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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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 Probability-and-statistics/266359: A recent study of 300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels, and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following: a. An alcoholic with elevated cholesterol b. A nonalcoholic c. A nonalcoholic with nonelevated cholesterol level. Thanks!1 solutions Answer 195764 by stanbon(57984)   on 2010-02-06 20:58:27 (Show Source): You can put this solution on YOUR website!A recent study of 300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels, and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following: ---- Procedure: 1st: I sketched a contingency table with 2 rows(alc and non-alc) and 2 columns (high choles and low choles) --- 2nd: I put the given numbers into the contingency table and filled in the missing numbers. ------- Find the probability that the patient is the following: a. An alcoholic with elevated cholesterol: 87/300 b. A nonalcoholic: 200/300 c. A nonalcoholic with nonelevated cholesterol level: 43/300 ================================================================ Cheers, Stan H.
 Age_Word_Problems/266447: Jennifer is twice as old as Ramon. The sum of their ages 7 years ago was 13. How old are they now?1 solutions Answer 195759 by stanbon(57984)   on 2010-02-06 20:47:10 (Show Source): You can put this solution on YOUR website! Jennifer is twice as old as Ramon. The sum of their ages 7 years ago was 13. How old are they now? --- Equations: J = 2R (J-7)+(R-7) = 13 ------- Substitute for "J" and solve for "R": 2R-7 + R-7 = 13 3R - 14 = 13 3R = 27 R = 9 (Ramon's age now) ------ J = 2R = 18 (Jennifer's age now) =================================== Cheers, Stan H.
 Probability-and-statistics/266372: A company manufactures calculators in batches of 45 and claims that the rate of defects is 4%. Find the probability of getting exactly 2 defects in a batch of 45 if the rate of defects is 4%. If a store receives a batch of 45 calculators and finds that there are 2 defective calculators, do they have any reason to doubt the company's claimed rate of defects? Possible answers: a. 0.263; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators. b. 0.548; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators. c. 0.0166; Yes. If the rate of defects is really 4%, the probability of finding 2 defects in a batch of 45 calculators is very small. d. 0.274; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.1 solutions Answer 195756 by stanbon(57984)   on 2010-02-06 20:39:28 (Show Source): You can put this solution on YOUR website!A company manufactures calculators in batches of 45 and claims that the rate of defects is 4%. Find the probability of getting exactly 2 defects in a batch of 45 if the rate of defects is 4%. Binomial Problem: n = 45 ; p = 0.04 ; x=2 P(x=2) = 45C2(0.4)^2(0.96)^43 = 0.2738 ----------------------------------------- Ans: d ----------- If a store receives a batch of 45 calculators and finds that there are 2 defective calculators, do they have any reason to doubt the company's claimed rate of defects? No, the probability is better than 27% that 2 defects would be found in a batch of 45. ========================================================================== Cheers, Stan H. ========================================================================== Possible answers: a. 0.263; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators. b. 0.548; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators. c. 0.0166; Yes. If the rate of defects is really 4%, the probability of finding 2 defects in a batch of 45 calculators is very small. d. 0.274; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
 Polynomials-and-rational-expressions/266446: The following problem is from my college algebra class using the book "Introduction to Algebra." A polynomial in x has a degree 3. The coefficient of x squared is 3 less than the coefficient of x to the 3rd.? The coefficient of x is three times the coefficient of x squared. The remaining coefficient is 2 more than the coefficient of x to the third. The sum of the coefficients is -4. What is the polynomial? I honestly don't even know where to begin, I started by using simple guesses and it got me nowhere. They assign us the most difficult question in the exercise set even though the text in no way prepares us for the answer. Please help!1 solutions Answer 195751 by stanbon(57984)   on 2010-02-06 20:27:46 (Show Source): You can put this solution on YOUR website!A polynomial in x has a degree 3. The coefficient of x squared is 3 less than the coefficient of x to the 3rd. The coefficient of x is three times the coefficient of x squared. The remaining coefficient is 2 more than the coefficient of x to the third. The sum of the coefficients is -4. What is the polynomial? ------------- y = kx^3 + (k-3)x^2 + (3k-9)x +(k+2) ---------------------------------------- Equation: k + (k-3) + 3k-9 + k+2 = -4 6k -10 = -4 6k = 6 k = 1 ---- Polynomial: y = x^3 - 2x^2 -6x + 3 ============================= Cheers, Stan H.
