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# Recent problems solved by 'stanbon'

stanbon answered: 57239 problems
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 , 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 Travel_Word_Problems/545831: damian left the airport travelling at an average speed of 35km/h. Jasmine left the airport at the same time and travelled in the opposite direction with an average speed of 65km/h. Find the number of hours Jasmine must travel before thet are 59.4km apart1 solutions Answer 355750 by stanbon(57307)   on 2011-12-12 08:00:07 (Show Source): You can put this solution on YOUR website! damian left the airport travelling at an average speed of 35km/h. Jasmine left the airport at the same time and travelled in the opposite direction with an average speed of 65km/h. Find the number of hours Jasmine must travel before thet are 59.4km apart ---- They are separating at a rate of (35+65) = 100 km/hr ---- time = distanc/rate ---- Your Problem: time = 59.4/100 = 0.594 hrs = 0.594*60 = 35.64 minutes ================ Cheers, Stan H. ================
 Functions/545813: Let f(x)= sqrt (1-cosx) , what is the domain of f(x)? More than just the answer, I need a good explanation to the answer. Please help. 1 solutions Answer 355749 by stanbon(57307)   on 2011-12-12 07:57:34 (Show Source): You can put this solution on YOUR website!Let f(x)= sqrt (1-cosx) , what is the domain of f(x)? ---- Since you want the square root, 1-cos(x) must not be negative. --- Solve 1-cos(x) >= 0 cos(x) <= 1 ---- But -1 <= cos(x) <= 1 for all "x". ---- So Domain is All Real Numbers. ============== Cheers, Stan H. ==============
 Probability-and-statistics/545763: Find the probability. A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a black card that is not a face card?1 solutions Answer 355747 by stanbon(57307)   on 2011-12-12 07:45:57 (Show Source): You can put this solution on YOUR website!Find the probability. A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a black card that is not a face card? --- # of ways to succeed: 20 # of random outcomes: 52 --- P(black AND not face) = 20/52 =============================== Cheers, Stan H. ==============
 Probability-and-statistics/545779: The accompanying table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. ---------Allergy ------Present-----Absent Male----15----------36 Female--40----------39 Suppose that the selection of a person is considered a trial and the presence of the allergy is considered a success. For each case, identify the numerical value of p and find the required probability. Two males and two females are selected at random. What is the probability that none has the allergy? This problem is going to due soon. Please help me solve this problem ASAP. Thank you so much for your effort.1 solutions Answer 355746 by stanbon(57307)   on 2011-12-12 07:42:52 (Show Source): You can put this solution on YOUR website!The accompanying table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. ---------Allergy ------Present-----Absent-----Total Male----15----------36-------51 Female--40----------39-------79 Total---55----------75-------130 Suppose that the selection of a person is considered a trial and the presence of the allergy is considered a success. For each case, identify the numerical value of p and find the required probability. Two males and two females are selected at random. What is the probability that none has the allergy? P(2 males absent) = 15C2/51C2 = 0.0824 P(2 females absent) = 40C2/79C2 = 0.2532 ---- P(2males AND 2females absent) = 0.0824*0.26532 = 0.0209 =================== Cheers, Stan H. ===================
