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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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 Polynomials-and-rational-expressions/89396: Write the inverse variation equation of the following. Y varies inversely with x and y = 9 when x = 14. 1 solutions Answer 64998 by stanbon(57962)   on 2007-07-21 15:45:01 (Show Source): You can put this solution on YOUR website!Write the inverse variation equation of the following. Y varies inversely with x and y = 9 when x = 14. --------------- Equation form: y=k/x Need to find k if y=9 when x=14. 9 = k/14 k = 126 ----------- INVERSE VARIATION EQUATION: y = 126/x ================== Cheers, stan H.
 Coordinate-system/89407: Determine the domain of the function f(x) = A. all real numbers B. all positive real numbers C. x 6 D. x < 6 1 solutions Answer 64996 by stanbon(57962)   on 2007-07-21 15:39:45 (Show Source): You can put this solution on YOUR website!What is the function; it didn't get posted. Cheers, Stan H.
 Quadratic_Equations/89408: /Word problem to solve - very confused Okay here goes!!! It is a launch of a cannon ball Cannon ball should have initial vertical velocity of 15 feet per second. the cannon is on a hill that is 10 ft high. Keep in mind that the barrel of teh cannon is 4 ft. off the ground (on the hill) and the cannon ball is launched from the top of the cannon. Okay - I need to use the following model: h=-16t^+vt + h h=height v=initial vertical velocity (ft per second) h=inital height (ft) t-time in motion - (seconds) I have to find a function that models the path of the cannon ball Graph of the path Maximum height of the cannon ball above level ground and how long after the cannon ball is launched does it reach its max height i can't believe this - HELP!!!!!!!!!!!!!!!1 solutions Answer 64995 by stanbon(57962)   on 2007-07-21 15:38:28 (Show Source): You can put this solution on YOUR website!Cannon ball should have initial vertical velocity of 15 feet per second. the cannon is on a hill that is 10 ft high. Keep in mind that the barrel of teh cannon is 4 ft. off the ground (on the hill) and the cannon ball is launched from the top of the cannon. Okay - I need to use the following model: h=-16t^+vt + h h=height v=initial vertical velocity (ft per second) h=inital height (ft) t-time in motion - (seconds) I have to find a function that models the path of the cannon ball h(t) = -16t^2 + 15t + 14 ------------------------- Graph of the path ------------------------- Maximum height of the cannon ball above level ground and how long after the cannon ball is launched does it reach its max height Max occurs at time t= -b/2a = -15/-32 seconds H(15/32) = -16(15/32)^2+15(15/32)+14 = 17.516 ft ============= Cheers, Stan H.
 Probability-and-statistics/89212: Here is the 3/3 question i need hlep on. Provide an appropirate responce. A) Describe some situations wher ethe mode is the best average to use to describe data. B) A test can have grades from 0 to 100, inclusive. If 17 students take the test, is the median necessarily 50? Explain show work if possible C) The set of grades from different classes is recorded. In the first class, the mean is 80 and the standard deviation is 2. In the second class, thte mean is 70 and the standard deviation is 5. IN the third class, the mean is 72 and the standard deviation is 4. In which class does it appear that a student is most likely to recieve a grade of 90 or higher? D) Give a normal distribution, is it more likely that a value is within one standard deviation above the mean or within one standard deviation below the mean? or are both equally likely?1 solutions Answer 64993 by stanbon(57962)   on 2007-07-21 15:27:25 (Show Source): You can put this solution on YOUR website!A) Describe some situations where the mode is the best average to use to describe data. A description of typical family income in a country is better described by the mode than by the mean because a few huge income families would skew the mean figure upwards. ------------------------ B) A test can have grades from 0 to 100, inclusive. If 17 students take the test, is the median necessarily 50? Explain show work if possible No, the median is the score below which 50% of the scores lies. --------------------------- C) The set of grades from different classes is recorded. In the first class, the mean is 80 and the standard deviation is 2. In the second class, the mean is 70 and the standard deviation is 5. IN the third class, the mean is 72 and the standard deviation is 4. In which class does it appear that a student is most likely to receive a grade of 90 or higher? For each class find the score below which 90% of the scores lie. First class: score = 82.56 Second class: score = 76.41 Third class: score = 77.13 ----------------- In the second class the student will need a score of 76.41 or better to score in the top 10% of the class. ==================== D) Give a normal distribution, is it more likely that a value is within one standard deviation above the mean or within one standard deviation below the mean? or are both equally likely? It is the same----appoximately 34% ===================== Cheers, Stan H.
