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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 , 57180..57209 , 57210..57239, >>Next

 Square-cubic-other-roots/234288: Find all real and imaginary solutions w^2 = -225 Could someone please help me with this, I am drawing a blank!1 solutions Answer 172771 by stanbon(57282)   on 2009-11-02 18:20:06 (Show Source): You can put this solution on YOUR website!Find all real and imaginary solutions --- Factors of a^2+b^2 are (a+bi) and (a-bi) ----------------------- Your problem: w^2 = -225 w^2+225 = 0 --- w^2+15^2 = 0 --- (w+15i)(w-15i) = 0 w = -15i or w = +15i =================== Cheers, Stan H.
 Miscellaneous_Word_Problems/234289: Please help me solve this word problem: Find three consecutive odd integers such that three times the second minus the third is 17 more than the first. ----Thank you =)1 solutions Answer 172768 by stanbon(57282)   on 2009-11-02 18:16:08 (Show Source): You can put this solution on YOUR website!Find three consecutive odd integers such that three times the second minus the third is 17 more than the first. ----------------------- 1st: 2x-1 2nd: 2x+1 3rd: 2x+3 ---------------- Equation: 3(2x+1)-(2x+3) = (2x-1)+17 4x = 2x+16 2x = 16 x = 8 ------------ 1st: 2x-1 = 15 2nd: 17 3rd: 19 ==================== Cheers, Stan H.
 Geometry_Word_Problems/234287: Find the missing dimension in each rectangle. 12cm. width. area=276cm 2 squared, find missing dimension. 25ft. width. area=1125ft. 2 squared, find missing dimension1 solutions Answer 172765 by stanbon(57282)   on 2009-11-02 18:13:06 (Show Source): You can put this solution on YOUR website!Find the missing dimension in each rectangle. 12cm. width. area=276cm 2 squared, find missing dimension. Divide 276 by 12 to get the length ---------------------------------------------- 25ft. width. area=1125ft. 2 squared, find missing dimension Divide 1125 by 25 to get the length ================================================ Cheers, Stan H.
 Square-cubic-other-roots/234285: Simplify and reduce to lowest terms 1/(√t-5)-3/(√t+5)1 solutions Answer 172762 by stanbon(57282)   on 2009-11-02 18:09:54 (Show Source): You can put this solution on YOUR website!Simplify and reduce to lowest terms 1/(√t-5)-3/(√t+5) --- (sqrt(t+5) -3sqrt(t-5))/(t-25) ==================================== Cheers, Stan H.
 Travel_Word_Problems/234236: #5 EllEN WISHES TO MIX CANDY WORTH \$1.85 PER POUND WITH CANDY WORTH \$3.33 PER POUND TO FORM 29 POUNDS OF A MIXTURE WORTH \$2.62 PER POUND. HOW MANY POUNDS OF THE MORE EXPENSIVE CANDY SHOULD SHE USE?1 solutions Answer 172759 by stanbon(57282)   on 2009-11-02 18:07:18 (Show Source): You can put this solution on YOUR website!EllEN WISHES TO MIX CANDY WORTH \$1.85 PER POUND WITH CANDY WORTH \$3.33 PER POUND TO FORM 29 POUNDS OF A MIXTURE WORTH \$2.62 PER POUND. HOW MANY POUNDS OF THE MORE EXPENSIVE CANDY SHOULD SHE USE? ---------------------------------- Equation: value + value = value 1.85x + 3.33(29-x) = 2.62*29 Multiply thru by 100 to get: 185x + 333*29 - 333x = 262*29 -148x = -71*29 --- x = 13.91 lb (amount of \$1.85 candy needed in the mix) -------------- 29-x = 29-13.91 = 15.09 lb (amount of \$3.33 candy needed in the mix) ======================== Cheers, Stan H.
 Rational-functions/234192: g/g^2+6g-7-6/g-11 solutions Answer 172717 by stanbon(57282)   on 2009-11-02 16:08:07 (Show Source): You can put this solution on YOUR website!g/(g^2+6g-7) - 6/(g-1) --------------------------- Factor: g/[(g+7)(g-1)] - 6/(g-1) ------------------------ gcd = (g+7)(g-1) ------------------------ Rewrite each fraction with the gcd as its denominator. g/gcd - 6(g+7)/gcd ------------------------- Combine over the gcd: (g-6)/[g+7)(g-1)] =========================== Cheers, Stan H.
