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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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 Finance/729463: Find the amount if \$500 is invested at 15% compounded monthly for 17 months. Amount = \$ 1 solutions Answer 445879 by stanbon(57387)   on 2013-03-22 15:16:13 (Show Source): You can put this solution on YOUR website!Find the amount if \$500 is invested at 15% compounded monthly for 17 months. --------- A(t) = P(1+(r/n))^(nt) --- A(17/12) = 500(1+(0.15/12))^(12(17/12) ----- A(17/12) = 500(1.0125)^(17)= \$617.57 ------------------------ Cheers, Stan H. =================
 Polynomials-and-rational-expressions/729474: please show me the work for this problem. (3x-2)(x2-6x +5)1 solutions Answer 445878 by stanbon(57387)   on 2013-03-22 15:06:28 (Show Source): You can put this solution on YOUR website!(3x-2)(x2-6x +5) --------------- = 3x(x^2-6x+5) - 2(x^2-6x+5) ------ = 3x^3 - 18x^2 + 15x - 2x^2 + 12x - 10 ----- = 3x^3 -20x^2 +27x - 10 ============= Cheers Stan H.
 Age_Word_Problems/729473: brittany is 5 years older than three times the age of her brother. The sum of their ages is 21. if x represents the age of her brother, write an equation that represents this situation1 solutions Answer 445877 by stanbon(57387)   on 2013-03-22 15:01:33 (Show Source): You can put this solution on YOUR website!brittany is 5 years older than three times the age of her brother. The sum of their ages is 21. if x represents the age of her brother, write an equation that represents this situation ----- Equations: t = 3b + 5 t + b = 21 ------- Substitute for "t" and solve for "b": 3b+5+b = 21 4b = 16 Brother's age = 4 years Brit's age = 3*4+5 = 17 years ============================== Cheers, Stan H
 percentage/729471: Can you please help me with this? Thank you so much for your time! Tyrone pays \$5 for a lottery ticket. There is a .1% chance that he will win \$200, a 1% chance that he will win \$50, and a 5.2% chance that he will win \$25 (Otherwise he wins nothing). Find his expected payoff. How much can he expect to win or lose on average? Don't forget to include the price of the ticket!1 solutions Answer 445871 by stanbon(57387)   on 2013-03-22 14:51:32 (Show Source): You can put this solution on YOUR website!Tyrone pays \$5 for a lottery ticket. There is a .1% chance that he will win \$200, a 1% chance that he will win \$50, and a 5.2% chance that he will win \$25 (Otherwise he wins nothing). Find his expected payoff. How much can he expect to win or lose on average? Don't forget to include the price of the ticket! ----- Random Winning values: ......195......45.....20.........-5 Probabilities::::::::: .......1/100...1/100..5.2/100...92.8/100 -------------- Expected winnings = [195 + 45 + 104 -464]/100 = -120/100 = -\$1.20 ------------------- Cheers, Stan H. ===================
 Probability-and-statistics/729303: Two dice are rolled in a game you pay \$1.00 to play. If a total lower than 5 comes up, you win \$5.00, if a total greater than 9 comes up you win \$2.00, otherwise you lose your dollar for playing. Calculate the expected value of playing,and the price of the game making it fair. Good luck, I'm not einstein.1 solutions Answer 445809 by stanbon(57387)   on 2013-03-21 22:50:55 (Show Source): You can put this solution on YOUR website!Two dice are rolled in a game you pay \$1.00 to play. -------------------------------------------------------- If a total lower than 5 comes up, you win \$5.00, ways to do that: 1/1,1/2,1/3,2/1,2/2,3/1 -----6 ways -------------------------------------------------------- if a total greater than 9 comes up you win \$2.00, Ways to do that: 4/6----------------------1 5/5,5/6------------------2 6/4,6/5,6/6--------------3 Total-----------------------------------------6 ways otherwise you lose your dollar for playing. Total-----------------------------------------24 ways =========================================================== Calculate the expected value of playing, Random Value:.....