 Linear-equations/89406: This question is from textbook In England, sons of members of the Labor Party vote Labor with probability 0.5, vote Conservative with probability 0.4, and vote Liberal with probability 0.1. The probabilities for sons of Conservative Party members are 0.7 Conservative, 0.2 Labor, and 0.1 Liberal. For the sons of Liberals the probabilities are 0.2 Conservative, 0.4 Labor, and 0.4 Liberal. Given these statistics, what is the probability that the grandson of a Liberal will vote Labor?1 solutions Answer 64992 by stanbon(57962)   on 2007-07-21 14:27:32 (Show Source): You can put this solution on YOUR website!In England, sons of members of the Labor Party vote Labor with probability 0.5, vote Conservative with probability 0.4, and vote Liberal with probability 0.1. The probabilities for sons of Conservative Party members are 0.7 Conservative, 0.2 Labor, and 0.1 Liberal. For the sons of Liberals the probabilities are 0.2 Conservative, 0.4 Labor, and 0.4 Liberal. Given these statistics, what is the probability that the grandson of a Liberal will vote Labor? ---------------
 Functions/89379: 3. In captivity, the average life span of a grizzly bear is 9 years more than that of a tiger. The sum of the two average life spans is 41 years. Find the average life span of a tiger in captivity. a. Define the variables. b. Write the expression for the life span of a grizzly bear in terms of the life span of a tiger. c. Write an equation for the sum of their life spans in term of one variable. d. Solve the equation for the life span of a tiger. 4. George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now? a. Define the variables. b. Write an expression for the age of George in terms of Jeannie's age. c. Write an equation for the sum of their ages in 5 years from now. d. Solve the equation for the age of Jeannie now. 5. Mandy begins bicycling west at 20mph. Liz leaves from the same point 1 hour later bicycling west at 30mph. When will she catch up with Mandy? a. Define the variables. b. Make a chart. distance=rate x time Rate Time Distance Mandy 20 t 20t Liz 30 t -1 30(t-1) c. Set the distances equal to one another (they travel the same distance) and solve the equation for t. d. What does t represent? 1 solutions Answer 64979 by stanbon(57962)   on 2007-07-21 12:19:21 (Show Source): You can put this solution on YOUR website!3. In captivity, the average life span of a grizzly bear is 9 years more than that of a tiger. The sum of the two average life spans is 41 years. Find the average life span of a tiger in captivity. a. Define the variables. Let t be tiger's life span and b be the bear's life span. --------------- b. Write the expression for the life span of a grizzly bear in terms of the life span of a tiger. g=t+9 c. Write an equation for the sum of their life spans in term of one variable. t+t+9 = 41 ------------ d. Solve the equation for the life span of a tiger. 2t = 32 t=16 --------------- 4. George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now? a. Define the variables. George's age is g ; Jeannie's age if j. ------------------------- b. Write an expression for the age of George in terms of Jeannie's age. g = j-12 --------------- c. Write an equation for the sum of their ages in 5 years from now. g+5 + j+5 = 50 ----------------- d. Solve the equation for the age of Jeannie now. (j-12)+5 + j+5 = 50 2j - 2 = 50 2j = 52 j = 26 yrs old ------------------------------- 5. Mandy begins bicycling west at 20mph. Liz leaves from the same point 1 hour later bicycling west at 30mph. When will she catch up with Mandy? a. Define the variables Mandy's time is t; Liz's time is t-1. b. Make a chart. distance=rate x time Rate Time Distance Mandy: rate = 20 mph ; time = t ; distance= 20t Liz..: rate = 30 mph ; time = t -1 ; distance = 30(t-1) c. Set the distances equal to one another (they travel the same distance) and solve the equation for t. 20t = 30(t-1) 20t = 30t-30 10t = 30 t = 3 hrs ============================ d. What does t represent? Mandy's time. ================= Cheers, Stan H.
 Numbers_Word_Problems/89358: The price of an item is fiven by p=2x^2-100. Find the polynomial that represents the revenue generated from the sale of x items.1 solutions Answer 64976 by stanbon(57962)   on 2007-07-21 10:45:39 (Show Source): You can put this solution on YOUR website!Revenue = price*quantity Just multiply the price by "x". =========== Cheers, Stan H.
