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 5βˆ’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 5βˆ’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>xβˆ’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} (9βˆ’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} 8βˆ’x2βˆ’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(βˆ’1 - \\frac{βˆ’1^3}{3} - \\frac{βˆ’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>= \\left16βˆ’frac83βˆ’2right - \\leftβˆ’8+frac13βˆ’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\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>122=144\u003C/mathβˆ’field>\u003C/mathβˆ’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 Δ‡e \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 jednadΕΎbu: \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 doΔ‘e 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+Bβˆ’29=678","First, simplify the equation:\u003Cbr />\n\u003Cbr />\n1. Start with the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>431 + Bβˆ’29 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Distribute and simplify: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>431 + B - 29 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Combine like terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B + 402 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Isolate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B\u003C/math-field>\u003C/math-field> by subtracting 402 from both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 678 - 402\u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Calculate the right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 276\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nFinal answer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 276\u003C/math-field>\u003C/math-field>",1140,228,"431-b-29-678",{"id":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>133βˆ’1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify the expression inside the parentheses:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3 - 1 = 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Therefore, the factored expression is: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13 \\times 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplified result: \u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13 \\times 2 = 26\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThus, the expression \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>39 - 13\u003C/math-field>\u003C/math-field> factors to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>132\u003C/math-field>\u003C/math-field> or simplifies to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26\u003C/math-field>\u003C/math-field>.",373,75,"factor-the-expression-using-gcf-39-13",{"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},[219,223,227,231,235,239,243,247,251,255,259,263,267,271,275,279,283,286,290,294],{"id":220,"category":36,"text_question":221,"slug":222},532003,"A particular employee arrives at work sometime between 8:00 a.m. and 8:40 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:40 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:30 a.m. Round your answer to four decimal places, if necessary.","a-particular-employee-arrives-at-work-sometime-between-8-00-a-m-and-8-40-a-m-based-on-past-experience-the-company-has-determined-that-the-employee-is-equally-likely-to-arrive-at-any-time-between-8-0",{"id":224,"category":36,"text_question":225,"slug":226},532006,"a to the power of 2 minus 16 over a plus 4, what is the result?","a-to-the-power-of-2-minus-16-over-a-plus-4-what-is-the-result",{"id":228,"category":36,"text_question":229,"slug":230},532029,"reduction method 2x-y=13 x+y=-1","reduction-method-2x-y-13-x-y-1",{"id":232,"category":36,"text_question":233,"slug":234},532044,"a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate.\r\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",{"id":236,"category":36,"text_question":237,"slug":238},532056,"5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight","5-squirrels-were-found-to-have-an-average-weight-of-9-3-ounces-with-a-sample-standard-deviation-is-1-1-find-the-95-confidence-interval-of-the-true-mean-weight",{"id":240,"category":36,"text_question":241,"slug":242},533898,"A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had","a-car-that-starts-from-rest-moves-for-11-min-reaching-a-speed-of-135-km-h-calculate-the-acceleration-it-had",{"id":244,"category":36,"text_question":245,"slug":246},533922,"A consulting company charges a fee of 50perhourforconsulting.Iftheirmonthlyfixedcostsare1,000 and they want to make a monthly profit of 2,500, how many consulting hours should they bill per month?","a-consulting-company-charges-a-fee-of-50-per-hour-for-consulting-if-their-monthly-fixed-costs-are-1-000-and-they-want-to-make-a-monthly-profit-of-2-500-how-many-consulting-hours-should-they-bill",{"id":248,"category":36,"text_question":249,"slug":250},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":252,"category":36,"text_question":253,"slug":254},533988,"If eight basketball teams participate in a tournament, find the number of different ways that first, second, and third places can be decided assuming that no ties are allowed.","if-eight-basketball-teams-participate-in-a-tournament-find-the-number-of-different-ways-that-first-second-and-third-places-can-be-decided-assuming-that-no-ties-are-allowed",{"id":256,"category":36,"text_question":257,"slug":258},533993,"Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.","two-events-e-and-f-are-if-the-occurrence-of-event-e-in-a-probability-experiment-does-not-affect-the-probability-of-event-f",{"id":260,"category":36,"text_question":261,"slug":262},534029,"A job takes  9\n  workers  92\n  hours to finish. How many hours would it take  5\n  workers to complete the same job?","a-job-takes-9-workers-92-hours-to-finish-how-many-hours-would-it-take-5-workers-to-complete-the-same-job",{"id":264,"category":36,"text_question":265,"slug":266},534048,"To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:","to-celebrate-the-five-year-anniversary-of-a-consultancy-specializing-in-information-technology-the-administrator-decided-to-draw-3-different-qualification-courses-among-its-10-employees-considering",{"id":268,"category":36,"text_question":269,"slug":270},534105,"A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?","a-pair-of-die-is-thrown-and-the-absolute-difference-of-the-two-scores-is-recorded-what-is-the-probability-of-the-absolute-difference-being-4-or-more",{"id":272,"category":36,"text_question":273,"slug":274},534193,"(1) July 1, 2008: Receives25,000 from Quinn Zealick for 25,000 shares of the stock\n common face value 1fromthebookstore.\n(2)July1,2008:Obtains30,000 loan from local bank for needs\n of working capital. The loan earns 6% interest per year. The loan is payable\n with interest on June 30, 2009.\n 3 July 1, 2008: Sign a three-year rental agreement at an annual rent of 20,000\nPaythefirstyearβ€²srentinadvance.\n(4)July1,2008:Purchasesshelvesfor4,000 in cash. The shelves have\n an estimated useful life of five years and zero residual value.\n 5 July 1, 2008: Purchase computers for 10,000incash.Thecomputers\nTheyhaveanestimatedusefullifeofthreeyearsand1,000 in residual value.\n 6 July 1, 2008: Makes guarantee deposits with various book distributors for\n a total of 8,000.DepositsarerefundableonJune30,2009ifthebookstorepays\nontimeallamountspayableforbookspurchasedfromdistributorsbetween\nJuly2008andJune30,2009.\n(7)During2008:Purchasesbooksonaccountfromvariousdistributorsforacostof160,000.\n 8During 2008: Sells books costing 140,000to172,800. Of the total sales,\n 24,600correspondstocashand148,200 is on account.\n 9 During 2008: Returns unsold books and books ordered in error for a cost of\n 14,600.Thecompanyhadnotyetpaidforthesebooks.\n(10)During2008:Collected142,400 from sales on account.\n 11 During 2008: Pays employees salaries of 16,700.\n(12)During2008:Pays139,800 to book distributors of the amounts payable for\n purchases on account.\n 13 December 28, 2008: Receives customer advances of 850duetoorderbooks\nspecialthatthebookstorewillorderandexpectstoreceiveduring2009.\n(14)December31,2008:Recordthecorrespondingamountofinterestexpenseonthe\nloanin(2)for2008.\n(15)December31,2008:Recordthecorrespondingamountofrentalexpensefor2008.\n(16)December31,2008:Recordthecorrespondingamountofdepreciationexpense\nontheshelvesin(4).