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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 Numbers_Word_Problems/582681: i have been trying to figure this out but no luck! 3 times the sum of a number and 4 is 8 less than one half the number 1 solutions Answer 372161 by stanbon(57984)   on 2012-03-05 19:11:50 (Show Source): You can put this solution on YOUR website!3 times the sum of a number and 4 is 8 less than one half the number ----- 3(x+4) = (1/2)x-8 ---- 3x+12 = (1/2)x - 8 (5/2)x = -20 x = (2/5)(-20) --- x = -8 ----------------------------- Cheers, Stan H.
 Mixture_Word_Problems/582679: 15 ml of 25% acid solution must be mixed with how much 30% acid to yield a 27% acid solution?1 solutions Answer 372157 by stanbon(57984)   on 2012-03-05 19:09:12 (Show Source): You can put this solution on YOUR website!15 ml of 25% acid solution must be mixed with how much 30% acid to yield a 27% acid solution? ---- Equation: acid + acid = acid 0.25*15 + 0.30x = 0.27(15+x) ---- Multiply thru by 100 to get: 25*15 + 30x = 27*15 + 27x 3x = 2*15 x = 10 ml (amt. of 30% solution needed) ===================== Cheers, Stan H. =============
 Equations/582667: Graph the function below. Determine the domain, range, and horizontal asymptote. Please show all of your work. f(x) = (3/4)^(x+3)1 solutions Answer 372154 by stanbon(57984)   on 2012-03-05 19:05:20 (Show Source): You can put this solution on YOUR website!Graph the function below. Determine the domain, range, and horizontal asymptote. Please show all of your work. f(x) = (3/4)^(x+3) -------- Domain: All Real Numbers. Range: Since (3/4) is positive f(x) cannot be negative or zero. So Range is "All Real Numbers greater than zero". ------ Horizontal Asymptote: f(x) will get closer and closer to zero as x gets larger. HA: y = 0 ================== Cheers, Stan H. ==================
 Circles/582659: I am getting 30 baby chickens. I am going to keep them in a brooder that consist of a cardboard roll that has been rolled out into a circle. The only thing is I'm not sure how big to make the circle. I read that there should be 1/2 a square foot per chick. What would the area and diameter be of this circle?1 solutions Answer 372151 by stanbon(57984)   on 2012-03-05 18:58:31 (Show Source): You can put this solution on YOUR website!I am getting 30 baby chickens. I am going to keep them in a brooder that consist of a cardboard roll that has been rolled out into a circle. The only thing is I'm not sure how big to make the circle. I read that there should be 1/2 a square foot per chick. What would the area and diameter be of this circle? ---- 30 chicks would need 30(1/2) = 15 sq yrds of area ------ Area of a circle is (pi)r^2 --- Solve: (pi)r^2 = 15 r^2 = 15/(pi) r = sqrt(4.7746) = 2.1851 yrds. ----- Diameter = 2(2.1851) = 4.36 yrds. ====================================== Cheers, Stan H. ================
 test/582658: Deleted1 solutions Answer 372146 by stanbon(57984)   on 2012-03-05 18:51:35 (Show Source):
 Trigonometry-basics/582651: An airplane flying at an altitude of 32000 feet is headed toward an airport. To guide the airplane to a safe? landing, the airport landing system sends radar signals from the runway at a 10 degree angle above the runway. Measured along the ground, how far is the airplane from the airport runway to the nearest foot? 0 seconds ago - 4 days left to answer. 1 solutions Answer 372142 by stanbon(57984)   on 2012-03-05 18:45:25 (Show Source): You can put this solution on YOUR website!An airplane flying at an altitude of 32000 feet is headed toward an airport. To guide the airplane to a safe? landing, the airport landing system sends radar signals from the runway at a 10 degree angle above the runway. Measured along the ground, how far is the airplane from the airport runway to the nearest foot? ---- Draw the picture. You have a right triangle with a 10 degree angle at the ground and a 32000 ft side opposite the 10 degree angle. ---- Solve for the base. ---- tan(10) = 32000/base base = 32000/tan(10) = 181481.0182 ft. ==================== Cheers, Stan H. =================
