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Recent problems solved by 'stanbon'

stanbon answered: 57283 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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Probability-and-statistics/397044: what are the odds that the card is not the ace of spades? 1 solutions Answer 281463 by stanbon(57356)   on 2011-01-19 20:51:28 (Show Source): You can put this solution on YOUR website! what are the odds that the card is not the ace of spades? ----- P(it is an ace) = 1/4 P(it is not an ace) = 3/4 ---- odds it is not an ace = (3/4)/(1/4) = 3:1 ===== Cheers, Stan H. ======

Inequalities/396999: Solve the inequality. x^3+x^2 is less than or equal to 16x+16 Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution". 1 solutions Answer 281455 by stanbon(57356)   on 2011-01-19 20:22:45 (Show Source): You can put this solution on YOUR website! x^3+x^2 is less than or equal to 16x+16 --------------- x^3+x^2-16x-16 < 0 --- Find the zeroes because they are the boundaries for the solution intervals. --- x = -1 is one of the zeroes. ---- -1)....1....1....-16....-16 ........1.....0.....-16....|..0 --- The quotient is x^2-16 --- So the other zeroes are +4 and -4 ====================================== Plot x = -4,-1, and 1 on a number line. -- Test a value from each interval to find the solution set for (x+1)(x-4)(x+4)<0 --- If x = -10 you get -*-*- < 0; true so solutions in (-inf,-4) If x = -2 you get -*-*+ < 0; false If x = 0 you get +*-*+ < 0; true so solutions in (-1,1) If x = 10 you get +*+*+ < 0; false ------ Solution: (-inf,-4)U(-1,1) ============================= Cheers, Stan H.

Graphs/396989: when graphing a logarithmic function, what does a reflection across the x-axis of that function look like? 1 solutions Answer 281451 by stanbon(57356)   on 2011-01-19 20:11:29 (Show Source): You can put this solution on YOUR website! An exponential function. --- Cheers, Stan H.

Exponents/396998: Please Help Simplify ((-2x^2)^3)*(4x^3)^-1 1 solutions Answer 281450 by stanbon(57356)   on 2011-01-19 20:09:52 (Show Source): You can put this solution on YOUR website! ((-2x^2)^3)*(4x^3)^-1 ------- = [(-8x^6)]/(4x^3) --- = -2x^3 =========== Cheers, Stan H. ===========

Quadratic_Equations/396995: how do you write a quadratic function in standard form whose graph passes through the given points: (2,7) (3,2) and (5,4)? 1 solutions Answer 281447 by stanbon(57356)   on 2011-01-19 20:07:22 (Show Source): You can put this solution on YOUR website! how do you write a quadratic function in standard form whose graph passes through the given points: (2,7) (3,2) and (5,4)? ------------- Use ax^2+bx+c = y You need to find a,b, and c. --- Substitute each of the points into the quadratic form to get three equations with three variables. --- Solve the system and find the formula. =============== Cheers, Stan H. =============

Graphs/396996: The sum of two numbers is and the difference is . What are the numbers? 1 solutions Answer 281443 by stanbon(57356)   on 2011-01-19 20:03:33 (Show Source): You can put this solution on YOUR website! numbers are missing in your post.

Linear-equations/396994: The measure of an angle and its complement are in the ratio 4:11. what is the measure of the two angles? I tried 4x and 11x so far but lost my way of getting to the answer :( 1 solutions Answer 281442 by stanbon(57356)   on 2011-01-19 20:02:35 (Show Source): You can put this solution on YOUR website! The measure of an angle and its complement are in the ratio 4:11. what is the measure of the two angles? --- Let the angle be "x". Its complement is "90-x" ---- Equation: x/(90-x) = 4/11 11x = 4(90-x) 11x = 360-4x 15x = 360 ---- x = 24 degrees --- 90-x = 66 degrees =================== Cheers, Stan H. =============

Functions/396993: solve: D(h)=5e^(-0.4(1)) 1 solutions Answer 281440 by stanbon(57356)   on 2011-01-19 19:59:19 (Show Source): You can put this solution on YOUR website! Solve for what?