 Quadratic_Equations/234184: For this problem I need to complete the square, and find the roots of the quadratic equation x^2 + 16x = 01 solutions Answer 172716 by stanbon(57282)   on 2009-11-02 16:03:29 (Show Source): You can put this solution on YOUR website!complete the square, and find the roots of the quadratic equation x^2 + 16x = 0 --- x^2 + 16x + 64 = 64 (x+8)^2 = 64 x+8 = 8 or x+8 = -8 x = 0 or x = -16 --------------------- Cheers, Stan H.
 Inequalities/234199: suppose it costs 5 dollars to enter a carnival. Each ride costs 1.25 dollars. you have 15 dollars to spend at the carnival. What is the greatest number of rides that you can go on?1 solutions Answer 172713 by stanbon(57282)   on 2009-11-02 15:57:46 (Show Source): You can put this solution on YOUR website!suppose it costs 5 dollars to enter a carnival. Each ride costs 1.25 dollars. you have 15 dollars to spend at the carnival. What is the greatest number of rides that you can go on? ------------- Let # of rides you can go on = "x": Equation: 5 + 1.25x = 15 1.25x = 10 x = 8 ============ Cheers, Stan H.
 Linear-systems/234195: What is the solution set to the following equations: 3x-2y=4,4x+5y=281 solutions Answer 172711 by stanbon(57282)   on 2009-11-02 15:54:09 (Show Source): You can put this solution on YOUR website!What is the solution set to the following equations: 3x-2y=4 4x+5y=28 ---------- Multiply thru the 1st equation by 5; Multiply thru the 2nd by 2 --------- 15x-10y=20 8x+10y=56 --------------- Add the two equations and solve for "x": 23x = 76 x = 76/23 --------------------- Substitute into 3x-2y = 4 to solve for "y": 3(76/23) - 2y = 4 (228/23) - 2y = (92/23) 2y = 136/23 y = 68/23 ==================== Cheers, Stan H.
 Quadratic_Equations/234186: I need to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. (it is not necessary to find the roots; just determine the number and types of solutions) x^2 + 6x - 7 = 01 solutions Answer 172707 by stanbon(57282)   on 2009-11-02 15:46:55 (Show Source): You can put this solution on YOUR website!I need to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. (it is not necessary to find the roots; just determine the number and types of solutions) x^2 + 6x - 7 = 0 ------------------------ discriminant = b^2-4ac = 6^2-4*1*-7 = 36+28 = 64 ----------- Since the discriminant is positive, the quadratic has 2 unequal Real Number solutions. ====================================== Cheers, Stan H.
 Triangles/234188: Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 401 solutions Answer 172702 by stanbon(57282)   on 2009-11-02 15:32:15 (Show Source): You can put this solution on YOUR website!Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40 ------------------ Ans: 22 Why? because 14+22=34 Those three side lengths would give you a line segment 34 long. They would not form a triangle. Cheers, Stan H.
 Geometry_Word_Problems/234189: If the area a of a triangle is 60 sq m and the base is 20 m what is the altitude1 solutions Answer 172700 by stanbon(57282)   on 2009-11-02 15:29:54 (Show Source): You can put this solution on YOUR website!If the area a of a triangle is 60 sq m and the base is 20 m what is the altitude ------------- Area = (1/2)bh 60 = (1/2)*20h 60 = 10h h = 6 meters =================== Cheers, Stan H.