 Probability-and-statistics/266373: Use the Poisson Distribution to find the indicated probability. The town of Fastville has been experiencing a mean of 68.7 car accidents per year. Find the probability that on a given day the number of car accidents in Fastville is 3. (Assume 365 days in a year.) Possible answers: a. 0.000921 b. 0.000801 c. 0.00103 d. 0.000120 1 solutions Answer 195746 by stanbon(57984)   on 2010-02-06 20:20:26 (Show Source): You can put this solution on YOUR website!The town of Fastville has been experiencing a mean of 68.7 car accidents per year. Find the probability that on a given day the number of car accidents in Fastville is 3. (Assume 365 days in a year.) ----- Using a TI84 I get poissonpdf(68.7/365,3) = 0.000921... Cheers, Stan H. Possible answers: a. 0.000921 b. 0.000801 c. 0.00103 d. 0.000120
 Probability-and-statistics/266375: Use the Poisson Distribution to find the indicated probability. The number of calls received by a car towing service averages 19.2 per day (per 24-hour period). After finding the mean number of calls per hour, find the probability that in a randomly selected hour the number of calls is 2. a. 0.15816 b. 0.14379 c. 0.11503 d. 0.17973 1 solutions Answer 195744 by stanbon(57984)   on 2010-02-06 20:15:52 (Show Source): You can put this solution on YOUR website!Use the Poisson Distribution to find the indicated probability. The number of calls received by a car towing service averages 19.2 per day (per 24-hour period). After finding the mean number of calls per hour, find the probability that in a randomly selected hour the number of calls is 2. ----- I used the poissonpdf((19.2/24),2) function on a TI-84 and got 0.14379 ================== Cheers, Stan H. ================== a. 0.15816 b. 0.14379 c. 0.11503 d. 0.17973
 Roman-numerals/266348: Three-quarters of a certain number exceeds two-thirds of it by 3.Find the number 1 solutions Answer 195689 by stanbon(57984)   on 2010-02-06 14:35:26 (Show Source): You can put this solution on YOUR website!Three-quarters of a certain number exceeds two-thirds of it by 3.Find the number ---------------------- Let the number be "x": Equation: (3/4)x = (2/3)x + 3 --- [(3/4)-(2/3)]x = 3 (1/12)x = 3 x = 36 ------------- Cheers, Stan H.
 Equations/266346: L=a+(n-1)d ;d=?1 solutions Answer 195687 by stanbon(57984)   on 2010-02-06 14:32:05 (Show Source): You can put this solution on YOUR website!L=a+(n-1)d ;d=? ----------------- L - a = (n-1)d d = (L-a)/(n-1) ================== Cheers, Stan H.
 Probability-and-statistics/266344: Student has 10 question test with 5 choices for each answer. He needs to answer 60% or > to pass. If he randomly guesses, what is the % probability he will pass? thank you Choices are: 0.006 0.377 0.0601 solutions Answer 195686 by stanbon(57984)   on 2010-02-06 14:29:31 (Show Source): You can put this solution on YOUR website!Student has 10 question test with 5 choices for each answer. He needs to answer 60% or > to pass. If he randomly guesses, what is the % probability he will pass? thank you Choices are: 0.006 0.377 0.060 ---- Binomial Problem: n = 10, p(correct) = 1/5, q(wrong) = 4/5 --- Find P(6 <= x <=10) = 1 - binomcdf(10,1/5,5) = 0.0064 ============= Cheers, Stan H.
 Linear-equations/266334: Please explain this problem step by step Solve each system of inequalities by graphing: 2x+y<(less than or equal to) 4 y+1>(greater than or equal to) -2x1 solutions Answer 195683 by stanbon(57984)   on 2010-02-06 14:19:22 (Show Source): You can put this solution on YOUR website!Solve each system of inequalities by graphing: 2x+y<(less than or equal to) 4 y+1>(greater than or equal to) -2x -------------------------------------------- ALWAYS graph the boudary of the inequality first: Graph y = -2x+4 with a solid line because = is included in your equation. Then shade the area BELOW the boundary because you want y LESS than -2x+4 ------------------------ Graph y = -2x-1 with a solid line. Then shade the half-plane ABOVE the boundary because you want y GREATER than -2x-1 ------------------------ The solution set is the intersection of the two graphs. ========================================================= Cheers, Stan H.
