Question

A cylinder contains gas at a pressure of 3 atm and a volume of 6 L. If the pressure is decreased to 1 atm, what will be the new volume of the gas, assuming the temperature remains constant?

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Answer to a math question A cylinder contains gas at a pressure of 3 atm and a volume of 6 L. If the pressure is decreased to 1 atm, what will be the new volume of the gas, assuming the temperature remains constant?

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Bud
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92 Answers
1. Start with Boyle's Law: P_1 V_1 = P_2 V_2
2. Substitute known values: 3 \text{ atm} \cdot 6 \text{ L} = 1 \text{ atm} \cdot V_2
3. Solve for V2: V_2 = \frac{3 \text{ atm} \cdot 6 \text{ L}}{1 \text{ atm}}
4. Compute the value of V2: V_2 = 18 \text{ L}

Answer: V_2 = 18 \text{ L}

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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 52x+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 52x+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>x2x+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} (9x2 - 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} 8x2x \\, 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>= \\left16frac832right - \\left8+frac13frac12right\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\u003Cmathfieldreadonlydefaultmode=\"inlinemath\"class=\"mathexpression\">\u003Cmathfieldreadonly>122=144\u003C/mathfield>\u003C/mathfield>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+B29=678","First, simplify the equation:\u003Cbr />\n\u003Cbr />\n1. Start with the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>431 + B29 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Distribute and simplify: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>431 + B - 29 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Combine like terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B + 402 = 678\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Isolate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B\u003C/math-field>\u003C/math-field> by subtracting 402 from both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 678 - 402\u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Calculate the right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 276\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nFinal answer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = 276\u003C/math-field>\u003C/math-field>",1140,228,"431-b-29-678",{"id":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>1331\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify the expression inside the parentheses:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3 - 1 = 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Therefore, the factored expression is: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13 \\times 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplified result: \u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>13 \\times 2 = 26\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThus, the expression \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>39 - 13\u003C/math-field>\u003C/math-field> factors to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>132\u003C/math-field>\u003C/math-field> or simplifies to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26\u003C/math-field>\u003C/math-field>.",373,75,"factor-the-expression-using-gcf-39-13",{"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},{"id":218,"category":36,"slug":219,"text_question":220,"photo_question":8,"text_answer":221,"step_text_answer":8,"step_photo_answer":8,"views":222,"likes":223,"expert":224},537055,"a-cylinder-contains-gas-at-a-pressure-of-3-atm-and-a-volume-of-6-l-if-the-pressure-is-decreased-to-1-atm-what-will-be-the-new-volume-of-the-gas-assuming-the-temperature-remains-constant","A cylinder contains gas at a pressure of 3 atm and a volume of 6 L. If the pressure is decreased to 1 atm, what will be the new volume of the gas, assuming the temperature remains constant?","1. Start with Boyle's Law: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> P_1 V_1 = P_2 V_2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Substitute known values: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3 \\text{ atm} \\cdot 6 \\text{ L} = 1 \\text{ atm} \\cdot