 Probability-and-statistics/234143: To test the null hypothesis that the average lifetime for a particular brand of bulb is 725 hours versus the alternative that the average lifetime is different from 725 hours, a sample of 90 bulbs is used. If the standard deviation is 75 hours and α is equal to 0.05, what values for will result in rejection of the null hypothesis (show all work). Thanks for all your help!!1 solutions Answer 172699 by stanbon(57282)   on 2009-11-02 15:27:33 (Show Source): You can put this solution on YOUR website!To test the null hypothesis that the average lifetime for a particular brand of bulb is 725 hours versus the alternative that the average lifetime is different from 725 hours, a sample of 90 bulbs is used. -------------------------------------------------------------- If the standard deviation is 75 hours and α is equal to 0.05, what values for will result in rejection of the null hypothesis (show all work). ------------ A two-tail test is implied. The rejection interval is a function of alpha = 5% and the degrees of freedom. --- invT(0.025,89) = -1.0987 ----------------------------------- The rejection interval is (-inf,-1.0987)U(1.0987,+inf) ============================================================ Cheers, Stan H.
 Equations/234056: Which of the following pairs of equations has no solution? A}k+2j=6,k-2j=4 B}k+2j=6,k+2j=4 C}k+2j=6,k+4j=12 d}k+2j=6,k-4j=12 1 solutions Answer 172630 by stanbon(57282)   on 2009-11-02 07:21:06 (Show Source): You can put this solution on YOUR website!Which of the following pairs of equations has no solution? In each case check the slopes and the intercepts. ======================== A}k+2j=6,k-2j=4 k = -2j+6 k = 2j+4 Slopes different so has a solution ------------------------------------- B}k+2j=6,k+2j=4 k = -2j+6 k = -2j+4 Slopes equal so no solution -------------------------------------- C}k+2j=6,k+4j=12 slopes different --------------------- d}k+2j=6,k-4j=12 slopes different ======================== Cheers, Stan H.
 Equations/234055: Please help me to solve the system: r+d=9 r-d=-5 1 solutions Answer 172629 by stanbon(57282)   on 2009-11-02 07:16:58 (Show Source): You can put this solution on YOUR website!solve the system: r+d=9 r-d=-5 ----------- Add the two equations and solve for "r": 2r = 4 r = 2 ------------- Substitute into r+d = 9 to solve for "d": 2+d = 9 d = 7 ------------------- Cheers, Stan H.
 Exponential-and-logarithmic-functions/234053: What are the steps to finding 4(log9 of X)^2 - 2(log9 of X^2)=3?1 solutions Answer 172628 by stanbon(57282)   on 2009-11-02 07:14:29 (Show Source): You can put this solution on YOUR website!What are the steps to finding 4(log9 of X)^2 - 2(log9 of X^2)=3? ------------------ It is a quadratic with w = (log9 (x)) ------------- Rewrite as: 4w^2 - 2w - 3 = 0 -- w = [2 +- sqrt(4 -4*4*-3)]/8 --- w = [2 +- sqrt(52)]/8 --- w = [2 +- 2sqrt(13)]/8 --- w = [(1/4) + (1/4)sqrt(13)] or w = [(1/4) - (1/4)sqrt(13)] ---------------- Now solve for "x" log9 (x) = [(1/4) + (1/4)sqrt(13)] or log9 (x) = [(1/4) - (1/4)sqrt(13)] --- x = 9^[(1/4) + (1/4)sqrt(13)] or x = 9^[(1/4) - (1/4)sqrt(13)] --- x = 12.55.. or x = 0.239... ================================= Cheers, Stan H.
 Probability-and-statistics/233963: Question: A die is rolled and a spiner (4 sides) is spun. Find the probability: P ( an even number and C) P ( 2 or 5 and B or D) P ( a number less than 5 and B or D) One card is drawn from a standard deck of 52 cards. Find each probability P( Jack or ten) P(queen or Club) ( (diamond or black)1 solutions Answer 172627 by stanbon(57282)   on 2009-11-02 06:49:27 (Show Source): You can put this solution on YOUR website!Question: A die is rolled and a spiner (4 sides) is spun. Find the probability: P ( an even number and C) = (3/6)*(1/4) P ( 2 or 5 and B or D) = (2/6)*(2/4) P ( a number less than 5 and B or D)= (4/6)*(2/4) One card is drawn from a standard deck of 52 cards. Find each probability P( Jack or ten)= (4/52) + (4/52) P(queen or Club) = (4/52) + (13/52) - (1/52) ( (diamond or black)= (13/52) + (26/52) ============================================== Cheers, Stan H.
