The most popular questions on the topic of general

.\u003Cbr />\n2. Determine the profit function: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Profit} = \\text{Revenue} - \\text{Cost} \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Use mathematical models and optimization techniques to maximize or minimize the function.\u003Cbr />\n4. Analyze results and adjust business strategies accordingly.\u003Cbr />\n\u003Cbr />\nAnswer: Profit maximization and cost minimization involve optimizing the function \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Profit} = \\text{Revenue} - \\text{Cost} \u003C/math-field>\u003C/math-field> by increasing revenue or decreasing cost through mathematical modeling.",1365,273,"discuss-the-role-of-maximization-and-minimization-in-business",{"id":44,"category":36,"text_question":45,"photo_question":38,"text_answer":46,"step_text_answer":8,"step_photo_answer":8,"views":47,"likes":48,"slug":49},537786,"in the file room there are 800 offender files. Your sergeant tells you to take out 30 per cent of the files and put them in the next room. How many files should you put into the next room?","Solution:\u003Cbr />\n1. Total number of files: 800\u003Cbr />\n2. Percentage to move: 30%

$or 0.30 as a decimal$ \u003Cbr />\n3. Calculate the number of files to move:\u003Cbr />\n- Multiply the total number of files by the percentage as a decimal.\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>800 \\times 0.30 = 240\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Therefore, the number of files to put into the next room is 240.",1058,212,"in-the-file-room-there-are-800-offender-files-your-sergeant-tells-you-to-take-out-30-per-cent-of-the-files-and-put-them-in-the-next-room-how-many-files-should-you-put-into-the-next-room",{"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},537785,"At the end of the day, the sergeant has 400 offender files that have been processed and 100 that still need to be processed. What percentage of the 500 files have not been processed?","Solution:\u003Cbr />\n1. Total files: 500\u003Cbr />\n2. Files not processed: 100\u003Cbr />\n\u003Cbr />\n3. Calculate the percentage of files not processed:\u003Cbr />\n- Percentage formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Percentage} = \\left

$\\frac{\\text{Part}}{\\text{Whole}}\\right$ \\times 100\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Substitute the known values:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Percentage} = \\left

$\\frac{100}{500}\\right$ \\times 100\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Percentage} = 0.2 \\times 100\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Percentage} = 20\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Therefore, the percentage of files that have not been processed is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20\\%\u003C/math-field>\u003C/math-field>.",1258,252,"at-the-end-of-the-day-the-sergeant-has-400-offender-files-that-have-been-processed-and-100-that-still-need-to-be-processed-what-percentage-of-the-500-files-have-not-been-processed",{"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},537783,"You notice these two old suitcases stacked in the closet. The smaller suitcase is 25 in x 8 in x 9in, and the larger suitcase is 75 in x 20 in x 18in.\n\nThe big suitcase is how many times larger than the smaller suitcase?","1. Find the volume of the smaller suitcase:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_{\\text{small}} = 25 \\times 8 \\times 9 = 1800 \\, \\text{cubic inches} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Find the volume of the larger suitcase:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V_{\\text{large}} = 75 \\times 20 \\times 18 = 27000 \\, \\text{cubic inches} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate how many times larger the larger suitcase is by dividing the volume of the larger suitcase by the volume of the smaller suitcase:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Ratio} = \\frac{27000}{1800} = 15 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nSo, the larger suitcase is 15 times larger than the smaller suitcase.",1190,238,"you-notice-these-two-old-suitcases-stacked-in-the-closet-the-smaller-suitcase-is-25-in-x-8-in-x-9in-and-the-larger-suitcase-is-75-in-x-20-in-x-18in-the-big-suitcase-is-how-many-times-larger-than-t",{"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},537782,"You notice these two old suitcases stacked in the closet. The smaller suitcase is 25 in x 8 in x 9in, and the larger suitcase is 75 in x 20 in x 18in.\n\nThe big suitcase is 15 times larger than the small suitcase.\n\nYou decide to use the larger suitcase to transport rectangular prism watermelons back home.\nThough their dimensions vary, the average rectangular watermelon has a volume of roughly 720 cubic inches. If one of these watermelons is about 10 inches long and 9 inches wide, about how tall would it be?","1. The formula for the volume of a rectangular prism is: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\text{length} \\times \\text{width} \\times \\text{height} \u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Given: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Volume} = 720 \\, \\text{cubic inches}, \\, \\text{length} = 10 \\, \\text{inches}, \\, \\text{width} = 9 \\, \\text{inches} \u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Substitute the known values and solve for height:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 720 = 10 \\times 9 \\times \\text{height} \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Simplify and solve:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{height} = \\frac{720}{10 \\times 9} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{height} = \\frac{720}{90} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{height} = 8 \\, \\text{inches} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nAnswer: 8 inches",317,63,"you-notice-these-two-old-suitcases-stacked-in-the-closet-the-smaller-suitcase-is-25-in-x-8-in-x-9in-and-the-larger-suitcase-is-75-in-x-20-in-x-18in-the-big-suitcase-is-15-times-larger-than-the-sma",{"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},537781,"9. You draw three cards from a deck of cards. Explain the difference in the probability of drawing three kings from the deck if you pull and replace the card versus you pull and don't replace the card.","1. **With Replacement:**\u003Cbr />\n - Calculate the probability of drawing a king each time with replacement.\u003Cbr />\n - Each time, the probability of a king is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{4}{52} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n - Thus, the combined probability for three draws is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left

$\\frac{4}{52} \\right$ \\times \\left

$\\frac{4}{52} \\right$ = \\left

$\\frac{1}{13} \\right$ ^3 = \\frac{1}{2197} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. **Without Replacement:**\u003Cbr />\n - Calculate the probability of drawing a king each time without replacement.\u003Cbr />\n - First draw: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{4}{52} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n - Second draw: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{3}{51} \u003C/math-field>\u003C/math-field> since one king is gone.\u003Cbr />\n - Third draw: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{2}{50} \u003C/math-field>\u003C/math-field> since two kings are gone.\u003Cbr />\n - Thus, the combined probability for three draws is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{4}{52} \\times \\frac{3}{51} \\times \\frac{2}{50} = \\frac{24}{132600} = \\frac{1}{5525} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. **Answer:**\u003Cbr />\n - Probability with replacement: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{2197} \u003C/math-field>\u003C/math-field>\u003Cbr />\n - Probability without replacement: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{5525} \u003C/math-field>\u003C/math-field>",987,197,"9-you-draw-three-cards-from-a-deck-of-cards-explain-the-difference-in-the-probability-of-drawing-three-kings-from-the-deck-if-you-pull-and-replace-the-card-versus-you-pull-and-don-t-replace-the-card",{"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},537780,"Give the domain and range of the relation\n\n{

