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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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 Radicals/179911: please write (x^2/3 y-1/4)^-4 in the simpliest form.. thanks.. can you please sheps too cuz i dnt understand this and need diretions.. thanks bunches1 solutions Answer 134810 by stanbon(57347)   on 2009-02-03 09:03:07 (Show Source): You can put this solution on YOUR website!write (x^(2/3) y^(-1/4))^-4 in the simplest form ------------------------ 1st: Multiply (2/3) -4 and (-1/4) by -4 to get: = (x^(-8/3) y^(1)) 2nd: Put x^(8/3) in the denominator: = y/[x^(8/3)] ====================== Cheers, Stan H.
 Linear-equations/179900: Solve using method: x=7/2y+5 2x-7y=13 a (-6,11) b (5,13) c (-5,11) d (-4,10) e the system is inconsistent f the system are dependent how did you conclude your answer1 solutions Answer 134804 by stanbon(57347)   on 2009-02-03 07:55:50 (Show Source): You can put this solution on YOUR website!Solve using method: x=(7/2)y+5 2x-7y=13 ------------ Rearrange: y = (2/7)x - (10/7) y = (2/7)x - (13/7) ------------------------ Slopes are the same and intercepts are different, so the lines are parallel. The system has no solution and is called inconsistent. ======================================= Cheers, Stan H. ================================================ a (-6,11) b (5,13) c (-5,11) d (-4,10) e the system is inconsistent f the system are dependent how did you conclude your answer
 Linear-equations/179901: Write an equation of the line that passes through the given point (0,6) and is parallel to 7y-35x=4. Write the answer in slope intercept form: a) y=5x+6 b) y=5x-6 c) -1/6x+4 d) -1/5x+6 e) y=-1/5x+4 explain your answer1 solutions Answer 134803 by stanbon(57347)   on 2009-02-03 07:50:09 (Show Source): You can put this solution on YOUR website!Write an equation of the line that passes through the given point (0,6) and is parallel to 7y-35x=4. Write the answer in slope intercept form. ---------- Form of the equation is y = mx + b You need to find m and b. -------- The given equation can be written in the form y = (35/7)x + (4/7) So the slope is (35/7) = 5 --- You know y = 6 when x = 0 and you know m = 5, so solve for "b" 6 = 5*0 + b b = 6 ------- Equation: y = 5x + 6 ==================== Cheers, Stan H. ====================
 Probability-and-statistics/179875: This question is from textbook Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned? Certainty Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total 0–9 12 8 3 23 10–59 8 4 10 22 60 or more 1 7 11 19 Col Total 21 19 24 64 1 solutions Answer 134802 by stanbon(57347)   on 2009-02-03 07:42:30 (Show Source): You can put this solution on YOUR website!Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned? Certainty Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total 0–9................ 12................ 8.......... 3.......... 23 10–59............... 8................ 4.......... 10......... 22 60 or more.......... 1................ 7.......... 11......... 19 Col Total.......... 21............... 19.......... 24......... 64 --------------------------------- Ho: Row and column factors are independent (not related) Ha: they are dependent ----------------------- Run a Chi-Square test on the 3x3 data set to get: Test Statistic: Chi-Sq. = 14.764 p-value: 0.00522 df= (3-1)(3-1) = 4 --------------------- Conclusion: Since the p-value is less than 1%, Reject Ho The row and column factors are statistically related (dependent). ======================================================= Cheers, Stan H.
 Probability-and-statistics/179859: A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it. 1 solutions Answer 134765 by stanbon(57347)   on 2009-02-02 22:12:43 (Show Source): You can put this solution on YOUR website!A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. --- Ho: p = 1/2 Ha: p > 1/2 ---------------- p-hat = 38/60 = 0.63333... --- Critical value for one-tail z-test with alpha=10% is z=1.28 Reject Ho if test statistic is greater than 1.28 ------------------- Test statistic = z(0.63333) = (0.633333-0.5)/sqrt[(1/2)(1/2)/(60)] = 2.0655 ---------- (b) Calculate a p-value and interpret it. p-value = P(z>2.0655) = 0.01944 Interpretation: Less than 1.944% of test results could provide stronger evidence for rejecting Ho. ====================================== Cheers, Stan H.
