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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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 Probability-and-statistics/575154: 4. The amounts of money requested small business loan applications at GetBuckets Fantake Commercial Savings Bank follows the normal distribution, with a mean of \$70,000 and a standard deviation of \$20,000. What is the probability that the amount requested is \$80,000 or more? a. .3500 b. .3085 c. .2902 d. .5987 5. Using Problem #4, what is the probability the amount requested is between \$65,000 and \$80,000? a. .4500 b. .2902 c. .5987 d. None of the above 1 solutions Answer 369400 by stanbon(57219)   on 2012-02-20 07:26:35 (Show Source): You can put this solution on YOUR website!4. The amounts of money requested small business loan applications at GetBuckets Fantake Commercial Savings Bank follows the normal distribution, with a mean of \$70,000 and a standard deviation of \$20,000. What is the probability that the amount requested is \$80,000 or more? a. .3500 b. .3085 c. .2902 d. .5987 --- normalcdf(80000,10^10,70000,20000) = 0.3085 ===================================================== 5. Using Problem #4, what is the probability the amount requested is between \$65,000 and \$80,000? a. .4500 b. .2902 c. .5987 d. None of the above normalcdf(65000,80000,70000,20000) = 0.2902 ========== Cheers, Stan H. ==========
 Probability-and-statistics/575152: A normal distribution has a mean of 80 and a standard deviation of 14. Compute the probability of a value between 75.0 and 90.0. a. .2022 b. .3595 c. .4017 d. None of the above 1 solutions Answer 369399 by stanbon(57219)   on 2012-02-20 07:21:01 (Show Source): You can put this solution on YOUR website!A normal distribution has a mean of 80 and a standard deviation of 14. Compute the probability of a value between 75.0 and 90.0. a. .2022 b. .3595 c. .4017 d. None of the above --- Using a TI-84 you get: normalcdf(75,90,80,14) = 0.4020 ============= Cheers, Stan H. ==============
 Probability-and-statistics/575155: 10. The Ho and Ha for a given problem are as follows: Ho: Mean or u = 999 Ha: Mean or u NE 999 This is a two-tailed test. a. True b. False c. Not enough information to make a decision on the direction of the tail. d. The direction of the tail is decided after the significance level is settled between the researcher and the sponsor of the research. 1 solutions Answer 369398 by stanbon(57219)   on 2012-02-20 07:18:06 (Show Source): You can put this solution on YOUR website!The Ho and Ha for a given problem are as follows: Ho: Mean or u = 999 Ha: Mean or u NE 999 This is a two-tailed test. a. True b. False c. Not enough information to make a decision on the direction of the tail. d. The direction of the tail is decided after the significance level is settled between the researcher and the sponsor of the research. --- Ha ALWAYS determines the type of test. "not equal to" implies a 2-tail test. Cheers, Stan H.
 Age_Word_Problems/575153: a 48 year old man is two times as old as his son. How old was the father when he was three times as old as his son?1 solutions Answer 369397 by stanbon(57219)   on 2012-02-20 07:16:09 (Show Source): You can put this solution on YOUR website!a 48 year old man is two times as old as his son. How old was the father when he was three times as old as his son? -------------- father = 48 son = 24 ------------------------------- Equation: (48+x) = 3(24+x) 48 + x = 72 + 3x 2x = -24 x = -12 ---- Father was 48-12 = 36 Son was 24-12 = 12 ============================= Cheers, Stan H.
 Angles/575148: Let p, q, and r be the following statements: p: Jamie is on the train. q: Sylvia is at the park. r: Nigel is in the car. Translate the following statement into English: (~q ^ p) arrow ~r (Points : 4) 1 solutions Answer 369396 by stanbon(57219)   on 2012-02-20 07:12:28 (Show Source): You can put this solution on YOUR website!Let p, q, and r be the following statements: p: Jamie is on the train. q: Sylvia is at the park. r: Nigel is in the car. Translate the following statement into English: (~q ^ p) arrow ~r ----- If Sylvia is not at the park and Jamie is on the train then Nigel is not in the car. --------- Cheers, Stan H.
