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Recent problems solved by 'stanbon'

stanbon answered: 57911 problems
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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Rate-of-work-word-problems/397960: One pump can empty a tank three times as another. working together they can complete a job in four hours, find the rate of each pump 1 solutions Answer 281974 by stanbon(57984)   on 2011-01-21 17:27:36 (Show Source): You can put this solution on YOUR website! One pump can empty a tank three times as another. working together they can complete a job in four hours, find the rate of each pump --- One pump rate: 1/x job/hr Other pump rate: 1/(3x) job/hr ----- Together rate: 1/4 job/hr ================================ Equation: rate + rate = together rate 1/x + 1/(3x) = 1/4 --- Multiply thru by 12x to get: 12 + 4 = 3x 3x = 16 ----- One pump DATA: x = 16/3 hr Pump rate = (3/16) job/hr ----- Other pump DATA: time = 3x = 16 hr Pump rate = 1/16 job/hr ============================= Cheers, Stan H. ============

Polynomials-and-rational-expressions/397957: A particular hybrid car travels approximately 312 miles on 6 gallons of gas. Find the amount of gas required for a 936 mile trip? 1 solutions Answer 281966 by stanbon(57984)   on 2011-01-21 17:13:26 (Show Source): You can put this solution on YOUR website! A particular hybrid car travels approximately 312 miles on 6 gallons of gas. Find the amount of gas required for a 936 mile trip? ------- gas/miles = gas/miles x/936 = 6/312 x = 936(6/312) --- x = 3*6 x = 18 gallons ======================= Cheers, Stan H.

Complex_Numbers/397904: The point (-5+bi) has been plotted on the complex plane and r=9. If 0°≤θ≤180° find the value of b. Leave your answer as a radical. Thank you all for your time and assistance! -ClanMacniall 1 solutions Answer 281945 by stanbon(57984)   on 2011-01-21 16:20:32 (Show Source): You can put this solution on YOUR website! The point (-5+bi) has been plotted on the complex plane and r=9. If 0°≤θ≤180° find the value of b. Leave your answer as a radical. ----------- With that range for theta, (-5+bi) must be in the 2nd Quadrant and b must be positive. ---- x = -5 and r = 9 --- Solve for "y" 9^2 = [5^2+y^2] 81 = 25 + y^2 y^2 = 56 y = sqrt(56) ---- b = y = sqrt(56) =================== Cheers, Stan H.

Rate-of-work-word-problems/397942: elsa can complete a typing job in six hours. She was given a helper and together they finish the job in only four days. How long would it take the helper had he worked alone 1 solutions Answer 281941 by stanbon(57984)   on 2011-01-21 16:12:26 (Show Source): You can put this solution on YOUR website! elsa can complete a typing job in six hours. She was given a helper and together they finish the job in only four hours. How long would it take the helper had he worked alone ------ Elsa rate = 1/6 job/hr Helper's rate = 1/x job/hr Together rate = 1/4 job/hr -------------------------------- Equation: rate + rate = together rate 1/6 + 1/x = 1/4 --- Multiply thru by 12x to get: 2x + 12 = 3x x = 12 hrs (time for helper to do job alone) ============================== Cheers, Stan H.

Complex_Numbers/397891: Hi, I am having a hard time with these two complex numbers problems. Can anyone help? Thanks. Directions: Without using a graph, find the endpoint of the vector that satisfies the following questions. 1. (-5-3i)+(20-7i) 2. (7+8i)-(6+9i) 1 solutions Answer 281940 by stanbon(57984)   on 2011-01-21 16:09:18 (Show Source): You can put this solution on YOUR website! Without using a graph, find the endpoint of the vector that satisfies the following questions. 1. (-5-3i)+(20-7i) = (-5+20)+(-3-7)i = 15-10i ------------------- 2. (7+8i)-(6+9i) = 1-i ====== cheers, Stan H.

real-numbers/397940: iF I have 4x^2+5=6x^3 how would i solve for a real number solutions? 1 solutions Answer 281939 by stanbon(57984)   on 2011-01-21 16:05:28 (Show Source): You can put this solution on YOUR website! 4x^2+5=6x^3 6x^3-4x^2-5 = 0 ----- I graphed it and found a Real solution at x = 1.223423... Cheers, Stan H.

