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Determine the face value of a zero coupon bond whose maturity is 3 years, its IRR is 4% and has a present value of $8,420

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Answer to a math question Determine the face value of a zero coupon bond whose maturity is 3 years, its IRR is 4% and has a present value of $8,420

Expert avatar
Jon
4.6
108 Answers
1. The formula for the present value PV of a zero-coupon bond is given by:
PV = \frac{FV}{(1 + r)^n}
where:
- PV is the present value
- FV is the face value
- r is the interest rate IRR
- n is the number of years to maturity

2. Rearrange the formula to solve for the face value FV:
FV = PV \times (1 + r)^n

3. Substitute the given values into the formula:
FV = 8,420 \times (1 + 0.04)^3

4. Perform the calculation:
FV = 8,420 \times (1.04)^3
FV = 8,420 \times 1.124864
FV \approx 9478.40

Answer: FV \approx 9478.40

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Round to the nearest tenth:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 113.1 \\, \\text{m}^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, the volume of the sphere is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 113.1 \\, \\text{m}^3 \u003C/math-field>\u003C/math-field> .",1203,241,"r-3m-calculate-the-volume-of-the-sphere-round-to-the-nearest-tenth-if-necessary",{"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},538084,"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":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},538083,"Calculate the volume (to the nearest tenth of a cubic centimeter) of a golf ball whose diameter is 4.267cm","1. The formula for the volume of a sphere is given by \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>\u003Cbr>2. The diameter of the golf ball is given as 4.267 cm, so the radius is half of that: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{4.267}{2} = 2.1335 \\, \\text{cm}\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>3. Substitute the radius into the volume formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{4}{3} \\pi (2.1335)^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>4. Calculate the cube of the radius: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(2.1335)^3 = 9.707432537375\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>5. Substitute this back into the formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V=\\frac{4}{3}\\pi\\times9.707432537375\\approx40.7\\,\\text{cm}^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>6. The volume of the golf ball is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>40.7\\,\\text{cm}^3\u003C/math-field>\u003C/math-field> .",1440,288,"calculate-the-volume-to-the-nearest-tenth-of-a-cubic-centimeter-of-a-golf-ball-whose-diameter-is-4-267cm",{"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},538082,"Find the length of each base edge (to the nearest tenth of a meter) of the 24m tall glass square pyramids of the Muttart Conservatory in Alberta, Canada, if each contains 5280m^3 of space","1. Volume V of a square pyramid is given by the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{1}{3} B h\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>where B is the area of the base and h is the height of the pyramid.\u003Cbr>\u003Cbr>2. Given that the height h = 24 m and the volume V = 5280 m^3.\u003Cbr>\u003Cbr>3. The base is square, so if the side length of the base is s, then:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = s^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substituting into the volume formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5280 = \\frac{1}{3} s^2 \\times 24\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify and solve for s^2:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5280 = 8 s^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s^2 = \\frac{5280}{8} = 660\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Solve for s:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{660} \\approx 25.7\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. To find the length of each base edge to the nearest tenth of a meter, compute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s \\approx 25.7 \\, \\text{m}\u003C/math-field>\u003C/math-field>",418,84,"find-the-length-of-each-base-edge-to-the-nearest-tenth-of-a-meter-of-the-24m-tall-glass-square-pyramids-of-the-muttart-conservatory-in-alberta-canada-if-each-contains-5280m-3-of-space",{"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},538081,"An observer is 150 meters away\n distance of a hot air balloon online\n straight line at ground level. From your position,\n measures an elevation angle of 40° up to\n the base of the balloon. At what height is\n find the hot air balloon?","Solution:\u003Cbr />\n1. Dado:\u003Cbr />\n- Distancia horizontal desde el observador hasta la base del globo: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>d = 150 \\ m\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Ángulo de elevación: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta = 40^{\\circ}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Usamos la función