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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/454119: . In 2005, John G. Roberts was nominated by President Bush and confirmed by the Senate to be the 17th U.S. Supreme Court Chief Justice. During the nomination process, John G. Roberts's career as a lawyer and judge was the subject of many studies. For example, Kenneth Manning, associate professor of political science at the University of Massachusetts-Dartmouth presented a research paper titled “How Right Is He?” at the 2005 meeting of the American Political Science Association. In cases where Judge Roberts participated, the study categorized the cases into three types: criminal justice, civil rights, and economic activity. In each case, the study also labeled Judge Roberts's vote as either liberal or conservative. Forty-five cases that could not be clearly categorized for the study were not included. At the 0.01 significance level can we conclude Judge Roberts is more conservative in some types of cases? Criminal Justice Civil Rights Economic Activity Liberal 6 2 39 Conservative 38 11 49 1 solutions Answer 311894 by stanbon(57377)   on 2011-05-25 18:57:27 (Show Source): You can put this solution on YOUR website!At the 0.01 significance level can we conclude Judge Roberts is more conservative in some types of cases? Criminal Justice Civil Rights Economic Activity Liberal 6 2 39 Conservative 38 11 49 ------------------------------- Ho: row and column factors are independent Ha: they are dependent ----------------------------- I ran a Chi-Sq on the 2 by 3 matrix of data and got the following: Chi-Sq = 14.496... p-value = 0.0007119 ===== Since the p-value is less than 1%, reject Ho. Roberts opinion position tends to depend on the type of case. ===================== Cheers, Stan H. =====================
 Probability-and-statistics/454125: Imagine you have two dice, one red and one white. You roll the dice at the same time. a) How many possible outcomes are there? Explain how you get your answer. b) What is the probability that the dice show a total of 8? c) What is the probability that the dice show a total less than 5? HELP! :(1 solutions Answer 311892 by stanbon(57377)   on 2011-05-25 18:45:46 (Show Source): You can put this solution on YOUR website!Imagine you have two dice, one red and one white. You roll the dice at the same time. a) How many possible outcomes are there? Explain how you get your answer. # of sum results: 6 x 6 = 36 ------------------------------------ b) What is the probability that the dice show a total of 8? 2/6;3/5;4/4;5/3;6/2 P(sum is 8) = 5/36 ------------------------------------ c) What is the probability that the dice show a total less than 5? 1/1;1/2;1/3 2/1;2/2 3/1 --- P(sum < 5) = 6/36 = 1/6 ================================= Cheers, Stan H. =================================
 Probability-and-statistics/454120: . A survey by USA Today investigated the public's attitude toward the federal deficit. Each sampled citizen was classified as to whether they felt the government should reduce the deficit, increase the deficit, or if they had no opinion. The sample results of the study by gender are reported below. Gender Reduce the Deficit Increase the Deficit No Opinion Female 244 194 68 Male 305 114 25 At the .05 significance level, is it reasonable to conclude that gender is independent of a person's position on the deficit? 1 solutions Answer 311890 by stanbon(57377)   on 2011-05-25 18:36:47 (Show Source): You can put this solution on YOUR website!A survey by USA Today investigated the public's attitude toward the federal deficit. Each sampled citizen was classified as to whether they felt the government should reduce the deficit, increase the deficit, or if they had no opinion. The sample results of the study by gender are reported below. Gender Reduce the Deficit Increase the Deficit No Opinion Female 244 194 68 Male 305 114 25 At the .05 significance level, is it reasonable to conclude that gender is independent of a person's position on the deficit? ------------- Ho: row and column factors are independent Ha: they are dependent ---- I ran a Chi-Sq test on the 2 by 3 matrix and got the following; Chi-Sq = 43.578... p-value = 0.0000000003445 ===================== Since the p-value is less than 1%, reject Ho at the 1% level of significance. The test result does not support the independence of the factors; it supports the conclusion that gender and position are dependent. ============================ Cheers, Stan H.