 Probability-and-statistics/233879: The average lifespan for batteries is 90 hours with a standard deviation of 12 hours. Construct a confidence interval at the 95% confidence level.1 solutions Answer 172626 by stanbon(57282)   on 2009-11-02 06:43:46 (Show Source): You can put this solution on YOUR website!The average lifespan for batteries is 90 hours with a standard deviation of 12 hours. Construct a confidence interval at the 95% confidence level. ----------- sample mean: 90 standard error: 1.96*12 = 23.52 95% CI: 90-23.52 < u < 90+23.52 95% CI: 66.48 < u < 113.52 ================================= Cheers, Stan H.
 Probability-and-statistics/233967: a menu has three choices for salad, six main dishes, and four desserts. how many different meals are available if you select a salad, a main dish, and a dessert?1 solutions Answer 172625 by stanbon(57282)   on 2009-11-02 06:03:42 (Show Source): You can put this solution on YOUR website!Ans: 3*6*4 = 72 Cheers, Stan H.
 Probability-and-statistics/233772: In testing the hypothesis, and , using the p-value approach, a p-value of 0.0668 was obtained. If σ = 9.2, find a sample mean which produced this p-value given that the sample of size n = 45 was randomly selected (show all work). 1 solutions Answer 172624 by stanbon(57282)   on 2009-11-02 06:02:09 (Show Source): You can put this solution on YOUR website!In testing the hypothesis, and , using the p-value approach, a p-value of 0.0668 was obtained. If σ = 9.2, find a sample mean which produced this p-value given that the sample of size n = 45 was randomly selected (show all work). ---------------- That depends on whether the hypothesis is = , >= , or <=. Cheers, Stan H.
 Probability-and-statistics/233773: A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 150 was taken, and the mean amount spent was \$225. Assuming a standard deviation equal to \$50, find the 95% confidence interval for μ, the mean for all such families (show all work). 1 solutions Answer 172623 by stanbon(57282)   on 2009-11-02 05:58:10 (Show Source): You can put this solution on YOUR website!A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 150 was taken, and the mean amount spent was \$225. Assuming a standard deviation equal to \$50, find the 95% confidence interval for μ, the mean for all such families (show all work). -------------------- sample mean: 225 standard error: 1.96*50/(sqrt(150) = 8 ---------------------- 95% CI: 225-8 < u < 225+8 Ans: (217,233) ==================== Cheers, Stan H.
 Probability-and-statistics/234041: What is the probability of Jonah picking a vowel if he randomly chooses a letter from the word "CAT" ? Express your answer as a common fraction.1 solutions Answer 172622 by stanbon(57282)   on 2009-11-02 05:54:28 (Show Source): You can put this solution on YOUR website!Ans: 1/3 Cheers, Stan H.
 Probability-and-statistics/233778: Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 80 hours. 1 solutions Answer 172621 by stanbon(57282)   on 2009-11-02 05:53:11 (Show Source): You can put this solution on YOUR website!Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 80 hours. ------------------- Ho: u >= 80 Ha: u < 80 =============== Cheers, Stan H.
 Probability-and-statistics/233780: Write a correct alternative hypothesis that tests the claim that the mean distance a student commutes to campus is no less than 7.5 miles1 solutions Answer 172620 by stanbon(57282)   on 2009-11-02 05:51:10 (Show Source): You can put this solution on YOUR website!Write a correct alternative hypothesis that tests the claim that the mean distance a student commutes to campus is no less than 7.5 miles -------------------- "No less than" means greater than or equal to. So the alternate hypothesis is u < 7.5 Cheers, Stan H.
 Probability-and-statistics/233782: If you are constructing a 95% confidence interval using the information: n = 50, = 65.4, s = 2.1 and E = 0.65. What is the middle value of the interval? 1 solutions Answer 172619 by stanbon(57282)   on 2009-11-02 05:48:38 (Show Source): You can put this solution on YOUR website!If you are constructing a 95% confidence interval using the information: n = 50, = 65.4, s = 2.1 and E = 0.65. What is the middle value of the interval? ----------------- The middle value is the sample mean, Your data left out the symbol but I think you meant to list 65.4 as the sample mean. Cheers, Stan H.
