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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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 Quadratic_Equations/138591: The midpoint of AB is (3sqrt5,2sqrt3). If the coordinates of the endpoint B are (-sqrt5,1/2sqrt3), then what are the coordinates of endpoint A?1 solutions Answer 101157 by stanbon(57953)   on 2008-04-25 23:22:48 (Show Source): You can put this solution on YOUR website!The midpoint of AB is (3sqrt5,2sqrt3). If the coordinates of the endpoint B are (-sqrt5,1/2sqrt3), then what are the coordinates of endpoint A? ----------------------- Let the coordinates of A be (x,y) -------------------- Note: The coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints. --------------------- EQUATIONS: (x + (-sqrt5))/2 = 3sqrt5 x - sqrt5 = 6sqrt5 x = 7sqrt5 ---------------- (y + 2sqrt3)/2 = (1/2)sqrt3 y + 2sqrt3 = sqrt3 y = -sqrt3 ------------------------- The coordinates of A are (7sqrt5 , -sqrt3) ======================== Cheers, Stan H.
 Trigonometry-basics/138612: Solve the equation on [0,2pie). Approximate the solution(s) to four decimal places, if necessary. 2cos^2x-cosx-1=01 solutions Answer 101156 by stanbon(57953)   on 2008-04-25 23:16:16 (Show Source): You can put this solution on YOUR website!Solve the equation on [0,2pie). Approximate the solution(s) to four decimal places, if necessary. 2cos^2x-cosx-1=0 ----------------------------- Factor to get: (2cosx + 1)(cosx - 1) = 0 cosx = -1/2 or cosx = 1 x = pi/3 radians or -pi/3 radians or 0 radians ============================= Cheers, Stan H.
 Probability-and-statistics/138607: To Stanbon, Using the first problem you solved on z-score please check this problem I tried to solve: The mean weight of 545 women is 99lbs. and s is 5, Assuming that the wts. of women are normally distributed, how many would you expect to weigh less than 105? Z= 105-99/5 z=1.2 from table: Z score = .3848 or 38.48% will weigh more than 105 that is 210 women computing for women who will weigh less than 105: 100-38.48 = 61.52% 545x.6152 = 335 women who will weigh less 105 lbs. Thanks again. 1 solutions Answer 101155 by stanbon(57953)   on 2008-04-25 23:12:30 (Show Source): You can put this solution on YOUR website!The mean weight of 545 women is 99lbs. and s is 5, Assuming that the wts. of women are normally distributed, how many would you expect to weigh less than 105? Z= (105-99)/5 z=1.2 That is correct. ----------------- P(0 < x < 105) = P(-19.8 < z < 1.2) = 0.8848 or 88.48% from table: Z score = .3848 or 38.48% will weigh more than 105 ------------------------------------------------------------- No: 38.48% will weigh more than the MEAN score of 99 lbs. You have to include the 50% who weigh less than 99 lbs. What that means is you need a z-score for "0" lbs. z(0) = (0-99)/5 = -19.8 --------------------------- Then 88.48% of 545 is 482 ladies who will weigh less than 105 lbs. So 545-482 = 63 will weight more than 105 lbs. --------------------------- Recommendation: I think if you draw the normal curve and put the problem values on the horizontal axis and shade the area under the curve that corresponds to the probability you are looking for, you will avoid some errors you might otherwise make when you only manipulate the numbers. You will be able to see how your answers make sense,or don't. -------------------------------- Cheers, Stan H.
 Finance/138599: Use the compound interest formula above to compute the total amount after \$3000 is invested at 4% over 2 years compounded daily. (Use n=360). 1 solutions Answer 101152 by stanbon(57953)   on 2008-04-25 21:23:41 (Show Source): You can put this solution on YOUR website!Use the compound interest formula above to compute the total amount after \$3000 is invested at 4% over 2 years compounded daily. (Use n=360). ----------------------------- A(t) = P(1+(r/n))^(nt) A(2) = 3000(1+(0.04/360))^(360*2) A(2) = 3000(1.00011111)^(720) A(2) = 3000*1.08328.. A(2) = \$3249.85 ==================== Cheers, Stan H.