$12,2$ ;

$11,10$ ;

$18,0$ ;

$19,1$ ;

$13,4$ }","Solution:\u003Cbr />\n1. Identify the domain:\u003Cbr />\n - The domain consists of all the first elements

$x-values$ from the ordered pairs.\u003Cbr />\n\u003Cbr />\n2. List the x-values from the relation:\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12, 11, 18, 19, 13\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Identify the range:\u003Cbr />\n - The range consists of all the second elements

$y-values$ from the ordered pairs.\u003Cbr />\n\u003Cbr />\n4. List the y-values from the relation:\u003Cbr />\n - \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2, 10, 0, 1, 4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, \u003Cbr />\n* Domain: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\{12, 11, 18, 19, 13\\}\u003C/math-field>\u003C/math-field>\u003Cbr />\n* Range: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\{2, 10, 0, 1, 4\\}\u003C/math-field>\u003C/math-field>",1203,241,"give-the-domain-and-range-of-the-relation-12-2-11-10-18-0-19-1-13-4",{"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},537779,"Use a graphing calculator to make a table of values for f

$x$ =x^2-1","Solution:\u003Cbr />\n1. Choose a set of x-values. Typically, for a quadratic function like \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$x$ = x^2 - 1\u003C/math-field>\u003C/math-field>, we use a symmetric range around zero. Let's use \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -3, -2, -1, 0, 1, 2, 3\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Calculate the corresponding \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y\u003C/math-field>\u003C/math-field>-values for each \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n* For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -3\u003C/math-field>\u003C/math-field>: \u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$-3$ =

$-3$ ^2 - 1 = 9 - 1 = 8\u003C/math-field>\u003C/math-field>\u003Cbr />\n* For \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 * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$-2$ =

$-2$ ^2 - 1 = 4 - 1 = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n* For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field>: \u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$-1$ =

$-1$ ^2 - 1 = 1 - 1 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n* For \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 * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$0$ = 0^2 - 1 = -1\u003C/math-field>\u003C/math-field>\u003Cbr />\n* For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 1\u003C/math-field>\u003C/math-field>: \u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$1$ = 1^2 - 1 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n* For \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 * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$2$ = 2^2 - 1 = 4 - 1 = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n* For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 3\u003C/math-field>\u003C/math-field>: \u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$3$ = 3^2 - 1 = 9 - 1 = 8\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Create the table:\u003Cbr />\n\u003Cbr />\nColumn \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>-3\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-1\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nColumn \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>f

