supposed 60 of the register voters in a country or democrat if a sample of 793 voters is selected what is the probability
Question
Supposed 60% of the register voters in a country or democrat. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64% round your answer to four decimal places
143
likes
714 views
Answer to a math question Supposed 60% of the register voters in a country or democrat. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64% round your answer to four decimal places
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},[217,221,225,229,233,237,241,245,249,253,257,261,265,269,273,277,281,285,289,293],{"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},532051,"Eight acts are scheduled to perform in a variety show how many different ways are there to schedule their appearances show your work","eight-acts-are-scheduled-to-perform-in-a-variety-show-how-many-different-ways-are-there-to-schedule-their-appearances-show-your-work",{"id":226,"category":36,"text_question":227,"slug":228},532064,"12-6x=4x+2","12-6x-4x-2",{"id":230,"category":36,"text_question":231,"slug":232},532078,"Solve: −3(−2x+23)+12=6(−4x+9)+9.","solve-3-2x-23-12-6-4x-9-9",{"id":234,"category":36,"text_question":235,"slug":236},533919,"a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?","a-bank-finds-that-the-balances-in-its-savings-accounts-are-normally-distributed-with-a-mean-of-500-and-a-standard-deviation-off-of-40-what-is-the-probability-that-a-randomly-selected-account-has-a",{"id":238,"category":36,"text_question":239,"slug":240},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":242,"category":36,"text_question":243,"slug":244},534090,"If you randomly selected one person from the 900 subjects in this study, what is the probability that \nthe person exhibits the minimum BMI?","if-you-randomly-selected-one-person-from-the-900-subjects-in-this-study-what-is-the-probability-that-the-person-exhibits-the-minimum-bmi",{"id":246,"category":36,"text_question":247,"slug":248},534125,"There were no defectives in a sample of 1 light bulb does this sample provide sufficient evidence that in the warehouse with millions of light bulbs fewer than 10% are defective?","there-were-no-defectives-in-a-sample-of-1-light-bulb-does-this-sample-provide-sufficient-evidence-that-in-the-warehouse-with-millions-of-light-bulbs-fewer-than-10-are-defective",{"id":250,"category":36,"text_question":251,"slug":252},534129,"Determine the general equation of the straight line that passes through the point P (2;-3) and is parallel to the straight line with the equation 5x – 2y 1 = 0:","determine-the-general-equation-of-the-straight-line-that-passes-through-the-point-p-2-3-and-is-parallel-to-the-straight-line-with-the-equation-5x-2y-1-0",{"id":254,"category":36,"text_question":255,"slug":256},534193,"(1) July 1, 2008: Receives $25,000 from Quinn Zealick for 25,000 shares of the stock\n common face value $1 from the bookstore.\n (2) July 1, 2008: Obtains $30,000 loan from local bank for needs\n of working capital. The loan earns 6% interest per year. The loan is payable\n with interest on June 30, 2009.\n (3) July 1, 2008: Sign a three-year rental agreement at an annual rent of $20,000\n Pay the first year's rent in advance.\n (4) July 1, 2008: Purchases shelves for $4,000 in cash. The shelves have\n an estimated useful life of five years and zero residual value.\n (5) July 1, 2008: Purchase computers for $10,000 in cash. The computers\n They have an estimated useful life of three years and $1,000 in residual value.