 Travel_Word_Problems/575063: I rowed 20 km up a river that had a steady current in 5 hours and returned downstream in 2.5 hours. How fast would I have rowed the boat in still water, and what is the speed of the current? Let x be the speed of the boat in still water and y the speed of the current (km/h). The speed of the boat going upstream is (x –y) km/h and the speed of the boat going downstream is (x+y) km/h,. 1 solutions Answer 369365 by stanbon(57219)   on 2012-02-19 22:19:19 (Show Source): You can put this solution on YOUR website!I rowed 20 km up a river that had a steady current in 5 hours and returned downstream in 2.5 hours. How fast would I have rowed the boat in still water, and what is the speed of the current? Let x be the speed of the boat in still water and y the speed of the current (km/h). The speed of the boat going upstream is (x –y) km/h and the speed of the boat going downstream is (x+y) km/h,. --- Upstream DATA: distance = 20 km ; rate = (x-y)km/h ; time = 20/(x-y) hr ------------------ Downstream DATA: distance = 20 km ; rate = (x+y)km/h ; time = 20/(x+y) hr ---- Equation: 20/(x-y) = 5 hrs 20/(x+y) = 2.5 hrs --------------------------- x-y = 4 x+y = 8 ____ Add and solve for "x": 2x = 12 x = 6 km/h (boat speed in calm water) ----- Solve for "y": x+y = 8 y = 2 km/h (current speed) ================================ Cheers, Stan H. ===========================
 Polynomials-and-rational-expressions/574911: Can someone please help me sovle this problem...Thanks, find all numbers for which the rational expression is undefined x^2+17 over x^2-2x-31 solutions Answer 369326 by stanbon(57219)   on 2012-02-19 16:12:15 (Show Source): You can put this solution on YOUR website!find all numbers for which the rational expression is undefined x^2+17 over x^2-2x-3 ---- Undefined when that denominator is zero. ---- Solve x^2-2x-3 = 0 Factor: (x-3)(x+1) = 0 Undefined when x = 3 or x = -1 ================================= Cheers, Stan H.
 Rate-of-work-word-problems/574909: If 5 girls and 2 boys work together they can paint a house in a day. Three girls and 6 boys working together can also paint the house in a day. How long would it take one boy to paint the house by himself?1 solutions Answer 369325 by stanbon(57219)   on 2012-02-19 16:07:59 (Show Source): You can put this solution on YOUR website!If 5 girls and 2 boys work together they can paint a house in a day. Three girls and 6 boys working together can also paint the house in a day. How long would it take one boy to paint the house by himself? ----- Let girl rate = g Let boy's rate = b ---- Equations: 5g + 2b = 1 3g + 6b = 1 ------- Multiply thru 1st equation by 3 Multiply thru 2nd equation by 5 -------------------------- 15g + 6b = 3 15g + 30b = 5 ---- Subtract and solve for "b": 24b = 2 b = 1/12 job/day ---- Time for a boy to do the job alone 12 days/job =================================================== Cheers, Stan H.
 Volume/574908: A cube has a volume of 64-cubic inches. What’s the length of one side of the cube? 1 solutions Answer 369324 by stanbon(57219)   on 2012-02-19 16:01:13 (Show Source): You can put this solution on YOUR website!A cube has a volume of 64-cubic inches. What’s the length of one side of the cube? --- Vol = side^3 --- side = Vol^(1/3) ----- Your problem: side = 64^(1/3) = 4 inches ============================ Cheers, Stan H.
