309,"created_at":8,"updated_at":8,"rating":310,"total_answer":311},"Ali","https://api.math-master.org/img/experts/10/10.webp","I’m Aileen, a licensed civil engineer. I started to become interested in Mathematics while I was in gradeschool. I used to be very careless in solving simple math problems, but with the right guidance and consistent effort, I was able to overcome my carelessness. I enjoyed solving algebra problems, since there is not much to memorize. From gradeschool to college, I used to join several mathematics competitions. My favorite fields of mathematics are algebra, geometry, probability and differential calculus. ",4.4,86,{"data":313},{"questions":314},[315,319,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387,391],{"id":316,"category":36,"text_question":317,"slug":318},532029,"reduction method 2x-y=13 x+y=-1","reduction-method-2x-y-13-x-y-1",{"id":320,"category":36,"text_question":321,"slug":322},532043,"a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate.\nAt this rate, what fraction of the distance between the two ports can the ferry travel in one hour.","a-ferry-travels-1-6-of-the-distance-between-two-ports-in-3-7-hour-the-ferry-travels-at-a-constant-rate-at-this-rate-what-fraction-of-the-distance-between-the-two-ports-can-the-ferry-travel-in-one-h",{"id":324,"category":36,"text_question":325,"slug":326},532059,"-63x−4=-6","6-3x-4-6",{"id":328,"category":36,"text_question":329,"slug":330},532071,"A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?","a-normally-distributed-population-has-a-mean-of-118-with-a-standard-deviation-of-18-what-score-separates-the-lowest-72-of-the-distribution-from-the-rest-of-the-scores",{"id":332,"category":36,"text_question":333,"slug":334},532083,"Let X be a discrete random variable with range {1, 3, 5} and whose probability function is fx = PX=x. If it is known that PX=1 = 0.1 and PX=3 = 0.3. What is the value of PX=5?","let-x-be-a-discrete-random-variable-with-range-1-3-5-and-whose-probability-function-is-f-x-p-x-x-if-it-is-known-that-p-x-1-0-1-and-p-x-3-0-3-what-is-the-value-of-p-x-5",{"id":336,"category":36,"text_question":337,"slug":338},532307,"Write 32/25 as a percent","write-32-25-as-a-percent",{"id":340,"category":36,"text_question":341,"slug":342},532308,"90 divided by 40","90-divided-by-40",{"id":344,"category":36,"text_question":345,"slug":346},533976,"Which of the following is the product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths?","which-of-the-following-is-the-product-of-multiplying-twenty-seven-and-twenty-five-hundredths-by-nine-and-twenty-seven-hundredths",{"id":348,"category":36,"text_question":349,"slug":350},534025,"You have been hired to estimate the average weight of quarters in circulation. Based on the sample of quarters you collect below, create a 90% confidence interval for the weight of quarters in circulation.