 Polynomials-and-rational-expressions/582626: There are three types of bikes. A bicycle, tricycle, and tandem bikes. A bicycle as 2 wheels, 2 pedals, and 1 seat. A tricycle has 3 wheels, 2 pedals, and 1 seat. A tandem bike has 2 wheels, 4 pedals, and 2 seats. How many of each are there if there are 144 front steering handlebars, 378 pedals, and 320 wheels? How many bicycles, tricycles, and tandem bikes? Can you tell me the equation to find it? It's been bugging me for a while.1 solutions Answer 372137 by stanbon(57984)   on 2012-03-05 18:37:32 (Show Source): You can put this solution on YOUR website!A bicycle as 2 wheels, 2 pedals, and 1 seat. A tricycle has 3 wheels, 2 pedals, and 1 seat. A tandem bike has 2 wheels, 4 pedals, and 2 seats. How many of each are there if there are 144 front steering handlebars, 378 pedals, 320 wheels? ------------------------------------------------ How many bicycles, tricycles, and tandem bikes? ---- Wheels Eq: 2b + 3t + 2tb = 320 Pedals Eq: 2b + 2t + 4tb = 378 HandbarEq: 1b + 1t + 1tb = 144 ---------------------------- I used the Matrix function on my TI-84 to get: b = 67 bikes t = 32 tricycles tb = 45 tandem bikes =========================== Cheers, Stan H. =================
 Quadratic_Equations/582617: Determine whether the graph of y = x^2 − 6x + 3 has a maximum or minimum point, then find the maximum or minimum value.1 solutions Answer 372128 by stanbon(57984)   on 2012-03-05 18:19:06 (Show Source): You can put this solution on YOUR website!Determine whether the graph of y = x^2 − 6x + 3 has a maximum or minimum point, then find the maximum or minimum. -------- Since the coefficient of x^2 is positive, y will increase as x gets larger and larger both positively and negatively. So the graph has a minimum point. ------- The minimum occurs where x = -b/(2a) = 6/(2*1) = 3 --- The minimum y-value = f(3) = 3^2-6*3+3 = 9-18+3 = -6 ------------------- Cheers, Stan H.
 Equations/582620: Solve for x. 90=x/x+151 solutions Answer 372126 by stanbon(57984)   on 2012-03-05 18:09:00 (Show Source): You can put this solution on YOUR website!90 = x/(x+15) ----- 90(x+15) = x 90x + 135 = x 89x = -135 x = -135/89 ===================== Cheers, Stan H.
 Radicals/582615: i need your help on this text brfore tommoroww so can u help me withab tho the 1/3 power and 1 solutions Answer 372123 by stanbon(57984)   on 2012-03-05 18:05:47 (Show Source): You can put this solution on YOUR website!with ab to the 1/3 power --------- = ab^(1/3) ============= Cheers, Stan H.
 Exponents-negative-and-fractional/582605: how do you write -o.125z to the negative third power without using a negative exponent?1 solutions Answer 372121 by stanbon(57984)   on 2012-03-05 18:03:01 (Show Source): You can put this solution on YOUR website!how do you write -o.125z to the negative third power without using a negative exponent? --- Note: 0.125 = 1/8 -------------------- -0.125z^(-3) = -(1/8)z^(-3) = -(1/8)(1/z^3) = -1/(8z^3) ====================== Cheers, Stan H. =============
 Trigonometry-basics/582595: Please help me solve this equation for all the solutions in the interval [0, 2 pi) sin^2x+sinx=01 solutions Answer 372116 by stanbon(57984)   on 2012-03-05 17:56:00 (Show Source): You can put this solution on YOUR website!Please help me solve this equation for all the solutions in the interval [0, 2 pi) sin^2x+sinx=0 --- Factor: sin(x)[sinx+1] = 0 --- sin(x) = 0 or sin(x) = -1 ---- x = 0, or pi, or (3/2)pi ============================= Cheers, Stan H.