 Linear-equations/89366: Find the equation of this line in slope-intercept form. y = 3x + 2. can anyone explain an easier way to find the slope intercept? 1 solutions Answer 64975 by stanbon(57962)   on 2007-07-21 10:43:07 (Show Source): You can put this solution on YOUR website!It's already in slope-intercept form. Cheers, Stan H.
 Polynomials-and-rational-expressions/89367: 1: \$52 monthly fee plus \$10/hour for court rental 2: No monthly fee but \$9.50/hour for court rental. Let x = hours per month of court rental time. Write a mathematical model representing the total monthly cost, C, in terms of x for the following: 1: C=_________________ 2: C=_________________ How many hours would you have to rent the court so the monthly cost of 1. is less than 2.? Set up an inequality and show your work algebraically using the information in part a. 1 solutions Answer 64974 by stanbon(57962)   on 2007-07-21 10:40:26 (Show Source): You can put this solution on YOUR website!1: \$52 monthly fee plus \$10/hour for court rental 2: No monthly fee but \$9.50/hour for court rental. Let x = hours per month of court rental time. Write a mathematical model representing the total monthly cost, C, in terms of x for the following: 1: C= 52+10x 2: C= 9.5x How many hours would you have to rent the court so the monthly cost of 1. is less than 2.? Set up an inequality and show your work algebraically using the information in part a. 52+10x<9.5x 0.5x< -52 x < -104 This doesn't make much sense; it appears that Plan 1 will never be less costly than plan 2. ============= Cheers, Stan H.
 Coordinate-system/89371: what is the solution of finding the range and the domain in these equations? 1. (x,y)/y=7x-1 2. (x,y)/y=-4x-8 3. y=-8 4. x=1/4 5. (x,y)/y=4x raise to 2 6. ( x,y)/y=-5xsquared+7 7. (x,y)/x=ysquared+3 i hope you'll answer it immediately because i need it now. thank you.1 solutions Answer 64972 by stanbon(57962)   on 2007-07-21 10:30:57 (Show Source): You can put this solution on YOUR website!what is the solution of finding the range and the domain in these equations? 1. (x,y)/y=7x-1 Domain is all Real numbers; Range is all Real numbers 2. (x,y)/y=-4x-8 Domain and Range are all Real numbers 3. y=-8 Domain is all Real numbers; Range is {-8} 4. x=1/4 Domain is {1/4}; Range is all Real numbers 5. (x,y)/y=4x raise to 2 Domain is all Real numbers: Range is all Real >=0 6. ( x,y)/y=-5xsquared+7 Domain is all Real numbers : Range is all Real <=0 7. (x,y)/x=ysquared+3 Domain is all Real numbers >=3; Range is all Real numbers ======== Cheers, Stan H.
 Quadratic_Equations/89374: Find the x intercepts y=x^2-2x+4 Thanks for any help1 solutions Answer 64970 by stanbon(57962)   on 2007-07-21 10:18:44 (Show Source): You can put this solution on YOUR website!Find the x intercepts y=x^2-2x+4 ----------- Let y=0 and solve for "x". x^2-2x+4=0 x=[2+-sqrt(4-4*4)]/2 x=[2+-sqrt(-12)]/2 x=[1+-isqrt(3)] x=[1+isqrt3] or x=[1-isqrt3]/ ==================== Cheers, Stan H.
 Polynomials-and-rational-expressions/89347: I need help with this problem Add. express your answer in simplist form X-13/X^2-X-12+3x-3/x^2-X-12 Thank you1 solutions Answer 64924 by stanbon(57962)   on 2007-07-20 22:27:08 (Show Source): You can put this solution on YOUR website!Use parentheses so we can tell where numerators and denominators begin and end. Cheers, Stan H.
 Inverses/89356: 9x+7=5x-31 solutions Answer 64923 by stanbon(57962)   on 2007-07-20 22:22:55 (Show Source): You can put this solution on YOUR website!9x+7=5x-3 4x = 10 x=5/2 ============ Cheers, Stan H.
 Square-cubic-other-roots/89345: Can you help me with this problem. Find the solution sets for (sqrt2x+1) - (sqrt x) = 11 solutions Answer 64921 by stanbon(57962)   on 2007-07-20 22:19:52 (Show Source): You can put this solution on YOUR website!(sqrt2x+1) - (sqrt x) = 1 ---------- Square both sides to get: 2x+1 -2sqrt(x(2x+1)) + x = 1 Simplify and isolate the remaining radical, as follows: 2sqrt(2x^2+x) =3x Square both sides to get: 4(2x^2+x) = 9x^2 8x^2+4x = 9x^2 x^2-4x=0 x(x-4)=0 x=0 or x=4 Check the answer in the original equation:(sqrt2x+1) - (sqrt x) = 1 Does x=0? : sqrt(1)-sqrt(1)=1 : False Does x=4? ; sqrt(9)-sqrt(4) = 1 : True -------------- Final Answer: x=4 ===================== Cheers, Stan H.