$x$ = x^2 - 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-1\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8\u003C/math-field>\u003C/math-field>",1219,244,"use-a-graphing-calculator-to-make-a-table-of-values-for-f-x-x-2-1",{"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},537776,"plot -3x+y=-6","Solution:\u003Cbr />\n1. Rewrite the equation in slope-intercept form, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = mx + b\u003C/math-field>\u003C/math-field>:\u003Cbr />\n * Start with: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-3x + y = -6\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field> to both sides: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 3x - 6\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Identify the slope and the y-intercept:\u003Cbr />\n * Slope \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>m = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Y-intercept \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b = -6\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Create a table of points:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\begin{array}{cc} \\text{X-Coordinate} & \\text{Y-Coordinate} \\\\ 0 & -6 \\\\ 1 & -3 \\\\ 2 & 0 \\end{array}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Plot the points and draw the line:\u003Cbr />\n * Plot the points: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(0, -6), (1, -3), (2, 0)\u003C/math-field>\u003C/math-field>.\u003Cbr />\n * Draw a straight line through these points.",1076,215,"plot-3x-y-6",{"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},537775,"40 percent of 56300","Solution:\u003Cbr />\n1. Express '40 percent' as a decimal:\u003Cbr />\n * 40% = 0.40\u003Cbr />\n\u003Cbr />\n2. Multiply 0.40 by 56300 to find 40 percent of 56300:\u003Cbr />\n * Calculation: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.40 \\times 56300 = 22520\u003C/math-field>\u003C/math-field>",810,162,"40-percent-of-56300",{"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},537774,"Write in slope-intercept form the equation of the line passing through the points (3,0) and (5,0).","Solution:\u003Cbr />\n1. Given points: \u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x_1, y_1) = (3, 0)\u003C/math-field>\u003C/math-field> \u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x_2, y_2) = (5, 0)\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Calculate the slope (m) using the formula:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>m = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{0 - 0}{5 - 3} = \\frac{0}{2} = 0.\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. The slope-intercept form of a line is given by:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = mx + b\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n4. Substitute the slope (m) into the equation:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 0x + b\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Simplifies to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = b\u003C/math-field>\u003C/math-field>.\u003Cbr />\n \u003Cbr />\n5. Since both points lie on the x-axis, the y-coordinate is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0\u003C/math-field>\u003C/math-field>. Thus \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>b = 0\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n6. The equation of the line in slope-intercept form is:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 0\u003C/math-field>\u003C/math-field>.",884,177,"write-in-slope-intercept-form-the-equation-of-the-line-passing-through-the-points-3-0-and-5-0",{"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},537773,"Explain Factorization in Mathematics in German","Lösung:\u003Cbr />\n1. Definition: \u003Cbr />\n- Faktorisierung bedeutet, einen mathematischen Ausdruck in ein Produkt von einfacheren Ausdrücken, sogenannten Faktoren, zu zerlegen. Diese Faktoren sind oft Primzahlen oder algebraische Ausdrücke mit geringeren Graden.\u003Cbr />\n\u003Cbr />\n2. Beispiele:\u003Cbr />\n- Faktorisierung von Zahlen: \u003Cbr />\n - Nehmen wir die Zahl \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12\u003C/math-field>\u003C/math-field>. Die Faktorisierung von \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12\u003C/math-field>\u003C/math-field> als Produkt von Primzahlen lautet \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2^2 \\times 3\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Algebraische Faktorisierung:\u003Cbr />\n - Betrachten wir den Ausdruck \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 - 5x + 6\u003C/math-field>\u003C/math-field>. Die Faktorisierung lautet \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x - 2)(x - 3)\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Zweck:\u003Cbr />\n- Die Hauptziele der Faktorisierung sind die Vereinfachung von Ausdrücken, das Lösen von Gleichungen und die Erleichterung der Multiplikation, Addition oder Subtraktion von Brüchen.\u003Cbr />\n\u003Cbr />\n4. Praktische Anwendung:\u003Cbr />\n- Faktorisierung ist eine wichtige Technik zur Lösung quadratischer Gleichungen: \u003Cbr />\n - Zum Beispiel: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 - 5x + 6 = 0\u003C/math-field>\u003C/math-field> wird durch Faktorisierung zu \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x - 2)(x - 3) = 0\u003C/math-field>\u003C/math-field>, was die Lösungen \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field> und \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 3\u003C/math-field>\u003C/math-field> ergibt.",669,134,"explain-factorization-in-mathematics-in-german",{"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},537767,"If 𝑃 𝑥; 𝑦 = 5𝑥𝑦– 2𝑦 + 3𝑥, then 𝑃(– 1; 1)","1. Start with the given function: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(x; y) = 5xy - 2y + 3x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Substitute \$x = -1\$ and \$y = 1\$ into the function:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(-1; 1) = 5(-1)(1) - 2(1) + 3(-1)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate each term:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5(-1)(1) = -5\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>-2(1) = -2\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>3(-1) = -3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Add the results: \u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-5 - 2 - 3 = -10\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Thus, the value of the function at \$x = -1\$ and \$y = 1\$ is:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(-1; 1) = -10\u003C/math-field>\u003C/math-field>",930,186,"if-p-x-y-5xy-2y-3x-then-p-1-1",{"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},537766,"the negation of the statement \" some oranges are tart\" is \" some oranges are not tart\"","It is false. \nthe negation of the statement \" some oranges are tart\" is \" No oranges is tart\"",699,140,"the-negation-of-the-statement-some-oranges-are-tart-is-some-oranges-are-not-tart",{"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},537765,"Solve and check x-4(x-3)+7=6-(x-4)","Solution:\u003Cbr />\n1. Expand the equation:\u003Cbr />\n- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x - 4(x - 3) + 7 = x - 4x + 12 + 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6 - (x - 4) = 6 - x + 4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Simplify both sides:\u003Cbr />\n- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x - 4x + 12 + 7 = -3x + 19\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6 + 4 - x = 10 - x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Set the simplified equations equal:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-3x + 19 = 10 - x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Rearrange the equation to isolate terms involving \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>-3x + x = 10 - 19\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2x = -9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. 