 Square-cubic-other-roots/138603: i'm a freshman i college not real good with math..just wanted to know if i was on the right track..9v=15...i came up with 6/1.. 1 solutions Answer 101150 by stanbon(57953)   on 2008-04-25 21:18:31 (Show Source): You can put this solution on YOUR website!5√75 – √48 + 8√3 = 5sqrt(25*3) - sqrt(16*3) + 8sqrt3 = 5*5sqrt3 -4sqrt3 + 8sqrt3 = (25 - 4 + 8)sqrt3 =29sqrt(3) You are correct. 29√3 I think is the answer, if so can it be simlified even more? Cannot be further simplified. ===================================== 59 – 33 ÷ (13 - 4²) – 8 = 59 - 33 /(-3) -8 = 59 + 11 -8 =62 ================ multiplication and division must be done before addition and subtraction. ================ Cheers, Stan H.
 Surface-area/138604: What is the surface area of a cube if it has an edge of 6 inches? 1 solutions Answer 101148 by stanbon(57953)   on 2008-04-25 21:12:47 (Show Source): You can put this solution on YOUR website!Each face is 6^2 =36 sq in. ---------------------------- There are 6 faces, so a total of 6*36 = 216 sq. in. ===================== Cheers, Stan H.
 logarithm/138602: This question is from textbook College Algebra graph the function: f(x)=log base 2 x/21 solutions Answer 101147 by stanbon(57953)   on 2008-04-25 21:10:07 (Show Source): You can put this solution on YOUR website!graph the function: f(x)=log base 2 x/2 ------------ You have to graph it as a fraction: f(x) = (log(x/2))/[(log2)) ------------- Cheers, Stan H.
 Quadratic_Equations/138601: 2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it. (HELP can you please help) a) The sales representative here tells you they also have two floor plans available, but they only have 38 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively. x = 19, y = 19, is this correct? b) The representative tells you that floor plan #1 sells for \$175,000 and floor plan #2 sells for \$200,000. She also mentions that all the available houses combined are worth \$7,200,000. Write an equation that illustrates this situation. Use the same variables you used in part a. x=\$175,000, y = \$200,000 is this correct???? 1 solutions Answer 101146 by stanbon(57953)   on 2008-04-25 21:04:49 (Show Source): You can put this solution on YOUR website!a) The sales representative here tells you they also have two floor plans available, but they only have 38 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively. x = 19, y = 19, is this correct? Ans: This is a quantity equation: x + y = 38 ----------------------- b) The representative tells you that floor plan #1 sells for \$175,000 and floor plan #2 sells for \$200,000. She also mentions that all the available houses combined are worth \$7,200,000. Write an equation that illustrates this situation. Use the same variables you used in part a. x=\$175,000, y = \$200,000 is this correct???? Ans: This is a Value equation: 175000x + 200000y = 7200000 =================================
 Probability-and-statistics/138510: The mean science achievement score of a group of Grade 8 students is 78 and s of 10. Granting that the scores of these students are normally distributed, how many would you expect to score less than 85? If the number of students who took the test is 200, how many would that be? How many students would score more than 85?1 solutions Answer 101145 by stanbon(57953)   on 2008-04-25 20:56:06 (Show Source): You can put this solution on YOUR website!The mean science achievement score of a group of Grade 8 students is 78 and s of 10. Granting that the scores of these students are normally distributed, how many would you expect to score less than 85? Find the z-score of 85. z(85)=(85-78)/10 = -0.7 P(0 < x < 85) = P(0 < z < -0.7) = 0.2580 ------------------------------------------------- If the number of students who took the test is 200, how many would that be? How many students would score more than 85? ------- 0.2580*200 = 51.6;rounding down you get 51 students scored below 85 200-51 = 149 students scored above 85 ================= Cheers, Stan H.