 Numeric_Fractions/89348: Estimate the following sum. 4 1/9 + 7 9/10 + 2 1/7 + 5 7/8 1 solutions Answer 64918 by stanbon(57962)   on 2007-07-20 22:09:16 (Show Source): You can put this solution on YOUR website!Estimate the following sum. 4 1/9 + 7 9/10 + 2 1/7 + 5 7/8 = about 10 + about 10 = about 20 =================================== Cheers, Stan H.
 Money_Word_Problems/89310: \$1,000 is being compounded for 3 years, so your balance on January 1, 2007, is \$1,259.71: FV to the lower n power = PV(1+i)^n = \$1000(1+0.08)^3 = 1259.71 I need some help with this Please. Thanks. 1 solutions Answer 64916 by stanbon(57962)   on 2007-07-20 21:11:56 (Show Source): You can put this solution on YOUR website!What you posted is true. What is your question? Cheers, Stan H.
 Radicals/89354: Okay, I am completely confused here....x^2+18x+81 is a perfect square because (x+9)(x+9), However, I need help with figuring out if x^2-2x-1 is a perfect square, so far I am thinking that it's not? But is it? Please help...Thanks1 solutions Answer 64914 by stanbon(57962)   on 2007-07-20 21:02:25 (Show Source): You can put this solution on YOUR website!No. It would have to be x^2-2x+1 which is (x-1)(x-1) Cheers, Stan H.
 Numbers_Word_Problems/89349: In 1975 the population of the Earth was approximately 4 billion and doubling every 35 years. The formula for the population P in year Y for this doubling rate is P(in billions)=4X2^[(y-1975)/35] What will the population of the US be in 2025 if this growth rate continues1 solutions Answer 64911 by stanbon(57962)   on 2007-07-20 20:40:10 (Show Source): You can put this solution on YOUR website!The formula for the population P in year Y for this doubling rate is P(in billions)=4X2^[(y-1975)/35] What will the population of the US be in 2025 if this growth rate continues ----------- P = 4*2^[(2025-1975)/35] P = 4 * [2.6918000...] P = 10.76720... billion ============== Cheers, stan H.
 Miscellaneous_Word_Problems/89325: how do you do this type of problem? Gary has figured that he needs to take home \$30,400 a year to live comfortably. If the government gets 24% of Gary's income, then what must his income be for him to live comfortably?1 solutions Answer 64905 by stanbon(57962)   on 2007-07-20 20:16:18 (Show Source): You can put this solution on YOUR website!Gary has figured that he needs to take home \$30,400 a year to live comfortably. If the government gets 24% of Gary's income, then what must his income be for him to live comfortably? -------------------------- Let his salary be "x" EQUATION: x - 0.24x = 30,400 (1-0.24)x = 30,400 0.76x = 30,400 x = \$40,000 (Amount of salary he needs) Cheers, stan H.
 Money_Word_Problems/89268: PLEASE HELP!!! I need help with the following question. I am using the formula PMT= iFV/(1+i)^n. However, I can't get to the final answer which I feel is \$2096. Mary and Joe would like to save up \$10,000 by the end of three years from now to buy new furniture for their home. They currently have \$2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be? Show all work for each assignment and explain each step carefully. Thanks in advance - lj 1 solutions Answer 64903 by stanbon(57962)   on 2007-07-20 19:07:09 (Show Source): You can put this solution on YOUR website!I am using the formula PMT= iFV/(1+i)^n. However, I can't get to the final answer which I feel is \$2096. Mary and Joe would like to save up \$10,000 by the end of three years from now to buy new furniture for their home. They currently have \$2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be? -------------------------------- PMT= iFV/(1+i)^n I think the formula should be PMT = iFV/[(1+i)^n -1] FV = \$10,000-2500 = \$7500 n = 3 i = 0.08 ------------- The \$2500 that is in the account in the beginning will grow at a compounded rate of 8% yearly to have a value of 2500(1+0.08)^3 = 3149.28 So the account has to gain an increased value of 10000-3149.28= \$6850.72 Therefore FV = \$6850.72 PMT = 0.08*6850.72/[(1+0.08)^3 - 1] PMT = 548.06 / [1.259712 -1] PMT = \$2110.25 ===================== Cheers, Stan H.
