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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Probability-and-statistics/291796: You are dealt 2 cards from a shuffled deck of 52 cards, without replacement. There are four suits of 13 cards each in a deck of cards; two of them are black and two of them are red. What is the probability that both cards are red? 1 solutions Answer 211063 by stanbon(57241)   on 2010-04-14 07:48:09 (Show Source): You can put this solution on YOUR website!You are dealt 2 cards from a shuffled deck of 52 cards, without replacement. There are four suits of 13 cards each in a deck of cards; two of them are black and two of them are red. What is the probability that both cards are red? --------------- Ans: 26C2/52C2 = 325/1326 = 0.2451 ========================== Cheers, Stan H. ==========================
 Probability-and-statistics/291857: A room contains five men and four women. Two people are selected at random with no replacements between selections. 1. Find the probability that the first person selected is a man and the second is a woman. 2. Find the probability that all the people selected are men. 3. Find the probability that the second person selected is a woman, given that the first to be selected was a woman. 4. Find the probability that one man and one woman are selected.1 solutions Answer 211062 by stanbon(57241)   on 2010-04-14 07:43:08 (Show Source): You can put this solution on YOUR website!A room contains five men and four women. Two people are selected at random with no replacements between selections. 1. Find the probability that the first person selected is a man and the second is a woman. Ans: (5/9)(4/8) = 20/72 = 5/18 --------------------------------------- 2. Find the probability that all the people selected are men. Ans: 5C2/9C2 = 10/36 = 5/18 ---------------------------------------- 3. Find the probability that the second person selected is a woman, given that the first to be selected was a woman. Ans: P(w|w) = P(2 women)/P(women) = [4C2/9C2]/[4/9] = (6/36)/(4/9) = 3/8 ----------------------------------------------------- 4. Find the probability that one man and one woman are selected. P(1m and 1 w) = 1-[P(2men)+P(2women)] = 1-[(5/18)+(1/6)] = 10/18 = 5/9 ================================================================ Cheers, Stan H.
 Probability-and-statistics/291889: Suppose you select 2 letters at random from the word "pacific". find each probability P(2 vowels) P(2 consonants) P(1 vowel, 1 consonant)1 solutions Answer 211058 by stanbon(57241)   on 2010-04-14 07:33:07 (Show Source): You can put this solution on YOUR website!Suppose you select 2 letters at random from the word "pacific". vowels: a,i,i consonants: p,c,f,c ----------- find each probability P(2 vowels) = 3C2/7C2 = 3/21 = 1/7 -------------- P(2 consonants) = 4C2/7C2 = 6/21 = 2/7 -------------- P(1 vowel, 1 consonant) = 1 - [1/7 + 2/7] = 4/7 ===================================================== Cheers, Stan H.
 Probability-and-statistics/292053: The following hypotheses are given. H0: p = 0.40 H1: p ≠ 0.40 A sample of 120 observations revealed that p = 0.30 At the 0.05 significance level, can the null hypothesis be rejected? a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis? 1 solutions Answer 211055 by stanbon(57241)   on 2010-04-14 07:28:36 (Show Source): You can put this solution on YOUR website!The following hypotheses are given. H0: p = 0.40 H1: p ≠ 0.40 A sample of 120 observations revealed that p = 0.30 At the 0.05 significance level, can the null hypothesis be rejected? a. State the decision rule. If z > 1.96 or less than -1.96, reject Ho. ------------------------------------- b. Compute the value of the test statistic. z(0.30) = (0.30-0.40)/sqrt[0.4*0.6/120] = -2.2361 ------------------------------------- c. What is your decision regarding the null hypothesis? Since the test stat is in the reject interval, reject Ho. ============================================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/291935: you have to factor the polynomial completely (25a^2-1)1 solutions Answer 210984 by stanbon(57241)   on 2010-04-13 21:04:52 (Show Source): You can put this solution on YOUR website!factor the polynomial completely (25a^2-1) ----- = (5a-1)(5a+1) =================== Cheers, Stan H. ===================