\$4......\$1......-1 Probabilities.....1/6.....1/6.....4/6 ---- Expected gain: (4 + 1 - 4)/6 = 1/6 or 16 2/3 cents -------- and the price of the game making it fair. You should pay \$1.67 to play Then your expected winning would be zero and the game would be fair. ================================ Cheers, Stan H
 Probability-and-statistics/729292: 3. A box contains 40 computer disks, 5 of which are defective. Three disks are selected from the box (without replacement and regard to order). What is the probability that (a) all three of the disks are defective? (b) none of the three disks are defective? (c) exactly one of the three disks is defective? (d) at least one of the three disks works? 1 solutions Answer 445808 by stanbon(57387)   on 2013-03-21 22:31:52 (Show Source): You can put this solution on YOUR website!A box contains 40 computer disks, 5 of which are defective. Three disks are selected from the box (without replacement and regard to order). What is the probability that ------------------------------------ (a) P(all three of the disks are defective) = 5C3/40C3 ----------------------------------------------------- (b) P(none of the three disks are defective) = 35C3/40C3 ----------------------------------------------------- (c) P(exactly one of the three disks is defective) = [5*35*34]/[40*39*38] ============ ================ (d) P(at least one of the three disks works) = 1 - (answer to b) ================= Cheers, Stan H.
 Linear-equations/729289: FIND ANY TWO LINEAR EQUATIONS PASSING THROUGH THE POINT (-1,-1/2). HOW MANY SUCH EQUATIONS ARE POSSIBLE 1 solutions Answer 445800 by stanbon(57387)   on 2013-03-21 22:09:13 (Show Source): You can put this solution on YOUR website! FIND ANY TWO LINEAR EQUATIONS PASSING THROUGH THE POINT (-1,-1/2). HOW MANY SUCH EQUATIONS ARE POSSIBLE ----- Form: y = mx + b --- Let the slope be "m". Solve for "b": -1/2 = m(-1) + b b = m-(1/2) ----- Equation: y = mx + m-1/2) ---- y = m(x+1)-(1/2 ==================== Cheers, stan H. ================
 Exponential-and-logarithmic-functions/729290: How do I solve f(x)= (x-4)^2 where x is less than equal to 4? I'm having trouble solving and finding the domain?1 solutions Answer 445799 by stanbon(57387)   on 2013-03-21 22:05:47 (Show Source): You can put this solution on YOUR website! How do I solve f(x)= (x-4)^2 where x is less than equal to 4? I'm having trouble solving and finding the domain? ------- You can graph it but you can't "solve" it. ---------------------------------- The graph looks like the left-half of a parabola with vertes at (4,0) and opening upward. ---------------------------- If x is less than or equal to 4, that IS the domain. ---- Cheers, Stan H. ================
 Geometry_proofs/729283: Suppose tanθ=-3/4 and π/2<θ<π. Evaluate the five remaining trigonometric functions of θ.1 solutions Answer 445797 by stanbon(57387)   on 2013-03-21 22:02:30 (Show Source): You can put this solution on YOUR website!Suppose tanθ=-3/4 and π/2<θ<π. Evaluate the five remaining trigonometric functions of θ. ---- Theat is in QII where x is negative, y is positive, r is always positive. ---- Since tan(theta) = y/x = -3/4, y = 3 and x = -4 --- Then r = sqrt(3^2 + 4^2] = 5 ---- sin = y/r = 3/5 cos = x/r = -4/5 tan = -3/4 csc = r/y = 5/3 sec = r/x = -5/4 cot = -4/3 ============ Cheers, Stan H.
