where IQR =Q3-Q1\nFind the lower bound if Q1 =66 and Q3=85\nRound to one decimal place","Solution:\u003Cbr />\n1. Calculate the interquartile range IQR:\u003Cbr />\n * Given:\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Q1 = 66\u003C/math-field>\u003C/math-field>\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Q3 = 85\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>IQR = Q3 - Q1 = 85 - 66 = 19\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Apply the formula for the lower outlier bound:\u003Cbr />\n * Lower Bound = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Q1 - 1.5 \\times IQR\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Lower Bound = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>66 - 1.5 \\times 19\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Lower Bound = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>66 - 28.5\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Lower Bound = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>37.5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. The lower outlier bound rounded to one decimal place is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>37.5\u003C/math-field>\u003C/math-field>",1392,278,"the-formula-for-finding-the-lower-outlier-bound-in-a-data-set-is-lower-bound-q1-1-5-iqr-where-iqr-q3-q1-find-the-lower-bound-if-q1-66-and-q3-85-round-to-one-decimal-place",{"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},537937,"Hannah’s chess board is divided into 64 smaller squares and has an area of 256 inches square. Write and solve an equation to find the dimensions of each small square","1. Calculate the area of one small square: \u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Area of one small square} = \\frac{256}{64} = 4 \\text{ square inches}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Set up the equation for the side length of the small square:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 = 4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Solve for \\( x \\) by taking the square root:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\sqrt{4}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Therefore, the side length is:\u003Cbr />\n\u003Cbr />\n \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 />\nThus, the dimensions of each small square are 2 inches by 2 inches.",1077,215,"hannah-s-chess-board-is-divided-into-64-smaller-squares-and-has-an-area-of-256-inches-square-write-and-solve-an-equation-to-find-the-dimensions-of-each-small-square",{"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},537936,"There is a 6% probability that a randomly selected employed person has more than one job. There is 40% probability that a randomly selected employed person is male, given that the person has more than one job. What is the probability that a randomly selected employee is a man with more than one job? What is the probability that a randomly selected employee is a man and has more than one job?","1. Identify the probability that a person has more than one job: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(M) = 0.06\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Identify the probability that a person is a male given they have more than one job: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(A|M) = 0.40\u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Use the conditional probability formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(A \\cap M) = P(A|M) \\times P(M)\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Calculate: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.40 \\times 0.06 = 0.024\u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Therefore, the probability that a randomly selected employee is a man with more than one job is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.024\u003C/math-field>\u003C/math-field>.",1114,223,"there-is-a-6-probability-that-a-randomly-selected-employed-person-has-more-than-one-job-there-is-40-probability-that-a-randomly-selected-employed-person-is-male-given-that-the-person-has-more-tha",{"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},537935,"A={x/x is a real number and x squared= 0","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- A real number \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> such that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 = 0\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. 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- Since \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 = 0\u003C/math-field>\u003C/math-field> implies that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\cdot x = 0\u003C/math-field>\u003C/math-field>, the only real number that satisfies this equation is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 0\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Therefore, the set \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A\u003C/math-field>\u003C/math-field> consists only of the number zero.