 Linear_Algebra/291929: What is the answer if you solve each system of equation by substitution? 4y+3x=-3 y=5x-51 solutions Answer 210981 by stanbon(57241)   on 2010-04-13 20:55:00 (Show Source): You can put this solution on YOUR website!What is the answer if you solve each system of equation by substitution? 4y+3x=-3 y=5x-5 --------------------------- Substitute for "y" and solve for "x": 4(5x-5)+3x = -3 20x-20+3x = -3 23x = 17 x = 17/23 ------------------------------ Substitute for "x" and solve for "y": y = 5(17/23)-5 y = 85/23 - 115/23 y = 200/23 ================================= Cheers, Stan H. =================================
 Quadratic_Equations/291921: Please help me solve the equation b^4+13b^2+36=0 Find all real and imaginery solutions to this problem1 solutions Answer 210979 by stanbon(57241)   on 2010-04-13 20:47:57 (Show Source): You can put this solution on YOUR website!b^4+13b^2+36=0 --- b^4 + 9b^2 + 4b^2 + 36 = 0 -------- b^2(b^2+9) + 4(b^2+9) = 0 -------- (b^2+9)(b^2+4) = 0 ---- (b+3i)(b-3i)(b+2i)(b-2i) = 0 ---- b = 3i or b = -3i or b = 2i or b = -2i ================================================ Cheers, Stan H. ================================================
 Graphs/291688: How do i: Find the value of "C" to make g(squared)-18g+c a perfect square? Please explain.1 solutions Answer 210869 by stanbon(57241)   on 2010-04-13 12:47:24 (Show Source): You can put this solution on YOUR website!Find the value of "C" to make g(squared)-18g+c a perfect square? --------------------- Perfect Square: q^2 - 18q + (18/2)^2 ----------- C = (18/2)^2 = 9^2 = 81 ============================= Cheers, Stan H. =============================
 Travel_Word_Problems/291683: charles started a trip by car averaging 49 miles per hour samantha started a trip by car from the same place and in the same direction averaging 51 miles per hour if samantha left 24 mintues later how long will it take samantha to catch up to charles1 solutions Answer 210868 by stanbon(57241)   on 2010-04-13 12:44:04 (Show Source): You can put this solution on YOUR website!charles started a trip by car averaging 49 miles per hour samantha started a trip by car from the same place and in the same direction averaging 51 miles per hour if samantha left 24 mintues later how long will it take samantha to catch up to charles --- Charles DATA: rate = 49 mph; time = x hrs ; distance = 49x miles ---------------------------- Samantha DATA: rate = 51 mph; time = (x-24/60) ; distance = 51x - 20.4 miles --------------------- Equation: distance = distance 49x = 51x-20.4 -2x = -20.4 x = 10.2 hrs ---- x-(24/60) = 10.2-0.4 = 9.8 hrs = 9 hrs 48 minutes ==================================================== Cheers, Stan H. ====================================================
 Square-cubic-other-roots/291684: what is the square root of 108 divided by the square root of 31 solutions Answer 210865 by stanbon(57241)   on 2010-04-13 12:36:46 (Show Source): You can put this solution on YOUR website!what is the square root of 108 divided by the square root of 3 --------------------- (sqrt(108))/(sqrt(3)) --- (sqrt(36*3))/sqrt(3) --- (6*sqrt(3))/(sqrt(3) ---- = 6 ========================= Cheers, Stan H.
 Quadratic_Equations/291678: Please help to answer the follwing question. If the profit function for a commodity is p=6400x-18x^2-(1/3)x^3-40,000 dollars, selling how many units, x, will result in a maximum profit? Find the maximum profit. (I am having troublw getting past this: p'=6400-36x-x^2=0 Thanks!1 solutions Answer 210864 by stanbon(57241)   on 2010-04-13 12:31:30 (Show Source): You can put this solution on YOUR website!If the profit function for a commodity is p=6400x-18x^2-(1/3)x^3-40,000 dollars, selling how many units, x, will result in a maximum profit? Find the maximum profit. p'(x) = 6400 - 36x - x^2 ---- Solve x^2 + 36x + 6400 = 0 (x+100)(x-64) = 0 Poxitive solution: x = 64 p(64) = \$208,491 ---------------------- Cheers, Stan H. ----------------------
 Linear-equations/291551: Find the average rate of change for the function over the given interval. y=√2x-1 between x=1 x=5 Answer is 1/2 Could you please show steps for this!! √ = squareroot1 solutions Answer 210835 by stanbon(57241)   on 2010-04-13 09:17:53 (Show Source): You can put this solution on YOUR website!Find the average rate of change for the function over the given interval. y=√2x-1 between x=1 x=5 Answer is 1/2 -------------------- Average change = (change in y values)/(change in x values) =(f(5) - f(1))/(5-1) --- = (sqrt(9)-sqrt(1))/(4) --- = (3-1)/4 = 1/2 ============== Cheers, Stan H.