 Polynomials-and-rational-expressions/89270: I need help with this word problem During rush hour, Bill can drive 15 miles using the side roads in the same time that it takes to travel 10 miles on the freeway. If Bills rate on the side roads is 8 miles hour faster than hr rate on the freeway, find his rate in the side roads.1 solutions Answer 64895 by stanbon(57962)   on 2007-07-20 18:19:18 (Show Source): You can put this solution on YOUR website!During rush hour, Bill can drive 15 miles using the side roads in the same time that it takes to travel 10 miles on the freeway. If Bills rate on the side roads is 8 miles hour faster than his rate on the freeway, find his rate in the side roads. ---------------- Side roads DATA: distance = 15 miles ; rate = x+8 mph ; time = d/r = 15/(x+8) ---------------- Freeway DATA: distance = 10 miles ; rate = x mph ; time = d/r = 10/x ----------------- EQUATION: time = time 15/(x+8) = 10/x 15x = 10x+80 5x = 80 x = 16 mph (rate on freeway) x+8 = 24 mph (rate on side roads) ========== Cheers, Stan H.
 Polynomials-and-rational-expressions/89338: solve by completing the square x^2-6x-3=01 solutions Answer 64893 by stanbon(57962)   on 2007-07-20 18:12:23 (Show Source): You can put this solution on YOUR website!solve by completing the square x^2-6x-3=0 --------- x^2-6x + (6/2)^2 = 3+(6/2)^2 x^2-6x+9 = 12 Factor the left side to get: (x-3)^2 = 12 Take the square root of both sides to get: (x-3) = 2sqrt3 or (x-3) = -2sqrt3 Solve for x: x= 3+2sqrt3 or x= 3-2sqrt3 =============== Cheers, Stan H.
 Radicals/89329: I don't know how to do these. I just figured out how to simplify radical expressions, now I need to know how to add, subtr, mult, and divide them. These are example problems: 3 and the sqrt of 8 + 4 and the sqrt of 50 sqrt of 12^2y^3 - the sqrt of 27x^4y 5th root of 4x^3y^4 * 5th root of 8x^2y^3 Sqrt of 3x^3/4y^2 * sqrt of 9x^2/2y^4 sqrt of 3x^4 divided by the sqrt of 9xy^5 1 solutions Answer 64891 by stanbon(57962)   on 2007-07-20 18:05:19 (Show Source): You can put this solution on YOUR website!3 and the sqrt of 8 + 4 and the sqrt of 50 Do you mean 3sqrt8 + 4sqrt50 If it is the problem unfolds this way: =3sqrt4*sqrt2 + 4sqrt25*sqrt2 = 3*2sqrt2 + 4*5sqrt2 = 6sqrt2 + 20sqrt2 = 26sqrt2 ---------------------------------- sqrt of 12^2y^3 - the sqrt of 27x^4y = sqrt(12^2y^2)*sqrty - sqrt(9x^4)*sqrt(3y) = 12y*sqrt(y) - 3x^2*sqrt(3y) ---------------------------------- 5th root of 4x^3y^4 * 5th root of 8x^2y^3 = 5th root (32x^5y^7) = 2xy*5th rt. of y^2 ------------------------------------ Sqrt of 3x^3/4y^2 * sqrt of 9x^2/2y^4 = sqrt[27x^5/8y^6] = [(3/4)x^2/y^3]*sqrt[(3/2)x] ------------------------------------- sqrt of 3x^4 divided by the sqrt of 9xy^5 = [x^2sqrt(3)] /[3y^2sqrt(xy)] Multiply numerator and denominator by sqrt(xy) to get: = [x^2sqrt(3xy)] / [3y^2(xy)] Cancel factors common to numerator and denominator to get: = [xsqrt(3xy)] / [3y^3] ====================== Cheers, Stan H.