\u003Cbr />\n\u003Cbr />\n3. Conclusion:\u003Cbr />\n- The set \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A\u003C/math-field>\u003C/math-field> can be represented as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A = \\{0\\}\u003C/math-field>\u003C/math-field>.",964,193,"a-x-x-is-a-real-number-and-x-squared-0",{"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},537933,"Find the largest two consecutive integers whose sum is less than 46","1. Let the two consecutive integers be \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n \u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n+1 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Their sum is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n + (n+1) = 2n + 1 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. To find the largest such integers, solve \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2n + 1 \u003C 46 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n4. Subtract 1 from both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2n \u003C 45 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n5. Divide by 2: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n \u003C 22.5 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n6. Since \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n \u003C/math-field>\u003C/math-field> must be an integer, the largest possible value for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> n \u003C/math-field>\u003C/math-field> is 22.\u003Cbr />\n\u003Cbr />\nThus, the integers are 22 and 23.",808,162,"find-the-largest-two-consecutive-integers-whose-sum-is-less-than-46",{"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},537932,"Write and solve inequality for:\nWhat hourly wage must Johannes make if he works 40hr a week and wants to earn at least $350 each week?","1. Set up the inequality:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 40x \\geq 350 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Solve for \\( x \\) by dividing both sides by 40:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\geq \\frac{350}{40} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate the division:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\geq 8.75 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, Johannes must make at least $8.75 per hour.",1258,252,"write-and-solve-inequality-for-what-hourly-wage-must-johannes-make-if-he-works-40hr-a-week-and-wants-to-earn-at-least-350-each-week",{"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},537931,"Write an inequality for:\nThe total bill for a lawnmower and 15 drawer pulls was within the family’s $400 budget. If he the lawnmower cost $325, find the maximum cost of each drawer pull","1. Write down the inequality for the total cost: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 325 + 15x \\leq 400 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Subtract the cost of the lawnmower from both sides to isolate the drawer pulls' cost: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 15x \\leq 400 - 325 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 15x \\leq 75 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Divide both sides by 15 to solve for x :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\leq \\frac{75}{15} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\leq 5 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>The maximum cost of each drawer pull is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\leq 5 \u003C/math-field>\u003C/math-field> .",900,180,"write-an-inequality-for-the-total-bill-for-a-lawnmower-and-15-drawer-pulls-was-within-the-family-s-400-budget-if-he-the-lawnmower-cost-325-find-the-maximum-cost-of-each-drawer-pull",{"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},537930,"Find the smallest two consecutive integers such that five times the smaller is at least eight more than three the larger","1. Let x be the smallest integer,\u003Cdiv>Set up the expression for the problem: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x \\geq 3(x+1) + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Distribute and simplify: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x \\geq 3x + 3 + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Combine like terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x \\geq 3x + 11\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Isolate the variable: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x \\geq 11\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Solve for the smallest integer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x \\geq 5.5\u003C/math-field>\u003C/math-field> , so the smallest integer is 6.