MATH MADE EASY - MathMaster

.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",4.7,91,{"data":47,"links":120,"meta":122},[48,57,64,71,78,85,92,99,106,113],{"id":49,"category":50,"text_question":51,"photo_question":52,"text_answer":53,"step_text_answer":8,"step_photo_answer":8,"views":54,"likes":55,"slug":56},538084,"general","Width of 12 in. Calculate the volume of the sphere. Round to the nearest tenth if necessary","","1. Identify the radius of the sphere. Given the width is 12 inches, the diameter is 12 inches. Therefore, the radius is half of the diameter:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = \\frac{12}{2} = 6 \\, \\text{in} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the formula for the volume of a sphere:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi r^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute the radius into the formula:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi

$6$ ^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi \\times 216 = \\frac{864}{3} \\pi = 288 \\pi \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Approximate using \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\pi \\approx 3.1416 \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 288 \\times 3.1416 = 904.8 \\, \\text{in}^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. The volume of the sphere, rounded to the nearest tenth, is approximately:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 904.8 \\, \\text{in}^3 \u003C/math-field>\u003C/math-field>",278,56,"width-of-12-in-calculate-the-volume-of-the-sphere-round-to-the-nearest-tenth-if-necessary",{"id":58,"category":50,"text_question":59,"photo_question":52,"text_answer":60,"step_text_answer":8,"step_photo_answer":8,"views":61,"likes":62,"slug":63},538080,"A plane ticket has gone up 18%, now costing

$4,720. How much did it cost before the increase?","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Solution:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> be the original price of the plane ticket.\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> increased by 18% means the new price is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P + 0.18P = 1.18P\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Set up the equation based on the problem statement:\u003Cbr />\n- The new price \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 4,720\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1.18P = 4,720\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Divide both sides by 1.18 to isolate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field>.\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\frac{4,720}{1.18}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P \\approx 4,000\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>\\text{Answer:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The original price of the plane ticket was approximately USD 4,000.",726,145,"a-plane-ticket-has-gone-up-18-now-costing-4-720-how-much-did-it-cost-before-the-increase",{"id":65,"category":50,"text_question":66,"photo_question":52,"text_answer":67,"step_text_answer":8,"step_photo_answer":8,"views":68,"likes":69,"slug":70},538074,"R=24 inches\nCalculate the surface area of the sphere","1. The formula to calculate the surface area of a sphere is given by: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 4 \\pi R^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the value of the radius \$ R = 24 \$ inches into the formula: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 4 \\pi (24)^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate the square of the radius:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (24)^2 = 576 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Multiply by 4:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4 \\times 576 = 2304 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. The surface area is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A=2304\\pi=7238.23\u003C/math-field>\u003C/math-field> square inches \u003Cbr>\u003Cbr>Therefore, the surface area of the sphere is 7238.23 square inches.",923,185,"r-24-inches-calculate-the-surface-area-of-the-sphere",{"id":72,"category":50,"text_question":73,"photo_question":52,"text_answer":74,"step_text_answer":8,"step_photo_answer":8,"views":75,"likes":76,"slug":77},537915,"Find the area between y = 9 - x^2 and y = x + 1 from x = -1 to x = 2","Solution:\u003Cbr />\n\u003Cbr />\n1. Given:\u003Cbr />\n- Curve 1: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 9 - x^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Curve 2: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = x + 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Interval for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Find points of intersection:\u003Cbr />\n- Set \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 9 - x^2\u003C/math-field>\u003C/math-field> equal to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = x + 1\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>9 - x^2 = x + 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Rearrange and simplify:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 + x - 8 = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Factor the quadratic equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x - 2)(x + 4) = 0\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2 \\quad \\text{and} \\quad x = -4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Valid intersection within the given interval is at \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Calculate area between curves from \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Integral of top curve minus bottom curve:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\int_{-1}^{2} ((9 - x^2) - (x + 1)) \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\int_{-1}^{2} (8 - x^2 - x) \\, dx\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve the integral:\u003Cbr />\n- Integrate term-by-term:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\left[ 8x - \\frac{x^3}{3} - \\frac{x^2}{2} \\right]_{-1}^{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Evaluate at upper and lower limits:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\left( 8(2) - \\frac{2^3}{3} - \\frac{2^2}{2} \\right) - \\left( 8(-1) - \\frac{(-1)^3}{3} - \\frac{(-1)^2}{2} \\right)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n- Simplify and calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\left( 16 - \\frac{8}{3} - 2 \\right) - \\left( -8 + \\frac{1}{3} - \\frac{1}{2} \\right)\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 14 - \\frac{8}{3} + 8 - \\frac{1}{3} + \\frac{1}{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 22 - \\frac{9}{3} + \\frac{3}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 22 - 3 + 0.5\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 19.5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. The area between the curves from \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = -1\u003C/math-field>\u003C/math-field> to \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field> is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\boxed{19.5}\u003C/math-field>\u003C/math-field>",1091,218,"find-the-area-between-y-9-x-2-and-y-x-1-from-x-1-to-x-2",{"id":79,"category":50,"text_question":80,"photo_question":52,"text_answer":81,"step_text_answer":8,"step_photo_answer":8,"views":82,"likes":83,"slug":84},537894,"What is the amount of an annuity if the payments are$ 60 at the end of each month for\n 10 years at 3.5% interest computed monthly?","Solution:\u003Cbr>\u003Cbr>1. Determine the number of payments and the interest rate per period:\u003Cbr>\u003Cbr>- Number of payments: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 10 \\times 12 = 120\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Monthly interest rate: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>i = \\frac{3.5\\%}{12} = 0.0029167\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Use the formula for the future value of an ordinary annuity:\u003Cbr>\u003Cbr>- Formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV = R \\times \\frac{