 Exponential-and-logarithmic-functions/582434: Hi, I'm having a lot of trouble with a couple of different questions. I did do the homework on this, but I feel like I did not do an example like this. A) (25u^2)^5/2 B) b^2/3b^2/3 / -b^1/3 C) Find the perimeter of the trapezoid. This one they gave us a problem like it, but they never made us set it up fully. So I'm not even sure how to set it up. Sides: 4 square root of 50, 2 square root of 72, 3 square root of 2, & the square root of 50.1 solutions Answer 372056 by stanbon(57984)   on 2012-03-05 13:05:02 (Show Source): You can put this solution on YOUR website!A) (25u^2)^(5/2) ----- The 2 in the exponent denominator means "take the square root". The 5 in the exponent numerator means "raise to the 5th power". ------ (25u^2)^(5/2) = (5u)^5 = 3125u^5 ====================================== B) b^2/3b^(2/3) / -b^(1/3) ------------ = [b^(4/3)/3] / [-b^(1/3) ----- = [b^(4/3)/[-3b^(1/3)] ---- = b/(-3) --- = (-1/3)b ============================= C) Find the perimeter of the trapezoid. This one they gave us a problem like it, but they never made us set it up fully. So I'm not even sure how to set it up. Sides: 4 square root of 50, 2 square root of 72, 3 square root of 2, & the square root of 50. ---- P = 2sqrt(50) + 2sqrt(72)+3sqrt(2)+sqrt(50) ---- P = 2*5sqrt(2) + 2*6sqrt(2) + 3 sqrt(2) + 5sqrt(2) ----- P = 30sqrt(2) ====================== Cheers, Stan H. =================
 Rectangles/582439: The ratio of the measures of a pair of sides of a rectangle is 7:12. If the perimeter of the rectangle is 95, what is the length of each side?1 solutions Answer 372054 by stanbon(57984)   on 2012-03-05 12:55:48 (Show Source): You can put this solution on YOUR website!The ratio of the measures of a pair of sides of a rectangle is 7:12. If the perimeter of the rectangle is 95, what is the length of each side? ------- Let width = 7x ; Then length = 12x ----- P = 2(length + width) ---- 95 = 2(12x + 7x) 19x = 95/2 x = 95/38 --- x = 2.5 ---- width = 7x = 7*2.5 = 17.5 ----- length = 12x = 12*2.5 = 30 ================================ Cheers, Stan ============
 test/582435: If A is a positive acute angle and sin A = the square root of 5/3 what is cos A1 solutions Answer 372052 by stanbon(57984)   on 2012-03-05 12:51:11 (Show Source): You can put this solution on YOUR website!If A is a positive acute angle and sin A = the square root of 5/3 what is cos A ----------------- A is in Q1. ---- sin(A) = sqrt(5)/3 ---- But sin(A) = y/4 So, y = sqrt(5) and r = 4 ----- Then x = sqrt[r^2-y^2] = sqrt[16-5] = sqrt(11) ---- cos(A) = x/r = sqrt(11)/4 ============================= Cheers, Stan H. =================
 Probability-and-statistics/582228: the sum of 450 and 250 is 6501 solutions Answer 371999 by stanbon(57984)   on 2012-03-04 22:15:56 (Show Source): You can put this solution on YOUR website!the sum of 450 and 250 is 650 ------ No 450 + 250 = 700 ----- Cheers, Stan H. ===========
 Linear_Equations_And_Systems_Word_Problems/582220: Hi, I am having trouble trying to write an equation for this question. Can you please help? You are running a concession stand. You are selling hotdogs and soda. Each hot dog costs \$ 1.50 and each soda costs \$ .50. You made a total of \$ 78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs and soda's sold. How many hot dogs and soda's were sold? Thanks1 solutions Answer 371998 by stanbon(57984)   on 2012-03-04 22:14:34 (Show Source): You can put this solution on YOUR website!Each hot dog costs \$ 1.50 and each soda costs \$ .50. You made a total of \$ 78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs and soda's sold. How many hot dogs and soda's were sold? ----- Quantity Equation: h + s = 87 Value Equation:: 1.5h+0.5s=78.50 -------------------------------------- Multiply thru the Quantity Equation by 15 Multiply thru the Value Equation by 10. -------------------- 15h + 15s = 15*87 15h + 5s = 785 ---------------------- Subtract and solve for "s": 10s = 520 s = 52 (# of soda's sold) ---- Solve for h: h + s = 87 h + 52 = 87 h = 35 (# of hot dog's sold) =============================== Cheers, Stan H. ==============
 Equations/582191: Please help me solve this. 3x=2y+7. And 5x=2y+13 Thank you. Sandy1 solutions Answer 371988 by stanbon(57984)   on 2012-03-04 21:09:35 (Show Source): You can put this solution on YOUR website!3x=2y+7 5x=2y+13 ------------------- --- Subtract to get: 2x = 6 x = 3 ------ Solve for "y": 3x = 2y + 7 9 = 2y + 7 2y = 2 y = 1 ------- Solution: (3,1) ================== Cheers, Stan H.