tangente para encontrar la altura \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h\u003C/math-field>\u003C/math-field> del globo aerostático. La tangente de un ángulo en un triángulo rectángulo es la razón entre la altura y la distancia horizontal:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan(\\theta) = \\frac{h}{d}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Sustituimos los valores conocidos en la ecuación:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan(40^{\\circ}) = \\frac{h}{150}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Resolvemos para \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h = 150 \\times \\tan(40^{\\circ})\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculamos el valor numérico:\u003Cbr />\n* Usando una calculadora, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan(40^{\\circ}) \\approx 0.8391\u003C/math-field>\u003C/math-field>\u003Cbr />\n* Entonces: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h \\approx 150 \\times 0.8391 = 125.865 \\ m\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nLa altura del globo aerostático es aproximadamente \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>125.865 \\ m\u003C/math-field>\u003C/math-field>.",667,133,"an-observer-is-150-meters-away-distance-of-a-hot-air-balloon-online-straight-line-at-ground-level-from-your-position-measures-an-elevation-angle-of-40-up-to-the-base-of-the-balloon-at-what-hei",{"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},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":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},538078,"H=8mm, r=2mm. Calculate the volume of the cone round to the nearest tenth if necessary","1. Use the formula for the volume of a cone: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi r^2 H \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the given values: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> H = 8 \\, \\text{mm}, \\, r = 2 \\, \\text{mm} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (2)^2 (8) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate \\( (2)^2 \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (2)^2 = 4 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substitute and compute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (4)(8) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (32) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Calculate the product: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{32}{3} \\pi \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Calculate:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V\\approx33.51032\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Round to the nearest tenth:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 33.5 \\, \\text{mm}^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>This is the answer: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 33.5 \\, \\text{mm}^3 \u003C/math-field>\u003C/math-field>",631,126,"h-8mm-r-2mm-calculate-the-volume-of-the-cone-round-to-the-nearest-tenth-if-necessary",{"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},538076,"Dividing 218 or 172 by the natural number n, you get a remainder of 11. Dividing n by 11, you get a remainder equal to:","** \u003Cbr>\u003Cbr>1. Since dividing 218 by n gives a remainder of 11, 218 - 11 = 207 is divisible by n : \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>207\\equiv0\\pmod{n}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Similarly, dividing 172 by n gives a remainder of 11, so 172 - 11 = 161 is divisible by n :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>161\\equiv0\\pmod{n}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. n must be a common divisor of 207 and 161. Find the greatest common divisor of 207 and 161:\u003Cbr>\u003Cbr>- First, find the difference: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 207 - 161 = 46 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Find the prime factorization of 46:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 46 = 2 \\times 23 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Prime factorization of 161:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 161 = 7 \\times 23 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Common factor is 23.\u003Cbr>\u003Cbr>4. Therefore, the possible value of n should be 23 (since other divisions have factors that don't divide both). Now, divide n = 23 by 11:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 23 \\div 11 = 2 \\, \\text{R} \\, 1 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Thus, the remainder of dividing n by 11 is 1\u003Cbr>\u003Cbr>",1233,247,"dividing-218-or-172-by-the-natural-number-n-you-get-a-remainder-of-11-dividing-n-by-11-you-get-a-remainder-equal-to",{"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},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":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},538073,"Andrés's age is three times Quan's.\n plus wins and both ages add up to 69 years. Nillar\n both ages.","Solution:\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> be the age of Andrés.