V_2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Solve for \\( V_2 \\): \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = \\frac{3 \\text{ atm} \\cdot 6 \\text{ L}}{1 \\text{ atm}} \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Compute the value of \\( V_2 \\): \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_2 = 18 \\text{ L} \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> V_2 = 18 \\text{ L} \u003C/math-field>\u003C/math-field>",1117,223,{"id":225,"name":226,"photo":227,"biography":228,"created_at":8,"updated_at":8,"rating":229,"total_answer":230},30,"Bud","https://api.math-master.org/img/experts/30/30.webp","I started my mathematics journey when i was in school and i went for a lot of competitions in mathematics back then and after worth, i proceeded into the university to study Electronics and Electrical Engineering and the course of studying it, i came across a lot of mathematics course which grounded me alot in mathematics.",4.6,92,{"data":232},{"questions":233},[234,238,242,246,250,254,258,262,266,270,274,278,282,286,290,294,298,302,306,310],{"id":235,"category":36,"text_question":236,"slug":237},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":239,"category":36,"text_question":240,"slug":241},532072,"Since one of the three integers whose product is (-60) is (+4), write the values that two integers can take.","since-one-of-the-three-integers-whose-product-is-60-is-4-write-the-values-that-two-integers-can-take",{"id":243,"category":36,"text_question":244,"slug":245},532076,"(x^2+3x)/(x^2-9)=","x-2-3x-x-2-9",{"id":247,"category":36,"text_question":248,"slug":249},532089,"Jose bought 3/4 of oil and his sister bought 6/8, which of the two bought more oil?","jose-bought-3-4-of-oil-and-his-sister-bought-6-8-which-of-the-two-bought-more-oil",{"id":251,"category":36,"text_question":252,"slug":253},533896,"What payment 7 months from now would be equivalent in value to a $3,300 payment due 23 months from now? The value of money is 2.7% simple interest. Round your answer to 2 decimal places.\nShow all work and how you arrive at the answer..","what-payment-7-months-from-now-would-be-equivalent-in-value-to-a-3-300-payment-due-23-months-from-now-the-value-of-money-is-2-7-simple-interest-round-your-answer-to-2-decimal-places-show-all-work",{"id":255,"category":36,"text_question":256,"slug":257},533907,"X^2 = 25","x-2-25",{"id":259,"category":36,"text_question":260,"slug":261},533979,"A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.","a-bird-randomly-chooses-to-land-on-1-of-12-perches-available-in-its-aviary-determine-the-probability-of-it-landing-on-a-perch-numbered-8-and-then-on-a-perch-marked-with-a-prime-number-take-into-acco",{"id":263,"category":36,"text_question":264,"slug":265},533999,"2x-4y=-6; -4y+4y=-8","2x-4y-6-4y-4y-8",{"id":267,"category":36,"text_question":268,"slug":269},534046,"Sean must chose a 6- digit PIN number for his online banking account.Each digit can be chosen from 0 to 9. How many different possible PIN numbers can sean chose.","sean-must-chose-a-6-digit-pin-number-for-his-online-banking-account-each-digit-can-be-chosen-from-0-to-9-how-many-different-possible-pin-numbers-can-sean-chose",{"id":271,"category":36,"text_question":272,"slug":273},534078,"is the x element (180,270), if tanx-3cotx=2, sinx ?","is-the-x-element-180-270-if-tanx-3cotx-2-sinx",{"id":275,"category":36,"text_question":276,"slug":277},534124,"Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)","substitute-a-2-and-b-3-and-c-4-to-evaluate-2ac-2b-2-a",{"id":279,"category":36,"text_question":280,"slug":281},534196,". What will be the osmotic pressure of a solution that was prepared at 91°F by dissolving 534 grams of aluminum hydroxide in enough water to generate 2.784 ml of solution.","what-will-be-the-osmotic-pressure-of-a-solution-that-was-prepared-at-91-f-by-dissolving-534-grams-of-aluminum-hydroxide-in-enough-water-to-generate-2-784-ml-of-solution",{"id":283,"category":36,"text_question":284,"slug":285},534246,"How to do 15 x 3304","how-to-do-15-x-3304",{"id":287,"category":36,"text_question":288,"slug":289},534299,"Three machines called A, B and C, produce 43%, 26% and 31% of the total production of\n a company, respectively. Furthermore, it has been detected that 8%, 2% and 1.6% of the product\n manufactured by these machines is defective.\n a) What is the probability that a product is not defective?