\n(17)December31,2008:Recordthecorrespondingamountofdepreciationexpense\naboutcomputersin(5).\n(18)December31,2008:Recordthecorrespondingamountofincometaxexpense.\nprofitsfor2008.Theincometaxrateis4075,000. He\n loan is payable on June 30, 2010, with 8% interest payable\n to the expiration.\n 4 July 1, 2009: Receives security deposits from book distributors.\n 5 July 1, 2009: Pay the rent corresponding to the period from July 1\n 2009 to June 30, 2010.\n 6 During 2009: Purchase books on account for a cost of 310,000.\n(7)During2009:Soldbooksforacostof286,400 for 353,700.Ofthetotalsales,\n24,900 corresponds to cash, 850correspondstospecialordersreceivedduringDecember\nof2008and327,950 are on account.\n 8 During 2009: Returns unsold books at a cost of 22,700.Thecompanyhasnotyet\nIhadpaidforthesebooks.\n(9)During2009:Collects320,600 from sales to accounts.\n 10 During 2009: Pays employees compensation of 29,400.\n(11)During2009:pays281,100 to book distributors for book purchases from\n account.\n 12 December 31, 2009: Declares and pays a dividend of 4,000.","1βˆ’julyβˆ’1βˆ’2008βˆ’receivesβˆ’25βˆ’000βˆ’fromβˆ’quinnβˆ’zealickβˆ’forβˆ’25βˆ’000βˆ’sharesβˆ’ofβˆ’theβˆ’stockβˆ’commonβˆ’faceβˆ’valueβˆ’1βˆ’fromβˆ’theβˆ’bookstoreβˆ’2βˆ’julyβˆ’1βˆ’2008βˆ’obtainsβˆ’30βˆ’000βˆ’loanβˆ’fromβˆ’localβˆ’bankβˆ’forβˆ’needsβˆ’ofβˆ’wor","id":276,"category":36,"textquestion":277,"slug":278,534239,"Themarketforeconomicstextbooksisrepresentedbythefollowingsupplyanddemandequations:\r\nP=5+2QsP=20βˆ’Qd\r\nWherePisthepriceinΒ£sandQsandQdarethequantitiessuppliedanddemandedinthousands.\r\nWhatistheequilibriumprice?","theβˆ’marketβˆ’forβˆ’economicsβˆ’textbooksβˆ’isβˆ’representedβˆ’byβˆ’theβˆ’followingβˆ’supplyβˆ’andβˆ’demandβˆ’equationsβˆ’pβˆ’5βˆ’2qsβˆ’pβˆ’20βˆ’qdβˆ’whereβˆ’pβˆ’isβˆ’theβˆ’priceβˆ’inβˆ’sβˆ’andβˆ’qsβˆ’andβˆ’qdβˆ’areβˆ’theβˆ’quantitiesβˆ’suppliedβˆ’andβˆ’deman","id":280,"category":36,"textquestion":281,"slug":282,534246,"Howtodo15x3304","howβˆ’toβˆ’doβˆ’15βˆ’xβˆ’3304","id":284,"category":36,"textquestion":285,"slug":285,534332,"392929βˆ’9","id":287,"category":36,"textquestion":288,"slug":289,534396,"GiveanexampleofafunctiondefinedinRthatiscontinuousin\nallpoints,exceptinthesetZofintegers.","giveβˆ’anβˆ’exampleβˆ’ofβˆ’aβˆ’functionβˆ’definedβˆ’inβˆ’rβˆ’thatβˆ’isβˆ’continuousβˆ’inβˆ’allβˆ’pointsβˆ’exceptβˆ’inβˆ’theβˆ’setβˆ’zβˆ’ofβˆ’integers","id":291,"category":36,"textquestion":292,"slug":293,534533,"8/9dividedby10/6","8βˆ’9βˆ’dividedβˆ’byβˆ’10βˆ’6","id":295,"category":36,"textquestion":296,"slug":297,534561,"Amembershiptothegymcost25 per person in 1995. The membership cost has increased by an average 6perpersonforeachyearsince1995.Writealinearequationforthecostofagymmembershipforonepersonsince1995.Whatisthecostofagymmembershipin2009?","aβˆ’membershipβˆ’toβˆ’theβˆ’gymβˆ’costβˆ’25βˆ’perβˆ’personβˆ’inβˆ’1995βˆ’theβˆ’membershipβˆ’costβˆ’hasβˆ’increasedβˆ’byβˆ’anβˆ’averageβˆ’6βˆ’perβˆ’personβˆ’forβˆ’eachβˆ’yearβˆ’sinceβˆ’1995βˆ’writeβˆ’aβˆ’linearβˆ’equationβˆ’forβˆ’theβˆ’costβˆ’ofβˆ’aβˆ’gymβˆ’membershipβˆ’fo","data":299,"id":300,"category":36,"slug":301,"textquestion":302,"photoquestion":8,"textanswer":303,"steptextanswer":8,"stepphotoanswer":8,"views":304,"likes":305,"expert":306,536365,"anβˆ’investmentβˆ’ofβˆ’currentβˆ’130βˆ’000βˆ’isβˆ’madeβˆ’andβˆ’accordingβˆ’toβˆ’calculationsβˆ’willβˆ’generateβˆ’theβˆ’indicatedβˆ’savingsβˆ’inβˆ’theβˆ’followingβˆ’yearsβˆ’yearβˆ’savingsβˆ’1βˆ’35βˆ’000βˆ’2βˆ’50βˆ’000βˆ’3βˆ’45βˆ’000βˆ’4βˆ’25βˆ’000βˆ’5βˆ’15","Aninvestmentofcurrent130,000 is made and, according to calculations, will generate the indicated savings in the following years:\n\n Year Savings\n 1 35,000\n250,000\n 3 45,000\n425,000\n 5 15,000\n\nWhatisthenetresultofthisinvestmentinpresentvaluetermsifitrequiresa9sicons":406},{"bxl:facebook-circle":407,"bxl:instagram":411,"mdi:web":413,"la:apple":415,"ph:google-logo-bold":418,"ph:google-logo":421},{"left":408,"top":408,"width":409,"height":409,"rotate":408,"vFlip":185,"hFlip":185,"body":410},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":408,"top":408,"width":409,"height":409,"rotate":408,"vFlip":185,"hFlip":185,"body":412},"\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 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