\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field> be the age of Quan.\u003Cbr />\n\u003Cbr />\n2. Set up the equations based on the problem:\u003Cbr />\n- Andrés is three times as old as Quan: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The sum of their ages is 69: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a + q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field> into the second equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3q + q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify the equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4q = 69\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>q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q = \\frac{69}{4}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Compute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q = 17.25\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> using the equation \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3 \\times 17.25\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Compute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 51.75\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore:\u003Cbr />\n- Quan is approximately 17.25 years old.\u003Cbr />\n- Andrés is approximately 51.75 years old.",553,111,"andres-s-age-is-three-times-quan-s-plus-wins-and-both-ages-add-up-to-69-years-nillar-both-ages",{"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},538072,"Andrew's age is three times John's plus nine years, and their ages add up to 69 years. Find both ages.","Solution:\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> be Juan's age.\u003Cbr />\n- Andrés' age is then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Set up the equation for the total age:\u003Cbr />\n- Juan's age \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> plus Andrés' age \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9\u003C/math-field>\u003C/math-field> equals 69.\u003Cbr />\n\u003Cbr />\n3. Equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + (3x + 9) = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify and 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 + 3x + 9 = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + 9 = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = 60\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 15\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Find Andrés' age:\u003Cbr />\n- Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 15\u003C/math-field>\u003C/math-field> into Andrés' age expression:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9 = 3(15) + 9 = 45 + 9 = 54\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the ages are:\u003Cbr />\n- Juan: 15 years\u003Cbr />\n- Andrés: 54 years",531,106,"andrew-s-age-is-three-times-john-s-plus-nine-years-and-their-ages-add-up-to-69-years-find-both-ages",{"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},538071,"Solve the following linear equations:\n 1) 5x-3= 3X+7","Solution:\u003Cbr />\n1. Given Equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3 = 3x + 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field> from both sides to simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3x - 3 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Combine like terms:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - 3 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Add 3 to both sides to isolate the term with the variable:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x = 10\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Divide both sides by 2 to 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 = 5\u003C/math-field>\u003C/math-field>",1382,276,"solve-the-following-linear-equations-1-5x-3-3x-7",{"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},538070,"Solve the following linear equations:\n\n 2) 2x+4- 5x = x+8-5×","1. Start with the original equation: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x + 4 - 5x = x + 8 - 5x\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Combine like terms on both sides:\u003Cbr>\u003Cbr>- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - 5x + 4 = -3x + 4\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x - 5x + 8 = -4x + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>So the equation becomes:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-3x + 4 = -4x + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x\u003C/math-field>\u003C/math-field> to both sides to get:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 4 = 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field> from both sides:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 4\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>",674,135,"solve-the-following-linear-equations-2-2x-4-5x-x-8-5",{"first":6,"last":177,"prev":8,"next":10},188,{"current_page":6,"from":6,"last_page":177,"links":179,"path":212,"per_page":213,"to":213,"total":214},[180,183,185,187,189,191,193,196,199,202,205,208,210],{"url":6,"label":181,"active":182},"1",true,{"url":10,"label":49,"active":184},false,{"url":13,"label":186,"active":184},"3",{"url":16,"label":188,"active":184},"4",{"url":19,"label":190,"active":184},"5",{"url":22,"label":192,"active":184},"6",{"url":194,"label":195,"active":184},7,"7",{"url":197,"label":198,"active":184},8,"8",{"url":200,"label":201,"active":184},9,"9",{"url":203,"label":204,"active":184},10,"10",{"url":206,"label":207,"active":184},187,"187",{"url":177,"label":209,"active":184},"188",{"url":10,"label":211,"active":184},"Next »","https://api.math-master.org/api/question",20,3742,{"data":216},{"questions":217},[218,222,226,230,234,238,242,246,250,254,258,262,266,270,274,278,282,286,290,294],{"id":219,"category":36,"text_question":220,"slug":221},532029,"reduction method 2x-y=13 x+y=-1","reduction-method-2x-y-13-x-y-1",{"id":223,"category":36,"text_question":224,"slug":225},532092,"-11+29-18","11-29-18",{"id":227,"category":36,"text_question":228,"slug":229},532308,"90 divided by 40","90-divided-by-40",{"id":231,"category":36,"text_question":232,"slug":233},533901,"For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.","for-a-temperature-range-between-177-degrees-celsius-to-213-degrees-celsius-what-is-the-temperature-range-in-degrees-fahrenheit",{"id":235,"category":36,"text_question":236,"slug":237},533909,"Express the following numbers in decimal system,\n where the subscript indicates the base: 110101 (SUBINDEX=2)","express-the-following-numbers-in-decimal-system-where-the-subscript-indicates-the-base-110101-subindex-2",{"id":239,"category":36,"text_question":240,"slug":241},534063,"A National Solidarity Bond offers A 5 year bond offering a gross return of 15%\r\n\r\nCalculate the AER for this investment. (Give your answer to two decimal places, no need for the percent or € sign in your answer)","a-national-solidarity-bond-offers-a-5-year-bond-offering-a-gross-return-of-15-calculate-the-aer-for-this-investment-give-your-answer-to-two-decimal-places-no-need-for-the-percent-or-sign-in",{"id":243,"category":36,"text_question":244,"slug":245},534117,"According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card","according-to-a-survey-in-a-country-27-of-adults-do-not-own-a-credit-card-suppose-a-simple-random-sample-of-800-adults-is-obtained-describe-the-sampling-distribution-of-p-hat-the-sample-proportion",{"id":247,"category":36,"text_question":248,"slug":249},534125,"There were no defectives in a sample of 1 light bulb does this sample provide sufficient evidence that in the warehouse with millions of light bulbs fewer than 10% are defective?","there-were-no-defectives-in-a-sample-of-1-light-bulb-does-this-sample-provide-sufficient-evidence-that-in-the-warehouse-with-millions-of-light-bulbs-fewer-than-10-are-defective",{"id":251,"category":36,"text_question":252,"slug":253},534135,"What is 28 marks out of 56 as a percentage","what-is-28-marks-out-of-56-as-a-percentage",{"id":255,"category":36,"text_question":256,"slug":257},534141,"v\r\nIs the following statement a biconditional?\r\nIf Shannon is watching a Tigers game, then it is on television.","v-is-the-following-statement-a-biconditional-if-shannon-is-watching-a-tigers-game-then-it-is-on-television",{"id":259,"category":36,"text_question":260,"slug":261},534198,"Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.","calculate-the-boiling-temperature-and-freezing-temperature-at-1-atmosphere-pressure-of-a-solution-formed-by-dissolving-123-grams-of-ferrous-oxide-in-1-890-grams-of-hcl",{"id":263,"category":36,"text_question":264,"slug":265},534245,"19) If the temperature of -8°C decreases by 12°C, how much will it be?\n\n a)-20°C\n\n -4°C\n\n c) 4°C\n\n d) 20°C","19-if-the-temperature-of-8-c-decreases-by-12-c-how-much-will-it-be-a-20-c-4-c-c-4-c-d-20-c",{"id":267,"category":36,"text_question":268,"slug":269},534288,"The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation","the-points-5-4-and-3-6-are-the-ends-of-the-diameter-of-the-circle-calculate-subequation",{"id":271,"category":36,"text_question":272,"slug":273},534348,"2.380× (1+0.05) / 0.95−0.05","2-380-1-0-05-0-95-0-05",{"id":275,"category":36,"text_question":276,"slug":277},534439,"A company has had the following data for two consecutive years.\n Total, asset item 3,100,500 euros 3,300,550 euros.\n Net amount of business figures 4,755,250 euros /5,100 euros\n Average number of workers employed during the year 64/70\n You can present a balance sheet in an abbreviated form","a-company-has-had-the-following-data-for-two-consecutive-years-total-asset-item-3-100-500-euros-3-300-550-euros-net-amount-of-business-figures-4-755-250-euros-5-100-euros-average-number-of-work",{"id":279,"category":36,"text_question":280,"slug":281},534447,"A diamond ring was reduced from $999.99 to $689.99. Find the percent reduction in the price. Round the answer to the nearest tenth of a percent, if necessary.","a-diamond-ring-was-reduced-from-999-99-to-689-99-find-the-percent-reduction-in-the-price-round-the-answer-to-the-nearest-tenth-of-a-percent-if-necessary",{"id":283,"category":36,"text_question":284,"slug":285},534452,"Write an expression using compatible numbers that can be used to estimate the quotient 629\\86","write-an-expression-using-compatible-numbers-that-can-be-used-to-estimate-the-quotient-629-86",{"id":287,"category":36,"text_question":288,"slug":289},534513,"Given a circle 