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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/382983: The lengthy of a rectangular garden is 2 yd greater than the width. The area is 80 yd squared. Find the length and width.1 solutions Answer 271310 by stanbon(57940)   on 2010-12-08 12:03:41 (Show Source): You can put this solution on YOUR website!The length of a rectangular garden is 2 yd greater than the width. The area is 80 yd squared. Find the length and width. ------------- Let width be "x" Then y = "x+2". ------- Equation: area = LW 80 yd^2 = x(x+2) x^2+2x-80 = 0 ----- Positive solution: x = 8 yd (width) x+2 = 10 yd (length) ================== Cheers, Stan H.
 Circles/382978: find the radius defined by the equation: x^2+y^2-2x-10y-23=0.1 solutions Answer 271305 by stanbon(57940)   on 2010-12-08 11:53:55 (Show Source): You can put this solution on YOUR website!find the radius defined by the equation: Complete the square on the x-terms and on the y-terms: x^2+y^2-2x-10y-23=0. ----- x^2-2x+1 + y^2-10y+25 = 23+1+25 ----- (x-1)^2 + (y-5)^2 = 49 ----- radius = sqrt(49) = 7 =============================== Cheers, Stan H.
 Functions/382970: A cat leaps trying to catch a flye. The motion of the cat can be modeled by h(d)=-32d^2+16d. The fly is staying at least 2.5 feet away from the ground. Will the cat get high enough to catch the fly? 1 solutions Answer 271304 by stanbon(57940)   on 2010-12-08 11:46:01 (Show Source): You can put this solution on YOUR website!A cat leaps trying to catch a fly. The motion of the cat can be modeled by h(d)=-32d^2+16d. The fly is staying at least 2.5 feet away from the ground. Will the cat get high enough to catch the fly? ----------------- h(d)=-32d^2+16d --- Maximum height occurs when d = -b/2a = -16/(2*-32) = 1/4 --- That maximum height is h(1/4) = -32(1/4)^2+16(1/4) = 2 ft. ---- I guess the cat is going to go hungry. ============================ Cheers, Stan H.
 Polynomials-and-rational-expressions/382976: Please help? Im missing a step somewhere. Find the product: (x+3)(x^2-3x+9)1 solutions Answer 271303 by stanbon(57940)   on 2010-12-08 11:41:40 (Show Source): You can put this solution on YOUR website!Find the product: (x+3)(x^2-3x+9) = x(x^2-3x+9)+3(x^2-3x+9) ---------- = x^3-3x^2+9x+3x^2-9x+27 ------ = x^3 + 27 ============================= cheers, Stan H.
 Probability-and-statistics/382972: In a recent survey, 63% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 5 of them favor the building of the police substation 1 solutions Answer 271302 by stanbon(57940)   on 2010-12-08 11:38:40 (Show Source): You can put this solution on YOUR website!In a recent survey, 63% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 5 of them favor the building of the police substation ------------------------- Binomial Problem with n = 14 and p = 0.63 ------- P(x=5) = 14C5(0.63)^5(0.37)^9 ---------- = binompdf(14,0.63,5) = 0.025822 =================================== Cheers, Stan H. ==============
 logarithm/382971: use a calculator to find the natural logarithm base e: ln 751 solutions Answer 271300 by stanbon(57940)   on 2010-12-08 11:29:56 (Show Source): You can put this solution on YOUR website!use a calculator to find the natural logarithm base e: ln 75 = 4.317488... Cheers, Stan H.
 logarithm/382966: express as the sum or difference in logarithms: log[9](5z)1 solutions Answer 271299 by stanbon(57940)   on 2010-12-08 11:28:02 (Show Source): You can put this solution on YOUR website!express as the sum or difference in logarithms: log[9](5z) --- = log9(5)+log9(z) ==================== Cheers, Stan H. ====================
 logarithm/382958: find an approximate solution 3^x=81 solutions Answer 271281 by stanbon(57940)   on 2010-12-08 11:10:22 (Show Source): You can put this solution on YOUR website!Try x = 2.5 =============== Cheers, Stan H.
