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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269, >>Next

 Probability-and-statistics/477209: Help! I got part of it, but I am boggled. Let μ = 160 and σ = 16. Find the z-score for the score 180 = 1.25 Find the z-score for the score 150 = -0.625 Find the score x if the z-score = 1 = x = ?????? PLEASE HELP Find the score x if the z-score = x = −0.875 ???????1 solutions Answer 327115 by stanbon(57342)   on 2011-08-02 17:31:53 (Show Source): You can put this solution on YOUR website!Let μ = 160 and σ = 16. Find the z-score for the score 180 = 1.25 Find the z-score for the score 150 = -0.625 ------ For the following problems, since z = (x-u)/s, x = zs + u -------------- Find the score x if the z-score = 1 x = 1*16 + 160 = 176 -------------------------- Find the score x if the z-score = x = −0.875 x = -0.875*16+160 = 146 ========================== Cheers, Stan H. ============
 Average/477166: two trains running in opposite direction with speeds 30 km/hr and 50km/hr crosees each other in 15 sec.what is the length of the fastest train?1 solutions Answer 327097 by stanbon(57342)   on 2011-08-02 16:17:42 (Show Source): You can put this solution on YOUR website!two trains running in opposite direction with speeds 30 km/hr and 50km/hr cross each other in 15 sec. what is the length of the fastest train? --- Combined speed = 80 (km/hr)(hr/3600 sec)(1000 m/km) = 22.22 meters.sec ---- 15(22.22) = 333.33 meters in 15 seconds ----- Equation: The ratio of the trains speeds is 5:3 5x + 3x = 333.33 8x = 333.33 x = 41.666. 5x = 208.33 meters (length of the faster train) ----- Cheers, Stan H.
 Points-lines-and-rays/477162: Find the equations for each of the following: a. The line containing P(3,0)and perpendicular to the x-axis b. The line containing P(-4,5)and parallel to the x-axis1 solutions Answer 327095 by stanbon(57342)   on 2011-08-02 16:01:38 (Show Source): You can put this solution on YOUR website!Find the equations for each of the following: a. The line containing P(3,0)and perpendicular to the x-axis Plot the point. Then draw the vertical thru the point. Do you see that it passes thru all points where x = 3? Equation: x = 3 ----------------------- b. The line containing P(-4,5)and parallel to the x-axis Plot the point. Draw a line thru it parallel to the x-axis. Do you see that it passes thru all the points where y = 5? Equation: y = 5 ======================== Cheers, Stan H.
 Expressions-with-variables/477131: I am trying to find the method of solving: ((x^2 + 4x) / (x^2 + 4)) * ((x + 2)^2 / x^2) = ((x + 4)(x + 2)^2) / (x^3 + 4x) I have tried simplifying and factoring. Though I do not end up with the correct answer.1 solutions Answer 327088 by stanbon(57342)   on 2011-08-02 14:44:55 (Show Source): You can put this solution on YOUR website!I am trying to find the method of solving: ((x^2 + 4x) / (x^2 + 4)) * ((x + 2)^2 / x^2) = ((x + 4)(x + 2)^2) / (x^3 + 4x) ------- ((x(x+4)) / (x^2 + 4)) * ((x + 2)^2 / x^2) = ((x + 4)(x + 2)^2) / (x(x^2+4)) ----- Cancel where you can: = (((x+4)) / (x^2 + 4)) * ((x + 2)^2 / x) = ((x + 4)(x + 2)^2) / (x(x^2+4)) ------ Multiply thru by x(x^2+4) to get: = (x+4)+(x+2)^2) = (x+4)(x+2)^2 ---- Solution: True for all Real Numbers except x = 0 =========================== Cheers, Stan H. ==============
 real-numbers/477132: how can i multiply 30%(-0.8)1 solutions Answer 327085 by stanbon(57342)   on 2011-08-02 14:31:39 (Show Source): You can put this solution on YOUR website!multiply 30%(-0.8) ---- = (30/100)(-8/10) --- = (3/10)(-8/10) ---- = -24/100 ---- = -0.24 ================ Cheers, Stan H.