\u003Cbr>\u003Cbr>6. The integers are 6 and 7.\u003Cbr>\u003Cbr>7. Answer: (6, 7) \u003C/div>",1172,234,"find-the-smallest-two-consecutive-integers-such-that-five-times-the-smaller-is-at-least-eight-more-than-three-the-larger",{"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},537928,"in a geometric sequence r=3 a2=12 find a10","1. Identify the given information in the problem:\u003Cbr />\n - Common ratio: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n - Second term: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_2 = 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the formula for the n-th term of a geometric sequence: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_n = a_1 \\cdot r^{n-1}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Find the first term \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_1\u003C/math-field>\u003C/math-field> using the second term:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_2 = a_1 \\cdot r^{1} \\Rightarrow 12 = a_1 \\cdot 3 \\Rightarrow a_1 = \\frac{12}{3} = 4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_1\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r\u003C/math-field>\u003C/math-field> into the formula for the 10th term:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10} = a_1 \\cdot r^{9} = 4 \\cdot 3^{9}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3^9 = 19683\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Multiply to find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10}\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10} = 4 \\cdot 19683 = 78732\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. The answer is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10} = 78732\u003C/math-field>\u003C/math-field>",791,158,"in-a-geometric-sequence-r-3-a2-12-find-a10",{"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},537927,"in a geometric sequence a1=125 and a3=5 find the common ratio","1. The formula for the \\(n\\)-th term of a geometric sequence is given by:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a_n = a_1 \\cdot r^{n-1} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Given \\( a_1 = 125 \\) and \\( a_3 = 5 \\). We can substitute into the formula for the third term:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a_3 = a_1 \\cdot r^{3-1} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Substitute the known values:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 5 = 125 \\cdot r^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Solve for \\( r^2 \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r^2 = \\frac{5}{125} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify the fraction:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r^2 = \\frac{1}{25} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Take the square root of both sides to solve for \\( r \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r=\\pm\\frac{1}{5}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Therefore, the common ratio is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r=\\pm\\frac{1}{5}\u003C/math-field>\u003C/math-field>",1383,277,"in-a-geometric-sequence-a1-125-and-a3-5-find-the-common-ratio",{"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},537926,"given the following sequence find a50 2,8,14,20,26","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>\u003Cmath-field read-only>a_{50}=2+6\\times 49\u003C/math-field> \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>\u003Cmath-field read-only>a_{50}=2+294\u003C/math-field> \u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>\u003Cmath-field read-only>a_{50}=296\u003C/math-field> \u003C/math-field>\n \u003Cbr>\n \u003C/div>",637,127,"given-the-following-sequence-find-a50-2-8-14-20-26",{"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},537925,"Write and solve an equation:\nFind a number such that tripling the sum of twice the number and 4 is 72.","1. Write the equation that represents the problem: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3(2x + 4) = 72 \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Expand the equation: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6x + 12 = 72 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Isolate the term with \\( x \\) by subtracting 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6x = 60 \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Solve for \\( x \\) by dividing both sides by 6: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 