 logarithm/574902: 2^(2x)-12*2^(x)+32=0 1 solutions Answer 369323 by stanbon(57219)   on 2012-02-19 15:57:45 (Show Source): You can put this solution on YOUR website!2^(2x)-12*2^(x)+32=0 --- That is a quadratic with variable = 2^x: ---- (2^x)^2 - 12(2^x) + 32 = 0 ----- Let w = 2^x ---- Substitute: w^2 - 12w + 32 = 0 Factor: (w-8)(w-4) = 0 w = 4 or w = 8 ----- Solve for "x": 2^x = 4 implies x = 2 2^x = 8 implies x = 3 ============================ Cheers, Stan H ===========
 Polynomials-and-rational-expressions/574904: I am so stuck on this problem. I need help i need someone to show me the steps so i can understand. Subtract. (-4x^2 + 2x) – (5x^2 +2x^6 +3) 1 solutions Answer 369321 by stanbon(57219)   on 2012-02-19 15:52:29 (Show Source): You can put this solution on YOUR website!I am so stuck on this problem. I need help i need someone to show me the steps so i can understand. Subtract. (-4x^2 + 2x) – (5x^2 +2x^6 +3) ------ -4x^2 + 2x -5x^2 -2x^6 - 3 ---- = -2x^6 -9x^2 + 2x - 3 ================================================================= Cheers, Stan H. ===========
 Geometry_Word_Problems/574903: 1. Find 2 summplementary angles such that the measure of the 1st angle is 34 degrees less than 3 times the measure of the second. I just need to double check on an answer if you could help me out. Thank you!1 solutions Answer 369319 by stanbon(57219)   on 2012-02-19 15:48:45 (Show Source): You can put this solution on YOUR website!Find 2 summplementary angles such that the measure of the 1st angle is 34 degrees less than 3 times the measure of the second. ----- Equations: x = 180-y x = 3y-34 ----- Substitute for "x" and solve for "y": 180-y = 3y -34 4y = 214 y = 53.5 degrees ---- x = 126.5 degrees ===================== Cheers, Stan H.
 test/574818: I have a big test and cannot firqure this out please help A cellular phone company offers a contract for which the cost C, in dollars, of T minutes of telephoning is given by C=0.25(t-600)+50.95, where it is assumed that t is greater then or equal to 600 minutes. What time keeps the cost between \$97.95 and \$123.45? for the cost to be between 97.95 and 123.45 the time must be between and minutes1 solutions Answer 369301 by stanbon(57219)   on 2012-02-19 11:55:51 (Show Source): You can put this solution on YOUR website!C=0.25(t-600)+50.95, where it is assumed that t is greater then or equal to 600 minutes. What time keeps the cost between \$97.95 and \$123.45? ----------- 97.95 <= 0.25(t-600)+50.95 <= 123.45 ---- Subtract 50.95 along the line: ---- 45 <= 0.25(t-600) <=72.50 --- Divide through by 0.25 to get: 180 <= t-600 <= 290 ---- Add 600 along the line: 780 <= t <=890 ================== Cheers, Stan H. ==================
 Travel_Word_Problems/574816: A boat can travel at a speed of 12km / h in still water. If it takes three hours to go 15km upstream and back, find the speed of the current.1 solutions Answer 369299 by stanbon(57219)   on 2012-02-19 11:38:14 (Show Source): You can put this solution on YOUR website!A boat can travel at a speed of 12km / h in still water. If it takes three hours to go 15km upstream and back, find the speed of the current. ----------------------- Upstream DATA: rate = 12-c km/h ; distance = 15 km ; time = 15/(12-c) hrs ------ Downstream DATA: rate = 12+c km/h ; distance = 15 km ; time = 15/(12+c) hrs -------- Equation: time + time = 3 hrs. 15/(12-c) + 15/(12+c) = 3 ----- [15(12+c) + 15(12-c) = 3(144-c^2) ----- 360 = 3(144-c^2 120 = 144-c^2 c^2 = 24 c = 2sqrt(6) km/h (speed of the current) ============== Cheers, Stan H. ===============
 Polynomials-and-rational-expressions/574814: Find all numbers for which the rational expression is undefined: 2/4w+71 solutions Answer 369298 by stanbon(57219)   on 2012-02-19 11:29:26 (Show Source): You can put this solution on YOUR website!Find all numbers for which the rational expression is undefined: 2/(4w+7) --- Undefined when the denominator = 0 ---- Solve: 4w+7 = 0 w = -7/4 ---- So, undefined when w = -7/4 ==================================== Cheers, Stan H.
 Linear-equations/574773: what is the y-intercept of 4x=5y+451 solutions Answer 369275 by stanbon(57219)   on 2012-02-19 09:08:48 (Show Source): You can put this solution on YOUR website!what is the y-intercept of 4x=5y+45 ------ Let x = 0, then 5y+45 = 0 y + 9 = 0 y = -9 --- y-intercept: (0,-9) ========================= Cheers, Stan H.