 Quadratic_Equations/138595: 1.Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. a)The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation. Would this be x= 1, y= 2 ? Is this right or should the number 56 be divided by x and y also? HELP1 solutions Answer 101144 by stanbon(57953)   on 2008-04-25 20:41:41 (Show Source): You can put this solution on YOUR website!The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation. --------------------------------------- Equation: x + y = 56 ================ Cheers, Stan H.
 Quadratic_Equations/138588: Solve: (logbase16 x)(logbase16 x)=1/41 solutions Answer 101142 by stanbon(57953)   on 2008-04-25 20:39:04 (Show Source): You can put this solution on YOUR website!Solve: (logbase16 x)(logbase16 x)=1/4 ------------------------------------------- (logbase16 x)^2 - 1/4 =0 Factor to get: (log16 x -1/2)(log16 x + 1/2 ) = 0 log16 x = 1/2 or log16 x = -1/2 x = 16^(1/2) or x = 16^(-1/2) x = 4 or x = 1/4 ===================== cheers, Stan H.
 Probability-and-statistics/138528: In a bumper test, three types of autos were delibertely crashed into a barrier at 5 mph, and the resulting damage(in dollars) was estimated. Five test vehicles of each type were crashed with the results showned below. Research question? Are the mean crash damages the same for these three vehicles? crash 1 Goliath 1,600, 760, 880, 1,950, 1,220 Vermint 1,290, 1,400, 1,390, 1,850, 950 Weasel 1,090, 2,100, 1,830, 1,250, 1,9201 solutions Answer 101139 by stanbon(57953)   on 2008-04-25 20:32:41 (Show Source): You can put this solution on YOUR website!All your problems have been answered and reside in the Prob and Stat category of this site. --------------- Go to www.algebra.com Use the search bar to find (one at a time) credits .....136383 Chucky.......135744 Hardtack.....136511 lovastation..136605 Coke.........136381 cockpit......133509 bumper.......136507 Mall cars....136384 ======================== cheers, Stan H.
 Probability-and-statistics/138547: Sherry Weinstein, a buyer, has decided that she will spend an extra \$7 per shirt for the next 10,000 T-shirts she buys for her chain of stores only if the vendor of the more expensive shirt can show conclusive evidence that its shirt can withstand at least 20 more times in the wash without fading. The vendor elected to set 1 as the mean number of washes without fading for the more expensive shirt. An appropriate null hypothesis for the vendor to test is: a. H0: u1 – u2<= 20. b. H0: u1 – u2 < 20. c. H0: u1 – u2 > 20. d. H0: u1 – u2<= 0. 1 solutions Answer 101136 by stanbon(57953)   on 2008-04-25 20:05:21 (Show Source): You can put this solution on YOUR website!Your posting was somewhat garbled. If u1 is the minimum number of extra washings the lady requires then Ho: u1-u2 >= 20 Ha: u1-u2 < 20 ====================== Cheers, Stan H.