10 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe answer is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 10 \u003C/math-field>\u003C/math-field>",380,76,"write-and-solve-an-equation-find-a-number-such-that-tripling-the-sum-of-twice-the-number-and-4-is-72",{"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},537924,"Write and solve an equation:\nFind a number such that 5 less than the opposite of the number is 3 times the sum of the number and -7","1. Write the equation: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-x - 5 = 3(x - 7)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Expand the right side: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-x - 5 = 3x - 21\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> to both sides: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-5 = 4x - 21\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Add 21 to both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>16 = 4x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Divide by 4:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 4\u003C/math-field>\u003C/math-field>",1033,207,"write-and-solve-an-equation-find-a-number-such-that-5-less-than-the-opposite-of-the-number-is-3-times-the-sum-of-the-number-and-7",{"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},537923,"Find two consecutive odd integers whose sum is 116","**\u003Cbr />\n\u003Cbr />\n1. Set up the equation based on the problem statement:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x + (x + 2) = 116 \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Simplify by combining like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x + 2 = 116 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Subtract 2 from both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x = 114 \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Divide both sides by 2 to solve for \\( x \\):\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 57 \u003C/math-field>\u003C/math-field>\u003Cbr />\n5. The first odd integer is 57, the next consecutive odd integer is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x + 2 = 59 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the two consecutive odd integers are \\( x = 57 \\) and \\( x + 2 = 59 \\).",1099,220,"find-two-consecutive-odd-integers-whose-sum-is-116",{"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},537922,"Find three consecutive integers whose sum is 84","1. Represent the consecutive integers as $x$, $x+1$, and $x+2$.\u003Cbr />\n\u003Cbr />\n2. Write the equation for their sum: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + (x+1) + (x+2) = 84\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Simplify and solve for $x$:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 3 = 84\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x = 81\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 27\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. The integers are $x = 27$, $x + 1 = 28$, $x + 2 = 29$.\u003Cbr />\n\u003Cbr />\n5. Therefore, the three consecutive integers are 27, 28, and 29.",1301,260,"find-three-consecutive-integers-whose-sum-is-84",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":132,"slug":153},537921,"A pilot flew 390 nautical miles in 45 minutes. Find his average speed in knots (nautical miles per hour)","1. Convert time from minutes to hours: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{{Time in hours}} = \\frac{45}{60} = 0.75 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Calculate average speed: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{{Average speed}} = \\frac{390}{0.75} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. The average speed of the pilot is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 520 \u003C/math-field>\u003C/math-field> knots.",1037,"a-pilot-flew-390-nautical-miles-in-45-minutes-find-his-average-speed-in-knots-nautical-miles-per-hour",{"id":155,"category":36,"text_question":156,"photo_question":38,"text_answer":157,"step_text_answer":8,"step_photo_answer":8,"views":158,"likes":159,"slug":160},537920,"Write and solve an equation:\nHow long does it take Kathryn to get to her grandmother’s house that is 180 mi away if she averages 45mi/hr on the trip","1. Use the formula for time: \\( t = \\frac{d}{s} \\).\u003Cbr />\n2. Plug in the distance: \\( d = 180 \\, \\text{miles} \\).\u003Cbr />\n3. Plug in the speed: \\( s = 45 \\, \\text{miles per hour} \\).\u003Cbr />\n4. Solve for time: \\( t = \\frac{180}{45} = 4 \\).