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{-9}{-2} = \\frac{9}{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Therefore, the solution for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{9}{2}\u003C/math-field>\u003C/math-field>",1350,270,"solve-and-check-x-4-x-3-7-6-x-4",{"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},537764,"Dhiya is painting her living room the total area that nees to be covered is 64.5 square feet each can of paint coat 15.25 and covers an area of 20square ft. How many cans will dhiya need to paint all 4 walls\nHow much will the paint coat her","1. Determine the number of cans needed by dividing the total area to be covered by the area each can covers:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{64.5}{20} = 3.225 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Since Dhiya cannot purchase a fraction of a can, she will need to round up to the nearest whole number, which is 4 cans.\u003Cbr />\n\u003Cbr />\n3. Calculate the total cost by multiplying the number of cans by the cost per can:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4 \\times 15.25 = 61.00 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, Dhiya will need 4 cans of paint, and the paint will cost her $61.00.",785,157,"dhiya-is-painting-her-living-room-the-total-area-that-nees-to-be-covered-is-64-5-square-feet-each-can-of-paint-coat-15-25-and-covers-an-area-of-20square-ft-how-many-cans-will-dhiya-need-to-paint-all",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":153,"slug":154},537763,"A new factory In a small town has an annual payroll of 6 million. It is expected 50% of this money will be spent in the town by factory personnel. The people in the town who receive this money are expected to spend 50% of what they receive in the town , and so on. What is the total of all of this spending , called the total economic impact on the town each year?","1. Identify the initial spending and the common ratio:\u003Cbr />\n - Initial Spending: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6,000,000 \u003C/math-field>\u003C/math-field>\u003Cbr />\n - Common Ratio, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = 0.5 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Substitute into the formula for the sum of an infinite geometric series:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> S = \\frac{\\text{Initial Spending}}{1 - r} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> S = \\frac{6,000,000}{1 - 0.5} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. This results in:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> S = \\frac{6,000,000}{0.5} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplify the division:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> S = 12,000,000 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the total economic impact is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 12,000,000 \u003C/math-field>\u003C/math-field>.",359,72,"a-new-factory-in-a-small-town-has-an-annual-payroll-of-6-million-it-is-expected-50-of-this-money-will-be-spent-in-the-town-by-factory-personnel-the-people-in-the-town-who-receive-this-money-are-e",{"id":156,"category":36,"text_question":157,"photo_question":38,"text_answer":158,"step_text_answer":8,"step_photo_answer":8,"views":159,"likes":160,"slug":161},537762,"X^2=81^1*1/2 \n Find x","Solution:\u003Cbr />\n1. Start with the equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X^2 = 81^{\\frac{1}{2}}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Recognize that \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>81^{\\frac{1}{2}}\u003C/math-field>\u003C/math-field> is the square root of 81:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>81^{\\frac{1}{2}} = \\sqrt{81}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate the square root of 81:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\sqrt{81} = 9\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>X^2 = 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X\u003C/math-field>\u003C/math-field> by taking the square root of both sides:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X = \\pm \\sqrt{9}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify the result:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X = \\pm 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Thus, the solutions for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X\u003C/math-field>\u003C/math-field> are:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X = 3\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>X = -3\u003C/math-field>\u003C/math-field>",411,82,"x-2-81-1-1-2-find-x",{"id":163,"category":36,"text_question":164,"photo_question":38,"text_answer":165,"step_text_answer":8,"step_photo_answer":8,"views":166,"likes":167,"slug":168},537761,"6/2 (1+2)=","Solution:\u003Cbr />\n1. Start with the expression: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{6}{2}(1+2)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Evaluate inside the parentheses first:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 + 2 = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute the result back into the expression:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{6}{2}(3)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Perform the division:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{6}{2} = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Multiply the result by 3:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3 \\times 3 = 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the evaluated result of the expression is 9.",858,172,"6-2-1-2",{"id":170,"category":36,"text_question":171,"photo_question":38,"text_answer":172,"step_text_answer":8,"step_photo_answer":8,"views":173,"likes":174,"slug":175},537760,"A discussion topic will be posted here shortly. You must reply to the question with your own response by Thurs Oct 31. You must also reply to the posts of 2 peers by Sunday, Nov 3. Please see the syllabus for discussion requirements. Each of your 3 posts should be a minimum of 300 words and use a properly formatted citation to support your ideas \nHere's this week's discussion: \nPart A: Describe a remote encounter, a phone encounter, and a face-to-face encounter that you have had recently. How did you evaluate the encounter, and what were the most important factors determining your satisfaction/dissatisfaction in each case?\nPart B: Think about a service organization that retains you as a loyal customer. Has your relationship with the company evolved over time? Why are you loyal to this provider? What are the benefits to you of staying loyal and not switching to another provider? What would it take for you to switch?","**Part A:**\n\n1. **Remote Encounter** \n Recently, I had a remote encounter with a customer service team via email regarding an issue with an online purchase. The response was quick and well-structured, and they provided clear steps to resolve the problem. I evaluated the encounter based on response time, clarity, and the helpfulness of the solution. My satisfaction stemmed from the quick turnaround and the ease with which I could follow their guidance.\n\n2. **Phone Encounter** \n I had a phone conversation with my bank to resolve a transaction issue. The representative was polite, but the hold time was long, and I had to repeat my details multiple times. I evaluated the encounter based on wait time, the representative’s helpfulness, and the resolution provided. My satisfaction was somewhat mixed; while the representative was helpful, the hold time and repeated explanations made the experience less efficient.