 Probability-and-statistics/138586: Statistical software is commonly used for problem solving in the workplace. It is useful to look at a computer generated output to understand the format of the output, how the computerized solution treats an ANOVA table, and so on. The ANOVA table is somewhat standardized among various software packages. Formulate the null and alternate hypothesis and decide whether or not to reject it from the ANOVA table data provided below. Group 1 5 7 4 5 4 6 8 5 6 7 Group 2 6 7 7 5 6 7 8 6 8 6 Group 3 7 8 9 8 9 9 10 11 10 9 One factor ANOVA Mean n Std. Dev 7.1 5.7 10 1.34 Group 1 7.1 6.6 10 0.97 Group 2 7.1 9.0 10 1.15 Group 3 7.1 30 1.81 Total ANOVA table Source SS df MS F p-value Treatment 58.20 2 29.100 21.53 2.57E-06 Error 36.50 27 1.352 Total 94.70 29 Post hoc analysis Tukey simultaneous comparison t-values (d.f. = 27) Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 5.7 Group 2 6.6 1.73 Group 3 9.0 6.35 4.62 critical values for experimentwise error rate: 0.05 2.49 0.01 3.18 p-values for pairwise t-tests Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 5.7 Group 2 6.6 .0949 Group 3 9.0 8.54E-07 .0001 1 solutions Answer 101135 by stanbon(57953)   on 2008-04-25 19:59:23 (Show Source): You can put this solution on YOUR website!The ANOVA table is somewhat standardized among various software packages. Formulate the null and alternate hypothesis and decide whether or not to reject it from the ANOVA table data provided below. ------------------------------------------ One factor ANOVA Mean n Std. Dev 7.1 5.7 10 1.34 Group 1 7.1 6.6 10 0.97 Group 2 7.1 9.0 10 1.15 Group 3 7.1 30 1.81 Total ANOVA table Source.. SS df MS F p-value Treatment 58.20 2 29.100 21.53 ...2.57E-06 Error ........36.50 27 1.352 Total ........94.70 29 Post hoc analysis Tukey simultaneous comparison t-values (d.f. = 27) Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 ........5.7 Group 2 ........6.6 1.73 Group 3 ........9.0 6.35 4.62 critical values for experimentwise error rate: 0.05 2.49 0.01 3.18 p-values for pairwise t-tests Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 ........5.7 Group 2 ........6.6 .0949 Group 3 ........9.0 8.54E-07 .0001 --------------------------------------------------- Ho: The means of the three Groups were all equal Ha: At least one of the means was different. Since p-value = 0.00000257, Reject Ho. Conclusion: At least one of the mean values is different. =============================== Cheers, Stan H.
 Probability-and-statistics/138546: The weekly sales (in thousands of dollars) the week before and the week after a new Internet sales location is installed are given in the following table for 8 different businesses. Sales Before Sales After 27 ------------ 32 35 ------------ 36 22 ------------ 23 13 ------------ 12 45 ------------ 48 55 ------------ 57 60 ------------ 58 18 ------------ 30 The alternative hypothesis is HA: d > 0, where d = sales after – sales before. For level of significance 0.10, what is the critical value and the value of the test statistic? a. 1.645 and 1.70 b. 1.70 and 1.645 c. 1.70 and 1.895 d. 1.895 and 1.70 1 solutions Answer 101127 by stanbon(57953)   on 2008-04-25 16:07:40 (Show Source): You can put this solution on YOUR website!The weekly sales (in thousands of dollars) the week before and the week after a new Internet sales location is installed are given in the following table for 8 different businesses. Sales Before Sales After 27 ------------ 32 35 ------------ 36 22 ------------ 23 13 ------------ 12 45 ------------ 48 55 ------------ 57 60 ------------ 58 18 ------------ 30 The alternative hypothesis is HA: d > 0, where d = sales after – sales before. For level of significance 0.10, what is the critical value and the value of the test statistic? ---------------- You have 8 pairs so df=7 You have alpha = 10% on a one-tail t-test so critical value is t=1.415 ------------- Comment: Since your HA is d>0 the implication is that you are conducting a one-tail test. But your four optional answers imply that you are conducting a two tail test. If they want it to be two tail with df=7 and alpha=10%, the critical values will be : +/-1.895. I think your text is confused. ------------- a. 1.645 and 1.70 b. 1.70 and 1.645 c. 1.70 and 1.895 d. 1.895 and 1.70 =================================== Cheers, Stan H.
 Quadratic_Equations/138539: Solve: -10 <_ 3x-9 <_ -2 (the _ are supposed to be under the <) {x | ?? <_ x <_ ??} (again the _ is supposedto be under the <) Can someone hlp me with this. Do i add 2 to each equation first?? 1 solutions Answer 101126 by stanbon(57953)   on 2008-04-25 15:58:48 (Show Source): You can put this solution on YOUR website!-10 <= 3x-9 <= -2 ----------------------- Since you want to solve for "x", you work from the inside out. Add 9 along the line to get: -1 <= 3x <= 7 Divide by 3 along the line to get: -1/3 <= x <= 7/3 ===================== Cheers, Stan H.