\n (6) July 1, 2008: Makes guarantee deposits with various book distributors for\n a total of $8,000. Deposits are refundable on June 30, 2009 if the bookstore pays\n on time all amounts payable for books purchased from distributors between\n July 2008 and June 30, 2009.\n (7) During 2008: Purchases books on account from various distributors for a cost of $160,000.\n (8)During 2008: Sells books costing $140,000 to $172,800. Of the total sales,\n $24,600 corresponds to cash and $148,200 is on account.\n (9) During 2008: Returns unsold books and books ordered in error for a cost of\n $14,600. The company had not yet paid for these books.\n (10) During 2008: Collected $142,400 from sales on account.\n (11) During 2008: Pays employees salaries of $16,700.\n (12) During 2008: Pays $139,800 to book distributors of the amounts payable for\n purchases on account.\n (13) December 28, 2008: Receives customer advances of $850 due to order books\n special that the bookstore will order and expects to receive during 2009.\n (14) December 31, 2008: Record the corresponding amount of interest expense on the\n loan in (2) for 2008.\n (15) December 31, 2008: Record the corresponding amount of rental expense for 2008.\n (16) December 31, 2008: Record the corresponding amount of depreciation expense\n on the shelves in (4).\n (17) December 31, 2008: Record the corresponding amount of depreciation expense\n about computers in (5).\n (18) December 31, 2008: Record the corresponding amount of income tax expense.\n profits for 2008. The income tax rate is 40%. The taxes are\n paid on March 15, 2009.\n\n\n (1) March 15, 2009: Pays 2008 income tax.\n (2) June 30, 2009: Pay off the bank loan with interest.\n (3) July 1, 2009: Obtains a new bank loan for $75,000. He\n loan is payable on June 30, 2010, with 8% interest payable\n to the expiration.\n (4) July 1, 2009: Receives security deposits from book distributors.\n (5) July 1, 2009: Pay the rent corresponding to the period from July 1\n 2009 to June 30, 2010.\n (6) During 2009: Purchase books on account for a cost of $310,000.\n (7)During 2009: Sold books for a cost of $286,400 for $353,700. Of the total sales,\n $24,900 corresponds to cash, $850 corresponds to special orders received during December\n of 2008 and $327,950 are on account.\n (8) During 2009: Returns unsold books at a cost of $22,700. The company has not yet\n I had paid for these books.\n (9) During 2009: Collects $320,600 from sales to accounts.\n (10) During 2009: Pays employees compensation of $29,400.\n (11) During 2009: pays $281,100 to book distributors for book purchases from\n account.\n (12) December 31, 2009: Declares and pays a dividend of $4,000.","1-july-1-2008-receives-25-000-from-quinn-zealick-for-25-000-shares-of-the-stock-common-face-value-1-from-the-bookstore-2-july-1-2008-obtains-30-000-loan-from-local-bank-for-needs-of-wor",{"id":258,"category":36,"text_question":259,"slug":260},534315,"Find each coefficient described. Coefficient of u^2 in expansion of (u - 3)^3","find-each-coefficient-described-coefficient-of-u-2-in-expansion-of-u-3-3",{"id":262,"category":36,"text_question":263,"slug":264},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":266,"category":36,"text_question":267,"slug":268},534365,"Calculate the difference between 407 and 27","calculate-the-difference-between-407-and-27",{"id":270,"category":36,"text_question":271,"slug":272},534388,"A contractor gives a bank note for $10250 at a rate of 1% for one month. How much interest\nis charged for 4 