\n b) A product is selected at random and found to be defective, what is the\n probability that it was manufactured on machine B?","three-machines-called-a-b-and-c-produce-43-26-and-31-of-the-total-production-of-a-company-respectively-furthermore-it-has-been-detected-that-8-2-and-1-6-of-the-product-manufactured-by-t",{"id":291,"category":36,"text_question":292,"slug":293},534437,"nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities.\n65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north","ni-exercises-65-68-the-latitudes-of-a-pair-of-cities-are-given-assume-that-one-city-si-directly-south-of-the-other-and-that-the-earth-is-a-perfect-sphere-of-radius-4000-miles-use-the-arc-length-for",{"id":295,"category":36,"text_question":296,"slug":297},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":299,"category":36,"text_question":300,"slug":301},534521,"Read the “Local Communities as Stakeholders: Does Amazon Really Need Tax Breaks?” example on p. 83 in Ch. 3 of Management: A Practical Introduction. In your response, discuss whether you feel that tax breaks for big companies benefit local communities. Describe ways to attract business to a region without having a negative impact on the larger community.","read-the-local-communities-as-stakeholders-does-amazon-really-need-tax-breaks-example-on-p-83-in-ch-3-of-management-a-practical-introduction-in-your-response-discuss-whether-you-feel-that-tax",{"id":303,"category":36,"text_question":304,"slug":305},534625,"Define excel and why we use it?","define-excel-and-why-we-use-it",{"id":307,"category":36,"text_question":308,"slug":309},534674,"Solve the system of equations by the addition method.\n\n0.01x-0.08y=-0.1\n0.2x+0.6y=0.2","solve-the-system-of-equations-by-the-addition-method-0-01x-0-08y-0-1-0-2x-0-6y-0-2",{"id":311,"category":36,"text_question":312,"slug":313},534689,"The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?","the-car-with-an-irresponsible-driver-starts-to-brake-when-it-goes-through-a-red-light-when-passing-the-traffic-light-he-does-so-at-a-speed-of-115-kph-in-the-right-lane-further-ahead-70-meters-from",{"data":315},{"questions":316},[317,321,325,329,333,337,341,345,349,353,357,361,365,369,373,377,381,385,389,393],{"id":318,"category":36,"text_question":319,"slug":320},532018,"Let 𝑢 = 𝑓(𝑥, 𝑦) = (𝑒^𝑥)𝑠𝑒𝑛(3𝑦). Check if 9((𝜕^2) u / 𝜕(𝑥^2)) +((𝜕^2) 𝑢 / 𝜕(𝑦^2)) = 0","let-u-f-x-y-e-x-sen-3y-check-if-9-2-u-x-2-2-u-y-2-0",{"id":322,"category":36,"text_question":323,"slug":324},533890,"Determine the correct value:\n A company knows that invoices pending collection have a normal distribution with a mean of $1.65 million, with a standard deviation of $0.2 million, then: The probability that an invoice pending collection has an amount that is within more than 2 deviations below the mean, is:","determine-the-correct-value-a-company-knows-that-invoices-pending-collection-have-a-normal-distribution-with-a-mean-of-1-65-million-with-a-standard-deviation-of-0-2-million-then-the-probability",{"id":326,"category":36,"text_question":327,"slug":328},533911,"The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that:\n Exactly 2 are not of high quality","the-lenovo-company-manufactures-laptop-computers-it-is-known-that-for-every-60-laptops-produced-54-go-on-the-market-with-the-highest-quality-standards-if-a-sample-of-15-laptops-is-taken-calculate",{"id":330,"category":36,"text_question":331,"slug":332},534011,"9b^2-6b-5","9b-2-6b-5",{"id":334,"category":36,"text_question":335,"slug":336},534026,"\"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?\"\n\n The answer is the number of response units.","if-three-wolves-catch-three-rabbits-in-three-hours-how-many-wolves-would-it-take-to-catch-a-hundred-rabbits-in-a-hundred-hours-the-answer-is-the-number-of-response-units",{"id":338,"category":36,"text_question":339,"slug":340},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":342,"category":36,"text_question":343,"slug":344},534112,"What is the total tolerance for a dimension from 1.996\" to 2.026*?","what-is-the-total-tolerance-for-a-dimension-from-1-996-to-2-026",{"id":346,"category":36,"text_question":347,"slug":348},534166,"calculate the area in square units of A rectangle with length 6cm and breadth 5cm","calculate-the-area-in-square-units-of-a-rectangle-with-length-6cm-and-breadth-5cm",{"id":350,"category":36,"text_question":351,"slug":352},534199,"A person decides to invest money in fixed income securities to redeem it at the end of 3 years. In this way, you make monthly deposits of R$300.00 in the 1st year, R$400.00 in the 2nd year and R$500.00 in the 3rd year. Calculate the amount, knowing that compound interest is 0.6% per month for the entire period.