 Functions/179845: I got 4 for this equation. Is it correct. -4x-10x=-561 solutions Answer 134739 by stanbon(57347)   on 2009-02-02 20:37:19 (Show Source): You can put this solution on YOUR website!I got 4 for this equation. Is it correct. -4x-10x=-56 ----- Substitute 4 in place of "x" and see if you get a true statement. -------------------------------- -4*4 -10*4 = -56 -16 - 40 = -56 -56 = -56 ----------------------- True, so 4 is a solution ================================ Cheers, Stan H.
 Unit_Conversion_Word_Problems/179837: how many centimeters are in an inch1 solutions Answer 134738 by stanbon(57347)   on 2009-02-02 20:30:35 (Show Source): You can put this solution on YOUR website!how many centimeters are in an inch ------------------ 1 inch = 2.54 cm ----------------- You can find answers for questions like that using Google. Search for inch centimeter and se what you get. Cheers, Stan H.
 Numeric_Fractions/179836: Hello, my daughter and I are working on a few math problems she brought home from school and It's been some time for me to do it without review...One one the problems is: 4/9v=1/4 we need to solve for v is that clear enough? I hope so and thank you so much for your help and the help of this website... Thank You, Seann 1 solutions Answer 134737 by stanbon(57347)   on 2009-02-02 20:19:41 (Show Source): You can put this solution on YOUR website!(4/9)v=1/4 we need to solve for v ------------------------ Multiply both sides by (9/4): (9/4)(4/9)v = (9/4)(1/4) Cancel numbers that are common to a numerator and a denominator. v = 9/16 ===================== Cheers, Stan H.
 Inverses/179838: What is an inverse? Like an inverse of 1,2,3,4? I have never heard of this? That is the question??? 1 solutions Answer 134736 by stanbon(57347)   on 2009-02-02 20:14:13 (Show Source): You can put this solution on YOUR website!What is an inverse? Like an inverse of 1,2,3,4? I have never heard of this? That is the question??? ------- There are two kinds of number inverses. One is the "additive inverse" ; for the number "a" the inverse is "-a" -------------- The other is the "multiplicative inverse" ; for the number "a" the inverse is "1/a". ---------------- Your problem Additive inverses: -1,-1,-3,-4 -------- Multiplicative inverses: 1/1, 1/2, 1/3, 1/4 ============================================== Cheers, Stan H.
 Probability-and-statistics/179831: Please show me how to do these problems and please explains. 1.) A farmer has four sheepdogs and three beagles. If he randomly chooses a dog to accompany him on a walk, what is the probability of him taking a walk with sheepdog? 2.) Gordon spins a spinner with equal-sized sections numbered 1-6. In one spin, what is the likelihood that the spinner will stop on a 1 or a 5? 3.) When two number cubes labeled 1-6 are rolled, what is the probability that the result will be two 4's ? 4.) Joanne is guessing which day in November is Bess's birthday. Joanne know that Bess's birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her first try? Thank you for your help.1 solutions Answer 134735 by stanbon(57347)   on 2009-02-02 20:08:25 (Show Source): You can put this solution on YOUR website!Please show me how to do these problems and please explains. 1.) A farmer has four sheepdogs and three beagles. If he randomly chooses a dog to accompany him on a walk, what is the probability of him taking a walk with sheepdog? Probability of event E = (# of ways E can happen)/(# of possible outcomes) ----- P(sheepdog) = 4/7 --------------------------------- 2.) Gordon spins a spinner with equal-sized sections numbered 1-6. In one spin, what is the likelihood that the spinner will stop on a 1 or a 5? P(1 or 5) = 2/6 = 1/3 --------------------------------- 3.) When two number cubes labeled 1-6 are rolled, what is the probability that the result will be two 4's ? P(two 4's) = 1/36 -------------------------------- 4.) Joanne is guessing which day in November is Bess's birthday. Joanne know that Bess's birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her first try? --- November has 30 days (15 even and 15 odd) P(Joanne chooses the correct day) = 1/15 ====================================================== Cheers, Stan H.