 Quadratic_Equations/582187: The profit P, in dollars, gained by selling x computers is modeled by the equation P= -5x^2 + 1000x + 5000. Find the number of computers that must be sold to obtain a profit of \$55,000.00? Using the quadratic equation, I came up with the computer cost being \$41.42 then divided \$55,000 by that and came out with 1327.86 computers needed to be sold to obtain that profit of \$55,000. Please help. Diana1 solutions Answer 371984 by stanbon(57984)   on 2012-03-04 20:59:39 (Show Source): You can put this solution on YOUR website!The profit P, in dollars, gained by selling x computers is modeled by the equation P= -5x^2 + 1000x + 5000. Find the number of computers that must be sold to obtain a profit of \$55,000.00? Using the quadratic equation, I came up with the computer cost being \$41.42 then divided \$55,000 by that and came out with 1327.86 computers needed to be sold to obtain that profit of \$55,000. ------------------- -5x^2 + 1000x + 5000 = 55000 Divide both sides by -5 to get ---- x^2 - 200x -1000 = -11000 ----------- x^2 - 200x + 10000 = 0 ----- x = 100 ============ Cheers, Stan H.
 Square-cubic-other-roots/582176: I don't know how to do this. Determine the values for the variable that will make each expression a real number. The problems are: √ 2x-1 √ 2x-10 √ 2x^2 √ x^2+17 √ x+51 solutions Answer 371982 by stanbon(57984)   on 2012-03-04 20:42:09 (Show Source): You can put this solution on YOUR website!Determine the values for the variable that will make each expression a real number. ------ For each, the radicand cannot be negative. ----------------- The problems are: √ 2x-1 Solve: 2x-1 >= 0 2x >= 1 x >= 1/2 ----------------- √ 2x-10 Solve: 2x-10 >= 0 2x >= 10 x >= 5 --------------------------------------- √ 2x^2 2x^2 >= 0 x^2 >= 0 x is All Real Numbers ------------------------------------------------------- Etc. Cheers, Stan H. ------------------------- √ x^2+17 All Real Numbers ---------------------------- √ x+5 x >= -5 =================== Cheers, Stan H.
 Age_Word_Problems/582180: the difference between Maria's age and her sister's age is 3. If Maria is seven years younger than twice her sister's age, how old is Maria?1 solutions Answer 371976 by stanbon(57984)   on 2012-03-04 20:28:09 (Show Source): You can put this solution on YOUR website!the difference between Maria's age and her sister's age is 3. If Maria is seven years younger than twice her sister's age, how old is Maria? ------ Equations: m - s = 3 m = 2s-7 ------------------ Sustitute for "m" and solve for "s": 2s-7-s = 3 s = 10 yrs (sister/s age) ---- Solve for "m": m = 2s-7 m = 2*10-7 m = 13 yrs (Maria's age) =========================== Cheers, Stan H.
 Quadratic_Equations/582171: The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag? I tried this several ways and still came up with 199.32 miles per hour which my teacher says is wrong. Please help.1 solutions Answer 371972 by stanbon(57984)   on 2012-03-04 20:20:12 (Show Source): You can put this solution on YOUR website!The number of horsepower, H, needed to overcome a wind drag on an automobile is given by H=0.005s^2 + 0.007s - 0.031, where s is the speed of the car in miles per hour. At what speed will the car need to travel to use 200 horsepower to overcome the wind drag? ---------------- 200 = 0.005s^2 + 0.007s - 0.031 ---- Multiply thru by 1000 to get: 5s^2 + 7s - 31 = 200000 --- 5s^2 + 7s - 200031 = 0 ------------------------- I graphed it and got s = 199.32 ===================================== Cheers, Stan H.