 Radicals/382931: ^3√250 the answer is 5^√2 but how??1 solutions Answer 271280 by stanbon(57940)   on 2010-12-08 11:08:21 (Show Source): You can put this solution on YOUR website!^3√250 the answer is 5^√2 but how?? ---- Your notation is completly comfusing. But I think I've figured it out. ---- cbrt(250) = cbrt(125)*cbrt(2) = 5*cbrt(2) ============================================= Cheers, Stan H.
 Expressions-with-variables/382944: Multiply. (s+1/3)(s+1/5)1 solutions Answer 271275 by stanbon(57940)   on 2010-12-08 11:01:14 (Show Source): You can put this solution on YOUR website!Multiply. (s+1/3)(s+1/5) ---- s^2 + [(1/3)+(1/5)]s + 1/15 ------ s^2 + (8/15)s + 1/15 ========================= Cheers, Stan H.
 Vectors/382952: my paper says to "list the steps for the algebraic addition of vectors and solve a problem of your choice" what would the steps be and can you give me a sample problem?1 solutions Answer 271273 by stanbon(57940)   on 2010-12-08 10:57:53 (Show Source): You can put this solution on YOUR website!Please use Google to search for "adding vectors". There you will see examples. Cheers, Stan H.
 logarithm/382926: find an approximate solution to 2^x=31 solutions Answer 271272 by stanbon(57940)   on 2010-12-08 10:53:02 (Show Source): You can put this solution on YOUR website!find an approximate solution to 2^x=3 ---- If you are just guessing you might say x = 1.5. --- I you want the answer take the log to get: x*log2 = log3 x = log(3)/log(2) x = 1.584963... Cheers, Stan H.
 logarithm/382929: Use a calculator to find the natural logarithm base e. ln 701 solutions Answer 271258 by stanbon(57940)   on 2010-12-08 09:53:18 (Show Source): You can put this solution on YOUR website!Use a calculator to find the natural logarithm base e. ln 70 ---- Note: A scientific calculator is available online. Use Google. --------------- ln(70) = 4.248495... Cheers, Stan H.
 Polynomials-and-rational-expressions/382925: (x^3+8/x^2-4)times(x^2-4x+4/x^2-2x+4) my math teacher said i got this wrong my answer was X(x-2)/-2x+4 he said you didnt solve the difference of squares correctly??1 solutions Answer 271257 by stanbon(57940)   on 2010-12-08 09:51:15 (Show Source): You can put this solution on YOUR website!(x^3+8/x^2-4)times(x^2-4x+4/x^2-2x+4) my math teacher said i got this wrong my answer was X(x-2)/-2x+4 he said you didnt solve the difference of squares correctly?? --------------- This is a "sum" .Factor x^3+8 = x^3+2^3 = (x+2)(x^2-x+2) ---- This is a "difference of squares": Factor x^2-4 = (x+2)(x-2) =============================== ============================== Your Problem: (x^3+8/x^2-4)times(x^2-4x+4/x^2-2x+4) ----- = [(x+2)(x^2-2x+4)/(x+2)(x-2)] ----- Cancel the (x+2) and (x-2) and (x^2-2x+4) factors to get: = [1*1/1*1] = 1/(x-2) ============== cheers, Stan H. Cheers, Stan H.
 Miscellaneous_Word_Problems/382915: I am trying to understand this question in easy terms and an example please. Why do you factor a quadratic equation before you solve? Thank you very much! Regards1 solutions Answer 271253 by stanbon(57940)   on 2010-12-08 09:45:13 (Show Source): You can put this solution on YOUR website! I am trying to understand this question in easy terms and an example please. Why do you factor a quadratic equation before you solve? Thank you very much! ---------------------- When you have a quadratic problem the "solution" is immediately seen by any person who can unravel the pattern expressed by the form. Most people cannot do that till the quadratic is factored. --- Example: When you see x^2+5x+6 = 0 do you "see" the solutions? Most people do not. --- So we factor the expression to get: (x+3)(x+2) = 0 ----- If you have studied algebra you see the product is zero so one of the factors must be zero. --- You say: x+3 = 0 or x+2=0 Maybe at this point you "see" the solutions. If not you solve each equation. x = -3 or x = -2 ---- Now you have the solutions. If you had "seen" them in the 1st place you would not have factored the problem. ---- So, factoring is a crutch we use to help us "see" the solutions. ================== cheers, Stan H.