 Expressions-with-variables/179832: My Problem Is: Y=2x+3 Y=4x-1 My teacher taught me today, but I left her room not understanding how to work this problem out. I'm not sure if they both start with "y" if the formula is the same or not. How do I do this problem?1 solutions Answer 134734 by stanbon(57347)   on 2009-02-02 19:49:04 (Show Source): You can put this solution on YOUR website!Y=2x+3 Y=4x-1 ----------- Since they are both equal to Y they must be equal to each other. 2x+3 = 4x-1 Substract 2x from both sides to get: 3 = 2x-1 Add 1 to both sides to get: 2x = 4 Divide both sides by 2 to get: x = 2 ============ Cheers, Stan H.
 Word_Problems_With_Coins/179804: Rico's collection of quarters and dimes contains \$32.85. There are 171 coins in all. How many quarters and how many dimes are in Rico's collection?1 solutions Answer 134729 by stanbon(57347)   on 2009-02-02 18:47:46 (Show Source): You can put this solution on YOUR website!Rico's collection of quarters and dimes contains \$32.85. There are 171 coins in all. How many quarters and how many dimes are in Rico's collection? ---------------------------- Equations: Quantity Equation: q + d = 171 Value Equation...:25q+10d = 3285 cents ------------------------- Modify to get: 10q + 10d = 1710 25q + 10d = 3285 ----------------------- Subtract 1st from 2nd to solve for "q": 15q = 1575 q = 105 (# of quarters) -------------- Substitute into q + d = 171 to solve for "d": 105 + d = 171 d = 66 (# of dimes) --------------------------- Cheers, Stan H.
 Number-Line/179815: This question is from textbook Algebra 1 I was wondering how to solve this problem. 4c=3d+3 c=d-1 4(d-1)=3d+3 = 4d-4=3d+3 subtract 3d to both sides d-4=3 Add 4 to both sides d=7 how do you post ?'s I got at least this far: 4(d-1)=3d+3 But now, I dont know if I'm soposed to find out what the variables are first or distribute. If I distribute, I dont kno how to distribute this equation. Can you help me?1 solutions Answer 134727 by stanbon(57347)   on 2009-02-02 18:39:23 (Show Source): You can put this solution on YOUR website!I was wondering how to solve this problem. 4c=3d+3 c=d-1 ----------------- Substitute and solve for "d": 4(d-1) = 3d + 3 4d - 4 = 3d + 3 d = 7 -------------- Since c = d-1, c = 7-1 = 6 ============================== Cheers, Stan H.
 Radicals/179813: please multiply and somplify.. thanks [ means [ square root. thanks so much.. 1. [18x^3 times [2x^2y^3 1 solutions Answer 134725 by stanbon(57347)   on 2009-02-02 18:34:29 (Show Source): You can put this solution on YOUR website![18x^3 times [2x^2y^3 = sqrt(18x^3) * sqrt(2x^2y^3) = 3xsqrt(2x) * xysqrt(2y) = 3x^2y*sqrt(4xy) = 3x^2y*2sqrt(xy) = 6x^2y^2*sqrt(xy) =========================== Cheers, Stan H.