\r\nQuarter Weights grams\r\n5.631 \t5.714 \t5.719 \t5.689 \t5.551 \t5.723 \t5.705 \t5.627 \t5.627 \t5.715 \t5.576\r\n5.632 \t5.641 \t5.676 \t5.660 \t5.699 \t5.609 \t5.634 \t5.713 \t5.591 \t5.674 \t5.675\r\n5.684 \t5.694 \t5.655 \t5.632 \t5.598 \t5.675 \t5.628 \t5.562 \t5.636 \t5.583 \t5.567\r\n5.551 \t5.649 \t5.708 \t5.696 \t5.614 \t5.637 \t5.601 \t5.628 \t5.711 \t5.566 \t5.653\r\n5.653 \t5.597 \t5.687 \t5.717 \t5.678 \t5.654 \t5.556 \t5.707 \t5.563 \t5.628 \t5.679\r\n5.714 \t5.555 \t5.719 \t5.634 \t5.647 \t5.717 \t5.612 \t5.705 \t5.657 \t5.670 \t5.607\r\n5.687 \t5.666 \t5.612 \t5.718 \t5.714 \t5.713 \t5.663 \t5.641 \t5.589 \t5.656 \t5.712\r\n5.639 \t5.577 \t5.580 \t5.674 \t5.636 \t5.625 \t5.597 \t5.616 \t5.591 \t5.616 \t5.700\r\n5.706 \t5.695 \t5.562 \t5.699 \t5.607 \t5.573 \t5.659 \t5.632 \t5.654 \t5.568 \t5.628\r\n5.687 \t5.605 \t5.689 \t5.687 \t5.554 \t5.618 \t5.701 \t5.681 \t5.645 \t5.714 \t5.665\r\n5.661 \t5.634 \t5.714 \t5.586 \t5.656 \t5.673 \t5.657 \t5.717 \t5.611 \t5.578 \t5.579\r\n5.614 \t5.644 \t5.724 \t5.647 \t5.566 \t5.697 \t5.558 \t5.586 \t5.586 \t5.611 \t5.573\r\n5.573 \t5.709 \t5.629 \t5.649 \t5.552 \t5.615 \t5.645 \t5.611 \t5.686 \t5.588 \t5.641\r\n5.704 \t5.703 \t5.696 \t5.557 \t5.551 \t5.725 \t5.608 \t5.725 \t5.603 \t5.677 \t5.638\r\n5.573 \t5.640 \t5.561 \t5.631 \t5.563 \t5.671 \t5.662 \t5.569 \t5.648 \t5.680 \t5.681\r\n5.551 \t5.555 \t5.578 \t5.701 \t5.645 \t5.670 \t5.574 \t5.594 \t5.705 \t5.633 \t5.719\r\n5.680 \t5.647 \t5.641 \t5.553 \t5.616 \t5.698 \t5.552 \t5.566 \t5.559 \t5.697 \t5.686\r\n5.560 \t5.629 \t5.701 \t5.622 \t5.615 \t5.553 \t5.608 \t5.637 \t5.663 \t5.696 \t5.714\r\n5.675 \t5.613 \t5.594 \t5.669 \t5.569 \t5.716 \t5.705 \t5.603 \t5.709 \t5.717 \t5.606\r\n5.581 \t5.575 \t5.601 \t5.600 \t5.664 \t5.715 \t5.705 \t5.583 \t5.586 \t5.592 \t5.550\r\n5.628 \t5.662 \t5.603 \t5.559 \t5.676 \t5.558 \t5.678 \t5.671 \t5.642 \t5.581 \t5.568\r\n5.706 \t5.665 \t5.712 \t5.574 \t5.602 \t5.699 \t5.716 \t5.693 \t5.711 \t5.635 \t5.612\r\n\r\nBLANK #1: Is this a question involving mean or proportion? ***ANSWER \"MEAN\" OR \"PROPORTION\" WITHOUTTHEQUOTATIONMARKS***\r\n\r\nBLANK #2: What is the LOW end of the estimate ***ANSWER TO 3 DECIMALS***\r\n\r\nBLANK #3: What is the HIGH end of the estimate ***ANSWER TO 3 DECIMALS***","you-have-been-hired-to-estimate-the-average-weight-of-quarters-in-circulation-based-on-the-sample-of-quarters-you-collect-below-create-a-90-confidence-interval-for-the-weight-of-quarters-in-cir",{"id":352,"category":36,"text_question":353,"slug":354},534082,"By direct proof, how can you prove that “The sum of any three consecutive even integers is\nalways a multiple of 6”.","by-direct-proof-how-can-you-prove-that-the-sum-of-any-three-consecutive-even-integers-is-always-a-multiple-of-6",{"id":356,"category":36,"text_question":357,"slug":358},534132,"123+7-5","12-3-7-5",{"id":360,"category":36,"text_question":361,"slug":362},534171,"Log5 625","log5-625",{"id":364,"category":36,"text_question":365,"slug":366},534202,"During a fishing trip Alex notices that the height h\r\n of the tide inmetres is given by\r\n\r\nh=1−1/2*cosπt/6\r\n \r\n\r\nwhere t\r\n is measued in hours from the start of the trip.