 Equations/574769: Determine if the following sets are closed under multiplication: a. {0} b. {1, 3, 5, 7, 9,...} c. {0, 1, 2}1 solutions Answer 369274 by stanbon(57219)   on 2012-02-19 09:06:59 (Show Source): You can put this solution on YOUR website!Determine if the following sets are closed under multiplication: a. {0} 0*0 = 0 ; closed under multiplication -------------------- b. {1, 3, 5, 7, 9,...} The product of any 2 odd numbers is an odd number: true So closed under multiplication. --------------------- c. {0, 1, 2} 0*0 or 1 or 2 is 0 1*0 = 0 ; 1*1 = 1 ; but 2*2 = 4 Not closed under multiplication. Cheers, Stan H.
 Age_Word_Problems/574770: one year ago, ram's age was 8 times his son's age.Now his age is equal to square of his son's age .find their present age.1 solutions Answer 369273 by stanbon(57219)   on 2012-02-19 09:03:04 (Show Source): You can put this solution on YOUR website!one year ago, ram's age was 8 times his son's age.Now his age is equal to square of his son's age .find their present age. ------- Equations: r-1 = 8(s-1) r = s^2 ---- Substitute for "r" and solve for "s": s^2-1 = 8s-8 s^2-8s+7 = 0 Factor: (s-7)(s-1) = 0 Acceptable solution: s = 7 yrs (son's age now) ---- r = s^2 = 49 (father's age now) ============== Cheers, Stan H. ===============
 percentage/574772: Need help solving...142 is what % of 460?1 solutions Answer 369272 by stanbon(57219)   on 2012-02-19 08:58:49 (Show Source): You can put this solution on YOUR website!Need help solving...142 is what % of 460? ------ x/100 = 142/460 --- x = 100(71/230) --- x = 7100/230 --- x = 30.87 So 142 is 30.87% of 460 ================== Cheers, Stan H.
 Sequences-and-series/574584: Can someone plz help me. plz show me how to work this problem. adding the polynomials. (1/8x^2 -1/4x -3/8) + (-1/2x^2 -1/4x -1/2)1 solutions Answer 369164 by stanbon(57219)   on 2012-02-18 13:00:01 (Show Source): You can put this solution on YOUR website!adding the polynomials. (1/8x^2 -1/4x -3/8) + (-1/2x^2 -1/4x -1/2) -------- = ((1/8)-(1/2))x^2 + ((-1/4)+(-1/4))x + ((-3/8)+(-1/2)) ------- = (-3/8)x^2 + (-1/2)x + (-7/8) ------- Cheers, Stan H. =======
 Polynomials-and-rational-expressions/574585: Find LCM for: 2x^3, 5x^2, 15xy^21 solutions Answer 369162 by stanbon(57219)   on 2012-02-18 12:51:07 (Show Source): You can put this solution on YOUR website!Find LCM for: 2x^3, 5x^2, 15xy^2 ----- LCM of 2,5,15 is 30 LCM of x^3,x^2,xy^2 is x^3y -------------- Ans: LCM is 30x^3y ====================== Cheers, Stan H. ======================
 Linear-equations/574598: Please help me solve this problem. A total of 508 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?1 solutions Answer 369160 by stanbon(57219)   on 2012-02-18 12:47:58 (Show Source): You can put this solution on YOUR website!Please help me solve this problem. A total of 508 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold? --- Quantity Eq: a + s = 508 Quantity Eq: s = 3a ----- Substitute for "s" and solve for "a": a + 3a = 508 4a = 508 a = 127 (# of adult tickets sold) ------ Solve for "s": s = 3a s = 3*127 s = 381 (# of student tickets sold) ===================================== Cheers, Stan H. ===============
 Triangles/574599: is a tiangle with sides that measure 9 cm, 40cm, and 41 cm a right triangle1 solutions Answer 369159 by stanbon(57219)   on 2012-02-18 12:43:47 (Show Source): You can put this solution on YOUR website!Yes because 41^2 = 9^2 + 40^2 --------------------------------- Cheers, Stan H. =============