 Radicals/179814: please divide and simply.. [ means square root.. 1. 3[18x^3 divide by 3[10xy^21 solutions Answer 134724 by stanbon(57347)   on 2009-02-02 18:29:48 (Show Source): You can put this solution on YOUR website!please divide and simply.. [ means square root.. 1. 3[18x^3 divide by 3[10xy^2 --- [3sqrt(18x^3)] / [3sqrt(10xy^2)] Can cel the common factor of 3 and simplify the radicals to get: = (3x*sqrt(2x)) / (y*sqrt(10x)): = (3x/y)sqrt(2x/10x) = (3x/y)sqrt(1/5) = (3x/5y)sqrt(5) ======================== Cheers, Stan H.
 Radicals/179812: rationalize the denominator of each expression... thanks key: [ means square roots 1. [5x/[3 2. 3[x2/3[4 1 solutions Answer 134723 by stanbon(57347)   on 2009-02-02 18:21:57 (Show Source): You can put this solution on YOUR website!rationalize the denominator of each expression... thanks key: [ means square roots 1. [5x/[3 = (5x)/sqrt(3) Multiply numerator and denominator by sqrt(3) to get: = [5xsqrt(3)]/3 = (5x/3)sqrt(3) ----------------------------- 2. 3[x2/3[4 = 3sqrt(x^2)/3sqrt(4) = (3x)/(3*2) = x/2 ==================== Cheers, Stan H.
 Trigonometry-basics/179810: (3/x+7) + (4/x-3) all over (3/x^2+4x-21) + (1/x-3)1 solutions Answer 134722 by stanbon(57347)   on 2009-02-02 18:17:22 (Show Source): You can put this solution on YOUR website!When you say (3/x+7) do you mean (3/x)+7 or do you mean 3/(x+7) ? Cheers, Stan H.
 Money_Word_Problems/179805: Airline fares for a flight from Elmwood to Palmdale are \$85 for first class. On Friday, 79 passengers paid a total of \$5290 to fly from Elmwood to Palmdale. How many of each type of ticket were sold?1 solutions Answer 134721 by stanbon(57347)   on 2009-02-02 18:14:11 (Show Source): You can put this solution on YOUR website!What was the alternate passenger cost? Cheers, Stan H.
 Miscellaneous_Word_Problems/179809: This question is from textbook Explain in your own words the law of large numbers. Provide an example to illustrate. 1 solutions Answer 134720 by stanbon(57347)   on 2009-02-02 18:07:17 (Show Source): You can put this solution on YOUR website!I suggest you use Google. Cheers, Stan H.
 Linear-equations/179807: A 50 word response to the following:How can you determine if two lines are perpendicular? 1 solutions Answer 134719 by stanbon(57347)   on 2009-02-02 18:04:56 (Show Source): You can put this solution on YOUR website!I would suggest you use Google to find words to answer your perpendicular and your parallel problems. Cheers, Stan H.
 Equations/179808: 2.65 x 10^31 solutions Answer 134718 by stanbon(57347)   on 2009-02-02 18:01:48 (Show Source): You can put this solution on YOUR website!2.65 x 10^3 When you multiply be 1000 move the decimal point 3 places to the right. ------------------ = 2650 ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/179795: This question is from textbook Algebra 2 Find each product. (2c - 3) (2c + 4)(2c - 1) 1 solutions Answer 134717 by stanbon(57347)   on 2009-02-02 17:58:29 (Show Source): You can put this solution on YOUR website!Find each product. (2c - 3) (2c + 4)(2c - 1) = (4c^2 + 8c - 6c -12)(2c-1) = (4c^2+2c-12)(2c-1) = (8c^3+4c^2-24c-4c^2-2c+12) = 8c^3 -26c + 12 ====================================== Cheers, Stan H.
 real-numbers/179799: write each rational number in the form a/b where a and b are integers and b = 0. a.) 0.3 b.)5 1/3 c.)0 d.)73 e.)-0.211 solutions Answer 134716 by stanbon(57347)   on 2009-02-02 17:32:41 (Show Source): You can put this solution on YOUR website!write each rational number in the form a/b where a and b are integers and b = 0. a.) 0.3 = 3/10 b.)5 1/3 = 16/3 c.)0 = 0/1 d.)73 = 73/1 e.)-0.21 = -21/100 ======================== Cheers, Stan H.