 Radicals/291615: I need help with this problem ∛-24x10y8 * ∛18x7y4 this is how far I got: ∛-24x10y8 * ∛18x7y4 = ∛-24x10y8 *18x7y4 =∛-432x17y12 = 1 solutions Answer 210832 by stanbon(57241)   on 2010-04-13 09:09:53 (Show Source): You can put this solution on YOUR website!∛-24x10y8 --------------- = cbrt(-24x^10y^8) --- = cbrt[(-8x^9y^6)(3xy^2)] --- = cbrt[-8x^9y^6]*cbrt[3xy^2] --- = -2x^3y^2*cbrt(3xy^2) =============================== Cheers, Stan H.
 Probability-and-statistics/291569: Because 10% of the reservation holders are 'no shows' a Canadian airline sells 400 tickets for a flight that can accommodate 375 passengers. a) Find the probability that one or more reservation holders will not be accomodated on the flight. b) Find the probability of fewer than 350 passengers on the flight.1 solutions Answer 210831 by stanbon(57241)   on 2010-04-13 09:05:24 (Show Source): You can put this solution on YOUR website!Because 10% of the reservation holders are 'no shows' a Canadian airline sells 400 tickets for a flight that can accommodate 375 passengers. a) Find the probability that one or more reservation holders will not be accomodated on the flight. --- Binomial Problem with n = 400, p = 0.1 P(x>375) = 1 - P(0<= x <=374) = 1 - 400C374(0.9)^374*(0.1)^26 = 0.0054... ----------------------------------------- b) Find the probability of fewer than 350 passengers on the flight. P(0<= x <=349) = 0.0436.. ----------------------------------------- Cheers, Stan H.
 Linear-equations/291613: By looking at two linear equations, how can you tell that the corresponding lines are parallel?1 solutions Answer 210828 by stanbon(57241)   on 2010-04-13 08:55:45 (Show Source): You can put this solution on YOUR website!If the slopes are the same and the y-intercepts are not equal, the lines are parallel. Cheers, Stan H.
 Probability-and-statistics/291590: H0: µ ≤ 10 H1: µ > 10 The sample mean is 12, and the sample size is 36. The population follows the normal distribution and the standard deviation is 3. Use a .02 significance level. 1 solutions Answer 210827 by stanbon(57241)   on 2010-04-13 08:54:17 (Show Source): You can put this solution on YOUR website!H0: µ ≤ 10 H1: µ > 10 The sample mean is 12, and the sample size is 36. The population follows the normal distribution and the standard deviation is 3. Use a .02 significance level. --------------------- t(12) = (12-10)/[3/sqrt(12)] = 2.3094... --- p-value: P(t> 2.3094 when df=11) = 0.02067 --- Whoa! That p-value is only 67/1000th above the significance mark. --- Conclusion: Since the p-value is greater than 2%, fail to reject Ho. ---- Also, you should do more testing. =============== Cheers, Stan H.
 Finance/291612: Find three consecutive odd integers such that three times the third is 7 more than the sum of the other two.1 solutions Answer 210825 by stanbon(57241)   on 2010-04-13 08:48:20 (Show Source): You can put this solution on YOUR website!Find three consecutive odd integers such that three times the third is 7 more than the sum of the other two. --- 1st: 2x-1 2nd: 2x+1 3rd: 2x+3 ---------------- Equality: 3(2x+3)= 4x+7 6x+9 = 4x+7 2x = -2 x = -1 ----- 1st: 2x-1 = -3 2nd: 2x+1 = -1 3rd: 2x+3 = 1 ----------------- Cheers, Stan H.