months?","a-contractor-gives-a-bank-note-for-10250-at-a-rate-of-1-for-one-month-how-much-interest-is-charged-for-4-months",{"id":274,"category":36,"text_question":275,"slug":276},534475,"94 divided by 8.75","94-divided-by-8-75",{"id":278,"category":36,"text_question":279,"slug":280},534552,"Solve for z:\n\n2z-6=10z+2","solve-for-z-2z-6-10z-2",{"id":282,"category":36,"text_question":283,"slug":284},534579,"What js the greatest 4-digit even number that can be formed by 3,6,1,4?","what-js-the-greatest-4-digit-even-number-that-can-be-formed-by-3-6-1-4",{"id":286,"category":36,"text_question":287,"slug":288},534599,"Today a father deposits $12,500 in a bank that pays 8% annual interest. Additionally, make annual contributions due of $2,000 annually for 3 years. The fund is for your son to receive an annuity and pay for his studies for 5 years. If the child starts college after 4 years, how much is the value of the annuity?\n\n solve how well it is for an exam","today-a-father-deposits-12-500-in-a-bank-that-pays-8-annual-interest-additionally-make-annual-contributions-due-of-2-000-annually-for-3-years-the-fund-is-for-your-son-to-receive-an-annuity-and-p",{"id":290,"category":36,"text_question":291,"slug":292},534609,"Sally’s sales for last Sunday were $1,278. That was an increase of 6.5% over her sales for the previous\nSaturday. What were her sales for the previous Saturday?","sally-s-sales-for-last-sunday-were-1-278-that-was-an-increase-of-6-5-over-her-sales-for-the-previous-saturday-what-were-her-sales-for-the-previous-saturday",{"id":294,"category":36,"text_question":295,"slug":296},534698,"Question 3\r\nA square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.","question-3-a-square-has-a-perimeter-given-by-the-algebraic-expression-24x-16-write-the-algebraic-expression-that-represents-one-of-its-sides",{"data":298},{"id":299,"category":36,"slug":300,"text_question":301,"photo_question":8,"text_answer":302,"step_text_answer":8,"step_photo_answer":8,"views":303,"likes":304,"expert":305},534008,"supposed-60-of-the-register-voters-in-a-country-or-democrat-if-a-sample-of-793-voters-is-selected-what-is-the-probability-that-the-sample-proportion-of-democrats-will-be-greater-than-64-round-your","Supposed 60% of the register voters in a country or democrat. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64% round your answer to four decimal places","0.0107",714,143,{"id":306,"name":307,"photo":308,"biography":309,"created_at":8,"updated_at":8,"rating":310,"total_answer":311},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp","I had very much interest from the Starting with simple addition and multiplication, my math journey led me to tackle more challenging problems. What I love most about math is how it's like a puzzle-solving adventure. It helps us understand things around us by finding patterns and connections. It's like a secret code that unveils the mysteries of the world, and I enjoy how each solution feels like a small victory. Math is like a playground for our imagination, where we can come up with creative ways to solve problems and learn new things. It's all about exploring, discovering, and having fun along the way.",4.9,92,{"data":313},{"questions":314},[315,319,323,327,331,335,339,343,347,351,355,359,363,367,371,372,376,380,384,388],{"id":316,"category":36,"text_question":317,"slug":318},532042,"The patient is prescribed a course of 30 tablets.\nThe tablets are prescribed “1 tablet twice a day”.