 Exponents-negative-and-fractional/179755: Please help me multiply these two fractions together. y^2 -6y + 9 over 8 multiplied by 4y + 12 over y^2 -9.1 solutions Answer 134669 by stanbon(57347)   on 2009-02-02 13:27:06 (Show Source): You can put this solution on YOUR website![(y^2 -6y + 9) /8] * [(4y + 12) / (y^2 -9)] Factor where you can: [(y-3)^2/8] * [4(y+3)/(y-3)(y+3)] Cancel any factor that is common to a numerator and a denominator, such as (y-3), 4, (y+3) : [1/2] * [1/1] = 1/2 ======================== Cheers, Stan H.
 Trigonometry-basics/179763: This question is from textbook Find the reference angle R of the given angles. Give your answer to the nearest hundredth. (a) 5 (b)-5 (c)3.5 (d)751 solutions Answer 134665 by stanbon(57347)   on 2009-02-02 13:20:18 (Show Source): You can put this solution on YOUR website!Find the reference angle R of the given angles. Give your answer to the nearest hundredth. (a) 5 Procedure: 5(180/pi) = 286.48 degrees 286-360 = -73.52 Referemce angle = 73.52 degrees = 1.283 radians ------------------------------------------------------- (b)-5 -5(180/pi) = -286.48 degrees 286 + 360 = 73.72 ------------------------------------------------------- (c)3.5 3.5(180/pi) = 200.53 degrees 200.53 - 180 = 20.53 20.53(pi/180) = 0.3584.. ============================ Cheers, Stan H. (d)75
 Probability-and-statistics/179648: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.1 solutions Answer 134652 by stanbon(57347)   on 2009-02-02 12:54:12 (Show Source): You can put this solution on YOUR website!A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 x-bar = 3.305 ; s =0.132.. ; n= 10 ----------------------------------------- (a) Construct a 90 percent confidence interval for the true mean weight. E = 1.645[0.132/sqrt(10)] = 0.069.. --- 90% CI: 3.305-0.069 < u < 3.305+0.069 ------------------------------------ (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence? n = [z*s/E]^2 = [1.645*0.132/0.03]^2 = 52.39; rounding up n = 53 ------------------------------------ (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. humidity level; machine variability; manufacture tolerance ============================================================== Cheers, Stan H.
 Probability-and-statistics/179742: 10.24 - 10.24 Below is a random sample of shoe sizes for 12 mothers and their daughters. (a) At α = .01, does this sample show that women’s shoe sizes have increased? State your hypotheses and show all steps clearly. (b) Is the decision close? (c) Are you convinced? (d) Why might shoe sizes change over time? (See The Wall Street Journal, July 17, 2004.) Shoe Size 2 1 2 3 4 5 6 7 8 9 10 11 12 Daughter 8 8 7.5 8 9 9 8.5 9 9 8 7 8 Mother 7 7 7.5 8 8.5 8.5 7.5 7.5 6 8 7 71 solutions Answer 134642 by stanbon(57347)   on 2009-02-02 12:03:41 (Show Source): You can put this solution on YOUR website!Below is a random sample of shoe sizes for 12 mothers and their daughters. Daughter 8 8 7.5 8 9 9 8.5 9 9 8 7 8 d-bar = 8.25 ; s = 0.657 ---- Mother 7 7 7.5 8 8.5 8.5 7.5 7.5 6 8 7 7 m-bar = 7.46 ; s = 0.721 ---------- (a) At α = .01, does this sample show that women’s shoe sizes have increased? State your hypotheses and show all steps clearly. Ho: ud-um = 0 Ha: ud-um < 0 (this for a right-tail test; you could reverse the inequality and make a left tail test) --- Critical Value: z = 2.326... Test statistic: z(8.25-7.46) = (0.79)/sqrt[(0.657)^2/12 + (0.721)^2/12] = 2.81 p-value: P(z>2.81) = 0.0025 ------- Conclusion: Since p-value < 1%, reject Ho. daughter's sizes are greater than mother's sizes --------------------------------------------------------- (b) Is the decision close? No. Less than (1/4) of 1% of test results could have provided stronger evidence for rejecting Ho. ----------- (c) Are you convinced? Yes ---------------- (d) Why might shoe sizes change over time? They don't; foot sizes change. ==================================== Cheers, Stan H.