 Exponents/454116: I am having difficulty solving this equation: [2^4*(4^5/4^2)]/[(6+7^-3)^0]1 solutions Answer 311888 by stanbon(57377)   on 2011-05-25 18:22:39 (Show Source): You can put this solution on YOUR website!I am having difficulty solving this equation: [2^4*(4^5/4^2)]/[(6+7^-3)^0] -------------- =[16(4^3)]/1 ---- = [2^4*2^6] --- = 1024 ============ Cheers, Stan H. ==============
 Quadratic-relations-and-conic-sections/454107: Hi, I am studying for a quiz on hyperbolas and one of the problems I am doing is this: Write an equation in standard form for each hyperbola. Length of transverse axis 10 and foci at (-7,18) and (-7,-8) So far, I understand that it is vertical therefore the equation would be in the (y-k)^2/a^2-(x-h)^2/b^2=1 I am pretty sure I also got the center which was (-7, 5) So now I have (y-5)^2/a^2-(x+7)^2/b^2=1 My problem is is that I don't know how to find what a and b are. I understand they come from the vertices and co-vertices but I don't think I fully understand the transverse axis.1 solutions Answer 311886 by stanbon(57377)   on 2011-05-25 18:18:44 (Show Source): You can put this solution on YOUR website!Write an equation in standard form for each hyperbola. Length of transverse axis 10 and foci at (-7,18) and (-7,-8) So far, I understand that it is vertical therefore the equation would be in the (y-k)^2/a^2-(x-h)^2/b^2=1 I am pretty sure I also got the center which was (-7, 5) So now I have (y-5)^2/a^2-(x+7)^2/b^2=1 My problem is is that I don't know how to find what a and b are. I understand they come from the vertices and co-vertices but I don't think I fully understand the transverse axis. ---------------------- Plot the foci points. The distance between the foci is 18--8 = 26 --- 2a + 2c = 26 But length of transverse axis = 2a = 10 So, a = 5 --- And 2c = 26-10 = 16 So c = 8 --- For a hyperbola a^2+b^2 = c^2 25 + b^2 = 16 b^2 = 9 b = 3 ---- Since (h,k) = (-7,5) Equation: (y-5)^2/25 - (x+7)^2/9 = 1 ================================= Cheers, Stan H. ============
 Permutations/454085: In how many ways can you choose a committee of four people from nine in the club?1 solutions Answer 311862 by stanbon(57377)   on 2011-05-25 17:00:25 (Show Source): You can put this solution on YOUR website!In how many ways can you choose a committee of four people from nine in the club? --- Ans: 9C4 = (9*8*7*6)/(1*2*3*4) = 126 --------------------- Cheers, Stan H. ==================
 Linear_Equations_And_Systems_Word_Problems/454082: on a jury there are 3 fewer men than twice the number of women. if there were 2 more women on the jury, the number of men and women would be equal. how many men are on the jury? solve by using a system of two equations in two variables.1 solutions Answer 311861 by stanbon(57377)   on 2011-05-25 16:56:24 (Show Source): You can put this solution on YOUR website!on a jury there are 3 fewer men than twice the number of women. if there were 2 more women on the jury, the number of men and women would be equal. how many men are on the jury? solve by using a system of two equations in two variables. --- Equations: m = 2w-3 w+2 = m ----------------- Substitute and solve for "w": 2w-3 = w+2 w = 5 (# of women) --- Solve for "m" m = w+2 = 7 (# of men) =========================== Cheers, Stan H.
 Graphs/454076: The lost value of equipment over a period of time is called depreciation. The simplest method for calculating depreciation is straight-lne depreciation. The annual straight-line depreciation D of an item that costs x dollars with a useful life of n years is D= (1/n)x. Find the depreciation for items with the given characteristics. Cost is \$15,968; life is 13 yr The annual straight-line depreciation is approximately \$_ per year. (Round to hte nearest cent.) Thankyou for your help it is much appreciated.1 solutions Answer 311860 by stanbon(57377)   on 2011-05-25 16:52:06 (Show Source): You can put this solution on YOUR website!The annual straight-line depreciation D of an item that costs x dollars with a useful life of n years is D= (1/n)x. Find the depreciation for items with the given characteristics. Cost is \$15,968; life is 13 yr ---- D(x) = (1/13)15968 = \$1228.31 --------------------------------------- The annual straight-line depreciation is approximately \$1228.31per year. (Round to hte nearest cent.) ================================= Cheers, Stan H. ===========
 Evaluation_Word_Problems/454074: shane wants to attend 3 concerts. She has a coice of 7.How many concert combinations are their?1 solutions Answer 311859 by stanbon(57377)   on 2011-05-25 16:46:59 (Show Source): You can put this solution on YOUR website!shane wants to attend 3 concerts. She has a coice of 7.How many concert combinations are their? ------------------ Ans: 7C3 = (7*6*5)/(1*2*3) = 35 ----------------------------------- Cheers, Stan H.