 Probability-and-statistics/89327: I need to find the classic probability of rolling a 1 (or any number) out of 8 dice. I'm not looking for the total face value, just the frequency of rolling a 1 out of 8 dice. So, "What is the probability that you will roll a single 1 out of 8 dice?", "What is the probability you will roll two 1s out of 8 dice?" and so on. What I have tried: (when rolling no 1s out of 8 dice) I used: (when rolling a single 1 out of 8 dice) I used: . (when rolling two 1s out of 8 dice) I used: Alternately, I tried the same thing without using powers in my formulas.... but this didn't seem to help. My total probability for the set did not add up to 1, so I think I must be missing a step? Please help!1 solutions Answer 64889 by stanbon(57962)   on 2007-07-20 17:29:42 (Show Source): You can put this solution on YOUR website!Your numbers have taken care of the independent nature of the event but not the mutually exclusive nature of the event. For example getting one "1" on the 8 dice is (1/6)^1(5/6)^7 takes care of getting the "1" on the 1st dice; but getting the one on the 2nd dice is a mututally exclusive event and has the same probability, and the same for a "1" on the 3rd dice etc. So the probability of getting one "1" is 8C1(1/6)(5/6)^7 = 8(1/6)(5/6)^7 ------------ Similarly the probability of getting two "1's" is 8C2(1/6)^2(5/6)^6= 28(1/6)^2(5/6)^6 ----------- If you continue this to 8C8(1/6)^8(5/6)^0 and add up the terms they will add up to one. ============ Cheers, Stan H.
 Radicals/89271: Please help. I'm really confused --I'm trying to simplify these radicals, but I'm lost as to what steps to take. My instructor gives a different method then I learned (I din't even have that down. We have a test and I don't think I'll pass this section unless I get some help. I'm not sure how to key the radical sign on my computor keyboard. Here's a few of the problems (sorry there's more than one, but I need to know the formulas, because I notice that not all problems can be solved just the same way, so here's one of every kind of problem I'm simplifying: The square root of 27x^3y^5 The cubed root 125x^9y^5/8x^3z^12 1/the square root of 5xy^2 2x/the 4th root of 3xy^2 x/3- the square root of x 1 solutions Answer 64878 by stanbon(57962)   on 2007-07-20 13:37:50 (Show Source): You can put this solution on YOUR website!The square root of 27x^3y^5 = [sqrt(9x^2y^4)[sqrt(3xy)] = [3xy^2][sqrt(3xy)] -------------------------- The cubed root 125x^9y^5/8x^3z^12 = cbrt[(125/8)x^6y^3 / z^12]*cbrt[y^2] =[(5/2)x^2y/z^4]*cbrt(y^2) -------------------------- 1/the square root of 5xy^2 Multiply numerator and denominator by sqrt(5x) to get: [sqrt(5x)] / [5xy] --------------- 2x/the 4th root of 3xy^2 Multiply numerator and denominator by 4th root of (3^3x^3y^2) to get: [2x*4th rt of (27x^3y^2)] / [3xy] Cancel the common factor of "x" to get: (2/3)[4th rt of (27x^3y^2)]/[3y] ============= x/[3- sqrt(x)] Multiply numerator and denominator by (3+sqr(x)) to get: [x(3+sqrtx]/[9-x] ================ Cheers, Stan H.
 Quadratic_Equations/89276: Simplify. Express your answer in simplified radical form. sqrt60/sqrt141 solutions Answer 64876 by stanbon(57962)   on 2007-07-20 13:02:35 (Show Source): You can put this solution on YOUR website!(sqrt60) / (sqrt14) = sqrt (30/7) = (1/7)sqrt(210) ======== cheers, Stan H.
 Equations/89296: Simplify the following: 1 3x2 + 4x + 3x2 - 4y 2. (5x - 2y) - (4x + 8y) 3. 3x3(2x2) 4. (-6a3b4)2 Can you PLEASE HELP ME WITH THESE! THANK YOU SO MUCH 1 solutions Answer 64875 by stanbon(57962)   on 2007-07-20 12:56:28 (Show Source): You can put this solution on YOUR website!Simplify the following: 1 3x2 + 4x + 3x2 - 4y = 6x^2 + 4x-4y ------------------- 2. (5x - 2y) - (4x + 8y) = x - 10y ============= 3. 3x3(2x2) = 6x^5 ------------ 4. (-6a3b4)2 = 36z^6b^8 =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/89224: hello, I know the answer to this problem, but I don't know how to figure the whole problem? would you please show me how? x^2-x-6/x^2-4=. I know you times them both by (x+2), but I can't figure out how to get to (x+2). Thanks1 solutions Answer 64859 by stanbon(57962)   on 2007-07-20 10:59:02 (Show Source): You can put this solution on YOUR website!x^2-x-6/x^2-4 Factor where you can to get: =[(x-3)(x+2)] / [(x+2)(x-2)] Cancel the factor common to numerator and denominator to get: = (x+3)(x-2) =========== Cheers, Stan H.