\n\n3. **Face-to-Face Encounter** \n Recently, I visited a local store for a product exchange. The staff was friendly and proactive in assisting me, making the process smooth and efficient. I evaluated the encounter based on their attentiveness, problem-solving ability, and the speed of service. I was very satisfied due to the friendly and proactive approach, which made the interaction feel personal and efficient.\n\n**Part B:**\n\nI am a loyal customer of Vodacom(or any service provider), a company I’ve used for several years for internet and streaming services. Over time, my relationship with them has grown as they’ve consistently met my needs by offering reliable service, competitive pricing, and regular loyalty rewards. I’m loyal because they’ve built trust by resolving any issues quickly and by providing occasional discounts or service upgrades. The benefit of staying loyal is the reliability and familiarity of the service, and I don’t need to re-establish my preferences with a new provider. However, if their service quality dropped, or if a competitor offered significantly better service at a lower price, I might consider switching.",1100,220,"a-discussion-topic-will-be-posted-here-shortly-you-must-reply-to-the-question-with-your-own-response-by-thurs-oct-31-you-must-also-reply-to-the-posts-of-2-peers-by-sunday-nov-3-please-see-the-syll",{"first":6,"last":177,"prev":178,"next":179},188,13,15,{"current_page":181,"from":182,"last_page":177,"links":183,"path":217,"per_page":218,"to":219,"total":220},14,261,[184,187,189,191,194,197,199,202,204,207,210,213,215],{"url":178,"label":185,"active":186},"« Previous",false,{"url":6,"label":188,"active":186},"1",{"url":10,"label":190,"active":186},"2",{"url":192,"label":193,"active":186},11,"11",{"url":195,"label":196,"active":186},12,"12",{"url":178,"label":198,"active":186},"13",{"url":181,"label":200,"active":201},"14",true,{"url":179,"label":203,"active":186},"15",{"url":205,"label":206,"active":186},16,"16",{"url":208,"label":209,"active":186},17,"17",{"url":211,"label":212,"active":186},187,"187",{"url":177,"label":214,"active":186},"188",{"url":179,"label":216,"active":186},"Next »","https://api.math-master.org/api/question",20,280,3742,{"data":222},{"questions":223},[224,228,232,236,240,244,248,252,256,260,264,268,272,276,280,284,288,292,296,300],{"id":225,"category":36,"text_question":226,"slug":227},532015,"a runner wants to build endurance by running 9 mph for 20 min. How far will the runner travel in that time period?","a-runner-wants-to-build-endurance-by-running-9-mph-for-20-min-how-far-will-the-runner-travel-in-that-time-period",{"id":229,"category":36,"text_question":230,"slug":231},532023,"find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.","find-the-value-of-the-tangent-if-it-is-known-that-the-cos-1-2-and-the-sine-is-negative-must-perform-procedures",{"id":233,"category":36,"text_question":234,"slug":235},532045,"5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15","5-2-5-8-9-1-7-2-5-2-5-8-15",{"id":237,"category":36,"text_question":238,"slug":239},532300,"A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.","a-hotel-in-the-algarve-had-to-offer-1-week-of-vacation-to-one-of-its-employees-as-an-easter-gift-in-a-random-choice-it-is-known-that-80-people-work-in-this-hotel-unit-41-of-whom-are-portuguese-and-3",{"id":241,"category":36,"text_question":242,"slug":243},533941,"If f(x) = 3x 2, what is the value of x so that f(x) = 11?","if-f-x-3x-2-what-is-the-value-of-x-so-that-f-x-11",{"id":245,"category":36,"text_question":246,"slug":247},534212,"A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free\nrate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an\nadditional $150 million which she plans to invest in several different stocks. After\ninvesting the additional funds, she wants to reduce the portfolio’s risk level so that once\nthe additional funds are invested the portfolio’s required return will be 9.20%. What\nmust the average beta of the new stocks added to the portfolio be (not the new\nportfolio’s beta) to achieve the desired required rate of return?","a-mutual-fund-manager-has-a-350-million-portfolio-with-a-beta-of-1-10-the-risk-free-rate-is-3-5-and-the-market-risk-premium-is-6-00-the-manager-expects-to-receive-an-additional-150-million-whic",{"id":249,"category":36,"text_question":250,"slug":251},534219,"The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis.\r\n\r\nDuring a client meeting we gathered these facts. There are 2 part-time employees that each earn $1000 per month. The utilities for the kennel area (water, electricity) are $200 per month. The average food cost for animals in the kennel is $800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs $6. \r\n\r\nAt the current cost of $50, how many animals must be adopted to break-even?\r\nWhat would break-even be at a $60 adoption fee? \r\nWhat would break-even be if the fee were lowered to $40?\r\nThe newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs $1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven?\r\nBased on what you have learned about elasticity, what price do you recommend for the adoption fee?","the-humane-society-has-asked-for-our-help-again-this-week-currently-they-are-charging-50-for-an-adoption-fee-unfortunately-they-just-pulled-this-number-out-of-the-air-and-do-not-know-why-they-are-c",{"id":253,"category":36,"text_question":254,"slug":255},534262,"7=-4/3y -1","7-4-3y-1",{"id":257,"category":36,"text_question":258,"slug":259},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":261,"category":36,"text_question":262,"slug":263},534326,"Professor Vélez has withdrawn 40 monthly payments of $3,275 from her investment account. If the\n investment account yields 4% convertible monthly, how much did you have in your investment account one month before making the first withdrawal?\n (Since you started making withdrawals you have not made any deposits.)","professor-velez-has-withdrawn-40-monthly-payments-of-3-275-from-her-investment-account-if-the-investment-account-yields-4-convertible-monthly-how-much-did-you-have-in-your-investment-account-one",{"id":265,"category":36,"text_question":266,"slug":267},534368,"In measuring the internal radius of a circular sewer the measurement is 2% too large. If this measurement is then used to calculate the circular cross-sectional area of the pipe:\nDetermine, by using the binomial theory, the percentage error that will occur compared to the true area.","in-measuring-the-internal-radius-of-a-circular-sewer-the-measurement-is-2-too-large-if-this-measurement-is-then-used-to-calculate-the-circular-cross-sectional-area-of-the-pipe-determine-by-using-t",{"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},534419,"Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.","determine-the-linear-function-whose-graph-passes-through-the-points-6-2-and-has-slope-3",{"id":277,"category":36,"text_question":278,"slug":279},534443,"The annual real property tax liability for a residential property is $4302 and has been paid by the seller in advance of closing. Using the 30-day month/260-day year method what will be the tax proration entry on the settlement statement round to the nearest dollar for a closing on Oct. 26 if the buyer owns the day of closing?