 Money_Word_Problems/729280: 6600 is compounded semiannually at a rate of 60% for 18 years?1 solutions Answer 445796 by stanbon(57387)   on 2013-03-21 21:53:08 (Show Source): You can put this solution on YOUR website!6600 is compounded semiannually at a rate of 60% for 18 years? ------ A(18) = 6600(1+(0.60/2))^(2*18) --- A(18) = \$83,465,842.45 ==================== cheers, Stan H. ===============
 logarithm/729266: Stars of magnitude m are visible through a telescope of minimum diameter d (in inches). the relationship is m=8.8 + 5.1 log d. Round your answer to one decimal place. 1. a telescope with diamter 75 inches can detect a star of magnitude m = ____. 2. a star of magnitude 10.6 can be detected using a telescope with lens diameter d = ______ inches for the firs problem I substituted 75 in for d. m= 8.8 + 5.1 log 75. I then solved for log 75 which is 1.875. m = 8.8 + 5.1(1.875). I then solved for m to be 18.4. the second problem I substituted 10.6 in for m. 10.6 = 8.8 + 5.1 log d. I didn't know what to do or if the first part is correct. Please help.1 solutions Answer 445795 by stanbon(57387)   on 2013-03-21 21:45:45 (Show Source): You can put this solution on YOUR website!Stars of magnitude m are visible through a telescope of minimum diameter d (in inches). the relationship is m(d) = 8.8 + 5.1 log d. Round your answer to one decimal place. 1. a telescope with diamter 75 inches can detect a star of magnitude m(75) = 8.8 + 5.1*log(75) = 18.37 ----------------------------------------- 2. a star of magnitude 10.6 can be detected using a telescope with lens Solve: 10.6 = 8.8+5.1*log(d) 5.1*log(d) = 1.8 log(d) = 0.3529 d = 10^0.3529 = 2.2539 inches ----------------------------------- Cheers, Stan H.
 Probability-and-statistics/729132: A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π=0.25). We would like to find the probability of 75 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor, what value would be used to calculate a z-score? 74.5 75 75.5 25 1 solutions Answer 445792 by stanbon(57387)   on 2013-03-21 21:20:25 (Show Source): You can put this solution on YOUR website!A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π=0.25). We would like to find the probability of 75 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor, what value would be used to calculate a z-score? --------------- 74.5 ; 75 ; 75.5 ; 25 ------- Ans: 74.5 ---------------- Cheers, Stan H.
 Probability-and-statistics/729141: "Suppose 100 customers were surveyed. How many of them rented between 6 and 10 movies?" I don't know how to do that. 1 solutions Answer 445785 by stanbon(57387)   on 2013-03-21 21:09:23 (Show Source): You can put this solution on YOUR website!"Suppose 100 customers were surveyed. How many of them rented between 6 and 10 movies?" I don't know how to do that. --- Ans: insufficient information. Cheers, Stan H.
 Probability-and-statistics/729221: Approximately 40% of the Wisconsin population have type O blood. If 4 persons are selected at random to be donors, find P[at least one type O]. Round your answer to four decimal places. 1 solutions Answer 445782 by stanbon(57387)   on 2013-03-21 20:57:10 (Show Source): You can put this solution on YOUR website!Approximately 40% of the Wisconsin population have type O blood. If 4 persons are selected at random to be donors, find P[at least one type O]. Round your answer to four decimal places. P(at least 1) = 1 - P(none) ----- = 1 - 0.6^4 ----- = 1 - 0.1296 ------- = 0.8704 ==================== Cheers, Stan H. ====================