 Quadratic_Equations/138554: Please help solve for vertex, axis of symmetry, y-intercept. (y=1/2x^2+4X+3)1 solutions Answer 101125 by stanbon(57953)   on 2008-04-25 15:55:20 (Show Source): You can put this solution on YOUR website!solve for vertex, axis of symmetry, y-intercept. (y=(1/2)x^2 + 4X + 3) ----------------------- Vertex and axis of symmetry occur where x = -b/2a = -4/(2*1/2)= -4 f(-4) = (1/2)16 -16+3 = -5 ------------------------------ y-intercept occurs where x = 0: y = 3 ====================================== Vertex: (-4,-5) Axis of sym: x = -4 y-intercept: y = 3 =========================== =========================== Cheers, Stan H.
 Probability-and-statistics/138548: A sample of 25 households in Prolific City revealed a mean of 7.5 residing members and a standard deviation of 3. If the mean household size for the nation is 4.2, what is the value of the test statistic? a. 27.5 b. 5.5 c. 1.1 d. 0.55 1 solutions Answer 101124 by stanbon(57953)   on 2008-04-25 15:47:14 (Show Source): You can put this solution on YOUR website!A sample of 25 households in Prolific City revealed a mean of 7.5 residing members and a standard deviation of 3. If the mean household size for the nation is 4.2, what is the value of the test statistic? ----------------- test statistic = t Assuming a 2-tail test with alpha = 5% you get: ts = 2.064[3/5] = 1.2384 ============================== Cheers, Stan H.
 Probability-and-statistics/138544: Help please.... Below are 3 groupings of data. Run an Analysis of Variance on these, and conclude if there is a statistical difference between the 3 groups. A 13, 16, 14, 16 B 10, 12 , 11, 12 C 14, 14, 15, 14 1 solutions Answer 101123 by stanbon(57953)   on 2008-04-25 15:42:04 (Show Source): You can put this solution on YOUR website!Below are 3 groupings of data. Run an Analysis of Variance on these, and conclude if there is a statistical difference between the 3 groups. A 13, 16, 14, 16 B 10, 12 , 11, 12 C 14, 14, 15, 14 ---------------------------- Ho: The three means are the same Ha: At least one of the means is different. ----------------------- I ran ANOVA on my TI calculator and generated the following: F = 12.585 p-value = 0.002 df = 2 Conclusion: Since p-value is less than 5%, reject Ho. At least one of the means is different. ============================= Cheers, Stan H.
 Probability-and-statistics/138545: A paired difference test is being conducted involving 19 pairs of observations. What is the number of degrees of freedom for the test statistic? a. 18 b. 19 c. 37 d. 38 1 solutions Answer 101122 by stanbon(57953)   on 2008-04-25 15:33:22 (Show Source): You can put this solution on YOUR website!You should use a t-test with 18 degrees of freedom. Cheers, Stan H.
 Graphs/138485: Ok..i dont know if anyone can help me with these, but please..i need help. Solve the systemof equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. x + y = 13 x - y =3 What is the solution of the system of equations? (Type an ordered pair. type N if there is no solution. Type R if the solution is all real numbers) Is the system consistent or inconsistent Are the equations dependent or independent.1 solutions Answer 101112 by stanbon(57953)   on 2008-04-25 09:14:12 (Show Source): You can put this solution on YOUR website!Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. --------- x + y = 13 x - y =3 What is the solution of the system of equations? (Type an ordered pair. type N if there is no solution. Type R if the solution is all real numbers) Is the system consistent or inconsistent ---------- Solve each equation for Y: y = -x+13 y = x -3 -------------- Graph the two equations on the same set of x/y axes ------------ ----------- The two lines meet at (8,5) The lines meet so the system is consistent. ------------- Cheers, Stan H.
 Equations/138484: 0.2[x-4]=x-5 over 51 solutions Answer 101111 by stanbon(57953)   on 2008-04-25 09:07:05 (Show Source): You can put this solution on YOUR website!0.2[x-4]=x-5 over 5 ------------ 0.2(x-4) = (x-5)/5 (1/5)(x-4) = (1/5)(x-5) x-4 = x-5 --------------- This is a contradiction. There is no solution. cheers, Stan H.