\n\na. $3525 credit to the buyer and $777 debit to the seller\nb. $777 debit to the buyer and $3525 debit to the seller\nc. $777 credit to the buyer and $777 debit to the seller\nd. $3525 debit to the buyer and $3525 credit to the seller\n\n*Can anyone help with this? I am studying for my real estate exam and am having trouble with some of the calculations :)","the-annual-real-property-tax-liability-for-a-residential-property-is-4302-and-has-been-paid-by-the-seller-in-advance-of-closing-using-the-30-day-month-260-day-year-method-what-will-be-the-tax-prorat",{"id":281,"category":36,"text_question":282,"slug":283},534457,"At the end of a lively discussion within your study group, your class neighbor, for the relevance of your points of view, asks your opinion on the subject of their debate which is the following question Am I the slave of my unconscious?\n Solve the problem posed by this subject in an argumentative production.","at-the-end-of-a-lively-discussion-within-your-study-group-your-class-neighbor-for-the-relevance-of-your-points-of-view-asks-your-opinion-on-the-subject-of-their-debate-which-is-the-following-questi",{"id":285,"category":36,"text_question":286,"slug":287},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":289,"category":36,"text_question":290,"slug":291},534502,"a) 6x − 5 > x + 20","a-6x-5-x-20",{"id":293,"category":36,"text_question":294,"slug":295},534526,"there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?","there-are-500-000-bacteria-at-the-end-of-a-pin-point-1000-bacteria-can-make-a-person-sick-then-bacteria-at-the-tip-of-a-pin-point-can-make-500-people-sick-also-many-people-do-not-know-that-bacteri",{"id":297,"category":36,"text_question":298,"slug":299},534605,"9n + 7(-8 + 4k) use k=2 and n=3","9n-7-8-4k-use-k-2-and-n-3",{"id":301,"category":36,"text_question":302,"slug":303},534675,"23,456 + 3,451","23-456-3-451",{"data":305},[306,316,325,334,346,355,364,372,384,391,401,409,420,429,436,443,451,462,470,480],{"id":307,"name":308,"photo":309,"certificates":310,"diplomas":312,"biography":313,"rating":314,"total_answer":315},19,"Seamus","https://api.math-master.org/img/experts/19/19.webp",[311],"https://api.math-master.org/img/experts/19/certificates/certif.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.",4.9,94,{"id":317,"name":318,"photo":319,"certificates":320,"diplomas":321,"biography":323,"rating":314,"total_answer":324},18,"Nash","https://api.math-master.org/img/experts/18/18.webp",[],[322],"https://api.math-master.org/img/experts/18/diplomas/diploma.webp","My interest in mathematics boomed in my school days which led me to choose mathematics as my core subject in college and later pursue Engineering in University. I have been working at MathMaster for 10 months now and the fact that I like solving math tasks makes me interested in this field. I can work part-time at any available shift for the day and not get exhausted. Moreover solving math tasks keep my brain sharp and focused.\n\n",85,{"id":179,"name":326,"photo":327,"certificates":328,"diplomas":330,"biography":332,"rating":314,"total_answer":333},"Miles","https://api.math-master.org/img/experts/15/15.webp",[329],"https://api.math-master.org/img/experts/15/certificates/2fd3f3a1-34c4-417d-a85a-1459c7fc0356.webp",[331],"https://api.math-master.org/img/experts/15/diplomas/diploma.webp","My name is Ali Haider and I hold a bachelor’s degree in Electrical Engineering and I am also certified Math Expert. I have been teaching Mathematics and Physics for the past 6 years at both the high school and college level. My pass rate for Mathematics is 100%.\nIn addition to teaching, I love playing badminton and video games.\n",108,{"id":13,"name":335,"photo":336,"certificates":337,"diplomas":341,"biography":343,"rating":344,"total_answer":345},"Timmothy","https://api.math-master.org/img/experts/3/3.webp",[338,339,340],"https://api.math-master.org/img/experts/3/certificates/14d1b957-4891-43e9-b5bc-07fdd4d9af21.webp","https://api.math-master.org/img/experts/3/certificates/27b13919-712a-4712-b27a-e09fc16c774f.webp","https://api.math-master.org/img/experts/3/certificates/b70a3a4e-33de-47d7-b0a5-9fbefe397734.webp",[342],"https://api.math-master.org/img/experts/3/diplomas/19c9addf-312a-4437-af41-e89bc3843209 (1).webp","Hello, I'm Jamil Omar, and I want to take you on a journey through my experience with math, from school to university.\nEarly School Years:\nHigh school marked the beginning of my mathematical journey, a journey that started with skepticism but transformed into something wonderful. At first, I wasn't a fan of math, until a special teacher changed everything. This teacher showed me the beauty of math, and suddenly, everything clicked.\nBecause of this teacher, I started enjoying math and even joined math competitions during my high school days. Surprisingly, I excelled and became a champion at both the provincial and regional levels. These wins boosted my confidence and made me realize that I could excel in math.\nThese victories also gave me the confidence to pursue an engineering degree in college. Thanks to that teacher and my successes in math, I knew I could conquer new challenges and make the most of my education journey.\nUniversity Journey:\nMy strong grasp of mathematics inspired me to pursue a bachelor's degree in Petroleum Engineering at Palawan State University. Confident in my mathematical foundation, I embarked on this academic journey.\nThroughout the course, I discovered that my solid background in mathematics was a true asset. It enabled me to better comprehend the intricate topics within Petroleum Engineering and successfully complete the program.\nMy enthusiasm for engineering led me to actively engage in quiz bee contests, where sharp mathematical skills are crucial for success. Our team's victory in these contests opened doors to a national quiz bee in our country. This experience not only honed my mathematical abilities but also granted us the privilege to participate in seminars related to our field of study.\nOne of my achievements was securing the top rank in our departmental exam for algebra. During my first year in college, I outperformed all other first-year students across the university. This accomplishment underscores the significant impact of mathematics on my academic journey.\nStudying math has proven to be invaluable, not just in terms of academic achievements but also in enhancing my analytical skills and enabling me to earn a degree in Petroleum Engineering.",4.8,96,{"id":347,"name":348,"photo":349,"certificates":350,"diplomas":351,"biography":353,"rating":344,"total_answer":354},22,"Hank","https://api.math-master.org/img/experts/22/22.webp",[],[352],"https://api.math-master.org/img/experts/22/diplomas/12.webp","When I was in elementary and middle school, I did not feel the importance and beauty of mathematics, but when I joined the secondary stage, I began to feel the beauty and importance of mathematics, and I excelled in mathematics. I joined the College of Education, Department of Mathematics, and now I am a mathematics teacher.\nThen after that, I got a master's degree and a doctorate in curricula and methods of teaching mathematics.",100,{"id":356,"name":357,"photo":358,"certificates":359,"diplomas":360,"biography":362,"rating":344,"total_answer":363},35,"Hester","https://api.math-master.org/img/experts/35/35.webp",[],[361],"https://api.math-master.org/img/experts/35/diplomas/03849782-84d8-46fb-b7ed-7e3204335b13.webp","Mathematics has been my favourite subject since childhood. I studied mathematics in secondary education and secured full marks in this subject which gave me great joy and boost as i was attached to this subject. Then I opted Pre-Engineering in my higher secondary education which was mainly about the mathematics. Then I got admission in Engineering University which is ranked as Number 1 Engineering University of my country and studied different subjects of mathematics there on graduate level. I really enjoy while solving the maths questions and get too much involved in the basics and different branches of maths as it is referred as mother of sciences and I am emotionally attached to this subject.