 Probability-and-statistics/574592: Show all work. A disc jockey has 7 songs to play. 5 are slow songs, and 2 are fast songs. each song is to be played only once. In how many ways can the disc jockey play the 7 songs if: a)the songs can be played in any order b)the first song must be a slow song and the last song must be a slow song c)the first two songs must be fast songs 1 solutions Answer 369158 by stanbon(57219)   on 2012-02-18 12:32:25 (Show Source): You can put this solution on YOUR website!A disc jockey has 7 songs to play. 5 are slow songs, and 2 are fast songs. each song is to be played only once. In how many ways can the disc jockey play the 7 songs if: a)the songs can be played in any order:: 7! = 5040 --------------------------------------------------------- b)the first song must be a slow song and the last song must be a slow song 1st song: 5 last song: 4 middle 5 songs: 5! --- # = 5*4*5! = 20*120 = 2400 --------------------------------------------------------- c)the first two songs must be fast songs 1st 2 songs: 2 last 5 songs: 5! --- # = 2*120 = 240 ========================== Cheers, Stan H. ==========================
 Probability-and-statistics/574595: Sow all work. Mary purchased a package of 18 different plants, but she only needed 12 plants for planting. In how many ways can she select the 12 plants from the package to be planted?1 solutions Answer 369156 by stanbon(57219)   on 2012-02-18 12:26:05 (Show Source): You can put this solution on YOUR website!Mary purchased a package of 18 different plants, but she only needed 12 plants for planting. In how many ways can she select the 12 plants from the package to be planted? ----- Ans: 18C12 = 18C6 = 18564 =============================== Cheers, Stan H. =============
 Matrices-and-determiminant/574590: 2x-3y+z=2 x-5y+5z=3 3x+y=3z=5 This is a matrices problem I am having difficutl solving it. I need help. Thank You Leticia1 solutions Answer 369154 by stanbon(57219)   on 2012-02-18 12:23:52 (Show Source): You can put this solution on YOUR website!2x-3y+z=2 x-5y+5z=3 3x+y-3z=5 ---------------- This is a matrices problem --- Using the matrix function on my TI-84 I get: x = 3 y = 2 z = 2 ================ Cheers, Stan H.
 Circles/574588: find the center and radius of a circle whose equation is x2-6x+8y-2001 solutions Answer 369150 by stanbon(57219)   on 2012-02-18 12:13:30 (Show Source): You can put this solution on YOUR website!find the center and radius of a circle whose equation is x2-6x+8y-200 = 0 -------------- That is the equation of a parabola, not a circle.
 Sequences-and-series/574587: Find the nth term of the sequence 1 2 5 10... 1 solutions Answer 369149 by stanbon(57219)   on 2012-02-18 12:09:44 (Show Source): You can put this solution on YOUR website!Find the nth term of the sequence 1 2 5 10... Assuming the next term is 17 a(n) = n^2-2n+2 ====================== Cheers, Stan H. =============
 Probability-and-statistics/574574: I really need help!!! thanks Suppose we want to estimate the average number of purchases in a given hour in a local convenience store. Using this example, describe how you would go about determining this average through: a. Drawing a random sample b. Drawing a systematic sample c. Drawing a convenience sample1 solutions Answer 369140 by stanbon(57219)   on 2012-02-18 11:26:14 (Show Source): You can put this solution on YOUR website!Answer: a Cheers, Stan H.
 Probability-and-statistics/574576: A machine has 9 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. 1 solutions Answer 369138 by stanbon(57219)   on 2012-02-18 11:24:52 (Show Source): You can put this solution on YOUR website!A machine has 9 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. ------- Binomial Problem with n = 9 and p(fail) = 0.02 --- P(0<= x <=3) = binomcdf(9,0.02,3) = 0.9993 ============================================ Cheers, Stan H. ==============
 Probability-and-statistics/574577: A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 21 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted1 solutions Answer 369137 by stanbon(57219)   on 2012-02-18 11:22:07 (Show Source): You can put this solution on YOUR website!A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 21 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted ------ Binomial problem with n = 21 and p(defect) = 0.06 --- P(0<= x <=2) = binomcdf(21,0.06,2) = 0.8716 ============== Cheers, Stan H. ==============