𝑘(𝑆; 𝑟 = 4 𝑐𝑚) and a line |𝐴𝐵| = 2 𝑐𝑚. Determine and construct the set of all\ncenters of circles that touch circle 𝑘 and have radius 𝑟 = |𝐴𝐵|","given-a-circle-k-s-r-4-cm-and-a-line-ab-2-cm-determine-and-construct-the-set-of-all-centers-of-circles-that-touch-circle-k-and-have-radius-r-ab",{"id":291,"category":36,"text_question":292,"slug":293},534579,"What js the greatest 4-digit even number that can be formed by 3,6,1,4?","what-js-the-greatest-4-digit-even-number-that-can-be-formed-by-3-6-1-4",{"id":295,"category":36,"text_question":296,"slug":297},534596,"calculate the product of 4 and 1/8","calculate-the-product-of-4-and-1-8",{"data":299},{"id":300,"category":36,"slug":301,"text_question":302,"photo_question":8,"text_answer":303,"step_text_answer":8,"step_photo_answer":8,"views":304,"likes":305,"expert":306},536313,"determine-the-face-value-of-a-zero-coupon-bond-whose-maturity-is-3-years-its-irr-is-4-and-has-a-present-value-of-8-420","Determine the face value of a zero coupon bond whose maturity is 3 years, its IRR is 4% and has a present value of $8,420","1. The formula for the present value (PV) of a zero-coupon bond is given by:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>PV = \\frac{FV}{(1 + r)^n}\u003C/math-field>\u003C/math-field>\u003Cbr />\nwhere:\u003Cbr />\n - \\(PV\\) is the present value\u003Cbr />\n - \\(FV\\) is the face value\u003Cbr />\n - \\(r\\) is the interest rate (IRR)\u003Cbr />\n - \\(n\\) is the number of years to maturity\u003Cbr />\n\u003Cbr />\n2. Rearrange the formula to solve for the face value \\(FV\\):\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV = PV \\times (1 + r)^n\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute the given values into the formula:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV = 8,420 \\times (1 + 0.04)^3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Perform the calculation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV = 8,420 \\times (1.04)^3\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV = 8,420 \\times 1.124864\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV \\approx 9478.40\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAnswer: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>FV \\approx 9478.40\u003C/math-field>\u003C/math-field>",1426,285,{"id":307,"name":308,"photo":309,"biography":310,"created_at":8,"updated_at":8,"rating":311,"total_answer":312},21,"Jon","https://api.math-master.org/img/experts/21/21.webp","I passed my matric from Govt.City Muslim school Faisalabad and got first division in school by getting 981/1000 marks.\nAfter matric i got admission in Shiblee Colege Faisalabad and got 883/1100 marks in degree of inter with Math.\nNow currently i'm student of BS Math and running my last semester.",4.6,108,{"data":314},{"questions":315},[316,320,324,328,332,336,340,344,348,352,356,360,364,368,372,376,380,381,385,389],{"id":317,"category":36,"text_question":318,"slug":319},532020,"Add.\n7/w²+18w+81 + 1/w²-81","add-7-w-18w-81-1-w-81",{"id":321,"category":36,"text_question":322,"slug":323},532075,"QUESTION l. An investigation has been carried out in a region to know the perception of "citizen insecurity" of its inhabitants. 1,270 people in the region were interviewed, of which 27.1% responded that it was a "serious" problem. Knowing that this opinion was previously held by 25.3% of the population of that region, we want to know if said opinion has changed significantly for a confidence level of 97.2%. Taking this statement into account, the following is requested: a) Critical value of the contrast statistic. b) Solve the hypothesis test and indicate what conclusion we can reach. c) P-value of contrast.","question-l-an-investigation-has-been-carried-out-in-a-region-to-know-the-perception-of-quot-citizen-insecurity-quot-of-its-inhabitants-1-270-people-in-the-region-were-interviewed-of-which-27-1-r",{"id":325,"category":36,"text_question":326,"slug":327},533904,"If O(3,-2) is reflected across x = 2. What are the coordinates of O","if-o-3-2-is-reflected-across-x-2-what-are-the-coordinates-of-o",{"id":329,"category":36,"text_question":330,"slug":331},533949,"Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number","consider-numbers-from-1-to-2023-we-delete-3-consecutive-numbers-so-that-the-avarage-of-the-left-numbers-is-a-whole-number",{"id":333,"category":36,"text_question":334,"slug":335},534032,"The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below.\r\n23.0\t21.2\t23.5\t23.6\r\n20.1\t24.3\t25.2\t26.9\r\n24.6\t22.6\t26.1\t23.1\r\n25.8\t24.6\t24.3\t24.1\r\n24.8\t22.1\t22.8\t24.5\r\n(a)\r\nFind the z-scores for the largest measurement. (Round your answers to two decimal places.)