\r\n\r",115,{"id":181,"name":365,"photo":366,"certificates":367,"diplomas":369,"biography":371,"rating":344,"total_answer":333},"Brice","https://api.math-master.org/img/experts/14/14.webp",[368],"https://api.math-master.org/img/experts/14/certificates/a53728ab-4dc7-40ba-8d75-9938dd4881d9.webp",[370],"https://api.math-master.org/img/experts/14/diplomas/240b3c4c-3403-49ef-aab8-6caa8f694f93.webp","Muhammad Farooq here. I have done Bachelor's in Electrical Engineering and in my institute mode of studying was in English. Though I don not posses and certificate of diploma in English as it costs much here in Pakistan and I was not required to submit this certificate anywhere, though my courses in English as well mathematics are mentioned in my School as well collage certificate so you can check my record in these certificates",{"id":373,"name":374,"photo":375,"certificates":376,"diplomas":379,"biography":381,"rating":382,"total_answer":383},28,"Esmeralda","https://api.math-master.org/img/experts/28/28.webp",[377,378],"https://api.math-master.org/img/experts/28/certificates/883 C.webp","https://api.math-master.org/img/experts/28/certificates/883 CC.webp",[380],"https://api.math-master.org/img/experts/28/diplomas/883 D.webp","From an early age, I've been captivated by the enchanting world of mathematics. It all began during my childhood when the mere sight of numbers and equations ignited a spark within me. This fascination evolved into a lifelong passion, shaping my journey into becoming a dedicated math enthusiast.\r\n\r\nThroughout my formative years in both primary and secondary school, I eagerly participated in various math contests, emerging victorious and accumulating a treasure trove of accolades that celebrated my mathematical prowess. As I embarked on my college journey, I chose a bachelor's degree program that seamlessly intertwined mathematics with computational problem-solving.\r\n\r\nStepping into the realm of teaching was a natural progression for me. Armed with a deep reservoir of mathematical knowledge and an innate ability to explain complex concepts in simple terms, I found myself guiding college entrance exam reviewees through the intricacies of algebra, geometry, trigonometry, and pre-calculus. In the interstices of my journey, I also dabbled in the realm of freelance mathematics. With the luxury of time, I engaged in tackling a diverse array of mathematical problems and coursework. This not only honed my skills further but also cemented my belief that mathematics, while a field of study, is also a boundless realm of exploration and creativity.",4.7,98,{"id":195,"name":385,"photo":386,"certificates":387,"diplomas":388,"biography":389,"rating":382,"total_answer":390},"Madelyn","https://api.math-master.org/img/experts/12/12.webp",[],[],"i am kishan kushavaha from india. i am completed my primary education from jawahar Navodaya vidhyalaya Rath hamirpur utter pradesh India. Currently I am pursuing Btech degree in computer science and engineering. Math my favorite subject i am feel very happyness solving the math problems.",86,{"id":178,"name":392,"photo":393,"certificates":394,"diplomas":398,"biography":399,"rating":382,"total_answer":400},"Maude","https://api.math-master.org/img/experts/13/13.webp",[395,396,397],"https://api.math-master.org/img/experts/13/certificates/664eea5b-1c59-4243-bed8-3a2ffba05ef7.webp","https://api.math-master.org/img/experts/13/certificates/bccb93ad-6ae1-4c1f-bc57-5c2fc5c479b5.webp","https://api.math-master.org/img/experts/13/certificates/cd4c4772-1927-4836-ad8e-340300efad86.webp",[],"i always fond of math ,TILL my matriculation to graduation math is my fvrt subject\nwhen i was in 9th class i had a teacher named as Sir Saleem this is now died but he was bestest teacher ever\nHe teach us each and every question of every exercise of my book of mathematics and what i do is write all those questions in my register as it is and practiced a lot this build my basics and keep them strong i am highly obliged to my sir May God give him high place in jannah ..\nso come to story i have digested too much math in my mind that when i gave math final exams of board i was too much confident and just revise definitions included in course and did not do any question by hand because every question is remembered by heart , i just go through by my register and believe me i got 74/75 marks . this was my initiation in math field that go wide and wide in other fields of math.\nMy interest in mathematics grew as it related to algorithms and data. I moved up into the complexity of algebra and geometry from arithmetic's simplicity because I was fascinated by their complexities. Calculus revealed the language of transformation, while number theory and abstract algebra drove me farther into abstraction. My ability to do rigorous and challenging analysis was put to the test, building a link to the very core of patterns and structures.\n\nThe applications of theory were made possible by probability, statistics, and discrete mathematics, demonstrating the usefulness of mathematical techniques. I incorporated mathematical ideas into my digital self as the digital era developed, optimizing, forecasting, and innovating.\n\n\n\nMy story is a never-ending quest that is inextricably linked to the beauty and logic of mathematics.",104,{"id":402,"name":403,"photo":404,"certificates":405,"diplomas":406,"biography":407,"rating":382,"total_answer":408},7,"Cristian","https://api.math-master.org/img/experts/7/7.webp",[],[],"I embarked on my academic journey as a sports enthusiast, prior to enrolling in my undergraduate studies. My enthusiasm for mathematics had always been muted, largely owing to the seemingly endless and purposeless calculations it often involved. However, a transformative experience awaited me during my time in college. It was there that I encountered a teacher who, in our very first class, presented a simple yet profound exercise: to complete the sentence \"Mathematics is _______\" with a single word that encapsulated our immediate perception of the subject.\nI hesitated briefly before filling the blank space with the word \"boring.\" To my surprise, my teacher chose the word \"beautiful.\" This striking contrast sparked my curiosity and set the stage for a remarkable journey of discovery. Guided by her teaching and insights, it took me a span of two to three months to truly grasp the hidden allure of mathematics. What I once considered mere calculations revealed themselves to be the building blocks of exquisite mathematical and geometric forms.\nThis revelation marked the turning point in my relationship with mathematics. I came to realize that nothing in the realm of mathematics is devoid of purpose or significance. Behind every calculation lies a tapestry of captivating patterns and shapes. As I delved deeper into the core concepts, my appreciation for the elegance and depth of mathematics grew exponentially.\nThis newfound passion became the bedrock of my academic pursuits. It paved the way for my entrance into the world of mathematical exploration, ultimately leading me to pursue a PhD in mathematics. The journey has brought me under the mentorship of an esteemed 80-year-old supervisor, a venerable professor renowned for his wisdom, at Jacobs University in Germany.