 Quadratic_Equations/454047: Solve the inequality below. Enter your answer as an inequality, such as w > 2/3 or s < -4. -9 < x - 71 solutions Answer 311849 by stanbon(57377)   on 2011-05-25 16:05:34 (Show Source): You can put this solution on YOUR website!Solve the inequality below. Enter your answer as an inequality, such as w > 2/3 or s < -4. ---------------------- -9 < x - 7 Add 7 to both sides to get: x > -9+7 x > -2 =============== Cheers, Stan H. ===============
 Equations/454054: State the domain of f(x)=(x-8)(x+2)/(x+2)(x-2)1 solutions Answer 311847 by stanbon(57377)   on 2011-05-25 15:59:13 (Show Source): You can put this solution on YOUR website!State the domain of f(x)=(x-8)(x+2)/(x+2)(x-2) --- x= -2 is a hole. x = 2 is a vertical asymptote. --- Domain is "all Real Numbers except x = +2 and x = -2". -------------- Cheers, Stan H. ==============
 Square-cubic-other-roots/454044: what is the square root of -54 in terms of i?1 solutions Answer 311846 by stanbon(57377)   on 2011-05-25 15:56:02 (Show Source): You can put this solution on YOUR website!what is the square root of -54 in terms of i? --- sqrt(-54) = sqrt(-9*6) = 3i*sqrt(6) = 3sqrt(6)i ================================================== Cheers, Stan H. =========
 Probability-and-statistics/453935: A teacher finds that the mean score of his class is 72 with a standard deviation of 8. Find the z-score corresponding to 501 solutions Answer 311843 by stanbon(57377)   on 2011-05-25 15:49:24 (Show Source): You can put this solution on YOUR website!A teacher finds that the mean score of his class is 72 with a standard deviation of 8. Find the z-score corresponding to 50 ----- z(50) = (50-72)/8 = -2.75 ==================================== Cheers, Stan H.
 Probability-and-statistics/453937: Of 200 grapes that were tested, 60 were decaying. In a random sample of 50 grapes, how many do you expect to be decaying?1 solutions Answer 311842 by stanbon(57377)   on 2011-05-25 15:46:59 (Show Source): You can put this solution on YOUR website!Of 200 grapes that were tested, 60 were decaying. In a random sample of 50 grapes, how many do you expect to be decaying? ----------- Use a proportion: decay/total = decay/total --- x/50 = 60/200 --- x = (50*60)/200 --- x = 3000/200 --- x = 15 ================= Cheers, Stan H.
 Probability-and-statistics/453941: A teacher has 20 students in her class. She randomly will select 4 students for a project. a)Find the probability that a specific group of 4 students is selected b)Mary is not to be in the selected group. Find the probability that Mary is in the selected group 1 solutions Answer 311839 by stanbon(57377)   on 2011-05-25 15:43:28 (Show Source): You can put this solution on YOUR website!A teacher has 20 students in her class. She randomly will select 4 students for a project. a)Find the probability that a specific group of 4 students is selected # of ways to get the "specific group: 1 # of ways to select a random group of 4: 20C4 ---- P(get specific grp of four) = 1/20C4 = 1/4845 ======================================================= b)Mary is not to be in the selected group. Find the probability that Mary is in the selected group --- Ans: zero ================================ Cheers, Stan H. =========
 Probability-and-statistics/453997: Wheel In Exercises 17–24, consider the following wheel. 1 & 8 is blue, 3 & 10 is yellow, 2,4,9,11 & 12 is purple and 5,6 &7 is red If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on an even number, given that the color is red. 1 solutions Answer 311838 by stanbon(57377)   on 2011-05-25 15:37:56 (Show Source): You can put this solution on YOUR website!consider the following wheel. ----------------- 1 & 8 is blue, 3 & 10 is yellow, 2,4,9,11 & 12 is purple and 5,6 &7 is red If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on an even number, given that the color is red. ---- P(the pointer lands on an even number| given that the color is red) --- = P(even and red)/P(red) --- = (1/12)/(3/12) --- = 1/3 ================= Cheers, Stan H. ======================
 Probability-and-statistics/454039: An urn contains green balls and red balls. If Tim chooses balls at random from the urn, what is the probability that he will select green balls and red balls? Round your answer to decimal places. 1 solutions Answer 311836 by stanbon(57377)   on 2011-05-25 15:32:22 (Show Source): You can put this solution on YOUR website!An urn contains green balls and red balls. If Tim chooses balls at random from the urn, what is the probability that he will select green balls and red balls? ---- the probability is zero because none of the balls can be green AND blue. =========================== Cheers, Stan H.