 Functions/477133: Given the function evaluate f(3). I did: =54+3 =57 so f(x)=57? Did I do that right? 1 solutions Answer 327084 by stanbon(57342)   on 2011-08-02 14:29:35 (Show Source): You can put this solution on YOUR website!f(x) = 2x^2+3x-5 evaluate f(3) ---------- f(3) = 2*3^2 + 3*3 - 5 --- f(3) = 18 + 9 - 4 --- f(3) = 23 ============== Cheers, Stan H. ==============
 Travel_Word_Problems/477137: If you are taking a 350-mile trip and for 70 miles you average 35 mph and the rest is at an average of 50 mph, how long will it take you to arrive at your destination? 1 solutions Answer 327083 by stanbon(57342)   on 2011-08-02 14:26:23 (Show Source): You can put this solution on YOUR website!If you are taking a 350-mile trip and for 70 miles you average 35 mph and the rest is at an average of 50 mph, how long will it take you to arrive at your destination? ------- Note: time = distance/rate ---- Equation: Total time = 70/35 + (350-70)/50 Total time = 2 + (280/50) Total time = 2 + 5.6 = 7.6 hrs. ============================= Cheers, Stan H.
 Exponents/477138: what is -(2p) squared, where p= 7?1 solutions Answer 327082 by stanbon(57342)   on 2011-08-02 14:21:45 (Show Source): You can put this solution on YOUR website!what is -(2p) squared, where p= 7? ---- = -(2*7)^2 --- = -(14)^2 --- = - 196 ============ Cheers, Stan H. ============
 Radicals/477136: Express in terms of i. - sqrt - 4961 solutions Answer 327081 by stanbon(57342)   on 2011-08-02 14:19:42 (Show Source): You can put this solution on YOUR website!Express in terms of i. - sqrt - 496 --- = -isqrt(496) = -4isqrt(31) ================ Cheers, Stan H. ================
 Rate-of-work-word-problems/477134: If one person can fill a pool in 30min another in 45min and another in 90min how long would it take if they all work together. i know the answer is 15 but i dont know the equation used to get the answer.1 solutions Answer 327080 by stanbon(57342)   on 2011-08-02 14:17:25 (Show Source): You can put this solution on YOUR website!If one person can fill a pool in 30min another in 45min and another in 90min how long would it take if they all work together. i know the answer is 15 but i dont know the equation used to get the answer. ---- Equation: rate + rate + rate = together rate 1/30 + 1/45 + 1/90 = 1/x ------ Multiply thru by 90x to get: 3x + 2x + x = 90 6x = 90 x = 15 minutes ==================== Cheers, Stan H.
 Inequalities/477135: 2x + 2>= 5x+ 11, then x a. x<= -3 b. x >= 12 c. x >= -3 d. x>= 31 solutions Answer 327079 by stanbon(57342)   on 2011-08-02 14:13:15 (Show Source): You can put this solution on YOUR website!2x + 2>= 5x+ 11, then x --- Subtract 2x from both sides: Subtract 11 from both sides: -9 >= 3x x <= -3 ------------------- Cheers, Stan H. =================== a. x<= -3 b. x >= 12 c. x >= -3 d. x>= 3
 Linear-equations/477054: equation of the line that passes through (5, 3) and is parallel to the line y = -2x + 21 solutions Answer 327060 by stanbon(57342)   on 2011-08-02 10:33:40 (Show Source): You can put this solution on YOUR website!equation of the line that passes through (5, 3) and is parallel to the line y = -2x + 2 Since the given line has a slope of -2 the parallel line must have a slope of -2. ---- Equation Form: y = mx + b -- You have x,y and m; solve for "b": 3 = -2*5 + b b = 3+10 b = 13 ---- Equation you want: y = -2x+13 ====================== cheers, Stan H. ======================
 Linear-equations/477041: Okay so I have two questions. I have tried to work them both the way our examples showed and the way a friend of mine showed and I cannot get the answer right. Please help I want to understand what I am doing wrong so I can finally get this right. Find the intercepts and then use them to graph the equation. 5y-15=5x Find the slope if it exists. y=-6x+81 solutions Answer 327057 by stanbon(57342)   on 2011-08-02 10:25:04 (Show Source): You can put this solution on YOUR website!Find the intercepts and then use them to graph the equation. 5y-15=5x Divide thru by 5 to simplify the work. y-3 = x Solve for "y": y = x+3 --- To get the intercepts: x-int?: Let y = 0, then x = -3 y-int?: Let x = 0, the y = 3 ---- Plot the intercepts and draw a lint thru them: Plot: (-3,0) and (0,3) Graph: ============================================== Find the slope if it exists. y=-6x+8 Since the equation is already in slope-intercept form, slope = -6 ================== cheers, Stan H.