 Exponents-negative-and-fractional/179694: I'm working on quadratic equations Equations and inequalities of one variable, in higher degree polynomial equations. Equation (5y-4)^-1/4 - 5(5y-4)^-4/3 =0. I understand that I must factor out (5y-4)^-4/3. I understand "factor out" as meaning to remove this from the equation. However, this results in (5y-4)^-4/3 ((5y-4)-4)=0, which I do not understand. Can someone explain what took place.1 solutions Answer 134625 by stanbon(57347)   on 2009-02-02 07:51:34 (Show Source): You can put this solution on YOUR website! (5y-4)^-1/4 - 5(5y-4)^-4/3 =0 (5y-4)^(-3/12) - 5(5y-4)^(-16/12) = 0 ---- [(5y-4)^(-16/12)][(5y-4)^(-12/12) - 5] = 0 [(5y-4)^(-16/12)][(5y-4)^-1 - 5] = 0 Solve for "y": (5y-4)^(-16/12) = 0 or (5y-4)^(-1) = 5 y cannot equal 4/5 because the exponent is negative: ----------- Solve (5y-4)^-1 = 5 Invert to get: 5y-4 = 1/5 5y = (1/5)+4 5y = 21/5 y = 21/25 ================= Cheers, Stan H.
 Miscellaneous_Word_Problems/179718: A gold smith combined an alloy that costs \$430 per gram with an alloy that costs \$180 per gram. How many grams of each were used to make a mixture of 200 grams that cost \$250 per gram?1 solutions Answer 134624 by stanbon(57347)   on 2009-02-02 07:39:22 (Show Source): You can put this solution on YOUR website!A gold smith combined an alloy that costs \$430 per gram with an alloy that costs \$180 per gram. How many grams of each were used to make a mixture of 200 grams that cost \$250 per gram? --- value + value = value 430x + 180(200-x) = 250*200 430x +180*200 - 180x = 250*200 250x = 70*200 x = 56 grams (amt. of \$430 alloy in the mixture) 200-56 = 144 grams (amt. of \$180 alloy in the mixture) ======================================================== Cheers, Stan H.
 Probability-and-statistics/179690: This question is from textbook Theoretical and Experimental Probability Please you help me solve these problems. How do you know? Can you write everything that you solve its? 6.) What is the probability that a random 2-digit number (00-99) does not end in 5? 8.) A clerk has 4 different letters that need to go in 4 different envelopes. What is the probability that all 4 letters are placed in the correct envelopes? Please answer me as soon as you could, Thank you.1 solutions Answer 134623 by stanbon(57347)   on 2009-02-02 07:31:57 (Show Source): You can put this solution on YOUR website!6.) What is the probability that a random 2-digit number (00-99) does not end in 5? ---- There are 100 numbers if you include 00. # that do not end in 5? 10 ways to pick the tens digit 9 ways to pick the ones digit So, 10*9 = 90 ways to have a two-digit number not ending in 5 --- Therefore P(2-digit not ending in 5) = 90/100 = 9/10 ============================================================ 8.) A clerk has 4 different letters that need to go in 4 different envelopes. What is the probability that all 4 letters are placed in the correct envelopes? -- # of possible arrangements: 4! = 24 # of correct arrangements: 1 --- Probability of getting the right arrangement: 1/24 ===================================================== Cheers, Stan H.