\r\nz =","the-miles-per-gallon-mpg-for-each-of-20-medium-sized-cars-selected-from-a-production-line-during-the-month-of-march-are-listed-below-23-0-21-2-23-5-23-6-20-1-24-3-25-2-26-9-24-6-22-6-26-1-23-1",{"id":337,"category":36,"text_question":338,"slug":339},534124,"Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)","substitute-a-2-and-b-3-and-c-4-to-evaluate-2ac-2b-2-a",{"id":341,"category":36,"text_question":342,"slug":343},534215,"Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.","calculate-the-value-of-a-so-that-the-vectors-2-2-1-3-4-2-and-a-2-3-are-coplanar",{"id":345,"category":36,"text_question":346,"slug":347},534217,"In the telephone exchange of a certain university, calls come in at a rate of 5 every\n 2 minutes. Assuming a Poisson distribution, the average number of calls per\n second is:\n a) 1/8\n b) 1/12\n c) 1/10\n d) 2/5\n e) 1/24","in-the-telephone-exchange-of-a-certain-university-calls-come-in-at-a-rate-of-5-every-2-minutes-assuming-a-poisson-distribution-the-average-number-of-calls-per-second-is-a-1-8-b-1-12-c-1-10",{"id":349,"category":36,"text_question":350,"slug":351},534271,"DuocUC\n\n 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function:\n\n (x+185) C(x)=81300-6x+ 20000\n\n a) It is known that C(90) 5.344. Interpret this result.\n\n (2 points)\n\n b) Calculate C'(x)\n\n (2 points)\n\n 3 x²+111x-0.87\n\n 20000 2000\n\n c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing.\n\n (3 points)\n\n d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost?\n\n (","duocuc-2-the-cost-c-in-pesos-for-the-production-of-x-meters-of-a-certain-fabric-can-be-calculated-through-the-function-x-185-c-x-81300-6x-20000-a-it-is-known-that-c-90-5-344-interpret",{"id":353,"category":36,"text_question":354,"slug":355},534278,"Use a pattern to prove that (-2)-(-3)=1","use-a-pattern-to-prove-that-2-3-1",{"id":357,"category":36,"text_question":358,"slug":359},534305,"User\n One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement.\n\n By deriving the time function we obtain the velocity function at time t, denoted by v(t).\n A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.","user-one-of-the-applications-of-the-derivative-of-a-function-is-its-use-in-physics-where-a-function-that-at-every-instant-t-associates-the-number-s-t-this-function-s-is-called-the-clockwise-functi",{"id":361,"category":36,"text_question":362,"slug":363},534413,"15.A newly married couple purchased a home with a $123710 down payment. They financed the remaining balance of the home with a mortgage. Their payments were $15395 at the end of every six months for 23 years and the interest rate was 10.6%, compounded semi-annually. How much did they purchase their home for.\n\nEnter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.","15-a-newly-married-couple-purchased-a-home-with-a-123710-down-payment-they-financed-the-remaining-balance-of-the-home-with-a-mortgage-their-payments-were-15395-at-the-end-of-every-six-months-for-2",{"id":365,"category":36,"text_question":366,"slug":367},534426,"2X+2=8","2x-2-8",{"id":369,"category":36,"text_question":370,"slug":371},534451,"Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?","pablo-has-a-balance-of-440-000-and-2-5-of-the-money-is-used-to-pay-bills-how-much-money-do-you-have-left-after-paying-the-bills",{"id":373,"category":36,"text_question":374,"slug":375},534503,"A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be \r\nNormally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and \r\nStandard deviation is measured in millimeters. \r\nWhat is the probability that an arbitrary route has a thickness less than 4.00 mm?","a-factory-produces-glass-for-windows-the-thickness-x-of-an-arbitrarily-selected-pane-of-glass-is-assumed-to-be-normally-distributed-with-expectation-u-4-10-and-standard-deviation-0-04-expect",{"id":377,"category":36,"text_question":378,"slug":379},534569,"the product of a 2-digit number and a 3-digit number is about 50000, what are these numbers","the-product-of-a-2-digit-number-and-a-3-digit-number-is-about-50000-what-are-these-numbers",{"id":295,"category":36,"text_question":296,"slug":297},{"id":382,"category":36,"text_question":383,"slug":384},534612,"Recall that with base- ten blocks, 1 long = 10 units, 1flat = 10 long, and\na block = 1 unit. Then what number does 5 flat, 17long and 5 units\nrepresent represent ?","recall-that-with-base-ten-blocks-1-long-10-units-1flat-10-long-and-a-block-1-unit-then-what-number-does-5-flat-17long-and-5-units-represent-represent",{"id":386,"category":36,"text_question":387,"slug":388},534651,"Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?","sarah-is-lining-a-square-tray-with-1-inch-square-tiles-the-side-length-of-the-tray-is-9-inches-how-many-tiles-does-sarah-need",{"id":390,"category":36,"text_question":391,"slug":392},534699,"Construct a set of six pieces of data with​ mean, median, and midrange of 67 and where no two pieces of data are the same.","construct-a-set-of-six-pieces-of-data-with-mean-median-and-midrange-of-67-and-where-no-two-pieces-of-data-are-the-same",{"data":394},[395,399,403],{"id":396,"question":397,"answer":398},114176,"What is the sum of the angles of an isosceles triangle with base angles measuring 40 degrees each?","The sum of the angles of the isosceles triangle is 180 degrees, since the base angles are congruent, each measuring 40 degrees, the third angle must be 180 - (40 + 40) = 100 degrees.",{"id":400,"question":401,"answer":402},117830,"What is the measure of angle BAC if angle BAE = 50° and angle EAC = 30°?","The measure of angle BAC is 80°, as the angle bisector divides angle BAE into two congruent angles. 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