\u003Cbr />\n5. Answer: \\( 4 \\, \\text{hours} \\).",668,134,"write-and-solve-an-equation-how-long-does-it-take-kathryn-to-get-to-her-grandmother-s-house-that-is-180-mi-away-if-she-averages-45mi-hr-on-the-trip",{"id":162,"category":36,"text_question":163,"photo_question":38,"text_answer":164,"step_text_answer":8,"step_photo_answer":8,"views":165,"likes":166,"slug":167},537919,"Write and solve an equation:\nFind a number such that the difference of 97 and eighteen times the number is five times one more than the number","1. Let the number be \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. According to the problem, the difference of 97 and eighteen times the number (\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 18x \u003C/math-field>\u003C/math-field>) is equal to five times one more than the number (\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 5(x+1) \u003C/math-field>\u003C/math-field>).\u003Cbr />\n\u003Cbr />\n The equation can be written as: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 97 - 18x = 5(x + 1) \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Expand the term on the right-hand side: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 5(x + 1) = 5x + 5 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Substitute back into the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 97 - 18x = 5x + 5 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Bring all terms involving \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field> to one side and constant terms to the other:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 97 - 5 = 18x + 5x \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 92 = 23x \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{92}{23} = 4 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the number is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 4 \u003C/math-field>\u003C/math-field>.",1373,275,"write-and-solve-an-equation-find-a-number-such-that-the-difference-of-97-and-eighteen-times-the-number-is-five-times-one-more-than-the-number",{"id":169,"category":36,"text_question":170,"photo_question":38,"text_answer":171,"step_text_answer":8,"step_photo_answer":8,"views":172,"likes":173,"slug":174},537918,"Find two consecutive integers such that four times the larger is 94 more than three times the smaller","1. Let the two consecutive integers be \\( x \\) and \\( x + 1 \\).\u003Cbr />\n2. According to the problem, four times the larger integer is 94 more than three times the smaller integer. Therefore, the expression becomes: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4(x + 1) = 3x + 94 \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Distribute and simplify: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4x + 4 = 3x + 94 \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Subtract \\( 3x \\) from both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x + 4 = 94 \u003C/math-field>\u003C/math-field>\u003Cbr />\n5. Subtract 4 from both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 90 \u003C/math-field>\u003C/math-field>\u003Cbr />\n6. The larger integer is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x + 1 = 90 + 1 = 91 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nAnswer: The larger integer is 91, so the consecutive integers are 90 and 91.",1053,211,"find-two-consecutive-integers-such-that-four-times-the-larger-is-94-more-than-three-times-the-smaller",{"first":6,"last":176,"prev":8,"next":10},181,{"current_page":6,"from":6,"last_page":176,"links":178,"path":211,"per_page":212,"to":212,"total":213},[179,182,185,187,189,191,193,196,199,202,205,207,209],{"url":6,"label":180,"active":181},"1",true,{"url":10,"label":183,"active":184},"2",false,{"url":13,"label":186,"active":184},"3",{"url":16,"label":188,"active":184},"4",{"url":19,"label":190,"active":184},"5",{"url":22,"label":192,"active":184},"6",{"url":194,"label":195,"active":184},7,"7",{"url":197,"label":198,"active":184},8,"8",{"url":200,"label":201,"active":184},9,"9",{"url":203,"label":204,"active":184},10,"10",{"url":90,"label":206,"active":184},"180",{"url":176,"label":208,"active":184},"181",{"url":10,"label":210,"active":184},"Next »","https://api.math-master.org/api/question",20,3613,{"data":215},{"questions":216},[217,221,225,229,233,237,241,244,248,252,256,260,264,268,272,276,280,284,288,292],{"id":218,"category":36,"text_question":219,"slug":220},532001,"A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.","a-normal-random-variable-x-has-a-mean-of-50-and-a-standard-deviation-of-10-would-it-be-unusual-to-see-the-value-x-0-explain-your-answer",{"id":222,"category":36,"text_question":223,"slug":224},532008,"1 + 1","1-1",{"id":226,"category":36,"text_question":227,"slug":228},532013,"Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps","using-a-remarkable-product-you-must-factor-the-expression-f-x-36x-2-324-and-you-are-entitled-to-5-steps",{"id":230,"category":36,"text_question":231,"slug":232},532091,"the