 Miscellaneous_Word_Problems/382916: please help me to answer this in simple terms so I can understand. Why are there usually two solutions in quadratic equations? Thank you!1 solutions Answer 271251 by stanbon(57940)   on 2010-12-08 09:34:01 (Show Source): You can put this solution on YOUR website!If you solve ax^2+bz+x = 0 you will get: x = [-b +- sqrt(b^2-4ac)]/(2a) --- You get two solutions because of the +- in the quadratic formula. ========================= x = [-b + sqrt(b^2-4ac)]/(2a) and x = [-b - sqrt(b^2-4ac)]/(2a) =========================== Cheers, Stan H.
 logarithm/382902: log(base4)x-2log3=1 How can I solve Logarithms with different bases? How can I change the bases and make it similar.1 solutions Answer 271250 by stanbon(57940)   on 2010-12-08 09:29:57 (Show Source): You can put this solution on YOUR website!log(base4)x-2log3=1 -------- log4(x) - log10(9) = 1 ---- log(x)/log(4) - log(9)/log(10) = 1 ----- log(x)/log(4) - log(9) = 1 ----- Multiply thru by log(4) to get: ----------- log(x) - log(9)*log(4) = log(4) ---------- log(x) = log(9)*log(4) + log(4) --- log(x) = 1.176571... x = 10^1.176571 x = 15.016587) ================== Cheers, Stan H. ==================
 Exponents/382911: Please solve using division 24x^5/3x^21 solutions Answer 271249 by stanbon(57940)   on 2010-12-08 09:22:55 (Show Source): You can put this solution on YOUR website!Please solve using division 24x^5/3x^2 ---- = (24/3)(x^5/x^2) --- = 8x^3 ======== Cheers, Stan H.
 Exponential-and-logarithmic-functions/382904: Seeing as I don't even know where to begin this is an extremely difficult question for me. The gravitational force on an object (or weight) varies inversely to the square of the distance the object from the center of the Earth. An object weighs 430 pounds when it is on the surface of the Earth, which means the object is 3960 miles from the center of the earth. a) calculate the value of k. b) determine the weight of the object, to the nearest pound, when it is 230 miles ABOVE the Earth's surface. so i know to start with something like y=k/w^2 I think??1 solutions Answer 271248 by stanbon(57940)   on 2010-12-08 09:21:16 (Show Source): You can put this solution on YOUR website!The gravitational force on an object (or weight) varies inversely to the square of the distance the object from the center of the Earth. -------------------------- f = k/d^2 ------ An object weighs 430 pounds when it is on the surface of the Earth, which means the object is 3960 miles from the center of the earth. a) calculate the value of k. 430 = k/3960^2 k = 430*3960^2 = 6743088000 ---------------------------------- b) determine the weight of the object, to the nearest pound, when it is 230 miles ABOVE the Earth's surface. f = (673088000)/(3960+230)^2 f = 384.09 lbs ---------------------------- Cheers, Stan H. =========
 Exponents/382894: (x+2)(x^2-2x+4) please solve using multiplication1 solutions Answer 271247 by stanbon(57940)   on 2010-12-08 08:58:32 (Show Source): You can put this solution on YOUR website!(x+2)(x^2-2x+4) ---- = x*(x^2-2x+4)+ 2*(x^2-2x+4) ---- = x^3 -2x^2 +4x + 2x^2 -4x +8 ------ = x^3 +8 =============== Cheers, Stan H.
 Probability-and-statistics/382862: a die is tossed 4 times. what is the odds in favor of the die showing a 6 all four times. 1 solutions Answer 271246 by stanbon(57940)   on 2010-12-08 08:55:43 (Show Source): You can put this solution on YOUR website!a die is tossed 4 times. what is the odds in favor of the die showing a 6 all four times. ------ P(6 four times) = (1/6)^4 P(not getting 6 four times) = 1 - (1/6)^4 ---------------------------------------------- Odds in favor of "6 four times" = [1/6^4]/[1 - (1/6^4)] = [1/6^4]/[(6^4-1)/6^4] -------------- = 1:1295 ================ Cheers, Stan H.