\nHow many days does a course of medication last?","the-patient-is-prescribed-a-course-of-30-tablets-the-tablets-are-prescribed-1-tablet-twice-a-day-how-many-days-does-a-course-of-medication-last",{"id":320,"category":36,"text_question":321,"slug":322},532085,"3(2+x)-2(2x+6)=20-4x","3-2-x-2-2x-6-20-4x",{"id":324,"category":36,"text_question":325,"slug":326},533891,"Investing equal amounts of money into each of five business ventures\n Let's say you plan. 20 to choose from\n If there are initiatives, how many different ones among 20 initiatives?\n five startups can be selected?","investing-equal-amounts-of-money-into-each-of-five-business-ventures-let-39-s-say-you-plan-20-to-choose-from-if-there-are-initiatives-how-many-different-ones-among-20-initiatives-five-startups",{"id":328,"category":36,"text_question":329,"slug":330},533902,"For a temperature range between -3 degrees Celsius to 5 degrees Celsius, what is the temperature range in degrees Farenheight","for-a-temperature-range-between-3-degrees-celsius-to-5-degrees-celsius-what-is-the-temperature-range-in-degrees-farenheight",{"id":332,"category":36,"text_question":333,"slug":334},533929,"Determine the equations of the recipes that pass through the following pairs of points\n P1 (2;-1) and p2 (4;-1)","determine-the-equations-of-the-recipes-that-pass-through-the-following-pairs-of-points-p1-2-1-and-p2-4-1",{"id":336,"category":36,"text_question":337,"slug":338},533949,"Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number","consider-numbers-from-1-to-2023-we-delete-3-consecutive-numbers-so-that-the-avarage-of-the-left-numbers-is-a-whole-number",{"id":340,"category":36,"text_question":341,"slug":342},533950,"Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that","consider-numbers-from-1-to-2023-we-want-to-delete-3-consecutive-so-that-the-avarage-of-the-left-numbers-is-a-whole-number-how-do-we-do-that",{"id":344,"category":36,"text_question":345,"slug":346},534174,"find f(x) for f'(x)=3x+7","find-f-x-for-f-x-3x-7",{"id":348,"category":36,"text_question":349,"slug":350},534324,"Solve equations by equalization method\n X-8=-2y\n 2x+y=7","solve-equations-by-equalization-method-x-8-2y-2x-y-7",{"id":352,"category":36,"text_question":353,"slug":354},534344,"Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9\r\n\r\nEnter the value of the function, not the value of x","find-the-minimum-value-of-the-function-y-4-x3-60-x2-252-x-8-for-values-of-x-between-x-0-and-x-9-enter-the-value-of-the-function-not-the-value-of-x",{"id":356,"category":36,"text_question":357,"slug":358},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":360,"category":36,"text_question":361,"slug":362},534471,"Log0","log0",{"id":364,"category":36,"text_question":365,"slug":366},534472,"In an economy with C= 10+0.8 Yd ; I= 20+0.1Y ; G= 100 ; X= 20 ; M=10+0.2Y ; T=-10+0.2Y and R= 10, when knew that Yd= Y-T+R. How much is the budget?\r\n\r\nA. -23.18\r\nB. -28.13\r\nC. -13.28\r\nD. -32.18","in-an-economy-with-c-10-0-8-yd-i-20-0-1y-g-100-x-20-m-10-0-2y-t-10-0-2y-and-r-10-when-knew-that-yd-y-t-r-how-much-is-the-budget-a-23-18-b-28-13-c-13-28-d-32-18",{"id":368,"category":36,"text_question":369,"slug":370},534473,"A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.","a-20-000-kg-school-bus-is-moving-at-30-km-per-hour-on-a-straight-road-at-that-moment-it-applies-the-brakes-until-it-comes-to-a-complete-stop-after-15-seconds-calculate-the-acceleration-and-the-forc",{"id":274,"category":36,"text_question":275,"slug":276},{"id":373,"category":36,"text_question":374,"slug":375},534503,"A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be \r\nNormally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and \r\nStandard deviation