value of sin 178°58'","the-value-of-sin-178-58-39",{"id":234,"category":36,"text_question":235,"slug":236},532304,"what is 9% of 307","what-is-9-of-307",{"id":238,"category":36,"text_question":239,"slug":240},533965,"In a store there are packets of chocolate, strawberry, tutti-frutti, lemon, grape and banana sweets. If a person needs to choose 4 flavors of candy from those available, how many ways can they make that choice?","in-a-store-there-are-packets-of-chocolate-strawberry-tutti-frutti-lemon-grape-and-banana-sweets-if-a-person-needs-to-choose-4-flavors-of-candy-from-those-available-how-many-ways-can-they-make-th",{"id":242,"category":36,"text_question":243,"slug":243},533975,"4x567",{"id":245,"category":36,"text_question":246,"slug":247},534045,"How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?","how-many-different-ways-can-a-psychology-student-select-5-subjects-from-a-pool-of-20-subjects-and-assign-each-one-to-a-different-experiment",{"id":249,"category":36,"text_question":250,"slug":251},534119,"What is the appropriate measurement for the weight of an African elephant?","what-is-the-appropriate-measurement-for-the-weight-of-an-african-elephant",{"id":253,"category":36,"text_question":254,"slug":255},534134,"find x in the equation\n 2x-4=6","find-x-in-the-equation-2x-4-6",{"id":257,"category":36,"text_question":258,"slug":259},534238,"Exercise 1\n\n An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares.\n\n Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables:\n\n Total available resource\n Water 15,000 m3\n Fertilizer 5,000 kg\n Labor 125 day laborers\n\n Requirements per cultivated hectare Corn Soybeans Wheat\n Water 15 25 20\n Fertilizer 5 8 7\n Labor** 1/8 1/5 1/4\n\n\n\n\n *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. *\n Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat.\n The objectives are to determine:\n • How many hectares of each crop must be allocated so that the profit is maximum. R=\n\n\n • The estimated profits for the ejidal cooperative in the next growing season. R=","exercise-1-an-ejidal-association-wishes-to-determine-the-distribution-for-the-three-different-crops-that-it-can-plant-for-the-next-season-on-its-available-900-hectares-information-on-the-total-av",{"id":261,"category":36,"text_question":262,"slug":263},534244,"A stunt man jumps horizontally from a building to the roof of a garage that is 2 meters lower. How fast does he need to be to land on the roof of the said garage that is 3 meters away from the building?","a-stunt-man-jumps-horizontally-from-a-building-to-the-roof-of-a-garage-that-is-2-meters-lower-how-fast-does-he-need-to-be-to-land-on-the-roof-of-the-said-garage-that-is-3-meters-away-from-the-buildin",{"id":265,"category":36,"text_question":266,"slug":267},534334,"Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.","next-c3-b3n-2c-we-are-given-a-series-of-tri-c3-a1angles-right-c3-a1angles-3cbr-2f-3ey-in-each-one-of-them-are-known-2-28two-29-measurements-of-sides-3cbr-2f-3elet-s-determine-all-trigonom-c3-a9tri",{"id":269,"category":36,"text_question":270,"slug":271},534391,"(X+2)(x+3)=4x+18","x-2-x-3-4x-18",{"id":273,"category":36,"text_question":274,"slug":275},534395,"Let f and g be defined in R and suppose that there exists M > 0 such that\n |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p,\n then f will also be continuous in p.","let-f-and-g-be-defined-in-r-and-suppose-that-there-exists-m-0-such-that-f-x-f-p-m-g-x-g-p-for-all-x-prove-that-if-g-is-continuous-in-p-then-f-will-also-be-continuous-in-p",{"id":277,"category":36,"text_question":278,"slug":279},534408,"Which statement best describes the key changes in perspectives on inclusion?\r\n\r\n\t\t\r\nAn inclusive program must consider the unique experiences of every child and family as well as the child's strengths and needs.\r\n\r\n\t\t\r\nThere is a shift in thinking about individual programs as \"inclusive programs\" to thinking about inclusion as something that reflects the cultural influence of the family.\r\n\r\n\t\t\r\nThere is a greater emphasis on barriers to full participation and the acknowledgement that all children are unique and must be fully and meaningfully engaged in a program.