 Probability-and-statistics/291606: suppose you are playing a game in which 2 fair die are rolled. you need a 9 to land on finish by an exact count or a 3 to land on "roll again" space. what is the probability of landing on the finish or rolling again. explain in detail. 1 solutions Answer 210823 by stanbon(57241)   on 2010-04-13 08:44:17 (Show Source): You can put this solution on YOUR website! suppose you are playing a game in which 2 fair die are rolled. you need a 9 to land on finish by an exact count or a 3 to land on "roll again" space. what is the probability of landing on the finish or rolling again. explain in detail. ------------- Rule: P(A or B) = P(A) + P(B) - P(A and B) --- Your Problem: The two events are mutually exclusive so P(A and B) is zero. --- Ways to get a 9: 6/3;5/4;4/5;3/6 P(get a 9) = 4/36 --- Ways to get a 3: 2/1;1/2 P(get a 3) = P(2/36) ---- Ans: P(9 or 3) = 4/36 + 2/36 = 6/36 = 1/6 ========================== Cheers, Stan H.
 Finance/291389: mary has \$3.75 in nickels,dimes,quarters. she has three more quarters than dimes. she has twice as many nickels as quarters. how many of each coin does she have?1 solutions Answer 210728 by stanbon(57241)   on 2010-04-12 19:34:38 (Show Source): You can put this solution on YOUR website!mary has \$3.75 in nickels,dimes,quarters. she has three more quarters than dimes. she has twice as many nickels as quarters. how many of each coin does she have? -------------------------------------------- Equations: Value Eq:::: 5n + 10d + 25q = 375 cents Quantity:::: q = d + 3 Quantity:::: n = 2q --------------------------------- Substitute for "d" dnd for "n" and solve for "q": 5(2q) + 10(q-3) + 25q = 375 10q + 10q - 30 + 25q = 375 45q = 405 q = 9 (# of quarters) n = 2q = 18 (# of quarters) d = q-3 = 6 (# of dimes) ============================ Cheers, Stan H.
 Quadratic_Equations/291381: Find the vertex for the graph of the quadratic function (x)= 5x squared - 38x + 211 solutions Answer 210727 by stanbon(57241)   on 2010-04-12 19:26:18 (Show Source): You can put this solution on YOUR website!Find the vertex for the graph of the quadratic function f(x)= 5x squared - 38x + 21 --- Vertex occurs where x = -b/2a = 38/(10) = 19/5 ----------------- f(19/5) = -51.2 or -256/5 -------------------------------- ------------------------------- Cheers, Stan H.
 Probability-and-statistics/291004: #3 (#23 e-text) Raising chickens in commercial chicken farms is a growing industry, as there is a shift from red meat to more white meat. New Jersey Red Chickens are a favorite chicken and the Feed is Us company has a new chicken food that they claim is excellent for increasing weight and naturally it costs more. You have heard this line before and therefore are skeptical but the potential pay off is huge. You buy a small amount and feed it to ten chickens, which you choose at random. Chicken Weights 4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39 At the .01 level of significance is there evidence that the chicken weight exceeds the average chicken weight of 4.35 pounds.1 solutions Answer 210724 by stanbon(57241)   on 2010-04-12 19:16:12 (Show Source): You can put this solution on YOUR website!Chicken Weights 4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39 At the .01 level of significance is there evidence that the chicken weight exceeds the average chicken weight of 4.35 pounds. --------------------------------------------------------- Ho: u = 4.35 Ha: u > 4.35 ---- I ran a t-test on the dat and got the following results: test statistic: t = 1.6777 p-value: 0.0639.. --- Conclusion: Since the p-value is greater than 1%, fail to reject Ho. ---------------------------------- Cheers, Stan H. ----------------------------------
 Equations/291353: write the standard form of an equation of the line that passes through each pair. (-2,7-) (1,2)1 solutions Answer 210709 by stanbon(57241)   on 2010-04-12 18:31:53 (Show Source): You can put this solution on YOUR website!write the standard form of an equation of the line that passes through each pair. (-2,7-) (1,2) --------------------- slope = (2-7)/(1--2) = -5/3 ---- Use the form y = mx + b to solve for "b": 2 = (-5/3)*1 + b b = 11/3 --------- y = (-5/3)x + (11/3) ======================== Cheers, Stan H.