 Miscellaneous_Word_Problems/266340: a trucker drove for 4 hours before he encountered icy road condition. He reduced his speed by 20 mph and continued driving for 3 more hours. Find his average speed during the first part of the trip if the entire trip was 325 miles.1 solutions Answer 195682 by stanbon(57984)   on 2010-02-06 14:02:50 (Show Source): You can put this solution on YOUR website!a trucker drove for 4 hours before he encountered icy road condition. He reduced his speed by 20 mph and continued driving for 3 more hours. Find his average speed during the first part of the trip if the entire trip was 325 miles. --- 1st segment DATA: time = 4 hrs. ; rate = x mph ; distance = rt = 4x miles ------------------ 2nd segment DATA: time = 3 hrs. ; rate = x-20 mph ; distance = rt = 3x-60 miles --------------------- Equation: distance + distance = 325 miles 4x + 3x-60 = 325 miles 7x = 385 x = 55 mph (rate during 1st segment) ============================= Cheers, Stan H.
 Probability-and-statistics/266302: I am having a hard time figuring this out. The null and alternative hypotheses are: HO: The cell categories are equal. H1: The cell categories are not equal. The significance level is 0.05. Category fo A 10 B 20 C 30 D 20 Compute the value of chi-square. 1 solutions Answer 195680 by stanbon(57984)   on 2010-02-06 13:57:56 (Show Source): You can put this solution on YOUR website!I am having a hard time figuring this out. The null and alternative hypotheses are: HO: The cell categories are equal. H1: The cell categories are not equal. The significance level is 0.05. Category fo A 10 B 20 C 30 D 20 Compute the value of chi-square. ----------------- The numbers you have for A,B,C etc. are the "observed" data values. The "expected" data values would be 20,20,20,20 since there are 80 data points and four categories. --- List the "observed" values in one set. List the expected values in another set. Run a Chi-Sq Goodness-of-Fit test on the two sets. --- I did and got: Chi-Sq = 10 p-value = 0.1886 --- Conclusion: Since the p-value is greater than 5% fail to reject Ho. ========================== Cheers, Stan H.
 Proportions/266292: 1:3/4 = 2/3:x what is x1 solutions Answer 195671 by stanbon(57984)   on 2010-02-06 10:33:23 (Show Source): You can put this solution on YOUR website!1:3/4 = 2/3:x what is x -------------- 1/(3/4) = (2/3)/x Cross-multiply to get: --- x = (3/4)(2/3) x = 1/2 =============== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/266276: I need to write a linear inequality for: A company manufactures and sells personalized stationery. The weekly fixed cost is \$3000 and it costs \$3.00 to produce each package of stationery. The selling price is \$5.50 per package. How many packages of stationery must be produced and sold each week for the company to have a profit? I am not sure where to start. I was thinking N=300x + 3000 and N=550x+3000 but I don't believe that is correct. Help?1 solutions Answer 195662 by stanbon(57984)   on 2010-02-06 09:18:41 (Show Source): You can put this solution on YOUR website!I need to write a linear inequality for: A company manufactures and sells personalized stationery. The weekly fixed cost is \$3000 and it costs \$3.00 to produce each package of stationery. The selling price is \$5.50 per package. How many packages of stationery must be produced and sold each week for the company to have a profit? --- Let the number of packs sold be "x". Revenue = 5.50x dollars Overhead = 3000 + 3.00x --------------- Inequality: Profit means Revenue > Overhead Solve 5.50x > 3000+3.00x for "x": 2.50x > 3000 x > 1200 (# of packs they need to sell to make a profit) ===================================== Cheers, Stan H. =====================================