 Exponents-negative-and-fractional/454015: how can i simplify this equation after raising the quanitity in the parenthesis using positive exponents? (-47x^-2y/141x^3y^-3)^31 solutions Answer 311825 by stanbon(57377)   on 2011-05-25 13:54:02 (Show Source): You can put this solution on YOUR website!how can i simplify this equation after raising the quanitity in the parenthesis using positive exponents? (-47x^-2y/141x^3y^-3)^3 --- = [(-47/141)(x^-2/x^3)(y/y^-3)]^3 ---- = [(1/3)(1/x^5)(1/y^4)]^3 --- = 1/[27x^5y^4] =========================== Cheers, Stan H. ==============
 logarithm/454012: how to simplify this expression 3log3(6x-4)1 solutions Answer 311824 by stanbon(57377)   on 2011-05-25 13:50:22 (Show Source): You can put this solution on YOUR website!simplify this expression 3log3(6x-4) --- I would say it's already simplified. You could rewrite it as = log3(6x-4)^3 but why? ------ Cheers, Stan H.
 Probability-and-statistics/454001: Chris owns 2 stocks, IBM & GE. The probability that IBM stock will increase in value next year is .5 and the probability that GE stock will increase in value next year is .7. Assume both stocks are independent. What is the probability that at least one of these stocks will increase in value during the next year? (This means that either one can increase or both). I have an answer of P(at least one)= (.5)(.3)+ (.5)(.7)+ (.7)(.5)=.85 Where does the (.5)(.3) come from?? mkatich@tampabay.rr.com1 solutions Answer 311822 by stanbon(57377)   on 2011-05-25 13:44:17 (Show Source): You can put this solution on YOUR website!Chris owns 2 stocks, IBM & GE. The probability that IBM stock will increase in value next year is .5 and the probability that GE stock will increase in value next year is .7. Assume both stocks are independent. What is the probability that at least one of these stocks will increase in value during the next year? (This means that either one can increase or both). I have an answer of P(at least one)= (.5)(.3)+ (.5)(.7)+ (.7)(.5)=.85 Where does the (.5)(.3) come from?? =========== P(IBM increases) = 0.5 ; P(IBM decreases) = 0.5 --- P(GE increases) = 0.7 ; P(GE decreases) = 0.3 --- So, (0.5)(0.3) is the probability that both decrease, or it could be the probability that IBM increases and IBM decreases. -------------------------- But, here's another way to do the problem: P(at least one increase) = 1-P(neither increase) = 1-(0.5*0.3) = 1-0.15 = 0.85 ------------ Cheers, Stan H.
 Linear_Algebra/453993: Find the values of a and b that make f continuous everywhere. f (x)= { x2−4x−2 if x<2 ax2−bx+3 if 2≤x<3 2x−a+b if x≥3 } I dont understand how i would solve this. Please help. Thank you. :)1 solutions Answer 311808 by stanbon(57377)   on 2011-05-25 12:38:12 (Show Source): You can put this solution on YOUR website!Find the values of a and b that make f continuous everywhere. f (x)= { 1. x^2−4x−2 if x<2 2. ax2−bx+3 if 2≤x<3 3. 2x−a+b if x≥3 } ----------------------------- Evaluate "1" at x = 2 f(2) = 2^2-4*2-2 = -6 -------------- Evaluate "3" at x = 3 g(3) = 2(3)-a+b = 6-a+b ---- So two of the points of "2" must be (2,-6) and (3,6-a+b) ____ Substitute those coordinates into "2" to solve for "a" and for "b". --- 2. ax2−bx+3 ---- (2,-6) gives you 4a-2b+3 = -6 2a - b = -9 --- (3,6-a+b) gives you a(9)-b(3)+3 = 6-a+b 10a - 4b = 3 -------------------- Solve the system: 2a - b = -9 10a -4b = 3 ---------------------- Multiply thru 1st equation by 5: 10a - 5b = -45 10a - 4b = 3 --- Subtract to get: b = 48 --- Solve for "a": 2a - b = -9 2a - 48 = -9 2a = 39 a = 39/2 --------------------- I'd suggest you check alll the arithmetic here as mistakes can creep in. ====================================== Cheers, Stan H.