\nLooking back, I can trace the evolution of my perspective from skepticism to fascination, all catalyzed by a single teacher's belief in the beauty that mathematics holds. With each step I take in my academic journey, I am reminded that the seeds of interest and passion can be sown in the most unexpected of places, transforming the trajectory of one's life in ways that are both profound and deeply fulfilling.",112,{"id":205,"name":410,"photo":411,"certificates":412,"diplomas":417,"biography":418,"rating":382,"total_answer":419},"\nClarabelle","https://api.math-master.org/img/experts/16/16.webp",[413,414,415,416],"https://api.math-master.org/img/experts/16/certificates/00f2469c-54a4-4a86-a1bd-058b62670da1.webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4 (1).webp","https://api.math-master.org/img/experts/16/certificates/82090cc4-0853-4d1d-88d0-3c33cd9dd4e4.webp","https://api.math-master.org/img/experts/16/certificates/f073e340-308d-4d20-ab38-8b2c9598137b.webp",[],"Hi,\nI've loved Mathematics and critical thinking for as long as I can remember. I started tutoring my fellow students in grade 6. I've studied Maths in the Faculty of Science. I started tutoring online 10 years ago. I've taken a lot of courses to help me teach the STEM curriculum better ever since.\nRegards\nRania",91,{"id":22,"name":421,"photo":422,"certificates":423,"diplomas":426,"biography":428,"rating":382,"total_answer":315},"Jett","https://api.math-master.org/img/experts/6/6.webp",[424,425],"https://api.math-master.org/img/experts/6/certificates/a05d6f13-1579-47ba-9f4d-1379fd868a32.webp","https://api.math-master.org/img/experts/6/certificates/fcc9c87f-66d3-4474-adfd-13fee92c6090.webp",[427],"https://api.math-master.org/img/experts/6/diplomas/ff175d15-b3af-4041-89fc-d9ac937be8d4.webp","Hello,\nI am pleased to introduce myself as a Mathmaster Expert 😊\nI am Engr. Paul Eejay Dy, a Registered Civil Engineer in the Philippines and Mathematics has always been my favorite subject.\nStudying Mathematics is a really difficult but fun experience for me and with the help of really great teachers and professors that helped me on this journey, I overcame all the obstacles that came my way until I achieved my dream profession.\nSo for all Mathmaster users, it is a great pleasure to be part of your journey into this rough but fulfilling journey of studying Mathematics. Study hard, and keep fighting for your dreams 😇🙏",{"id":19,"name":430,"photo":431,"certificates":432,"diplomas":433,"biography":434,"rating":382,"total_answer":435},"Rasheed","https://api.math-master.org/img/experts/5/5.webp",[],[],"Born with an insatiable curiosity, I began my journey with mathematics during my school years. From solving basic arithmetic problems to unraveling complex algebraic equations, I developed a deep passion for the subject. Upon entering university, my learnings diving into advanced topics like abstract algebra, numerical analysis and differential equations.\nIn retrospect, my journey through the realm of mathematics has been an exhilarating adventure of discovery, learning, and growth.\n",105,{"id":437,"name":438,"photo":439,"certificates":440,"diplomas":441,"biography":442,"rating":382,"total_answer":333},34,"Dexter","https://api.math-master.org/img/experts/34/34.webp",[],[],"I had done my schooling in SPHS, one of premier academic institutions in the city which covered all courses upto K-12. Mathematics had always been my forte, love & passion which earned me a good amount of reputation and accreditation at various phases of my career. My penchant in Maths was observed by my professors in school who did not hesitate to shower me the honour of one of the best mathematics students taught by them. I had a straight A in Mathematics and related sciences right from school to university level. After crossing the barrier of high school with elan, I did not hesitate to continue my graduation in Mathematics major from JU which enlists within the top 5 universities in the country. I stood first in my faculty in the final year of graduation with 85% score amounting to GPA 4.0. During the 3 year graduation, I silently earned the recognition of the top Mathematics student of the class in the eyes of my professors and my fellow students who used to crowd around me when they got stuck in any topic of maths. Overall my journey as a student of Mathematics was challenging, rewarding, enriching and a superbly enjoyable phase of my career. ",{"id":10,"name":444,"photo":445,"certificates":446,"diplomas":447,"biography":449,"rating":450,"total_answer":400},"Corbin","https://api.math-master.org/img/experts/2/2.webp",[],[448],"https://api.math-master.org/img/experts/2/diplomas/1ea09f59-7559-4ce7-8bad-50bcc43ea9ed.webp","My names is James Agustin Molina, I am from Philippines. Back when I in high school, I was not the best in Math in my class; but, If I were to compare my math skills to my other subjects, I think Math is my best subject. I always find solving and learning math techniques fun. Because I think my Math is the my best subject and I always fascinated in how things work, I took engineering in my college. In college, I really enjoyed math and thinking of pursuing a teaching career. I also took and passed my licensure exam right after graduation. Currently, I am taking my Masters Degree in Mathematics.",4.6,{"id":452,"name":453,"photo":454,"certificates":455,"diplomas":456,"biography":460,"rating":450,"total_answer":461},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp",[],[457,458,459],"https://api.math-master.org/img/experts/29/diplomas/458 2.webp","https://api.math-master.org/img/experts/29/diplomas/458 d.webp","https://api.math-master.org/img/experts/29/diplomas/458 dd.webp","In my school days I was not good in Mathematics but there was something which always attracted me towards Mathematics as playing with numbers and doing round of questions of different exercises of workbook was fun for me and as a hobby I inclined to Math's. I never thought of teaching mathematics and making a career out of it but somethings bound to happen.",106,{"id":463,"name":464,"photo":465,"certificates":466,"diplomas":467,"biography":468,"rating":450,"total_answer":469},30,"Bud","https://api.math-master.org/img/experts/30/30.webp",[],[],"I started my mathematics journey when i was in school and i went for a lot of competitions in mathematics back then and after worth, i proceeded into the university to study Electronics and Electrical Engineering and the course of studying it, i came across a lot of mathematics course which grounded me alot in mathematics.",95,{"id":471,"name":472,"photo":473,"certificates":474,"diplomas":475,"biography":478,"rating":450,"total_answer":479},31,"Frederik","https://api.math-master.org/img/experts/31/31.webp",[],[476,477],"https://api.math-master.org/img/experts/31/diplomas/344.webp","https://api.math-master.org/img/experts/31/diplomas/344D.webp","Hi, my name is Nitin,\r\nI started taking an interest in maths, because of my grandfather, who was a maths professor at HNBGU University, initially, I was not that good at maths, but with practice, I improved a lot, and I became pretty good at it when I got excellent marks in class 10th maths, I chose maths as my primary subject I completed my college and graduation, currently I am pursuing my master, I loved teaching maths, I also teach maths in a local school, and I want to become a professor in maths just like my grandfather.",97,{"id":481,"name":482,"photo":483,"certificates":484,"diplomas":486,"biography":488,"rating":450,"total_answer":333},21,"Jon","https://api.math-master.org/img/experts/21/21.webp",[485],"https://api.math-master.org/img/experts/21/certificates/41e2a05c-d94f-4bcc-9258-f2a7fe4c3c02.webp",[487],"https://api.math-master.org/img/experts/21/diplomas/9258cda6-9255-4b34-8806-23628b0a8153.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.",{"$sicons":490},{"bxl:facebook-circle":491,"bxl:instagram":495,"mdi:web":497,"la:apple":499,"ph:google-logo-bold":502,"ph:google-logo":505},{"left":492,"top":492,"width":493,"height":493,"rotate":492,"vFlip":186,"hFlip":186,"body":494},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":492,"top":492,"width":493,"height":493,"rotate":492,"vFlip":186,"hFlip":186,"body":496},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 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