Linear-equations/396991: find an equation of the line containing the points (-5,-2) and (-13,-7) 1 solutions Answer 281438 by stanbon(57356)   on 2011-01-19 19:58:05 (Show Source): You can put this solution on YOUR website! find an equation of the line containing the points (-5,-2) and (-13,-7) --------------- slope = (-7--2)/(-13--5) = -5/-8 = 5/8 ------------------------------------ Form: y = mx+b -2 = (5/8)(-5)+b -2 = -25/8 + b b = -16/8+25/8 --- b = 9/8 ---- Equation: y = (5/8)x+(9/8) ================== Cheers, Stan H. =====

test/396952: In a certain city a birth occurs on the average every 24 minutes and a death every half hour. A resident moves out of the city every 1.5 hours and a new person moves into the city every 4.5 hours. How long does it take on the average for the population to increase by 1 person? Please help me! 1 solutions Answer 281433 by stanbon(57356)   on 2011-01-19 19:37:01 (Show Source): You can put this solution on YOUR website! In a certain city a birth occurs on the average every 24 minutes and a death every half hour. A resident moves out of the city every 1.5 hours and a new person moves into the city every 4.5 hours. How long does it take on the average for the population to increase by 1 person? Please help me! ----- How many births in a day? 60 How many arrive in a day? 5 1/3 ----- Total in 24 hrs: 60 1/3 ==================================== How many deaths in a day? 48 How many leave in a day? 16 ----- Total in 24 hrs: 64 ----- So you have a gain of 1 1/3 in 24 hrs. ---- When do you have a gain of 1 person? Solve (4/3)/24 = 1/x (4/3)x = 24 x = 18 hrs. --- Every 18 hrs. the town gains one person. ============================================= Cheers, Stan H.

Functions/396938: For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other. f(x)= 2/x, x is not equal to 0 g(x)= 2/x, x is not equal to 0 f(g(x))= g(f(x))= Are they inverses of each other? Thanks 1 solutions Answer 281430 by stanbon(57356)   on 2011-01-19 19:07:01 (Show Source): You can put this solution on YOUR website! For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other. f(x)= 2/x, x is not equal to 0 g(x)= 2/x, x is not equal to 0 f(g(x))= f{2/x) = 2/(2/x) = x -------- g(f(x))= g(2/x) = 2/(2/x) = x ----------------------------------- Are they inverses of each other? Yes, because each of the functions undoes what the other does. Cheers, Stan H.

Triangles/396920: What type of triangle has an angle measures 2x degrees, x+15 degrees and 5x+15? 1 solutions Answer 281427 by stanbon(57356)   on 2011-01-19 18:58:10 (Show Source): You can put this solution on YOUR website! What type of triangle has an angle measures 2x degrees, x+15 degrees and 5x+15? --- Equation: 2x + x+15 + 5x+15 = 180 ---- 8x + 30 = 180 8x = 150 --- x = 150/8 = 18.75 degrees ---- 2x = 300/8 degrees = 37.5 degrees ---- x+15 = 15+(150/8)5 = 108.75 degrees ----- Ans: obtuse ================== Cheers, Stan H. ---- 5x+15 = 5(150/8)+15 =

Numeric_Fractions/396919: I need to know how to solve the following problem: 2X+4(18-X)=58 1 solutions Answer 281422 by stanbon(57356)   on 2011-01-19 18:23:17 (Show Source): You can put this solution on YOUR website! I need to know how to solve the following problem: 2X+4(18-X)=58 --- 2x + 72 - 4x = 58 -2x = -14 x = 7 ====== Cheers, Stan H.

Functions/396903: What is the domain of (5x+3)/(2x)? 1 solutions Answer 281421 by stanbon(57356)   on 2011-01-19 18:17:39 (Show Source): You can put this solution on YOUR website! What is the domain of (5x+3)/(2x)? ----- The denominator cannot be zero, so x cannot be zero. Domain: All Real Numbers except z = 0. ==================================== Cheers, stan H.

Mixture_Word_Problems/396896: How many cups of pure granola must be added to 16 cups of granola that is 15% raisins so that the percent of raisins in the resulting mixture will be 10%? 1 solutions Answer 281419 by stanbon(57356)   on 2011-01-19 18:08:46 (Show Source): You can put this solution on YOUR website! How many cups of pure granola must be added to 16 cups of granola that is 15% raisins so that the percent of raisins in the resulting mixture will be 10%? --------------------------- Equations: raisins + raisins = raisins --- 0*x + 0.15*16 = 0.10(x+16) --- Multiply thru by 100 to get: 0 + 15*16 = 10x + 10*16 10x = 5*16 x = 8 cups (amt. of pure granola needed for the mixture) ========================= Cheers, Stan H.