 Average/382751: The average of 12 numbers is 24. The average of 24 numbers is 12. What is the average of all 36 numbers?1 solutions Answer 271171 by stanbon(57940)   on 2010-12-07 22:08:36 (Show Source): You can put this solution on YOUR website!The average of 12 numbers is 24. The average of 24 numbers is 12. What is the average of all 36 numbers? ----- 12 numbers; ave. 24; total points 12*24 = 288 --- 24 numbers; ave. 12; total points 12*24 = 288 -------------------------------------------------- 36 numbers; total points = 576; average 576/36 = 16 ==================================================== Cheers, Stan H.
 Probability-and-statistics/382732: An official from the securities commission estimates that 75% of all investment bankers have profited from the use of insider information. Assume that 15 investment bankers are selected at random from the commission's registry. Using the Binomial Distribution, answer the following questions: a. Find the probability that at most 10 have profited from insider information. b. Find the probability that at least 6 have profited from insider information. c. Find the probability that all 15 have profited from insider information. d. What is the expected number of investment bankers who have profited from the use of insider information? e. Find the variance and standard deviation of the number of investment bankers who have profited from the use of insider information. 1 solutions Answer 271168 by stanbon(57940)   on 2010-12-07 22:03:52 (Show Source): You can put this solution on YOUR website!An official from the securities commission estimates that 75% of all investment bankers have profited from the use of insider information. Assume that 15 investment bankers are selected at random from the commission's registry. Using the Binomial Distribution, answer the following questions: -------------------------- Binomial Problems with n = 15 and p=0.75 ------- a. Find the probability that at most 10 have profited from insider information. P(0<= x <= 10) = binomcdf(15,0.75,10) = 0.3135 ----- b. Find the probability that at least 6 have profited from insider information. binomedf(15,0.75,6) = 0.0042 ---------------------------------------- c. Find the probability that all 15 have profited from insider information. 0.75^15 = 0.0134 ------------------- d. What is the expected number of investment bankers who have profited from the use of insider information? np = 15*0.75 = 11.25 --------------------- e. Find the variance and standard deviation of the number of investment bankers who have profited from the use of insider information. variance = npq = 15*0.75*0.252.8125 std = sqrt(variance) = 1.6771 -------------------------------- Cheers, Stan H.
 Probability-and-statistics/382740: 2 marbles are drawn without replacement from a box of 3 white 2 green 2 red and 1 blue marble. find the probablity 1. the second marble is blue given the first marble is red. so i got (rd) 1/4 and (blue) 1/7 so 1/4*1/7= 1/28 but my choices are 1/8 b. 1/4 c.1/7 or d. 2/7 so I am not sure what I am doing wrong. 2. the second marble is blue given the first marble is blue and I got 0 since there is only 1 marble is that correct?1 solutions Answer 271163 by stanbon(57940)   on 2010-12-07 21:51:41 (Show Source): You can put this solution on YOUR website!2 marbles are drawn without replacement from a box of 3 white 2 green 2 red and 1 blue marble. find the probablity 1. the second marble is blue given the first marble is red. so i got (rd) 1/4 and (blue) 1/7 so 1/4*1/7= 1/28 but my choices are 1/8 b. 1/4 c.1/7 or d. 2/7 so I am not sure what I am doing wrong. Ans:P(2nd is blue given the 1st is red) = 2/7 Comment: They don't want the probability of the 2 draw sequence only the probability getting a blue after a red has been drawn. ---------- 2. the second marble is blue given the first marble is blue and I got 0 since there is only 1 marble is that correct? Ans: CORRECT =============================== Cheers, Stan H.
 Probability-and-statistics/382737: I'm working on a homework assignment from my Topics in Mathematical Reasoning class and I've got an answer to this question, but there's no way for me to check the answer I have. The question is: A full house in poker consists of three of one kind and two of another kind in a five-card hand. For example, if a hand contains three Kings and two 5's, it is a full house. If 5 cards are dealt at random from a standard deck of 52 cards, without replacement, determine the probability of getting three Kings and two 5's. My answer is 1/108,2901 solutions Answer 271158 by stanbon(57940)   on 2010-12-07 21:39:41 (Show Source): You can put this solution on YOUR website! If 5 cards are dealt at random from a standard deck of 52 cards, without replacement, determine the probability of getting three Kings and two 5's. My answer is 1/108,290 ----- Ways to succeed: Pick 3 kings: 4C3 = 4 Pick 2 5's: 4C2 = 6 ---- Ways to succeed = 4*6 = 24 ------- Total number of 5-card hands: 52C5 -------- P(3K and 2 5's) = 24/52C5 = 0.0000092345 = 1/108,290 =========================================================== You have it. Cheers, Stan H.