Geometry_Word_Problems/397926: the dimensions of a rectangle are such that its length is 5 inches more than its width. If teh length were doubled and the width were decreases by 2 inches the area would be increases by 52 inches squared what are the length and width of teh rectangel 1 solutions Answer 281937 by stanbon(57984)   on 2011-01-21 16:01:00 (Show Source): You can put this solution on YOUR website! the dimensions of a rectangle are such that its length is 5 inches more than its width. If the length were doubled and the width were decreased by 2 inches the area would be increased by 52 inches squared. What are the length and width of the rectangel? --- Original dimensions: Let the width be "x". Then the length is "x+5" Area is x(x+5) = x^2+5x. -------------------------- New dimensions: width = x+2 length = 2(x+5) Area is 2(x+5)(x+2) = 2(x^2+7x+10) = 2x^2+14x+20 ---------------- Equation: New Area - Old Area = 52 sq. in. 2x^2+14x+20 -(x^2+5x) = 52 --- x^2+9x+20 = 52 x^2+8x-32 = 0 Use Quadratic formula to get a positive solution: x = 2.93 inches (width) x+5 = 7.93 inches (length) ================ Cheers, Stan H.

Geometry_proofs/397933: what kInd of process do you use to show that a statement must be true because it cannot be false ? 1 solutions Answer 281932 by stanbon(57984)   on 2011-01-21 15:48:30 (Show Source): You can put this solution on YOUR website! Indirect Proof. Cheers, Stan H.

Graphs/397931: Find the intervals where the graph of the function f(x)=x^2-4 is above the x-axis. 1 solutions Answer 281931 by stanbon(57984)   on 2011-01-21 15:47:29 (Show Source): You can put this solution on YOUR website! Find the intervals where the graph of the function f(x)=x^2-4 is above the x-axis. ---- Since the coefficient of x^2 is positive, the parabola opens up. --- Since x^2-4 = (x-2)(x+2) = 0 means the x-intercepts are x=-2 and x=+2. The vertex is inbetween -2 and +2 and is below the x-axis. So f(x) is positive in these intervals: (-inf,-2)U(2,+inf) ================================= Cheers, Stan H. =============

Complex_Numbers/397905: Express these complex numbers in standard form correct to one decimal place: If z=16(cos252°+i*sin252°) in trigonometric form find z in standard form. Thank you all for your time and assistance! -ClanMacniall 1 solutions Answer 281923 by stanbon(57984)   on 2011-01-21 15:24:17 (Show Source): You can put this solution on YOUR website! Express these complex numbers in standard form correct to one decimal place: If z=16(cos252°+i*sin252°) in trigonometric form find z in standard form. --- x = 16*cos(252) = -4.9 y = 16*sin(252) = -15.2 ----------------------------- z = -4.9-15.2i ==================== Cheers, Stan H.

Travel_Word_Problems/397922: how long to cover 92 miles traveling at 150mph 1 solutions Answer 281922 by stanbon(57984)   on 2011-01-21 15:20:14 (Show Source): You can put this solution on YOUR website! how long to cover 92 miles traveling at 150mph --- time = distance/rate --- time = 92/150 --- time = 46/75 = 36.8 minutes = 36min 48sec =========================================== Cheers, Stan H.

Square-cubic-other-roots/397928: 3^sqrt(81) 1 solutions Answer 281920 by stanbon(57984)   on 2011-01-21 15:16:24 (Show Source): You can put this solution on YOUR website! 3^sqrt(81) ------ cbrt(81) = cbrt(27)*cbrt(3) = 3*cbrt(3) ============ Cheers, Stan H.

Polynomials-and-rational-expressions/397929: Solve 4 - a-5/a+3 = a^2-1/a+3, and what does a=? 1 solutions Answer 281918 by stanbon(57984)   on 2011-01-21 15:14:31 (Show Source): You can put this solution on YOUR website! Solve 4 - a-5/a+3 = a^2-1/a+3, and what does a=? --- Multiply thru by (a+3) to get: 4(a+3) - (a-5) = a^2-1 ---- 4a+12 -a+5 = a^2-1 3a+17 = a^2-1 a^2-3a-18 = 0 ---- Factor: (a-6)(a+3) = 0 --- a = 6 or a = -3. ==== But a cannot be -3 as that would make a+3 be zero in the denominator. --- Only solution: a = 6 ========= Cheers, Stan H. =========

Polynomials-and-rational-expressions/397927: Solve 5/7+1/4=1/x, and what does x=? 1 solutions Answer 281917 by stanbon(57984)   on 2011-01-21 15:10:38 (Show Source): You can put this solution on YOUR website! Solve 5/7+1/4=1/x, and what does x=? --- lcm of 7,4,x is 28x --- Multiply thru by 28x to get: 20x + 7x = 28 27x = 28 x = 28/27 ---------- Cheers, Stan H.