 Evaluation_Word_Problems/453989: The total surface area of a cylinder of height 9.5 cm is estimated using the function f(r) = 6r2 + 60r, where r is the radius of the cylinder. If the radius of the cylinder is 5 cm, what is its total surface area? answers: a) 1200 cm(squared) b) 450 cm(squared) c) 187.5 cm(squared) d) 60 cm(squared) 1 solutions Answer 311804 by stanbon(57377)   on 2011-05-25 12:14:41 (Show Source): You can put this solution on YOUR website!The total surface area of a cylinder of height 9.5 cm is estimated using the function f(r) = 6r2 + 60r, where r is the radius of the cylinder. If the radius of the cylinder is 5 cm, what is its total surface area? -------- f(5) = 6*5^2+50*5 --- f(5) = 150+250 = 400 cm^2 ---------------------------- That's f(5). It doesn't show any relation to the 9.5 cm height which certainly is a factor in determining the total surface area. Cheers, Stan H. ======== answers: a) 1200 cm(squared) b) 450 cm(squared) c) 187.5 cm(squared) d) 60 cm(squared)
 Miscellaneous_Word_Problems/453988: Q: Joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag? I have answered 12...however that keeps coming back as wrong?...Help Please...thank you1 solutions Answer 311802 by stanbon(57377)   on 2011-05-25 12:03:52 (Show Source): You can put this solution on YOUR website! Joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag? ---------------------- Let original number be "x": Monday: x-(1/3)x = (2/3)x --- Tuesday: (2/3)x-(1/2)(2/3)x = (2/3)-(1/3)x = (1/3)x -- Equation (1/3)x = 2 x = 6 =============== Cheers, Stan H. =============== I have answered 12...however that keeps coming back as wrong?...
 Quadratic-relations-and-conic-sections/453917: Find the center of y^2/16-x^2/9=1. Thanks so much please show how.1 solutions Answer 311775 by stanbon(57377)   on 2011-05-25 10:20:01 (Show Source): You can put this solution on YOUR website!Find the center of y^2/16-x^2/9=1. ------ Put in standard form: (y-0)^2/16 - (x-0)^2/9 = 1 ----- The graph is a hyperbola with center at (h,k) = (0,0). ==== Cheers, Stan H.
 Complex_Numbers/453903: Hi, Solve: Thanks :)1 solutions Answer 311774 by stanbon(57377)   on 2011-05-25 10:16:37 (Show Source): You can put this solution on YOUR website!5-4x >= 15+3x Add 4x to both sides to get: 5 >= 17+7x --- Subtract 17 from both sides to get: -12 >= 7x --- Divide both sides by 7 to get: x <= -12/7 ===================== Cheers, Stan H.
 Probability-and-statistics/453849: I have three black beads and 3 white beads how many combinations can you get1 solutions Answer 311772 by stanbon(57377)   on 2011-05-25 10:13:14 (Show Source): You can put this solution on YOUR website!I have three black beads and 3 white beads how many combinations can you get ---- How many beads are you selecting. --- If you are selecting 2 the answer is 6C2 = (6*5)/(1*2) = 15 ============== Cheers, Stan H.
 Probability-and-statistics/453907: Help Please! This is my last math course and I'm afraid it will ruin my bursury. All the rest of my marks are in the high 80's and 90's. But math is a struggle for me . . . A new drug has been tested and is found to have a cure rate of 80%. The drug is given to a random sample of 100 patients for a further test. Using a normal approximation to the binomial distribution, find the probability that: a) at least 75 patients will be cured b) exactly 80 patients will be cured Thank you so much.1 solutions Answer 311770 by stanbon(57377)   on 2011-05-25 10:08:09 (Show Source): You can put this solution on YOUR website!A new drug has been tested and is found to have a cure rate of 80%. The drug is given to a random sample of 100 patients for a further test. Using a normal approximation to the binomial distribution, find the probability that: a) at least 75 patients will be cured mean = np = 100*0.80 = 80 std = sqrt(npq) = sqrt(80*0.2) = 4 --- z(74.5) = (74.5-80)/4 = -1.1 z(100.5) = (100.5-80)/4 = 20.5/4 = 5.125 ---------------- P(75<= x <=100) = P(-1.1< z < 5.125) = 0.8643 ====================================================== b) exactly 80 patients will be cured z(79.5) = (79.5-80)/4 = -0.125 z(80.5) = (80.5-80)/4 = +0.125 --- P(x = 80) = P(-0.125< z <0.125) = 0.0995 ========================= Cheers, Stan H.