 Miscellaneous_Word_Problems/266267: An escalator moves up at a rate of x steps per second. Walter walks up the escalator at the rate of one step per second and reaches the top in twenty seconds.The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds. How many steps does the escalator have? (A) 40 (B) 50 (C) 60 (D) 80 (E) none of these 1 solutions Answer 195659 by stanbon(57984)   on 2010-02-06 09:12:27 (Show Source): You can put this solution on YOUR website!An escalator moves up at a rate of x steps per second. Walter walks up the escalator at the rate of one step per second and reaches the top in twenty seconds. The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds. How many steps does the escalator have? ====== Assume the escalator has "s" steps --------- The escalator rate = x steps per second Walter's rate = 1 step per second --- In the 20 seconds it takes Walter from bottom to top at one step per second, the escalator has gone up 20x steps. Also Walter has gone up 20 steps. So 20x + 20 = s --- In the 16 seconds it takes Walter from bottom to top at 2x steps per second, the escalator has gone up 16x steps. Also Walter has gone up 2(16) steps. So 16x + 32 = s ---- Solve 20x+20 = 16x +32 for "x". 4x = 12 x = 3 steps per second --- Then s = 20x + 20 = 20*3 +20 = 80 (# of steps is 80) ========================================================= Cheers, Stan H. (A) 40 (B) 50 (C) 60 (D) 80 (E) none of these
 Numbers_Word_Problems/266270: Michelle receives a 10 percent raise every year. Her salary after four such raises has gone up by what percent? (A) between 30 and 35 percent (B) between 35 and 40 percent (C) between 40 and 45 percent (D) between 45 and 50 percent (E) none of these 1 solutions Answer 195654 by stanbon(57984)   on 2010-02-06 08:23:59 (Show Source): You can put this solution on YOUR website! Michelle receives a 10 percent raise every year. Her salary after four such raises has gone up by what percent? ---- If she starts at salary = x 1st raise she has x + 0.1x = (1.1)x 2nd raise she has (1.1)x + 0.1(1.1x) = (1.1)x(1.1) = (1.1)^2 x 3rd raise she has (1.1)^3 x 4th raise she has (1.1)^4x ---- 1.1^4 = 1.4641 1.4641x = x + 0.4641x % increase = 46.41% =========================== Cheers, Stan H. (A) between 30 and 35 percent (B) between 35 and 40 percent (C) between 40 and 45 percent (D) between 45 and 50 percent (E) none of these
 Numbers_Word_Problems/266272: The sum of three consecutive integers starting with x is 24 Write down and solve an equation to find the three integers.1 solutions Answer 195653 by stanbon(57984)   on 2010-02-06 08:18:29 (Show Source): You can put this solution on YOUR website!The sum of three consecutive integers starting with x is 24 Write down and solve an equation to find the three integers. --- 1st: x 2nd: x+1 3rd: x+2 ---------- Equation: 3x + 3 = 24 x+1 = 8 x = 7 --- 1st: 7 2nd: 8 3rd: 9 ============== Cheers, Stan H.
 Numbers_Word_Problems/266269: The sum of the square of 22 and the square of 19 equals the sum of the squares of two other two-digit numbers. Give the sum of four digits of the other two-digit numbers. (A) 11 (B) 12 (C) 18 (D) 21 (E) none of these 1 solutions Answer 195652 by stanbon(57984)   on 2010-02-06 08:16:17 (Show Source): You can put this solution on YOUR website!The sum of the square of 22 and the square of 19 equals the sum of the squares of two other two-digit numbers. Give the sum of four digits of the other two-digit numbers. --- 22^2 + 19^2 = x^2 + y^2 845 = x^2 + y^2 --- 845 = 169 + 676 845 = 13^2 + 26^2 --- Sum of digits = 1+3+2+6 = 12 =================================== Cheers, Stan H. =================================== (A) 11 (B) 12 (C) 18 (D) 21 (E) none of these
 Numeric_Fractions/266271: 1/X + 1/Y = -1/Z Y=2 and z=3 1/X + 1/2 = -1/3 - 1/2 -1/2 1/X = -5/6 X = -5/6 Please help is this correct??? Thanks 1 solutions Answer 195651 by stanbon(57984)   on 2010-02-06 08:08:16 (Show Source): You can put this solution on YOUR website!1/X + 1/Y = -1/Z Y=2 and z=3 1/X + 1/2 = -1/3 - 1/2 -1/2 1/X = -5/6 Invert both sides to solve for X: X = -6/5 ================ Cheers, Stan H.