 Angles/582173: Show all work. Mary purchased a package of 24 different plants, but she only needed 20 plants for planting. In how many ways can she select the 20 plants from the package to be planted? (Points : 3) 1 solutions Answer 371965 by stanbon(57984)   on 2012-03-04 20:06:52 (Show Source): You can put this solution on YOUR website!Show all work. Mary purchased a package of 24 different plants, but she only needed 20 plants for planting. In how many ways can she select the 20 plants from the package to be planted? ------------------------ Ans: 24C20 = 24C4 = (24*23*22*21)/(1*2*3*4) = 10626 ---------------------------- Cheers, Stan H. ==============
 Sequences-and-series/582136: A laptop manufacturer finds that the average time it takes an employee to load a laptop with software is 35 minutes with a standard deviation 15 minutes. Suppose you take a random sample of 64 employees. The standard deviation of the sample mean is:1 solutions Answer 371953 by stanbon(57984)   on 2012-03-04 19:03:34 (Show Source): You can put this solution on YOUR website!A laptop manufacturer finds that the average time it takes an employee to load a laptop with software is 35 minutes with a standard deviation 15 minutes. Suppose you take a random sample of 64 employees. The standard deviation of the sample mean is: ---- By the Central Limit Theorem the std of the sample means = 15/sqrt(64) = 15/8 =================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/582128: Write the following equation in standard form, then identify the type of conic 9x^2 - 4y^2 + 18x + 56y - 223 = 01 solutions Answer 371949 by stanbon(57984)   on 2012-03-04 18:55:55 (Show Source): You can put this solution on YOUR website!Write the following equation in standard form, then identify the type of conic 9x^2 - 4y^2 + 18x + 56y - 223 = 0 ---- 9(x^2+2x+1) -4(y^2-14y+49) = 223+9*1-4*49 ----- 9(x+1)^2 -4(y-7)^2 = 36 --- (x+1)^2/4 - (y-7)^2/9 = 1 ------------------------------ Hyperbola ================= Cheers, Stan H. =================
 Numeric_Fractions/582118: if an equation is 0.249=(2.61/2.53X) How do you find X1 solutions Answer 371944 by stanbon(57984)   on 2012-03-04 18:44:52 (Show Source): You can put this solution on YOUR website!if an equation is 0.249=(2.61/2.53X) How do you find X ------- Invert both sides to get: 2.53x/2.61 = 1/0.249 ------------------------------- Multiply both sides by 2.61 Then divide both sides by 2.53 to get: x = (2.61/2.53)(1/0.249) ---- x = 4.1431 ============================ Cheers, Stan H.
 Parallelograms/582117: how do I find the value of h in a parallelogram?1 solutions Answer 371943 by stanbon(57984)   on 2012-03-04 18:38:47 (Show Source): You can put this solution on YOUR website!insufficient information
 Polynomials-and-rational-expressions/582099: Does anyone have a easy way to factor? Her is a problem I just don't know how to do. 9ax^3+15ax^2-14ax1 solutions Answer 371941 by stanbon(57984)   on 2012-03-04 18:35:28 (Show Source): You can put this solution on YOUR website!9ax^3+15ax^2-14ax ---- = ax(9x^2 + 15x - 14 ----------- = ax(9x^2+21x-6x-14) ----------- = ax(3x(3x+7)-2(3x+7)) ----------- = ax(3x+7)(3x-2) =========================================== Cheers, Stan H.
 Rectangles/582092: The perimeter of a rectangle is 50 meters. The width of the rectangle is 5 meters less than the length. Determine the equation that would solve for the length and width of the rectangle1 solutions Answer 371936 by stanbon(57984)   on 2012-03-04 18:22:45 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 50 meters. The width of the rectangle is 5 meters less than the length. Determine the equation that would solve for the length and width of the rectangle ------- Let length be "x". The width is "x-5" ------- Perimeter = 2(length + width) 50 = 2(x + (x-5)) ================================== Cheers, Stan H. =====================