$1 + i$ ^n - 1}{i}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Where:\u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>R = 60\u003C/math-field>\u003C/math-field>

$monthly payment$ \u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>i = 0.0029167\u003C/math-field>\u003C/math-field>

$monthly interest rate$ \u003Cbr>\u003Cbr>- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 120\u003C/math-field>\u003C/math-field>

$total number of payments$ \u003Cbr>\u003Cbr>3. Calculate:\u003Cbr>\u003Cbr>- Substitute values: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV = 60 \\times \\frac{

$1 + 0.0029167$ ^{120} - 1}{0.0029167}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV\\approx8605.95\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Conclusion:\u003Cbr>\u003Cbr>- The future value of the annuity is approximately USD 8605.95.",1399,280,"what-is-the-amount-of-an-annuity-if-the-payments-are-60-at-the-end-of-each-month-for-10-years-at-3-5-interest-computed-monthly",{"id":86,"category":50,"text_question":87,"photo_question":52,"text_answer":88,"step_text_answer":8,"step_photo_answer":8,"views":89,"likes":90,"slug":91},537888,"Using dimensional analysis and showing your work calculate how many nickels are in twenty dollars","1. **Value of a nickel**: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 1 \\text{ nickel} = 0.05 \\text{ dollars} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. **Conversion to nickels**: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 20 \\text{ dollars} \\times \\frac{1 \\text{ nickel}}{0.05 \\text{ dollars}} \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> \\frac{20}{0.05} = 400 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n**Answer**: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 400 \\text{ nickels} \u003C/math-field>\u003C/math-field>",517,103,"using-dimensional-analysis-and-showing-your-work-calculate-how-many-nickels-are-in-twenty-dollars",{"id":93,"category":50,"text_question":94,"photo_question":52,"text_answer":95,"step_text_answer":8,"step_photo_answer":8,"views":96,"likes":97,"slug":98},537882,"8+5x4÷2x6÷5=","Solution:\u003Cbr />\n1. Given expression: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8 + 5 \\times 4 \\div 2 \\times 6 \\div 5\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Follow the order of operations

$PEMDAS/BODMAS$ :\u003Cbr />\n- First, perform multiplication and division from left to right.\u003Cbr />\n\u003Cbr />\n3. Evaluate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 \\times 4\u003C/math-field>\u003C/math-field>:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5 \\times 4 = 20\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Evaluate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20 \\div 2\u003C/math-field>\u003C/math-field>:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20 \\div 2 = 10\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Evaluate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>10 \\times 6\u003C/math-field>\u003C/math-field>:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>10 \\times 6 = 60\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Evaluate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>60 \\div 5\u003C/math-field>\u003C/math-field>:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>60 \\div 5 = 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Add the result to 8:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>8 + 12 = 20\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nThe simplified value of the expression is 20.",1124,225,"8-5x4-2x6-5",{"id":100,"category":50,"text_question":101,"photo_question":52,"text_answer":102,"step_text_answer":8,"step_photo_answer":8,"views":103,"likes":104,"slug":105},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

$61.00.",785,157,"dhiya-is-painting-her-living-room-the-total-area-that-nees-to-be-covered-is-64-5-square-feet-each-can-of-paint-coat-15-25-and-covers-an-area-of-20square-ft-how-many-cans-will-dhiya-need-to-paint-all",{"id":107,"category":50,"text_question":108,"photo_question":52,"text_answer":109,"step_text_answer":8,"step_photo_answer":8,"views":110,"likes":111,"slug":112},537622,"Factorize x^3 -2x^2-16 by x-2","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$ =x^{2}+\\frac{-16}{x-2}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$ =x^{2}-\\frac{16}{x-2}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1211,242,"factorize-x-3-2x-2-16-by-x-2",{"id":114,"category":50,"text_question":115,"photo_question":52,"text_answer":116,"step_text_answer":8,"step_photo_answer":8,"views":117,"likes":118,"slug":119},537611,"A jury pool consists of 26 people, 14 men and 12 women. Compute the probability that a randomly selected jury of 12 people is all male.","1. Total combinations of selecting any 12 people from 26:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\binom{26}{12} = 9657700 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Combinations of selecting 12 men from 14:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\binom{14}{12} = 91 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. The probability that the jury is all male:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{\\binom{14}{12}}{\\binom{26}{12}} = \\frac{91}{9657700} \\approx 9.42 \\times 10^{-6} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n Answer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{91}{9657700} \\approx 9.42 \\times 10^{-6} 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