 Probability-and-statistics/382639: For a segment of a radio show, the DJ can play 6 songs. If he has 87 songs to choose from how many ways can the program for this segment be arranged1 solutions Answer 271155 by stanbon(57940)   on 2010-12-07 21:32:55 (Show Source): You can put this solution on YOUR website!For a segment of a radio show, the DJ can play 6 songs. If he has 87 songs to choose from how many ways can the program for this segment be arranged --------------------- Ans: 87P6 = 87!/(81!*6!) = 3.635866x10^11 =================================================== Cheers, Stan H.
 Probability-and-statistics/382710: The scores on a standardized test had mean μ = 2.818 and standard deviation σ= 1.112. A teacher had 69 students take the test. Although the students were obviously not a random sample, she considered her students to be "typical" of all the national students. What is the probability that her students achieved an average score of at least 3?1 solutions Answer 271152 by stanbon(57940)   on 2010-12-07 21:11:33 (Show Source): You can put this solution on YOUR website!The scores on a standardized test had mean μ = 2.818 and standard deviation σ= 1.112. A teacher had 69 students take the test. Although the students were obviously not a random sample, she considered her students to be "typical" of all the national students. What is the probability that her students achieved an average score of at least 3? ------------------------------ t(3) = (3-2.818)/(1.112/sqrt(69)) = 1.3595 ---- P(x-bar > 3) = P(t >=1.350.089295 when df = 68) = 0.0892 ---------- Cheers, Stan H.
 Probability-and-statistics/382479: a bin contains 7 red chips , 9 green chips , 3 yellow chips, and 6 blue chips find each probability drawing a red chip replacing it then drawing a blue chip 1 solutions Answer 271078 by stanbon(57940)   on 2010-12-07 19:13:22 (Show Source): You can put this solution on YOUR website!a bin contains 7 red chips , 9 green chips , 3 yellow chips, and 6 blue chips find each probability drawing a red chip replacing it then drawing a blue chip ------- P(blue and red) = (7/25)(6/25) -------------------------------------- Cheers, Stan H.
 Probability-and-statistics/382560: during world war II, american bomber crews suffered about 2% losses each mission. Crews were required to fly 50 missions. some crew members claimed that this made a 100% chance of getting shot down. what's wrong with this (what was their actual chance of getting shot down)? 1 solutions Answer 271072 by stanbon(57940)   on 2010-12-07 18:57:54 (Show Source): You can put this solution on YOUR website!duplicate
 Probability-and-statistics/382593: Suppose that the annual rate of return for a stock is normally distributed with a mean of 7% and a standard deviation of 4% . Find the probability that the one-year return of this stock will be positive? Round your answer to at least four decimal places.1 solutions Answer 271069 by stanbon(57940)   on 2010-12-07 18:52:31 (Show Source): You can put this solution on YOUR website!Suppose that the annual rate of return for a stock is normally distributed with a mean of 7% and a standard deviation of 4% . Find the probability that the one-year return of this stock will be positive? Round your answer to at least four decimal places. ---- z(0) = (0-7)/4 = -1.75 --- P(x > 0) = P(z > -1.75) = 0.9599 =================================== Cheers, Stan H. =========
 Probability-and-statistics/382581: during world war II, american bomber crews suffered about 2% losses each mission. Crews were required to fly 50 missions. some crew members claimed that this made a 100% chance of getting shot down. what's wrong with this (what was their actual chance of getting shot down)? 1 solutions Answer 271068 by stanbon(57940)   on 2010-12-07 18:46:03 (Show Source): You can put this solution on YOUR website! during world war II, american bomber crews suffered about 2% losses each mission. Crews were required to fly 50 missions. some crew members claimed that this made a 100% chance of getting shot down. what's wrong with this (what was their actual chance of getting shot down)? ----- The probability of getting shot down is 2% on each mission. Cheers, Stan H.