Trigonometry-basics/397889: Please solve 1+3Sinx=0 Thank you 1 solutions Answer 281893 by stanbon(57984)   on 2011-01-21 13:16:56 (Show Source): You can put this solution on YOUR website! Please solve 1+3Sinx=0 3sin(x) = -1 sin(x) = -1/3 --- x = sin^-1(-1/3) = -19.47 degrees, if x is in the 4th Quadrant. If x is in the 3rd Quadrant the answer is 180+19.47 = 219.47 degrees. --------------- Cheers, Stan H.

Evaluation_Word_Problems/397886: Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? Please show each step and explain what you did.. Thank you soooo much! 1 solutions Answer 281891 by stanbon(57984)   on 2011-01-21 13:12:40 (Show Source): You can put this solution on YOUR website! Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? ----- Quantity Eq: x + y = 33000 dollars Interest Eq:0.04x + 0.025y = 970 dollars ------------------ Multiply thru Quantity Eq. by 4. Multiply thru Interest Eq. by 100. ------------------------------- 4x + 4y = 4*33000 4x + 2.5y = 97000 --------------------- Subtract the bottom from the top and solve for "y": 1.5y = 35000 y = $23,333.33 (amt. invested at 2.25%) --- Solve for "x": x+y = 33000 x + 23,333.33 = 33000 x = $9666.66 (amt. invested at 4%) ====================================== cheers, Stan H.

Mixture_Word_Problems/397848: The radiator in a car is filled with a solution of 70% antifreeze and 30% water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.5 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level? 1 solutions Answer 281863 by stanbon(57984)   on 2011-01-21 10:59:42 (Show Source): You can put this solution on YOUR website! The radiator in a car is filled with a solution of 70% antifreeze and 30% water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.5 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level? ---- Equation: water - water + water = water 0.30*3.5 - 0.30x + 1*x = 0.5*3.5 ---- Multiply thru by 100 to get: 30*3.5 - 30x + 100x = 50*3.5 70x = 20*3.5 --- x = 1 liter (amt. of solution that should be replaced) ============== Cheers, Stan H.

Polynomials-and-rational-expressions/397788: Divide and simplify. Simplify your answer. 1 solutions Answer 281860 by stanbon(57984)   on 2011-01-21 10:54:47 (Show Source): You can put this solution on YOUR website! [(3x-9)/(55)] / [(x-3)/(25x))] ------ Invert the denominator and multiply: ---- [(3(x-3))/(55)] * [(25x)/(x-3)] =========== Cancel the x-3 and 5 factors common to numerator and denominator to get: ----------- = [(3)/(11)] * [(5x)/(1)] --- = (15x)/11 ============== Cheers, Stan H. ============

Polynomials-and-rational-expressions/397834: A rectangle has an area given by A = x^2 + 5x + 6 Find an expression for the possible length of the rectangle. 1 solutions Answer 281849 by stanbon(57984)   on 2011-01-21 10:29:41 (Show Source): You can put this solution on YOUR website! duplicate

Polynomials-and-rational-expressions/397835: A rectangle has an area given by A = x^2 + 5x + 6 Find an expression for the possible width of the rectangle. 1 solutions Answer 281848 by stanbon(57984)   on 2011-01-21 10:28:34 (Show Source): You can put this solution on YOUR website! A rectangle has an area given by A = x^2 + 5x + 6 Find an expression for the possible width of the rectangle. --------------- Factor: A = (x+3)(x+2) ---- width could be x+3 or it could be x+2 ============= Cheers, Stan H. =============

Signed-numbers/397841: asssssssssssssssssssssssss 1 solutions Answer 281847 by stanbon(57984)   on 2011-01-21 10:26:45 (Show Source): You can put this solution on YOUR website!

Linear-equations/397840: Could you assist me with finding the slope and the y-intercept of the following: 6-1/5y=4x 1 solutions Answer 281846 by stanbon(57984)   on 2011-01-21 10:25:31 (Show Source): You can put this solution on YOUR website! the slope and the y-intercept of the following: 6-1/5y=4x ---- 6-(1/5)y = 4x --- Add (1/5)y to both sides to get: 6 = (1/5)y + 4x --- Subtract 4x from both sides to get: (1/5)y = -4x+6 --- Multiply both sides by 5 to get: y = -20x+30 --- slope = -20 intercept = 30 ==================== Cheers, Stan H.

Money_Word_Problems/397837: EE savings bond is sold at half face value, US Treasury guarantees it will double in value by 20 years from the issue date. What is the minimum APY for such a bond? 1 solutions Answer 281844 by stanbon(57984)   on 2011-01-21 10:22:05 (Show Source): You can put this solution on YOUR website! EE savings bond is sold at half face value, US Treasury guarantees it will double in value by 20 years from the issue date. What is the minimum APY for such a bond? ----- P(t) = P(0) + P(0)rt --- Let P(0) be $1. --- P(20) = 1 + 20r 2 = 1 + 20r 20r = 1 r = 1/20 r = 0.05 --- rate = 5% ========================= Cheers, Stan H.