\r\n\r\n\t\t\r\nIn an inclusive program all participants are accepted by their peers and other members of the community.","which-statement-best-describes-the-key-changes-in-perspectives-on-inclusion-an-inclusive-program-must-consider-the-unique-experiences-of-every-child-and-family-as-well-as-the-child-s-strengths",{"id":281,"category":36,"text_question":282,"slug":283},534415,"In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). \r\n\r\nCalculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1)\r\n )\r\n\r\n\r\n\r\n\r\n\r\nGive your answers to 4 decimal places and in a range between 0 and 1","in-a-24-hours-period-the-average-number-of-boats-arriving-at-a-port-is-10-assuming-that-boats-arrive-at-a-random-rate-that-is-the-same-for-all-subintervals-of-equal-length-i-e-the-probability-of-a",{"id":285,"category":36,"text_question":286,"slug":287},534451,"Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?","pablo-has-a-balance-of-440-000-and-2-5-of-the-money-is-used-to-pay-bills-how-much-money-do-you-have-left-after-paying-the-bills",{"id":289,"category":36,"text_question":290,"slug":291},534517,"solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0","solve-r-the-following-equation-4-x-squared-35-9-over-x-squared-is-equal-to-0",{"id":293,"category":36,"text_question":294,"slug":295},534670,"13/25+7/16","13-25-7-16",{"data":297},{"id":298,"category":36,"slug":299,"text_question":300,"photo_question":8,"text_answer":301,"step_text_answer":8,"step_photo_answer":8,"views":302,"likes":303,"expert":304},537789,"7-3-1-3","7-3 1/3","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$=3+\\frac{2}{3}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$=6\\frac{3}{3}-3\\frac{1}{3}$\n$=3\\frac{2}{3}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",362,72,{"id":305,"name":306,"photo":307,"biography":308,"created_at":8,"updated_at":8,"rating":309,"total_answer":310},21,"Jon","https://api.math-master.org/img/experts/21/21.webp","I passed my matric from Govt.City Muslim school Faisalabad and got first division in school by getting 981/1000 marks.\nAfter matric i got admission in Shiblee Colege Faisalabad and got 883/1100 marks in degree of inter with Math.\nNow currently i'm student of BS Math and running my last semester.",4.6,102,{"data":312},{"questions":313},[314,318,319,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387],{"id":315,"category":36,"text_question":316,"slug":317},532005,"A=m/2-t isolate t","a-m-2-t-isolate-t",{"id":222,"category":36,"text_question":223,"slug":224},{"id":320,"category":36,"text_question":321,"slug":322},532027,"-x+3x-2,si x=3","x-3x-2-si-x-3",{"id":324,"category":36,"text_question":325,"slug":326},532037,"Pedro bought 9 kg of sugar at the price of R$1.80 per kilogram, six packets of coffee at the price of R$3.90 per packet and 8 kg of rice at the price of R$2.70 per kilogram. Knowing that he paid for the purchases with a R$100.00 bill, how much change did he receive?","pedro-bought-9-kg-of-sugar-at-the-price-of-r-1-80-per-kilogram-six-packets-of-coffee-at-the-price-of-r-3-90-per-packet-and-8-kg-of-rice-at-the-price-of-r-2-70-per-kilogram-knowing-that-he-paid-for-t",{"id":328,"category":36,"text_question":329,"slug":330},533926,"(m²-121)","m-121",{"id":332,"category":36,"text_question":333,"slug":334},533956,"1 plus 1","1-plus-1",{"id":336,"category":36,"text_question":337,"slug":338},533999,"2x-4y=-6; -4y+4y=-8","2x-4y-6-4y-4y-8",{"id":340,"category":36,"text_question":341,"slug":342},534049,"(-5/6)-(-5/4)","5-6-5-4",{"id":344,"category":36,"text_question":345,"slug":346},534147,"2x+4x=","2x-4x",{"id":348,"category":36,"text_question":349,"slug":350},534263,"Scores are normally distributed with a mean of 25 and standard deviation of 5. Find the probability that sixteen randomly selected students have a mean score that is less than 24.","scores-are-normally-distributed-with-a-mean-of-25-and-standard-deviation-of-5-find-the-probability-that-sixteen-randomly-selected-students-have-a-mean-score-that-is-less-than-24",{"id":352,"category":36,"text_question":353,"slug":354},534311,"The two sides of the triangle are 12 cm and 5 cm, and the angle between the sides is 60°. Cover the area of the triangle!","the-two-sides-of-the-triangle-are-12-cm-and-5-cm-and-the-angle-between-the-sides-is-60-cover-the-area-of-the-triangle",{"id":356,"category":36,"text_question":357,"slug":358},534382,"Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will","twenty-five-students-in-a-class-take-a-test-for-which-the-average-grade-is-75-then-a-twenty-sixth-student-enters-the-class-takes-the-same-test-and-scores-70-the-test-average-grade-calculated-with",{"id":360,"category":36,"text_question":361,"slug":362},534431,"What is the value of f(-3) for the function X squared+5x-8=","what-is-the-value-of-f-3-for-the-function-x-squared-5x-8",{"id":364,"category":36,"text_question":365,"slug":366},534454,"We plan to test whether the mean mRNA expression level differs between two strains of\nyeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n\nsamples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene,\nusing an unpaired two-sample t-test for each gene (the particular type of test does not\nmatter).