 Polynomials-and-rational-expressions/138471: how do i divide this tutor plz help : 2x^3 - x^2 + 3x -1) ÷ (x + 2)1 solutions Answer 101110 by stanbon(57953)   on 2008-04-25 08:23:18 (Show Source): You can put this solution on YOUR website!2x^3 - x^2 + 3x -1) ÷ (x + 2) -------------------------------- Using synthetic division: -2)....2....-1....3....-1 ........2.....-5...13..|..-27 Quotient: 2x^2-5x+13 Remainder: -27 ======================== Cheers, Stan H.
 Trigonometry-basics/138472: This question is from textbook Algebra and Trigonometry Hi, the problem cos^2 2x - sin^2 2x=0 is giving me trouble. I don't know what to do to solve it. Please help me. Thank you.1 solutions Answer 101109 by stanbon(57953)   on 2008-04-25 08:19:58 (Show Source): You can put this solution on YOUR website!cos^2 2x - sin^2 2x=0 ---------------------------- cos^2(2x) - [ 1-cos^2(2x)] = 0 2cos^2(2x) = 1 cos^2(2x) = 1/2 --------------------- cos(2x) = sqrt(2)/2 2x = 45 degrees or -45 degrees x = 22.5 degrees or -22.5 degrees ==================== Cheers, Stan H.
 Probability-and-statistics/138432: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully. Any help is much appreciated. Thank you, Sean1 solutions Answer 101108 by stanbon(57953)   on 2008-04-25 08:15:08 (Show Source): You can put this solution on YOUR website!A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? = (0.02)^2 = 0.0004 (b) Neither will fail?= (0.98)^2 = 0.9604 (c) One or the other will fail? = 1-(0.004+0.9604) = 0.0392 --------------------------- Comment: The answers to this problem were previously posted. --------------------------- Cheers, Stan H.
 Unit_Conversion_Word_Problems/138478: A rectangular trench is to be dug which is to be 300 ft long, 36 ft wide and 10 ft deep. A large dump truck can carry 20 cubic yards in a load. How many truck loads will be required to remove the dirt from this trench?1 solutions Answer 101107 by stanbon(57953)   on 2008-04-25 08:10:33 (Show Source): You can put this solution on YOUR website!A rectangular trench is to be dug which is to be 300 ft long, 36 ft wide and 10 ft deep. A large dump truck can carry 20 cubic yards in a load. How many truck loads will be required to remove the dirt from this trench? --------------------------------------- volume = (300*36*10) = 108000 cu. ft each cubic yard = 3*3*3 = 27 cu ft 20 cu. yards = 20*27 cu ft. = 540 cu ft. ---------- # of truck loads = 108000/540 = 200 ============= Cheers, Stan H.
 Points-lines-and-rays/138482: The perimeter of a rectangle is 208 inches. The length exceeds the width by 32 inches. Find the length and the width. The length is ? (Type an integer or a decimal) The width is ? (Type an integer or a decimal) Help me please..Thank you so much in advance. 1 solutions Answer 101106 by stanbon(57953)   on 2008-04-25 08:04:24 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 208 inches. The length exceeds the width by 32 inches. Find the length and the width. ---------- Let the width be "x" in. ; then the length will be "x+32" in. ----------- Formula: Perimeter = 2(length + width) 208 = 2(x+32 + x) 104 = 2x+32 2x = 72 x = 36 in. (this is the width) x+32 = 68 in. (this is the length) ==================================== Cheers, Stan H. The length is ? (Type an integer or a decimal) The width is ? (Type an integer or a decimal)
 Linear-equations/138476: Given 2p-x=50 and p=8000/(x+370), how can you find x?1 solutions Answer 101105 by stanbon(57953)   on 2008-04-25 08:00:13 (Show Source): You can put this solution on YOUR website!Given 2p-x=50 and p=8000/(x+370), how can you find x? --------------------------------------- Substitute the "x expression" in place of "p". ------- 2[8000/(x+370)] - x = 50 16000/(x+370) - x = 50 16000 - x(x+370) = 50(x+370) 16000 -x^2+370x = 50x+ 18500 x^2 -320x + 2500 = 0 x = [320 +-sqrt(320^2-4*2500)]/2 x = [320 +- sqrt(92400)]/2 x = [320 +- sqrt(400*231)/2 x = [320 + - 20sqrt(231)]/2 x = [160 +- 10sqrt(231)] x = 160 + 10sqrt(231) or x = 160 - 10sqrt(231) Cheers, Stan H.