is measured in millimeters. \r\nWhat is the probability that an arbitrary route has a thickness less than 4.00 mm?","a-factory-produces-glass-for-windows-the-thickness-x-of-an-arbitrarily-selected-pane-of-glass-is-assumed-to-be-normally-distributed-with-expectation-u-4-10-and-standard-deviation-0-04-expect",{"id":377,"category":36,"text_question":378,"slug":379},534518,"Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.30, the probability that daily demand will be 200 cases is 0.40, and the probability that daily demand will be 300 cases is 0.30. Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case. (a) Draw a decision table for this problem (b) What do you recommend?","farm-grown-inc-produces-cases-of-perishable-food-products-each-case-contains-an-assortment-of-vegetables-and-other-farm-products-each-case-costs-5-and-sells-for-15-if-there-are-any-not-sold-by",{"id":381,"category":36,"text_question":382,"slug":383},534547,"2.3 X 0.8","2-3-x-0-8",{"id":385,"category":36,"text_question":386,"slug":387},534613,"How many digits are there in Hindu-Arabic form of numeral 26 × 1011","how-many-digits-are-there-in-hindu-arabic-form-of-numeral-26-1011",{"id":389,"category":36,"text_question":390,"slug":391},534665,"Let f(x)=-1/2x+5 evaluate f(-6)","let-f-x-1-2x-5-evaluate-f-6",{"data":393},[394,398,402],{"id":395,"question":396,"answer":397},161330,"What is the slope of the line passing through the points (2, 5) and (-3, 1)?","The slope can be found using the formula: slope = (y2 - y1) / (x2 - x1). Plugging the values, we get (1 - 5) / (-3 - 2) = -4 / -5 = 4/5. Therefore, the slope is 4/5.",{"id":399,"question":400,"answer":401},123554,"What is the slope-intercept form of a linear function with a slope of 3/4 and a y-intercept of 2?","The slope-intercept form is y = (3/4)x + 2, where the slope represents the rate of change and the y-intercept is the starting point.",{"id":403,"question":404,"answer":405},102450,"What is 35% expressed as a decimal?","To express 35% as a decimal, divide 35 by 100, which equals 0.35.",{"$sicons":407},{"bxl:facebook-circle":408,"bxl:instagram":412,"mdi:web":414,"la:apple":416,"ph:google-logo-bold":419,"ph:google-logo":422},{"left":409,"top":409,"width":410,"height":410,"rotate":409,"vFlip":184,"hFlip":184,"body":411},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":409,"top":409,"width":410,"height":410,"rotate":409,"vFlip":184,"hFlip":184,"body":413},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" d=\"M20.533 6.111A4.6 4.6 0 0 0 17.9 3.479a6.6 6.6 0 0 0-2.186-.42c-.963-.042-1.268-.054-3.71-.054s-2.755 0-3.71.054a6.6 6.6 0 0 0-2.184.42a4.6 4.6 0 0 0-2.633 2.632a6.6 6.6 0 0 0-.419 2.186c-.043.962-.056 1.267-.056 3.71s0 2.753.056 3.71c.015.748.156 1.486.419 2.187a4.6 4.6 0 0 0 2.634 2.632a6.6 6.6 0 0 0 2.185.45c.963.042 1.268.055 3.71.055s2.755 0 3.71-.055a6.6 6.6 0 0 0 2.186-.419a4.6 4.6 0 0 0 2.633-2.633c.263-.7.404-1.438.419-2.186c.043-.962.056-1.267.056-3.71s0-2.753-.056-3.71a6.6 6.6 0 0 0-.421-2.217m-1.218 9.532a5 5 0 0 1-.311 1.688a3 3 0 0 1-1.712 1.711a5 5 0 0 1-1.67.311c-.95.044-1.218.055-3.654.055c-2.438 0-2.687 0-3.655-.055a5 5 0 0 1-1.669-.311a3 3 0 0 1-1.719-1.711a5.1 5.1 0 0 1-.311-1.669c-.043-.95-.053-1.218-.053-3.654s0-2.686.053-3.655a5 5 0 0 1 .311-1.687c.305-.789.93-1.41 1.719-1.712a5 5 0 0 1 1.669-.311c.951-.043 1.218-.055 3.655-.055s2.687 0 3.654.055a5 5 0 0 1 1.67.311a3 3 0 0 1 1.712 1.712a5.1 5.1 0 0 1 .311 1.669c.043.951.054 1.218.054 3.655s0 2.698-.043 3.654z\"/>",{"left":409,"top":409,"width":410,"height":410,"rotate":409,"vFlip":184,"hFlip":184,"body":415},"\u003Cpath