 Surface-area/291344: if the area of a circular pond is 153.86 sq. yd. what is the circumference of the pond?1 solutions Answer 210705 by stanbon(57241)   on 2010-04-12 18:25:54 (Show Source): You can put this solution on YOUR website! if the area of a circular pond is 153.86 sq. yd. what is the circumference of the pond? ------------------------- Area = (pi)r^2 = 153.86 sq. yd. r^2 = 153.86/pi r = sqrt(48.98) ----- Circumference = 2(pi)r C = 2(pi)sqrt(48.98) C = 43.97... Cheers, Stan H.
 Linear-equations/291340: y+10x=-170 graph please1 solutions Answer 210701 by stanbon(57241)   on 2010-04-12 18:18:48 (Show Source): You can put this solution on YOUR website!y+10x=-170 graph please ---- x-intercept = ? Let y = zero, and solve for "x": 10x = -170 x = -17 --------------------- y-intercept = ? Let x = zero, and solve for "y": y = -170 --------------------- Plot the two points (0,-170) and (-17,0) ============================= ============================= Cheers, Stan H.
 Exponents/291336: how do i write 4.321 x neitive ten to the tenth power in standard notaion ?1 solutions Answer 210695 by stanbon(57241)   on 2010-04-12 18:09:59 (Show Source): You can put this solution on YOUR website!how do i write 4.321 x neitive ten to the tenth power in standard notaion ? ----- 4.321 x (-10)^10 --- = 4.321 x 10^10 Move the decimal point 10 steps to the right: --- = 43,210,000,000 ========================== Cheers, Stan H. ==========================
 Graphs/291335: what is the slope in 2y+4 = x+ 31 solutions Answer 210686 by stanbon(57241)   on 2010-04-12 18:00:20 (Show Source): You can put this solution on YOUR website!what is the slope in 2y+4 = x+ 3 ---------- 2y = x - 1 --- y = (1/2)x - (1/2) ----------------------- slope = 1/2 ========================== Cheers, Stan H.
 Numbers_Word_Problems/291334: The square of a number equals thirty-one times that number. Find the number.1 solutions Answer 210682 by stanbon(57241)   on 2010-04-12 17:56:28 (Show Source): You can put this solution on YOUR website!The square of a number equals thirty-one times that number. Find the number. ----------------- Equation: x^2 = 31x x^2-31x = 0 x(x-31) = 0 x = 0 or x = 31 -----------------------------
 Probability-and-statistics/291207: What is the probability that 6 people in 10 will agree on 7 out of 10 random answers, where the answer can be either a "yes" or a "no"?1 solutions Answer 210681 by stanbon(57241)   on 2010-04-12 17:53:52 (Show Source): You can put this solution on YOUR website!What is the probability that 6 people in 10 will agree on 7 out of 10 random answers, where the answer can be either a "yes" or a "no"? ---------------------------------------------------------- Binomial Problem with n = 10 ; p = 1/2 P(x = 6) = 10C6(1/2)^6*(1/2)^4 = 210(1/2)^10 = 0.2051 ===================== Cheers, Stan H.
 Linear-equations/291309: Write the linear equation x = 1/3 y – 2/3 in standard form. 1 solutions Answer 210677 by stanbon(57241)   on 2010-04-12 17:33:44 (Show Source): You can put this solution on YOUR website!Write the linear equation x = 1/3 y – 2/3 in standard form. ----- Multiply thru by 3 to get: 3x = y - 2 3x - y = -2 (standard form) ============================ Cheers, Stan H. ============================
 Probability-and-statistics/291273: Of the 400 students at a school, 35% have part-time jobs. Find the probability that two students selected at random have part-time jobs. Hello, I'm not sure what to do in this one. I was thinking maybe using a combination or permutation would work but I am just dumb founded. Thank you for your help.1 solutions Answer 210674 by stanbon(57241)   on 2010-04-12 17:29:50 (Show Source): You can put this solution on YOUR website!Of the 400 students at a school, 35% have part-time jobs. Find the probability that two students selected at random have part-time jobs. ----------------------------- P(2 of 2 have part-time jobs) = (0.35)^2 = 0.1225 ---------------------- Cheers, Stan H. ----------------------