 Probability-and-statistics/545783: A bag contains 20 blue and 15 green marbles. Two marbles, without replacement are drawn at random. What is the probability that both are blue? What is the probablity that at least one of them is blue?1 solutions Answer 355745 by stanbon(57307)   on 2011-12-12 07:31:39 (Show Source): You can put this solution on YOUR website!A bag contains 20 blue and 15 green marbles. Two marbles, without replacement are drawn at random. What is the probability that both are blue? What is the probablity that at least one of them is blue? ---- P(none are blue) = 15C2/35C2 = 105/595 ---- P(at least one is blue) = 1 - P(none is blue) = 1-0.1765 = 0.8235 ================ Cheers, Stan H. ================
 Probability-and-statistics/545817: A nationwide survey of 17,000 college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking. If 18 of those seniors are selected at random and asked their opinion, what is the probability that more than 9 but fewer than 14 disapprove of smoking pot daily?1 solutions Answer 355744 by stanbon(57307)   on 2011-12-12 07:28:27 (Show Source): You can put this solution on YOUR website!A nationwide survey of 17,000 college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking. If 18 of those seniors are selected at random and asked their opinion, what is the probability that more than 9 but fewer than 14 disapprove of smoking pot daily? ------ Binomial Problem with n = 18 and p(pot) = 0.7 --- P(10<= x <=13) = binomcdf(18,0.7,13)-binomcdf(18,0.7,9) = 0.6078 ============ Cheers, Stan H. ===========
 Mixture_Word_Problems/545690: George decides to mix grades of gasoline in his truck. He puts in 8 gallons of regular and 12 gallons of premium for a total cost of \$55.80. If premium gasoline costs \$0.15 more per gallon than regular, what was the price of each grade of gasoline.1 solutions Answer 355671 by stanbon(57307)   on 2011-12-11 21:24:54 (Show Source): You can put this solution on YOUR website! He puts in 8 gallons of regular and 12 gallons of premium for a total cost of \$55.80. If premium gasoline costs \$0.15 more per gallon than regular, what was the price of each grade of gasoline. ------------------- Equations: 8r + 12p = 55.80 p = r+ 0.15 ---- Substitute for "P" and solve for "r": 8r + 12(r+0.15) = 55.80 8r + 12r + 1.80 = 55.80 ---- 20r = 54 regular price = 2.70 --- Solve for "p": p = r + 0.15 premium price = 2.85 ======================== Cheers, Stan H. =============
 Linear-systems/545683: how do you solve x+y=-10 x=y+61 solutions Answer 355667 by stanbon(57307)   on 2011-12-11 21:20:11 (Show Source): You can put this solution on YOUR website!x+y=-10 x=y+6 --- Substitute for "x" and solve for "y": y+6+y = 10 2y = 4 y = 2 ---- Solve for "x": x = y+6 x = 2+6 x = 8 ------------ Solution: (8,2) -------- Cheers, Stan H.
 Exponents/545672: W = -0.0014x2 - 0.076x + 50 to find W for each x-value in the table. 1 solutions Answer 355663 by stanbon(57307)   on 2011-12-11 21:11:37 (Show Source): You can put this solution on YOUR website!No table posted.
 Money_Word_Problems/545669: how much must a man 35 years of age deposit in a savings account today in a bank paying 4 1/2 % compounded quarterly in order to have \$25000 in the account 25 years from now?1 solutions Answer 355659 by stanbon(57307)   on 2011-12-11 21:02:32 (Show Source): You can put this solution on YOUR website!how much must a man 35 years of age deposit in a savings account today in a bank paying 4 1/2 % compounded quarterly in order to have \$25000 in the account 25 years from now? ---- A(t) = P(1+(r/n))^(nt) ---- 25000 = P(1+(0.045/4))^(4*25) --- 250000 = P(3.0609) P = \$81674.51 ================== Cheers, Stan H. ====================