 test/477044: solve t^2 + 4t = 11 solutions Answer 327056 by stanbon(57342)   on 2011-08-02 10:19:03 (Show Source): You can put this solution on YOUR website!solve t^2 + 4t = 1 t^2 + 4t -1 = 0 Use the Quadratic Formula: t = [-b +- sqrt(b^2-4ac)]/(2a) --- t = [-4 +- sqrt(16-4*1*-1)]/2 --- t = [-4 +- sqrt(20)]/2 --- t = [4 +- 2sqrt(5)]/2 --- t = 2+sqrt(5) or t = 2-sqrt(5) ================================= Cheers, Stan H. ==========
 Money_Word_Problems/477052: Miranda's financial aid stipulates that her tuition not exceed \$1500. If her college charges a \$90 registration fee pluss \$250 per course, What is the greatest number of courses for which Miranda can register?1 solutions Answer 327054 by stanbon(57342)   on 2011-08-02 10:14:53 (Show Source): You can put this solution on YOUR website! Miranda's financial aid stipulates that her tuition not exceed \$1500. If her college charges a \$90 registration fee pluss \$250 per course, What is the greatest number of courses for which Miranda can register? ---- Solve: 90+250x <= 1500 250x <= 1410 x <= 5.64 --- round down to get # of courses = 5 ============ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/477048: Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 13% protein ?1 solutions Answer 327052 by stanbon(57342)   on 2011-08-02 10:11:39 (Show Source): You can put this solution on YOUR website!Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 13% protein ? ------ Equation: protein + protein = protein 0.16s + 0.08(320-s) = 0.13*320 --- Multiply thru by 100 to get: 16s + 8*320 - 8s = 13*320 8s = 5*320 s = 5*40 Amount of soybean meal needed is 200 lb Amount of cornmeal needed is 120 lb =========================== Cheers, Stan H.
 test/477045: . A person spins the pointer and is awarded the amount indicated by the pointer. pointer landed on \$2 1/2 is \$2, 1/4 is \$8, 1/4 is \$5 It costs \$6 to play the game. Determine: • The expectation of a person who plays the game. • The fair price to play the game. 1 solutions Answer 327050 by stanbon(57342)   on 2011-08-02 10:06:48 (Show Source): You can put this solution on YOUR website!A person spins the pointer and is awarded the amount indicated by the pointer. pointer landed on \$2 1/2 is \$2, 1/4 is \$8, 1/4 is \$5 It costs \$6 to play the game. Determine: • The expectation of a person who plays the game. --- E(gain) = (1/2)2+(1/4)8+(1/4)5-6 --- E(gain) = 1 + 2 + 5/4 - 6 E(gain) = 4.25 - 6 = -\$1.75 --- The player can expect to lose \$1.75 each time he plays the game. --- • The fair price to play the game. The fair price would be \$4.25 to play the game. ============== Cheers, Stan H.
 Probability-and-statistics/477047: Hi you all I really need help with this question.....Scores on the Standford-Binet I ntelligence scale have a mean of 100 and a standard deviation of 16, and are presuemd to be normally distributed. A person who scores 84 on this scale has what percentile rank within the population? Show all work as to how this is obtained. I dont even no where to begin or how can someone please help me and direct me with this question please!!!!!!!1 solutions Answer 327047 by stanbon(57342)   on 2011-08-02 09:57:59 (Show Source): You can put this solution on YOUR website!Scores on the Standford-Binet Intelligence scale have a mean of 100 and a standard deviation of 16, and are presumed to be normally distributed. A person who scores 84 on this scale has what percentile rank within the population? ---- z(84) = (84-100)/16 = -1 --- P(x < 84) = P(z < -1) = 0.1587 ---- So 15.87% of the population has a score less than 84. --- The person has percentile score of 15.87%ile or 16%ile if you found up. ==================== Cheers, Stan H.