\na) What are the null hypotheses in these tests (in words)? [2]\nb) If, in fact, the two strains are identical, how many of these tests do we expect to\nproduce a P-value exceeding 1/4? [2]","we-plan-to-test-whether-the-mean-mrna-expression-level-differs-between-two-strains-of-yeast-for-each-of-8-000-genes-we-will-measure-the-expression-levels-of-each-gene-in-n-samples-of-strain-1-and-m",{"id":368,"category":36,"text_question":369,"slug":370},534456,"When taking a test with m closed answers, a student knows the correct answer with probability p, otherwise he chooses one of the possible answers at random. What is the probability that the student knows the correct answer given that he answered the question correctly.","when-taking-a-test-with-m-closed-answers-a-student-knows-the-correct-answer-with-probability-p-otherwise-he-chooses-one-of-the-possible-answers-at-random-what-is-the-probability-that-the-student-kn",{"id":372,"category":36,"text_question":373,"slug":374},534471,"Log0","log0",{"id":376,"category":36,"text_question":377,"slug":378},534484,"00 piece jigsaw puzzle. the completed puzzle is 10x10. each piech connects to at least 2 other pieces. i plan to assemble by taking pieces out of box one by one. if i've already taken out 2 pieces that dont directly connect, what is the minimum number of additional pieces that i need to draw to in order to guarentee that the original 2 pieces connect?","00-piece-jigsaw-puzzle-the-completed-puzzle-is-10x10-each-piech-connects-to-at-least-2-other-pieces-i-plan-to-assemble-by-taking-pieces-out-of-box-one-by-one-if-i-ve-already-taken-out-2-pieces-tha",{"id":380,"category":36,"text_question":381,"slug":382},534488,"7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?","7-a-printing-company-found-in-its-investigations-that-there-were-an-average-of-6-errors-in-150-page-prints-based-on-this-information-what-is-the-probability-of-there-being-48-errors-in-a-1200-page",{"id":384,"category":36,"text_question":385,"slug":386},534572,"did an analysis of dropout from the nursing faculty at the Universidad Veracruzana. With a poblation of\n\n 122 students, it turned out that according to the gender data, the female sex predominates with 82%, and the male sex\n\n male is found with 12%. The main factors why students drop out are, first of all, \"Not\n\n \"re-enrolled\" at 49%, second place \"Personal reasons\" at 20%, third place \"change of school\"\n\n in 11%, \"lack of documents\" and \"economic reasons\" in 7%, change of residence and lack of social service in\n\n 3%. Of this sample, how many students dropped out for other reasons?","did-an-analysis-of-dropout-from-the-nursing-faculty-at-the-universidad-veracruzana-with-a-poblation-of-122-students-it-turned-out-that-according-to-the-gender-data-the-female-sex-predominates-wit",{"id":388,"category":36,"text_question":389,"slug":390},534597,"Arturo had hospitalization expenses of $8,300. Your policy for medical expenses\n Seniors have a deductible of $500 and expenses are paid at a 20% coinsurance.\n These are the first expenses ever this year, how much will Arturo have to pay in\n your bill for hospitalization expenses?","arturo-had-hospitalization-expenses-of-8-300-your-policy-for-medical-expenses-seniors-have-a-deductible-of-500-and-expenses-are-paid-at-a-20-coinsurance-these-are-the-first-expenses-ever-this-y",{"data":392},[393,397,401],{"id":394,"question":395,"answer":396},125632,"What is the value of y in the exponential function y = 2^x when x = 3?","The value of y is 8. For x = 3, substituting it into the function, y = 2^3, which equals 8.",{"id":398,"question":399,"answer":400},151807,"Math question: Find the 3rd derivative of f(x) = 2x^5 + 3x^4 - 7x^2 - 5x + 1.","Answer: To find the nth derivative, apply the power rule: f^(n)(x) = a(n!)(x^(n-m)), where a is the coefficient, n is the power, and m is the number of derivatives taken. The 3rd derivative is f'''(x) = 240x^2 + 72x - 28.",{"id":402,"question":403,"answer":404},156229,"Question: What is the integral of f(x) = 2x^3 + 5x^2 - 3x + 2 from x = 0 to x = 2 using the Fundamental Theorem of Calculus?","Answer: Applying the Fundamental Theorem of Calculus, the antiderivative of f(x) is F(x) = (1/2)x^4 + (5/3)x^3 - (3/2)x^2 + 2x + C. Evaluating from x = 0 to x = 2, we have F(2) - F(0). Substituting these values, we get [(1/2)(2)^4 + (5/3)(2)^3 - (3/2)(2)^2 + 2(2)] - [(1/2)(0)^4 + (5/3)(0)^3 - (3/2)(0)^2 + 2(0)]. Simplifying yields the numerical result.",{"$sicons":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":184,"hFlip":184,"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":184,"hFlip":184,"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 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" fill=\"currentColor\"/>\u003Cpath 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