 Probability-and-statistics/453909: Please help! This is my last math course and I am so afraid it will ruin my chances of getting my bursury. I am getting high 80's and 90's in my other courses, but math has been such a struggle through high school. The scholastic aptitude test (SAT) scores are normally distributed with a mean of 500 and a standard deviation of 100. a) What percentage of students obtain a score between 500 and 600? b) If you got 725 on this test what would your percentile rank be? Thanks so much!1 solutions Answer 311767 by stanbon(57377)   on 2011-05-25 09:58:31 (Show Source): You can put this solution on YOUR website!The scholastic aptitude test (SAT) scores are normally distributed with a mean of 500 and a standard deviation of 100. a) What percentage of students obtain a score between 500 and 600? b) If you got 725 on this test what would your percentile rank be? ------------------ z(500) = (500-500)/100 = 0 --- z(600) = (600-500)/100 = 100/100 = 1 ---- P(500< x <600) = P(0< z < 1) = 0.3413 ================ z(725) = (725-500)/100 = 225/100 = 2.25 -- %ile of 725 = P(z < 2.25) = 0.9878 = 99%ile ================================================= Cheers, Stan H.
 Functions/453910: The variables x and y vary directly. When x is 5, y is 15. If x is 25, what is y? a. 1/3 b. 3 c. 25/3 c. 751 solutions Answer 311765 by stanbon(57377)   on 2011-05-25 09:49:15 (Show Source): You can put this solution on YOUR website!The variables x and y vary directly. y = kx --- Solve for "k" using "When x is 5, y is 15". ---- 15 = k*5 k = 3 --- Equation: y = 3x ----- Solve: If x is 25, what is y? y = 3*25 y = 75 ================== Cheers, Stan H. ============ a. 1/3 b. 3 c. 25/3 c. 75
 Probability-and-statistics/453899: Help Please! It has been estimated that with a sophisticated mathematical strategy, a player can increase the probability of winning at black jack to 10/19. If you play with this strategy, what is the probability that you will win at least 8 games if you play 20? (Use normal approximation) Thank you1 solutions Answer 311764 by stanbon(57377)   on 2011-05-25 09:45:22 (Show Source): You can put this solution on YOUR website!It has been estimated that with a sophisticated mathematical strategy, a player can increase the probability of winning at black jack to 10/19. If you play with this strategy, what is the probability that you will win at least 8 games if you play 20? (Use normal approximation) ------------ mean = np = 20(10/19) = 10.526 std = sqrt(npq) = sqrt[20(10/19)(9/19)] = 2.233 ---- z(7.5) = (7.5-10.526)/2.233 = -1.355 z(20.5) = (20.5-10.526)/2.233 = 4.467 ======= P(8<= x <=20) = P(-1.355<= z <= 4.467) = 0.9123 =============== Cheers, Stan H.
 Travel_Word_Problems/453881: A plane is flying 240 mph heading N60°E. The wind is blowing S30°E at 30 mph. What is ground speed of the plane? What is the smallest angle in the triangle? What is the biggest angle in the triangle? What is the remaining angle in the triangle? What is the bearing of the plane?1 solutions Answer 311761 by stanbon(57377)   on 2011-05-25 09:15:24 (Show Source): You can put this solution on YOUR website!A plane is flying 240 mph heading N60°E. The wind is blowing S30°E at 30 mph. ------------------- Plane components: xp = 240cos(60) yp = 240sin(60) ----- Wind components: xw = 30cos(30) yw = 30sin(30) ----- What is ground speed of the plane? Actual plane position after one hour in the air: (240cos(6)+30cos(30);240sin(60)+30sin(3)) = (145.98,222.85) Ground speed = sqrt[145.98^2+222.85^2] = 266.40 mph =============================================================== What is the smallest angle in the triangle? What is the biggest angle in the triangle? What is the remaining angle in the triangle? --- Question: Which triangle? the given condition triangle or the resultant triangle? =========================== What is the bearing of the plane? tan^-1[222.85/145.98] = 56.77 degrees ========================================= Cheers, Stan H.