 Exponents-negative-and-fractional/233904: i don not understand this could you help me? my paper says simplify the expression. write your answer using exponents. 5^4 x 5^81 solutions Answer 172560 by stanbon(57282)   on 2009-11-01 20:07:29 (Show Source): You can put this solution on YOUR website!i don not understand this could you help me? my paper says simplify the expression. write your answer using exponents. 5^4 x 5^8 -------------------------------------- 5^4 means 5*5*5*5 5^8 means 5*5*5*5*5*5*5*5 ----- So 5^4*5^8 = 5^(4+8) = 5^12 ================================== Cheers, Stan H.
 Points-lines-and-rays/233901: A 25ft ladder is placed at an angle to a wall of a building. The top of the ladder is 28 ft above the ground.what is the distance of the foot of the ladder from the bottom of the building? Thanks n advance...1 solutions Answer 172554 by stanbon(57282)   on 2009-11-01 20:01:01 (Show Source): You can put this solution on YOUR website!A 25ft ladder is placed at an angle to a wall of a building. The top of the ladder is 28 ft above the ground.what is the distance of the foot of the ladder from the bottom of the building? --------------------- Draw the picture. You have a right triangle: the hypotenuse is 25 ft the height on the wall is 28 ft. ------------------ Comment: The conditions you posted are impossible. A leg of the triangle cannot be longer than the hypotenuse. ------------------ Cheers, Stan H.
 Expressions-with-variables/233899: Solve for X -5=3/8(x-1) 1 solutions Answer 172551 by stanbon(57282)   on 2009-11-01 19:56:33 (Show Source): You can put this solution on YOUR website!-5=(3/8)(x-1) --- Multiply both sides by 8 to get: -40 = 3(x-1) 3x-3 = -40 3x = -37 x = -37/3 ================== Cheers, Stan H.
 Expressions-with-variables/233895: Solve for X Not sure how to solve when you have a variable on each side of the equation X=2(X-1)+6 I got to the point of X=2X+4 but are not sure what to do next1 solutions Answer 172545 by stanbon(57282)   on 2009-11-01 19:52:02 (Show Source): You can put this solution on YOUR website!I got to the point of X=2X+4 but are not sure what to do next --- Subtract "X" from both sides to get: 0 = X + 4 Subtract 4 from both sides to get: X = -4 ============== Cheers, Stan H.
 Probability-and-statistics/233878: A local manufacturer wants to know how long to guarantee her toasters. A random sample of 16 toasters has an average lifespan of 1,000 hours with a standard deviation of 200 hours. If she doesn't want to replace any more than 10% of the toasters, for how long should she gaurantee her toasters?1 solutions Answer 172542 by stanbon(57282)   on 2009-11-01 19:47:50 (Show Source): You can put this solution on YOUR website!A local manufacturer wants to know how long to guarantee her toasters. A random sample of 16 toasters has an average lifespan of 1,000 hours with a standard deviation of 200 hours. If she doesn't want to replace any more than 10% of the toasters, for how long should she gaurantee her toasters? -------------------------------------- Find the z-value associated with a left tail of 10%. I used my TI-84 calculator to get: invNorm(0.10) = -1.2816 --------------------- Find the "x" value associated with that z value using x = zs + u x = -1.2816*200 + 1000 x = 743,69 hours ---------------------- She should guantee them for around 745 hrs. of use ======================================================== Cheers, Stan H.
 Probability-and-statistics/233872: The average flight from point A to B takes 40 minutes with a standard deviation of 5 minutes. What is the probability a random sample of 4 flights will take between 38 and 43 minutes? 1 solutions Answer 172533 by stanbon(57282)   on 2009-11-01 19:28:06 (Show Source): You can put this solution on YOUR website!The average flight from point A to B takes 40 minutes with a standard deviation of 5 minutes. What is the probability a random sample of 4 flights will take between 38 and 43 minutes? --------------------------------------------------------- z(38) = (38-40)/[5/[sqrt(4)] = -0.8 ---------- z(43) = (43-40)/[5/sqrt(4)] = 1.2 --------------------------- P(38 < x < 43) = P(-0.8 < z < 1.2) = 0.6731 ================================================== Cheers, Stan H. ------------