 Geometry_Word_Problems/266265: Two opposite sides of a square are increased by twenty-five percent while the other two are decreased by forty percent. Find the percent of decrease in the area of the square. (A) 15% (B) 25% (C) 30% (D) 32.5% (E) none of these 1 solutions Answer 195650 by stanbon(57984)   on 2010-02-06 08:05:43 (Show Source): You can put this solution on YOUR website! Two opposite sides of a square are increased by twenty-five percent while the other two are decreased by forty percent. Find the percent of decrease in the area of the square. Area of original square: s^2 where s is the length of a side Area of new rectangle: ((5/4)s)((6/10)s) = (3/4)s^2 Quantity of decrease = s^2 - (3/4)s^2 = (1/4) s^2 % of decrease = [(1/4)s^2]/s^2 = 1/4 = 25% ================= Cheers, Stan H. (A) 15% (B) 25% (C) 30% (D) 32.5% (E) none of these
 Polynomials-and-rational-expressions/266222: The two's are exponents I couldn't make them small. The -1 is also a exponent (b4)(b-6)-1 (b2)-2)1 solutions Answer 195629 by stanbon(57984)   on 2010-02-05 22:10:54 (Show Source): You can put this solution on YOUR website!The two's are exponents I couldn't make them small. The -1 is also a exponent (b^4)(b^-6)^-1 = b^4*b^6 = b^10 -------------- (b^2)^-2 = b^-4 = 1/b^4 -------------- Cheers, Stan H.
 percentage/266214: Mr hernandez had to interview a total of 63 households in his assignment. He has already finished 28. What percentage of the households in his assignment has he finished? ( Round the awnser to the nearest tenth of a percent.) The awnser is 44.5%. What work do I have to do to get this awnser, (the easiest work possible, because I would be out on the field and I would have to be able to estimate in my head.)1 solutions Answer 195627 by stanbon(57984)   on 2010-02-05 22:07:45 (Show Source): You can put this solution on YOUR website!Mr hernandez had to interview a total of 63 households in his assignment. He has already finished 28. What percentage of the households in his assignment has he finished? ( Round the awnser to the nearest tenth of a percent.) The awnser is 44.5%. ---- Quantity he has finished: 28 % he has finished: 28/63 = 0.4444 = 44.4% =========================================== Cheers, Stan H.
 Probability-and-statistics/266220: Three research departments have 6 , 7 , and 8 members, respectively. If each department is to select a delegate and an alternate to represent the department at a conference, in how many ways can this be done? 1 solutions Answer 195624 by stanbon(57984)   on 2010-02-05 22:02:39 (Show Source): You can put this solution on YOUR website!Three research departments have 6 , 7 , and 8 members, respectively. If each department is to select a delegate and an alternate to represent the department at a conference, in how many ways can this be done? ------------------------------------ Order matters if you are pickiing a person as delegate and another as alternate. ------------------------------------ # of ways: (6*5)*(7*6)*(8*7) = 70560 ============== Cheers, Stan H.
 Probability-and-statistics/266216: A fair die is rolled 6 times. What is the probability of having no 1 and no 2 among the rolls? Round your answer to three decimal places. 1 solutions Answer 195622 by stanbon(57984)   on 2010-02-05 21:55:43 (Show Source): You can put this solution on YOUR website!A fair die is rolled 6 times. What is the probability of having no 1 and no 2 among the rolls? Round your answer to three decimal places. --------------------- P(no1 and no 2) in one roll: 4/6 = 2/3 ------------- P(no1 and no2 in 6 rolls) = (2/3)^6 = 0.088 ================================================ Cheers, stan H.
 Probability-and-statistics/266215: Two cards are drawn with replacement from an ordinary deck of 52 playing cards. What is the probability that both cards are of the same value (for example, both cards are twos or queens or aces)? 1 solutions Answer 195621 by stanbon(57984)   on 2010-02-05 21:52:26 (Show Source): You can put this solution on YOUR website!Two cards are drawn with replacement from an ordinary deck of 52 playing cards. What is the probability that both cards are of the same value (for example, both cards are twos or queens or aces)? --- How to succeed: Pick a card type: 13 ways Pick 2 cards of that type: 4C2 = 6 ---------------------------------------- # of ways to succeed: 13*6 = 78 ----- # of possible selections: 52C2 = 650 ------ So, P(both cards are same value) = 78/650 = 0.12 =================================================== Cheers, Stan H.