Graphs/397828: write the equation of the line that contains the indicated pair of points. Express the final equation in standard form. (2,5),(8,12) 1 solutions Answer 281842 by stanbon(57984)   on 2011-01-21 09:31:13 (Show Source): You can put this solution on YOUR website! write the equation of the line that contains the indicated pair of points. Express the final equation in standard form. (2,5),(8,12) ----- slope = (12-5)/(8-2) = 7/6 ------------ Form: y = mx + b Substitite and solve for "b": 5 = (7/6)2+b b = 5-(7/3) b = (15/3)-(7/3) b = 8/3 ========= Equation: y = (7/6)x+(8/3) --------- Cheers, Stan H.

Miscellaneous_Word_Problems/397825: suppose that a city requires a 2.5% fall for a sewer pipe from the house to the main pipe at the street. How much vertical drop to the nearest foot must there be for a horizontal distance of 55 feet? 1 solutions Answer 281841 by stanbon(57984)   on 2011-01-21 09:26:39 (Show Source): You can put this solution on YOUR website! suppose that a city requires a 2.5% fall for a sewer pipe from the house to the main pipe at the street. How much vertical drop to the nearest foot must there be for a horizontal distance of 55 feet? ---------------------- Proportion: vert/hor = vert/hor x/55 = 2.5/100 --- x = 55(2.5/100) --- x = 1.375 ft. ================= Cheers, Stan H.

Miscellaneous_Word_Problems/397820: the grade of a highway up a hill is 3% how much change in horizontal distance is there if the vertical height of the hill is 10.5ft? 1 solutions Answer 281839 by stanbon(57984)   on 2011-01-21 09:23:48 (Show Source): You can put this solution on YOUR website! the grade of a highway up a hill is 3% how much change in horizontal distance is there if the vertical height of the hill is 10.5ft? ----- Proportion: hor/vert = hor/vert x/10.5 = 3/100 --- x = 10.5(100/3) --- x = 340 ft. =============== Cheers, Stan H.

Proportions/397822: How can I solve a proportion involving a missing number? 1 solutions Answer 281838 by stanbon(57984)   on 2011-01-21 09:19:34 (Show Source): You can put this solution on YOUR website! How can I solve a proportion involving a missing number? ---- Let's say the missing number is x: Proportion I made up. x/2 = 3/5 Cross-multiply to get: 5x = 2*3 --- Divide by 5 to get: x = 6/5 =========== Cheers, Stan H. ==========

Linear-equations/397821: write a equation of a line through the given points 1 solutions Answer 281837 by stanbon(57984)   on 2011-01-21 09:16:48 (Show Source): You can put this solution on YOUR website! Points not posted.

logarithm/397798: Given that y = ax^b and that y = 5 when x = 2 and y = 29 when x = 4, find the value of a and of b. :) =) 1 solutions Answer 281830 by stanbon(57984)   on 2011-01-21 08:12:01 (Show Source): You can put this solution on YOUR website! Given that y = ax^b and that y = 5 when x = 2 and y = 29 when x = 4, find the value of a and of b. ------------- Two Equations: 29 = a*4^b 5 = a*2^b -------------- divide to get 29/5 = (2^(2b))/(2^b) --- 29/5 = 2^b b(log2) = log(29/5) b = 0.7634/0.3010 --- b = 2.5362 ---- Solve for "a": 5 = a*2^2.5362 5 = a*5.80 a = 0.862 ==== Cheers, Stan H.

Rectangles/397795: Find a polynomial for the perimeter and for the area. The rectangle shows that the length is n+2 and that the width is n. The perimeter is ____. The area is ____. Simplify your answers but do not factor. 1 solutions Answer 281829 by stanbon(57984)   on 2011-01-21 08:03:25 (Show Source): You can put this solution on YOUR website! Find a polynomial for the perimeter and for the area. The rectangle shows that the length is n+2 and that the width is n. The perimeter is 2(length+width) = 2(n+2+n) = 2(2n+2) = 4n+4 ---- The area is n(n+2) = n^2+2n ============ Cheers, Stan H.

Equations/397794: What is 5(-17/29)+2y=-13 1 solutions Answer 281828 by stanbon(57984)   on 2011-01-21 08:00:57 (Show Source): You can put this solution on YOUR website! 5(-17/29)+2y=-13 ----- (-85/29) + 2y = -13 ---- 2y = (-13*29/29)+(85/29) --- 2y = (-292)/29 ---- y = -146/29 =============== Cheers, Stan H.