Polynomials-and-rational-expressions/396886: The speed of a passenger train is 10mph faster than the speed of a freight train. The passenger train travels 300 miles in the same time it takes the freight train to travel 250 miles. Find the speed of each train. 1 solutions Answer 281417 by stanbon(57356)   on 2011-01-19 17:55:11 (Show Source): You can put this solution on YOUR website! The speed of a passenger train is 10mph faster than the speed of a freight train. The passenger train travels 300 miles in the same time it takes the freight train to travel 250 miles. Find the speed of each train. ------------------------------- Passenger train DATA: distance = 300 miles ; rate = x+10 mph ; time = 300/(x+10) hrs. --------------------- Freight train DATA: distance = 250 miles ; rate = x mph ; time = 250/x hrs ----- Equation: time = time 300/(x+10) = 250/x --- 6/(x+10) = 5/x 6x = 5x + 50 x = 50 (rate of the freight train) x+10 = 60 (rate of the passenger train) =========================================== Cheers, Stan H.

Proportions/396867: What Dose Proportion mean? 1 solutions Answer 281416 by stanbon(57356)   on 2011-01-19 17:48:07 (Show Source): You can put this solution on YOUR website! What Does Proportion mean? --- Proportion relates to the fact that there are an infinite number of fractions that are equal to any give factor. --- 2/3 = 4/6 = 6/9 = 2k/3k where k is any integer except zero. -------- For additional information use Google to search for "Proportion examples". =============== Cheers, Stan H.

Equations/396864: Factor 15w^2+25w^3 1 solutions Answer 281414 by stanbon(57356)   on 2011-01-19 17:21:03 (Show Source): You can put this solution on YOUR website! Factor 15w^2+25w^3 ------ 5w^2(3+5w) ============= Cheers, Stan H.

expressions/396859: 1/x(x/y-1)- 1/y(1+Y/x) 1 solutions Answer 281413 by stanbon(57356)   on 2011-01-19 17:19:08 (Show Source): You can put this solution on YOUR website! (1/x)(x/y-1)- (1/y)(1+Y/x) ------ (1/y - 1/x)-(1/y+1/x) ----- (x-y)/xy -(x+y)/xy ---- [x-y+x+y]/(xy) ---- (2x)/xy --- = 2/y ========== Cheers, Stan H.

Travel_Word_Problems/396813: if you travel 190 km in 2 hours. what is your speed in km/h? 1 solutions Answer 281401 by stanbon(57356)   on 2011-01-19 16:02:06 (Show Source): You can put this solution on YOUR website! if you travel 190 km in 2 hours. what is your speed in km/h? ---- rate = distance/time ----- rate = 190/2 --- rate = 95 km/h ================= Cheers, Stan H.

Age_Word_Problems/396808: If a plane traves at 300 miles per hour how many miles does a plane travel in 20 minutes 1 solutions Answer 281399 by stanbon(57356)   on 2011-01-19 16:00:17 (Show Source): You can put this solution on YOUR website! If a plane travels at 300 miles per hour how many miles does a plane travel in 20 minutes --- Equation: distance = rate*time --- d = 300 mph*(20/60)hr --- d = 300*(1/3) --- d = 100 miles ================ Cheers, Stan H. ================

Linear_Equations_And_Systems_Word_Problems/396810: How do I solve the following: The three angles in a triangle always add up to 180 degrees. If one angle in a triangle is 72 degrees and the second is 2 times the third, what are the angles? 1 solutions Answer 281396 by stanbon(57356)   on 2011-01-19 15:54:47 (Show Source): You can put this solution on YOUR website! The three angles in a triangle always add up to 180 degrees. If one angle in a triangle is 72 degrees and the second is 2 times the third, what are the angles? ---- Let the third be "x". Then the 2nd is "2x". --- Equation: x + 2x + 72 = 180 3x = 108 x = 36 degrees 2x = 72 degree ===================== Cheers, Stan H.

Miscellaneous_Word_Problems/396809: determine whether y varies directly with x. if so, find the constant of variation k. 3y=-7x-18 1 solutions Answer 281394 by stanbon(57356)   on 2011-01-19 15:52:17 (Show Source): You can put this solution on YOUR website! determine whether y varies directly with x. if so, find the constant of variation k. 3y=-7x-18 y = (-7/3)x - 6 ---- constant of variation = slope = -7/3 ============================= Cheers, Stan H.

Linear_Algebra/396798: solve for b: 4b/8b=8-b i'm a parent trying to re-learn algebra to help my kids. 1 solutions Answer 281393 by stanbon(57356)   on 2011-01-19 15:50:38 (Show Source): You can put this solution on YOUR website! solve for b: 4b/8b=8-b ---- Reduce the fraction on the left side of the equation: 1/2 = 8-b Add b to both sides: b + (1/2) = 8 Subtract (1/2) from both sides to get: b = 7 1/2 ====================== Cheers, Stan H.