 Percentage-and-ratio-word-problems/138480: If a is 75% of b,b is 150% of c and d is 25% of c,then find a:d a)9:1 b)9:2 c)8:3 d)8:1 1 solutions Answer 101104 by stanbon(57953)   on 2008-04-25 07:48:07 (Show Source): You can put this solution on YOUR website!If a is 75% of b,b is 150% of c and d is 25% of c,then find a:d a)9:1 b)9:2 c)8:3 d)8:1 -------------------------------------- a=0.75b b=1.5c d=0.25c ------------- a = 0.75[1.5[d/0.25]] a = 4.5d a/d = 9/2 a:d = 9:2 ================= Cheers, Stan H.
 Linear-equations/138479: Hello please help me i have a test on linear equation and i don't understand it and my test is on sunday please help me . thank you 1 solutions Answer 101103 by stanbon(57953)   on 2008-04-25 07:43:17 (Show Source): You can put this solution on YOUR website!May I suggest you post a couple of the problems you have to understand. Cheers, Stan H.
 Linear-systems/138481: Please, ia m not even sure if i am in the right area. Wont someone help me please????? Solve the system by the elimination method of these: 1) 5x + 5y = -11 7x - 2y = 13 2) 0.3x - 0.2y = 4 0.2x + 0.5y = 1 3) 6x - 9y = 13.5 7y - 2x = -6.5 4) 0.05x + 0.25y = 11 0.15x + 0.05y = 12 On these it says "What is the solution of the system". (Type an order pair. Type an integer or a decimal. Type N if there is no solution. Type I if there are infinitely many solutions) Will someone, anyone, please help me. I am so confused. thank you in advance to anyone that will take the time to help.1 solutions Answer 101102 by stanbon(57953)   on 2008-04-25 07:41:52 (Show Source): You can put this solution on YOUR website!Solve the system by the elimination method of these: 1) 5x + 5y = -11 7x - 2y = 13 ------------------- Multiply thru the 1st equation by 7; Multiply thru the 2nd equation by 5 to get: 35x + 35y = -77 35x - 10y = 65 ----------------- Subtract the 2nd equation from the 1st so you can solve for "y": 25y = -142 y = -142/25 -------------------- Substitute that into 5x+5y=-11 so you can solve for "x": 5x + 5(-142/25) = -77 5x - (142/5) = -77 5x = -77 + (142/5) 5x = -243/5 x = -243/25 ======================= 2) 0.3x - 0.2y = 4 0.2x + 0.5y = 1 Multiply thru both equations by 10 to get rid of the decimals: --------------------- 3x - 2y = 40 2x + 5y = 10 ----------------- Multiply the 1st equation by 2; Multiply the 2nd equation by 3 to get: 6x -4y = 80 6x +15y = 30 ------------------ Subtract the 1st equation from the 2nd to get: 19y = -50 y = -50/19 ------------------ Substitute that into 3x-2y=40 to solve for "x": 3x-2(-50/19) = 40 3x + (100/19) = 40 3x = 660/19 x = 220/19 ======================= Comment: Maybe you can handle #'s 3 and 4 now. Cheers, Stan H. 3) 6x - 9y = 13.5 7y - 2x = -6.5 Ans: x = -57/34; y=-89/34 ========================== 4) 0.05x + 0.25y = 11 0.15x + 0.05y = 12 Ans: x=70 ; y = 30 ========================== Cheers, Stan H.