 Probability-and-statistics/729071: A probability experiment consist of two possible outcomes: Event A and Event B. Event A is 3 times more likely that Event B. Calculate the probability of Event A (rounded to two decimals).1 solutions Answer 445780 by stanbon(57387)   on 2013-03-21 20:48:04 (Show Source): You can put this solution on YOUR website!A probability experiment consist of two possible outcomes: Event A and Event B. Event A is 3 times more likely that Event B. Calculate the probability of Event A (rounded to two decimals). ------ Let P(A) = 3x Let P(B) = x ----- Equation: x + 3x = 1 4x = 1 x = 1/4 (Probability of B) 3x = 3/4 (Probability of A) --------------------------- Cheers, Stan H. ===================
 Mixture_Word_Problems/729079: How many pounds of salted nuts selling at \$1.60 per pound should be mixed with 2 pounds of salted nuts selling for \$2.20 per pound to obtain a mixture selling for \$1.72 per pound? 1 solutions Answer 445689 by stanbon(57387)   on 2013-03-21 16:01:23 (Show Source): You can put this solution on YOUR website! How many pounds of salted nuts selling at \$1.60 per pound should be mixed with 2 pounds of salted nuts selling for \$2.20 per pound to obtain a mixture selling for \$1.72 per pound? ---- Equation: value + value = value 1.6x + 2.2*2 = 1.72(x+2) ----- 160x + 220*2 = 172x + 172*2 ------------------- 12x = 48*2 x = 8 lbs. (amt. of \$1.60 per pound nuts needed) =============== Cheers, Stan H. ===============
 Quadratic_Equations/728609: Stuck and needs help with these math problems please help 1. Solve: x/3 = 3/x-8 2. Solve: 3x + 2/x + 2 - 1 = 2x 3. Solve: (x-2)(x-4)(x+1)<0 4. Solve: 3x/x-5 <51 solutions Answer 445561 by stanbon(57387)   on 2013-03-20 18:46:42 (Show Source): You can put this solution on YOUR website!1. Solve: x/3 = 3/x-8 x(x-8) = 9 x^2-8x-9 = 0 (x-9)(x+1) = 0 x = 9 or x = -1 ========================= 2. Solve: 3x + 2/x + 2 - 1 = 2x (3x+2)/(x+2) - 1 = 2x ----- 3x+2 - (x+2) = 2x(x+2) --- 3x+2 -x-2 = 2x^2+4x 2x^2 +2x + 2 = 0 x^2 + x + 1 = 0 Use the Quadratic formula. =============================== 3. Solve: (x-2)(x-4)(x+1)<0 Draw a Number Line. Plot: x = -1, x = 2, x = 4 --- Test a value in each interval. Test x = -10: -*-*- < 0 true Test x = 0 : -*-*+ < 0 false Test x = 3 : +*-*+ < 0 true Test x = 10 : +*+*+ < 0 false ---- Solution:(-oo,-1)U(2,4) =========== Cheers, Stan H. =============== 4. Solve: 3x/x-5 <5
 Quadratic_Equations/728619: how to factor x^2-7x-301 solutions Answer 445527 by stanbon(57387)   on 2013-03-20 16:06:11 (Show Source): You can put this solution on YOUR website!factor x^2-7x-30 --- Use reverse FOIL: --- x^2 -10x+3x -30 ===== x(x-10)+3(x-10) ----- = (x-10)(x+3) ================ Cheers, Stan H. ===============
 Circles/728616: Please help!!! The circumference of a circular plate is 94.2 centimeters. Find the radius of the plate. Use 3.14 as an approximation1 solutions Answer 445524 by stanbon(57387)   on 2013-03-20 16:03:51 (Show Source): You can put this solution on YOUR website!The circumference of a circular plate is 94.2 centimeters. Find the radius of the plate. Use 3.14 as an approximation ------ C = 2*pi*r ----- 94.2 = 2*(3.14)*r ---- r = 94.2/(6.28) ---- radius = 15 cm =================== Cheers, Stan H. =====================
 Trigonometry-basics/728615: hello, I am confused of which formula to use to find the value of x for tan 24 can you please help me 1 solutions Answer 445521 by stanbon(57387)   on 2013-03-20 15:59:35 (Show Source): You can put this solution on YOUR website!find the value of x for tan 24 ---- Please post the problem as it relates tan(24) to x. Cheers, Stan H.
 Equations/728610: Q=I^2Rt/J Solve for R?1 solutions Answer 445520 by stanbon(57387)   on 2013-03-20 15:57:45 (Show Source): You can put this solution on YOUR website!Q=I^2Rt/J Solve for R? -------------- I^2*Rt = QJ --- R = (QJ)/(I^2*t) ===================== Cheers, Stan H.