Inequalities/396800: A certain store has a fax machine available for use by its customers. The store charges $2.35 to send the first page and $.50 for each subsequent page. Use an inequality to dind the maximum number of pages that can be faxed for $8.35? 1 solutions Answer 281391 by stanbon(57356)   on 2011-01-19 15:46:01 (Show Source): You can put this solution on YOUR website! A certain store has a fax machine available for use by its customers. The store charges $2.35 to send the first page and $.50 for each subsequent page. Use an inequality to dind the maximum number of pages that can be faxed for $8.35? ------ cost = 2.35 + 0.50x --- Solve for "x": 2.35 + 0.50x = 8.35 0.50x = 6.00 x = 12 pages =================== Cheers, Stan H.

Mixture_Word_Problems/396802: How many milliliters of pure acid must be added to 150 milliliters of a 15% solution of acid to obtain a 25% solution? 1 solutions Answer 281388 by stanbon(57356)   on 2011-01-19 15:38:59 (Show Source): You can put this solution on YOUR website! How many milliliters of pure acid must be added to 150 milliliters of a 15% solution of acid to obtain a 25% solution? ---------- Equation: acid + acid = acid 1*x + 0.15*150 = 0.25(x+150) ----- Multiply thru by 100 to get: 100x + 15*150 = 25x + 25*150 75x = 10*150 ---- x = 20 mL (amount pure acid needed for the mixture) ========= Cheers, Stan H.

Triangles/396801: how to find the measure of an angle to the nearest degree that has no degree? 1 solutions Answer 281386 by stanbon(57356)   on 2011-01-19 15:35:22 (Show Source): You can put this solution on YOUR website! How about 0 degrees? Cheers, Stan H.

Equations/396799: A student scored 71, 83, and 96 on three algebra tests. What must he score on the fourth test in order to have an average of at least 85? 1 solutions Answer 281385 by stanbon(57356)   on 2011-01-19 15:33:44 (Show Source): You can put this solution on YOUR website! A student scored 71, 83, and 96 on three algebra tests. What must he score on the fourth test in order to have an average of at least 85? --- Let the 4th test score be "x": Equation: (71+83+96+x)/4 = 85 --- 250+x = 4*85 x = 90 ========== Cheers, Stan H.

Square-cubic-other-roots/396711: How do I find the total perimeter of 2 squares, one with an area of the square root of 5 and the other with a square root of 125? 1 solutions Answer 281355 by stanbon(57356)   on 2011-01-19 12:35:41 (Show Source): You can put this solution on YOUR website! How do I find the total perimeter of 2 squares, one with an area of the square root of 5 and the other with a square root of 125? ---- Area of a square = (side)^2 -------- 1st square: area = sqrt(5) Solve s^2 = sqrt(5) s = 5^(1/4) Perimeter = 4*5^(1/4) ----------------------------- 2nd sqruare: area = sqrt(125) = 5sqrt(5) Solve s^2 = 5sqrt(5) s = 5^(2/4)*5^(1/4) = 5^(3/4) Perimeter = 4*5^(3/4) =========================== Cheers, stan H.

Miscellaneous_Word_Problems/396703: of the 220 bakers at dennys 2/5 work full time. of the fulltime employees, 1/4 worked regularly overtime. how many employees at dennys worked regular overtime / 1 solutions Answer 281354 by stanbon(57356)   on 2011-01-19 12:30:33 (Show Source): You can put this solution on YOUR website! of the 220 bakers at dennys 2/5 work full time. of the fulltime employees, 1/4 worked regularly overtime. how many employees at dennys worked regular overtime --- (2/5)220 = 2*44 = 88 work full time. --- (1/4)88 = 22 worked regularly overtime ==== Cheers, Stan H.

Rational-functions/396705: simplify the expression using long division: find p(-4) and p(5) for the function p(x) =5x^5-5x^4-10x^2+6x-1 1 solutions Answer 281353 by stanbon(57356)   on 2011-01-19 12:18:51 (Show Source): You can put this solution on YOUR website! simplify the expression using long division: find p(-4) and p(5) for the function p(x) =5x^5-5x^4-10x^2+6x-1 ---------- ^2Using synthetic division: -4)....5....-5....0....-10....6....-1 ........5....-25...100..-410...1646..|..-6585 --- p(-4) = -6585 The quotient is 5x^4-25x^3+100x^2-410x+1646 =================================================== 5)....5....-5....0....-10....6....-1 ........5.....20....100...490...2456...12279 --- p(5) = 12279 The quotient is 5x^4+20x^3+100x^2+490x + 2456 =================================================== Cheers, Stan H.