 Subset/477027: what is the answer in (12+3)^2(4-2^2)+5(20/5)-21?1 solutions Answer 327039 by stanbon(57342)   on 2011-08-02 08:16:00 (Show Source): You can put this solution on YOUR website! (12+3)^2(4-2^2)+5(20/5)-21? --- (15^2)*(0) + 5(4)-21 --- = 0+20-21 --- = -1 ============== Cheers, Stan H.
 Equations/477028: Please help. Thanks. Simplify. Please show all of your work. 3c^2+4c+4-(c-6c^2-8) ---- 3c^2+4c+4-c+6c^2+8 ---- 9c^2+3c+12 ================== cheers, Stan H. 1 solutions Answer 327037 by stanbon(57342)   on 2011-08-02 08:13:19 (Show Source): You can put this solution on YOUR website!3c^2+4c+4-(c-6c^2-8) ---- 3c^2+4c+4-c+6c^2+8 ---- 9c^2+3c+12 ================== cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/477026: Twice the smallest of three consecutive even integers is four more than the largest. Find the integers.1 solutions Answer 327036 by stanbon(57342)   on 2011-08-02 08:10:32 (Show Source): You can put this solution on YOUR website!Twice the smallest of three consecutive even integers is four more than the largest. Find the integers. ---- 1st: 2x-2 2nd: 2x 3rd: 2x+2 ---- Equation: 2(2x-2) = 2x+2 + 4 --- 4x-4 = 2x+6 2x = 10 x = 5 --- 1st: 2x-2 = 8 2nd: 2x = 10 3rd: 2x+2 = 12 ================== Cheers, Stan H. ---------
 Geometry_proofs/477025: prove the identity: (1-tan'squared'a)/(1+tan'squared'a)= cos'squared'a-sin'squared'a1 solutions Answer 327035 by stanbon(57342)   on 2011-08-02 08:06:51 (Show Source): You can put this solution on YOUR website!prove the identity: (1-tan'squared'a)/(1+tan'squared'a)= cos'squared'a-sin'squared'a ------------------- (1-tan^2(a))/(1+tan^2(a)) ---- (1-(sin/cos)^2)/(1+sin/cos)^2) ---- [(cos^2-sin^2)/cos^2)]/[(cos^2+sin^2)/cos^2)] ----- Invert the denominator and multiply to get: [(cos^2-sin^2)/cos^2)]/[cos^2/(cos^2+sin^2)] --- Cancel the cos^2 factors and convert cos^2+sin^2 to 1 to get: --- = cos^2-sin^2 Which is the right side of your original problem. ==================== Cheers, Stan H. ==============
 Probability-and-statistics/477024: a traffic light is red for 25 sec, yellow for 5 sec, and green for 55 sec. What is the probability that when you reach the light, the light is yellow1 solutions Answer 327033 by stanbon(57342)   on 2011-08-02 07:58:47 (Show Source): You can put this solution on YOUR website!a traffic light is red for 25 sec, yellow for 5 sec, and green for 55 sec. What is the probability that when you reach the light, the light is yellow --- yellow time: 5 sec total recycle time: 85 sec --- P(yellow) = 5/85 = 1/17 ============================== Cheers, Stan H.
 Probability-and-statistics/476892: To people are selected from 6 freshman and 8 sophomores. Find the probability both are freshman or both are sophomores. 1 solutions Answer 326967 by stanbon(57342)   on 2011-08-01 21:45:54 (Show Source): You can put this solution on YOUR website!Two people are selected from 6 freshman and 8 sophomores. Find the probability both are freshman or both are sophomores. ---- P(2 frosh or 2 soph) = P(2frosh) + P(2soph) --- = [6C2 + 8C2]/14C2 ---- = [15 + 28]/91 --- = 43/91 ======================== Cheers, Stan H.
 Equations/476922: x^2+2x−15=01 solutions Answer 326966 by stanbon(57342)   on 2011-08-01 21:34:04 (Show Source): You can put this solution on YOUR website!x^2+2x−15=0 (x+5)(x-3) = 0 x = -5 or x = 3 ---------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/476918: The number of toys in the closet varies inversely with the number of children in the room. If there are 15 toys in the closet when there are 3 children in the room, how many toys are in the closet when 5 children are in the room ?1 solutions Answer 326965 by stanbon(57342)   on 2011-08-01 21:31:36 (Show Source): You can put this solution on YOUR website!The number of toys in the closet varies inversely with the number of children in the room. --- t = k/c --- Solve for "k" using "If there are 15 toys in the closet when there are 3 children in the room" 15 = k/3 k = 45 --- Equation: t = 45/c --- How many toys are in the closet when 5 children are in the room ? t = 45/5 # of toys = 9 ======================= Cheers, Stan H.