fill=\"currentColor\" d=\"M16.36 14c.08-.66.14-1.32.14-2s-.06-1.34-.14-2h3.38c.16.64.26 1.31.26 2s-.1 1.36-.26 2m-5.15 5.56c.6-1.11 1.06-2.31 1.38-3.56h2.95a8.03 8.03 0 0 1-4.33 3.56M14.34 14H9.66c-.1-.66-.16-1.32-.16-2s.06-1.35.16-2h4.68c.09.65.16 1.32.16 2s-.07 1.34-.16 2M12 19.96c-.83-1.2-1.5-2.53-1.91-3.96h3.82c-.41 1.43-1.08 2.76-1.91 3.96M8 8H5.08A7.92 7.92 0 0 1 9.4 4.44C8.8 5.55 8.35 6.75 8 8m-2.92 8H8c.35 1.25.8 2.45 1.4 3.56A8 8 0 0 1 5.08 16m-.82-2C4.1 13.36 4 12.69 4 12s.1-1.36.26-2h3.38c-.08.66-.14 1.32-.14 2s.06 1.34.14 2M12 4.03c.83 1.2 1.5 2.54 1.91 3.97h-3.82c.41-1.43 1.08-2.77 1.91-3.97M18.92 8h-2.95a15.7 15.7 0 0 0-1.38-3.56c1.84.63 3.37 1.9 4.33 3.56M12 2C6.47 2 2 6.5 2 12a10 10 0 0 0 10 10a10 10 0 0 0 10-10A10 10 0 0 0 12 2\"/>",{"left":409,"top":409,"width":417,"height":417,"rotate":409,"vFlip":184,"hFlip":184,"body":418},32,"\u003Cpath fill=\"currentColor\" d=\"M20.844 2c-1.64 0-3.297.852-4.407 2.156v.032c-.789.98-1.644 2.527-1.375 4.312c-.128-.05-.136-.035-.28-.094c-.692-.281-1.548-.594-2.563-.594c-3.98 0-7 3.606-7 8.344c0 3.067 1.031 5.942 2.406 8.094c.688 1.078 1.469 1.965 2.281 2.625S11.57 28 12.531 28s1.68-.324 2.219-.563c.54-.238.957-.437 1.75-.437c.715 0 1.078.195 1.625.438c.547.242 1.293.562 2.281.562c1.07 0 1.98-.523 2.719-1.188s1.36-1.519 1.875-2.343c.516-.824.922-1.633 1.219-2.282c.148-.324.258-.593.343-.812s.13-.281.188-.531l.188-.813l-.75-.343a5.3 5.3 0 0 1-1.5-1.063c-.625-.637-1.157-1.508-1.157-2.844A4.08 4.08 0 0 1 24.563 13c.265-.309.542-.563.75-.719c.105-.078.187-.117.25-.156c.062-.04.05-.027.156-.094l.843-.531l-.562-.844c-1.633-2.511-4.246-2.844-5.281-2.844c-.48 0-.82.168-1.25.25c.242-.226.554-.367.75-.624c.004-.004-.004-.028 0-.032q.018-.016.031-.031h.031a6.16 6.16 0 0 0 1.563-4.438L21.78 2zm-1.188 2.313c-.172.66-.453 1.289-.906 1.78l-.063.063c-.382.516-.972.899-1.562 1.125c.164-.652.45-1.312.844-1.812c.008-.012.023-.02.031-.032c.438-.5 1.043-.875 1.656-1.125zm-7.437 5.5c.558 0 1.172.21 1.812.468s1.239.594 2.094.594c.852 0 1.496-.336 2.25-.594s1.559-.469 2.344-.469c.523 0 1.816.333 2.906 1.344c-.191.172-.36.297-.563.531a6.2 6.2 0 0 0-1.53 4.094c0 1.906.831 3.34 1.718 4.25c.55.563.89.696 1.313.938c-.055.125-.086.222-.157.375a19 19 0 0 1-1.093 2.062c-.454.727-1.004 1.434-1.532 1.907c-.527.472-1 .687-1.375.687c-.566 0-.898-.156-1.468-.406S17.581 25 16.5 25c-1.137 0-1.977.336-2.563.594c-.585.258-.89.406-1.406.406c-.246 0-.777-.2-1.375-.688c-.597-.488-1.254-1.23-1.844-2.156c-1.183-1.851-2.093-4.394-2.093-7c0-3.941 2.199-6.343 5-6.343\"/>",{"left":409,"top":409,"width":420,"height":420,"rotate":409,"vFlip":184,"hFlip":184,"body":421},256,"\u003Cpath fill=\"currentColor\" d=\"M228 128a100 100 0 1 1-22.86-63.64a12 12 0 0 1-18.51 15.28A76 76 0 1 0 203.05 140H128a12 12 0 0 1 0-24h88a12 12 0 0 1 12 12\"/>",{"left":409,"top":409,"width":420,"height":420,"rotate":409,"vFlip":184,"hFlip":184,"body":423},"\u003Cpath fill=\"currentColor\" d=\"M224 128a96 96 0 1 1-21.95-61.09a8 8 0 1 1-12.33 10.18A80 80 0 1 0 207.6 136H128a8 8 0 0 1 0-16h88a8 8 0 0 1 8 8\"/>",{"oVhJaef6Ht":8,"t96FybqVTi":8,"5lK7LS5al0":8,"5oSQ2a90xd":8,"lVbrj4ov8c":8,"2QISyIzlyM":8,"HGsO2Ckakl":8},"/general/supposed-60-of-the-register-voters-in-a-country-or-democrat-if-a-sample-of-793-voters-is-selected-what-is-the-probability-that-the-sample-proportion-of-democrats-will-be-greater-than-64-round-your"] AppleWebKit/537.36 KHTML,likeGecko Chrome/64.0.3282.39 Safari/537.36",refreshOnResize:false}},app:{baseURL:"/",buildAssetsDir:"/_nuxt/",cdnURL:"https://gcdn.fx2.io/math-master.org/"}}