 Probability-and-statistics/266210: Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a freshman and an economics major? (b) Given that the student selected is a economics major, what is the probability that she is also an freshman? Write your responses as fractions. 1 solutions Answer 195619 by stanbon(57984)   on 2010-02-05 21:47:23 (Show Source): You can put this solution on YOUR website!Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a freshman and an economics major? ---- P(frosh and econ) = P(frosh) + P(econ) - P(frosh or econ) = 36/65 + 34/65 - (65-9)/65 --- = (36 + 34 - 56)/65 --- = 14/65 ----------------------------------------- (b) Given that the student selected is a economics major, what is the probability that she is also an freshman? P(frosh|econ) = P(frosh and econ)/P(econ) = (14/65)/(34/65) = 14/34 = 7/17 ============================================================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/266202: actually this problem is using the the Phythagorean Theorem this is the question I finished the whole assignment but I dont get this. 2. A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 10 feet across and 6 feet tall (see figure). Use the Pythagorean Theorem to calculate how long the pieces of PVC plumbing pipe should be? I dont know if the Triangle copied to you, but it is a triangle shaped like a tepee with a line down the middle which says height is 6ft, and the base width is 10ft. 1 solutions Answer 195615 by stanbon(57984)   on 2010-02-05 21:09:07 (Show Source): You can put this solution on YOUR website!A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 10 feet across and 6 feet tall (see figure). Use the Pythagorean Theorem to calculate how long the pieces of PVC plumbing pipe should be? I dont know if the Triangle copied to you, but it is a triangle shaped like a tepee with a line down the middle which says height is 6ft, and the base width is 10ft. ------------------------------- Sounds like you have a right triangle with vertical leg is 6 ft and horizontal leg is 5 ft (half of the total width of 10). ---- I don't see the figure but the slant height of the teepee can be determined using Pythagoras. --- (slant height)^2 = leg^2 + other leg^2 s^2 = 5^2 + 6^2 s^2 = 25 + 36 s^2 = 61 s = sqrt(61) is approximately 7.81 ft, ----------------------------------------------- Cheers, Stan H.
 Probability-and-statistics/266203: two coin and one six sided number cube are tossed together. What is the probability of getting two heads and a four?1 solutions Answer 195612 by stanbon(57984)   on 2010-02-05 21:03:28 (Show Source): You can put this solution on YOUR website!two coins and one six sided number cube are tossed together. What is the probability of getting two heads and a four? --------------------------------------------- The results are independent: P(2 heads) = 1/4 P(roll a 4) = 1/6 --------------------- P(2 heads and a 4) = (1/4)(1/6) = 1/24 ========================================= Cheers, Stan H.
 Inverses/266204: Please evaluate the following function or inverse; then write the ordered pair. f(x)=3x+1 and f^-1=(x-1)/3 f(2) = ( ) ( , ) Thank you for your help!1 solutions Answer 195610 by stanbon(57984)   on 2010-02-05 21:00:48 (Show Source): You can put this solution on YOUR website!Please evaluate the following function or inverse; then write the ordered pair. f(x)=3x+1 and f^-1=(x-1)/3 f(2) = 3*2+1 = 7 f^-1(x) = (x-1/3) f^-1(7) = (7-1)/3 = 2 =========================== (2,7) ===================== Cheers, Stan H.
 Complex_Numbers/266199: I have 2 question i have answered both but am not confident with the answers. (2+3i)(x+yi)=23+2i find values for x and y. express root 2 cis (5pi/4) in cartesian form. Thak you for your help.1 solutions Answer 195609 by stanbon(57984)   on 2010-02-05 20:57:48 (Show Source): You can put this solution on YOUR website!(2+3i)(x+yi)=23+2i find values for x and y. --- 2x +2yi +3xi -3y = 23 + 2i --- (2x-3y)+(3x+2y)i = 23 + 2i --- Equate the Real Parts and Equate the Imaginary Parts to get: 2x-3y = 23 3x+2y = 2 ------------------ Multiply 1st by 3; Multiply 2nd by 2 6x - 9y = 69 6x + 4y = 4 --------------- Subtract 1st from 2nd and solve for "y": 13y = -65 y = -5 ------------------- 2x-3y = 23 3x+2y = 2 --- Multiply 1st by 2; Multiply 2nd by 3 4x -6y = 46 9x +6y = 6 ----------- Add the two equations and solve for "x": 13x = 52 x = 4 =========================================== express root 2 cis (5pi/4) in cartesian form. --- = sqrt(2)[cos((5/4)pi)+ isin((5/4)pi)) = sqrt(2)[-1/sqrt(2) - i(1/sqrt(2)] = [-1 -i] ================== Cheers, Stan H.