 Age_Word_Problems/476920: Maria is 6yrs older than John, John is twice as old as Michael? if all their ages are added together it could be 102 how old is maria1 solutions Answer 326962 by stanbon(57342)   on 2011-08-01 21:24:42 (Show Source): You can put this solution on YOUR website!Maria is 6yrs older than John, John is twice as old as Michael? If all their ages are added together it could be 102 how old is maria ----------------------- Equations: m = j + 6 j = 2k m + j + k = 102 ---- Substitute and solve for "j": j+6 + j + j/2 = 102 --- (5/2)j = 96 j = (2/5)*96 j = 38.4 --- Maria = j+6 = 44.4 yrs old ---------------------- Cheers, Stan H. ===============
 Mixture_Word_Problems/476913: Someone please help and show me how to figure this--How many ounces of water should be added to 4g of 1:4 solution to make a 1:6 solution?1 solutions Answer 326958 by stanbon(57342)   on 2011-08-01 21:14:22 (Show Source): You can put this solution on YOUR website!How many ounces of water should be added to 4g of 1:4 solution to make a 1:6 solution? ------------- A 1:4 solution is 1/5 = 20% active ingrediant and 4/5 = 80% water --- A 1:6 solution is 1/7 = 14.29% active and 6/7 = 85.71% water ----- Equation: water + water = water x + 0.8*4 = 0.8571(x+4) ----- Multiply thru by 10,000 to get: 10000x + 800*4 = 8571x + 8571*4 --- 1429x = 7771*4 x = 21.7523 grams (amt of water to be added) ======================== Cheers, Stan H.
 Finance/476903: Each Sunday a newspaper agency sells x copies of a certain newspaper for \$1 per copy. The cost to the agency of each newspaper is \$0.50. The agency pays a fixed cost of storage, delivery and so on, of \$100 per Sunday. 1. How many newspapers need to be sold to break even? a) 100 c) 250 b) –200 d) 200 2. What is the profit for the agency if 150 newspapers sold for a particular Sunday? a) – 25 c) 25 b) – 150 d) 175 3. How many newspapers should the agency sell in order to realize a minimum profit of \$600? a) x = 1400 c) x = 600 b) x = 200 d) x = 1000 Is the answers as follows: can you please help me verify, Thank you 1. D (200) 2. A (-25) 3. A (x=1400) 1 solutions Answer 326953 by stanbon(57342)   on 2011-08-01 21:00:16 (Show Source): You can put this solution on YOUR website!Each Sunday a newspaper agency sells x copies of a certain newspaper for \$1 per copy. The cost to the agency of each newspaper is \$0.50. The agency pays a fixed cost of storage, delivery and so on, of \$100 per Sunday. 1. How many newspapers need to be sold to break even? Income = \$x of x newpapers Cost = 0.5x+100 ---- solve x = 0.5x+100 0.5x = 100 x = 200 -------------------------- a) 100 c) 250 b) –200 d) 200 ========================================== 2. What is the profit for the agency if 150 newspapers sold for a particular Sunday? Income = 150 dollars Cost = 0.5*150+100 = 175 Profit = -25 a) – 25 c) 25 b) – 150 d) 175 =========================================== 3. How many newspapers should the agency sell in order to realize a minimum profit of \$600? Profit = 0.5x-100 Solve 0.5x-100 = 600 0.5x = 700 x = 1400 a) x = 1400 c) x = 600 b) x = 200 d) x = 1000 Is the answers as follows: can you please help me verify, Thank you 1. D (200) 2. A (-25) 3. A (x=1400) ===================== All alright. Cheers, Stan H.
 Polygons/476900: If a pyramid has an octagon for a base, how many lateral faces does it have?1 solutions Answer 326952 by stanbon(57342)   on 2011-08-01 20:52:27 (Show Source): You can put this solution on YOUR website!If a pyramid has an octagon for a base, how many lateral faces does it have? --- Ans: eight ============== cheers, Stan H.