 Probability-and-statistics/728322: A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. The top tile in each stack is chosen. Find each probabillity. 1. P(neither is a horse) 2. P(exactly one is a fish) 1 solutions Answer 445517 by stanbon(57387)   on 2013-03-20 15:54:25 (Show Source): You can put this solution on YOUR website! A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. ---------- In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. -------- The top tile in each stack is chosen. Find each probabillity. ---- The events (selecting) are independent. ------- 1. P(neither is a horse) = (19/30)(25/30) = 0.5278 ---------------------------- 2. P(exactly one is a fish) = (1)(8/30) = 8/30 ==================================================== Cheers, Stan H.
 Probability-and-statistics/728559: An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second has a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently on the other. Presume a fire starts near a detector. What is the probability that both will work properly?1 solutions Answer 445515 by stanbon(57387)   on 2013-03-20 15:47:58 (Show Source): You can put this solution on YOUR website!An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second has a heat sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently on the other. Presume a fire starts near a detector. What is the probability that both will work properly? --- Their operation is an independent event. Ans: 0.98*0.95 = 0.931 ======================== Cheers, Stan H. ========================
 Equations/728520: I need to use the discriminant to determine the number and type of solutions for this equation: x^2+2x=-11 Thanks! 1 solutions Answer 445475 by stanbon(57387)   on 2013-03-20 12:48:18 (Show Source): You can put this solution on YOUR website! I need to use the discriminant to determine the number and type of solutions for this equation: x^2+2x=-11 ----- a = 1 b = 2 c = 11 ----- b^2-4ac = 2^2-4*1*11 = 4-44 < 0 --- Since the discriminant is negative there are 2 complex number solutions. ------------ Cheers, Stan H. ==============
 Exponents/728512: Find the power of i (-i)42 Possible answers: A) (-i)2 B) 1 C) i D) -i E) -11 solutions Answer 445474 by stanbon(57387)   on 2013-03-20 12:44:55 (Show Source): You can put this solution on YOUR website!(-i)^42 = (i^3)^(42) = i^(126) = (i^4)^31*i^2 = 1*(-1) = -1 ======================== Cheers, Stan H. ======================== Possible answers: A) (-i)2 B) 1 C) i D) -i E) -1
 Quadratic_Equations/728509: Write a quadratic equation having the given numbers as solutions. 8/5, 5/3 Possible answers: A) 3x2 -40x + 25=0 B) 3x2 + 25x + 40=0 C) 3x2 + 49/5x + 8=0 D) 3x2 -49/5x + 8=0 E) 3x2 + 40x + 25=01 solutions Answer 445472 by stanbon(57387)   on 2013-03-20 12:34:55 (Show Source): You can put this solution on YOUR website!Write a quadratic equation having the given numbers as solutions. 8/5, 5/3 Possible answers: f(x) = k(5x-8)(3x-5) f(x) = k(5x^2-49x+40) Let k = (3/5) Then f(x) = 3x^2 - (3/5)49x + (3/5)40 f(x) = 3x^2 - 29.4x + 24 ----------------- Comment: The optional answers do not match the posted problem. ------ Cheers, Stan H. ===================== A) 3x2 -40x + 25=0 B) 3x2 + 25x + 40=0 C) 3x2 + 49/5x + 8=0 D) 3x2 -49/5x + 8=0 E) 3x2 + 40x + 25=0
 Probability-and-statistics/728372: A hundred squash balls are tested by dropping from a height of 100 inches and measuring the height of the bounce. A ball is “fast” if it rises above 32 inches. The average height of bounce was 30 inches and the standard deviation was ¾ inches. What is the chance of getting a “fast” standard ball? PLEASE PROVIDE A STEP BY STEP SOLUTION FOR BETTER UNDERSTANDING1 solutions Answer 445471 by stanbon(57387)   on 2013-03-20 12:24:35 (Show Source): You can put this solution on YOUR website!A hundred squash balls are tested by dropping from a height of 100 inches and measuring the height of the bounce. A ball is “fast” if it rises above 32 inches. The average height of bounce was 30 inches and the standard deviation was ¾ inches. ------------------- What is the chance of getting a “fast” standard ball? z(32) = (32-30)/(3/4) = 8/3 ------- P(x > 32) = P(z > 8/3) = normalcdf(8/3,100) = 0.0038 ===================== cheers, Stan H. ============