\n The answer is 15,828.60","a-person-decides-to-invest-money-in-fixed-income-securities-to-redeem-it-at-the-end-of-3-years-in-this-way-you-make-monthly-deposits-of-r-300-00-in-the-1st-year-r-400-00-in-the-2nd-year-and-r-500-0",{"id":354,"category":36,"text_question":355,"slug":356},534241,"Let A, B, C and D be sets such that | A| = |C| and |B| = |D|. Prove that |A × B| = |C × D|","let-a-b-c-and-d-be-sets-such-that-a-c-and-b-d-prove-that-a-b-c-d",{"id":358,"category":36,"text_question":359,"slug":360},534269,"A researcher is interested in voting preferences on change of the governing constitution in a\r\ncertain country controlled by two main parties A and B. A questionnaire was developed and sent\r\nto a random sample of voters. The cross tabs are as follows\r\nFavour Neutral Oppose\r\nMembership: Party A 70 90 85\r\nParty B 50 50 155\r\nTest at α = 0.05 whether party membership and voting preference are associated and state the\r\nconditions required for chi-square test results to be valid.","a-researcher-is-interested-in-voting-preferences-on-change-of-the-governing-constitution-in-a-certain-country-controlled-by-two-main-parties-a-and-b-a-questionnaire-was-developed-and-sent-to-a-rand",{"id":362,"category":36,"text_question":363,"slug":364},534279,"Which of the methods below can be used to workout 95% of an amount?\na. Dividing the amount 100 and multiply by 95\nb. Working out 5% of the amount and taking it away from the full amount\nc. Dividing 95 by 100 and multiplying the answer by the amount\nd. Dividing the amount by 95 and then multiply by 100","which-of-the-methods-below-can-be-used-to-workout-95-of-an-amount-a-dividing-the-amount-100-and-multiply-by-95-b-working-out-5-of-the-amount-and-taking-it-away-from-the-full-amount-c-dividing-95",{"id":366,"category":36,"text_question":367,"slug":368},534328,"What is 75 percent less than 60","what-is-75-percent-less-than-60",{"id":370,"category":36,"text_question":371,"slug":372},534450,"In poker, a full house consists of five cards, where two of the cards have the\nsame number (or letter) and the remaining three also have the same number (or\nletter) as each other (but not as the previous two cards). Use a search engine or\nWikipedia to understand the concept better if necessary.\nIn how many different ways can one obtain a full house?","in-poker-a-full-house-consists-of-five-cards-where-two-of-the-cards-have-the-same-number-or-letter-and-the-remaining-three-also-have-the-same-number-or-letter-as-each-other-but-not-as-the-previ",{"id":374,"category":36,"text_question":375,"slug":376},534471,"Log0","log0",{"id":378,"category":36,"text_question":379,"slug":380},534522,"if y=1/w^2 yw=2-x; find dy/dx","if-y-1-w-2-yw-2-x-find-dy-dx",{"id":382,"category":36,"text_question":383,"slug":384},534528,"If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable.\n12, 18, 21, c, 13","if-the-mean-of-the-following-numbers-is-17-find-the-c-value-produce-an-algebraic-solution-guess-and-check-is-unacceptable-12-18-21-c-13",{"id":386,"category":36,"text_question":387,"slug":388},534585,"Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?","marc-jean-and-michelle-have-traveled-a-lot-marc-drove-twice-as-much-as-jean-but-it-was-michelle-who-drove-the-most-with-100km-more-than-marc-they-respected-their-objective-of-not-exceeding-1350km",{"id":390,"category":36,"text_question":391,"slug":392},534632,"What is the set-off agreement? Make your own example, describe and put in T accounts how you record transactions.","what-is-the-set-off-agreement-make-your-own-example-describe-and-put-in-t-accounts-how-you-record-transactions",{"id":394,"category":36,"text_question":395,"slug":396},534663,"x(squared) -8x=0","x-squared-8x-0",{"data":398},[399,403,407],{"id":400,"question":401,"answer":402},128144,"What is the value of f(x) = ∛(4x - 3) when x = -2?","The value of f(x) = ∛(4x - 3) when x = -2 is f(-2) = ∛(4(-2) - 3) = ∛(-11) = -∛11.",{"id":404,"question":405,"answer":406},113810,"What is the result of multiplying two vectors in a four-dimensional space?","The result of multiplying two vectors in a four-dimensional space is another vector that represents their combination in terms of magnitude and direction. 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