\r\n\r\n \r\n\r\na Enter the exact value of h\r\n at the start of the trip in the box below.","during-a-fishing-trip-alex-notices-that-the-height-h-of-the-tide-in-metres-is-given-by-h-1-1-2-cos-t-6-where-t-is-measued-in-hours-from-the-start-of-the-trip-a-ent",{"id":368,"category":36,"text_question":369,"slug":370},534329,"At the dance there are 150 boys the rest are girls. If 65% are girls what is the total amount in the room","at-the-dance-there-are-150-boys-the-rest-are-girls-if-65-are-girls-what-is-the-total-amount-in-the-room",{"id":372,"category":36,"text_question":373,"slug":374},534383,"Find the number of pounds of nails required for 17850 square feet of drywall if each thousand square feet requires 4.5 pounds of nails.","find-the-number-of-pounds-of-nails-required-for-17850-square-feet-of-drywall-if-each-thousand-square-feet-requires-4-5-pounds-of-nails",{"id":376,"category":36,"text_question":377,"slug":378},534440,"To find the increased amount on a standard term deposit with the following conditions:\n\nstarting amount: BGN 13000,\ntype of deposit: annual,\nannual compound interest rate: 1.4%,\nafter 4 years;","to-find-the-increased-amount-on-a-standard-term-deposit-with-the-following-conditions-starting-amount-bgn-13000-type-of-deposit-annual-annual-compound-interest-rate-1-4-after-4-years",{"id":380,"category":36,"text_question":381,"slug":382},534598,"draw the condensed formula fpr 3,3,4 triethylnonane","draw-the-condensed-formula-fpr-3-3-4-triethylnonane",{"id":384,"category":36,"text_question":385,"slug":386},534652,"A small box measures 10 in. by 4 in. by 6 in. high. Find the volume of the box.","a-small-box-measures-10-in-by-4-in-by-6-in-high-find-the-volume-of-the-box",{"id":388,"category":36,"text_question":389,"slug":390},534653,"Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?","mark-is-gluing-a-ribbon-around-the-sides-of-a-picture-frame-the-frame-is-11-inches-long-and-7-includes-wide-how-much-ribbon-does-mark-need",{"id":392,"category":36,"text_question":393,"slug":394},534655,"An export company grants a bonus of 100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?","an-export-company-grants-a-bonus-of-100-000-pesos-to-distribute-among-three-of-its-best-employees-so-that-the-first-receives-double-the-second-and-the-latter-receives-triple-the-third-how-much-did",{"data":396},[397,401,405],{"id":398,"question":399,"answer":400},145484,"Math question: What is the limit as x approaches 2 of (x^2 + 3x - 10) / (x - 2)?","Answer: Using algebraic simplification or factoring, we can rewrite the expression as (x + 5). Thus, the limit is 7, as x approaches 2.",{"id":402,"question":403,"answer":404},112540,"Question: What are the scalar components of the unit vector v = ⟨2/3, -1/3⟩?","Answer: The scalar components of the unit vector v are (2/3) and (-1/3). The vector is expressed as v = (2/3)i - (1/3)j.",{"id":406,"question":407,"answer":408},137277,"Question: What is the value of the sine function at 45 degrees on the unit circle?","Answer: The value of the sine function at 45 degrees on the unit circle is √2/2. In the first quadrant, the y-coordinate of the point on the unit circle corresponding to 45 degrees is √2/2, giving us the sine value.",{"sicons":410},{"bxl:facebook-circle":411,"bxl:instagram":415,"mdi:web":417,"la:apple":419,"ph:google-logo-bold":422,"ph:google-logo":425},{"left":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":185,"hFlip":185,"body":414},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":185,"hFlip":185,"body":416},"\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 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