 Money_Word_Problems/545664: Good evening, I need assistance with this interest problem and would greatly appreciate your help. Jim is able to sell a hand-carved statue for \$670 which was a 35% profit over his cost. How much did the statue originally cost him? A. \$496.30 B. \$512.40 C. \$555.40 D. \$574.90 E. \$588.20 the answer is A \$496.30 but I do not understand how they have got the solution to that problem. what I have gotten so far is that I multiplied 670 with .35 and the answer is 234.5 then I took the answer and subtracted it from 670 which the answer 435.5 1 solutions Answer 355654 by stanbon(57307)   on 2011-12-11 20:55:06 (Show Source): You can put this solution on YOUR website! Jim is able to sell a hand-carved statue for \$670 which was a 35% profit over his cost. How much did the statue originally cost him? ---- Let his cost be "x": Equation: x + 0.35x = 670 1.35x = 670 x = 670/1.35 x = \$496.30 ================= Cheers, Stan H. ================= A. \$496.30 B. \$512.40 C. \$555.40 D. \$574.90 E. \$588.20 the answer is A \$496.30
 Travel_Word_Problems/545658: a boat travels 66 miles in 2 hours. what is its rate in feet per minute1 solutions Answer 355652 by stanbon(57307)   on 2011-12-11 20:50:58 (Show Source): You can put this solution on YOUR website!a boat travels 66 miles in 2 hours. what is its rate in feet per minute ------------ 66 (miles/hour) (5280 ft/1 miles)(1 hr/60 min) ---- = (66*5280*1)/(1*1*60)(ft/min) --- = 5808 ft/min ================== Cheers, Stan H. ==================
 Radicals/545537: Solve for , where is a real number. (under a radical) -x+6 + (under a different radical) x-5 = 1 (If there is more than one solution, separate them with commas.) 1 solutions Answer 355616 by stanbon(57307)   on 2011-12-11 18:30:59 (Show Source): You can put this solution on YOUR website!(under a radical) -x+6 + (under a different radical) x-5 = 1 ---- sqrt(-x+6) + sqrt(x-5) = 1 --- Square both sides to get: (-x+6) + (x-5) + 2sqrt(-x^2+11x-30) = 1 --------- 2sqrt(-x^2+11x-30) = 0 --- sqrt(-x^2+11x-30) = 0 --- -x^2+11x-30 = 0 --- x^2-11x+30 = 0 --- Factor: (x-6)(x+5) = 0 ----- Acceptable answer: x = 6 ============ Cheers, Stan H. ===============
 Average/545540: If 9 and x have the same average as 3,7, and 14 what is the value of x?1 solutions Answer 355615 by stanbon(57307)   on 2011-12-11 18:21:22 (Show Source): You can put this solution on YOUR website!If 9 and x have the same average as 3,7, and 14 what is the value of x? ---- Average of 9 and x: (9+x)/2 ---- Average of 3,7,14: (3+7+14)/3 = 8 --- Solve (9+x)/2 = 8 9+x = 16 x = 7 =========== Cheers, Stan H. ===========
 Exponential-and-logarithmic-functions/545538: log base7 (3x-11)=21 solutions Answer 355614 by stanbon(57307)   on 2011-12-11 18:19:09 (Show Source): You can put this solution on YOUR website!log base7 (3x-11)=2 ----- log7(3x-11) = 2 ----- 3x-11 = 7^2 --- 3x-11 = 49 --- 3x = 60 x = 20 ============= Cheers, Stan H. =============
 Expressions-with-variables/545539: Please assist with the steps to solve this. I am solving for c. I know the answer. I want to see the steps to solve. Thanks Solve for c: 2a = 5b-c/3c+1 Answer should be: c = 5b-2a/6a+1 1 solutions Answer 355612 by stanbon(57307)   on 2011-12-11 18:17:27 (Show Source): You can put this solution on YOUR website!2a = 5b-c/3c+1 ----- 2a = (5b-c)/(3c+1) --- Cross-multiply: 6ac+2a = 5b-c 6ac+c = 5b-2a --- Factor out "c": c(6a+1) = (5b-2a) --- c = (5b-2a)/(6a+1) ============================ Cheers, Stan H. =============== Answer should be: c = 5b-2a/6a+1
 Travel_Word_Problems/545535: What does "n" equal? 3n-18 is at least 5n+21 1 solutions Answer 355611 by stanbon(57307)   on 2011-12-11 18:13:36 (Show Source): You can put this solution on YOUR website!What does "n" equal? 3n-18 is at least 5n+21 ------- 3n-18 >= 5n+21 2n <= -18-21 2n <= -39 n <= -39/2 ============== Cheers, Stan H. ==============
 Probability-and-statistics/545413: A class of first graders includes 7 girls and 14 boys, 2 students are selected at random to be the teachers assistant on a given day. What is the probability that both are boys?1 solutions Answer 355589 by stanbon(57307)   on 2011-12-11 15:50:09 (Show Source): You can put this solution on YOUR website!A class of first graders includes 7 girls and 14 boys, 2 students are selected at random to be the teachers assistant on a given day. What is the probability that both are boys? ------------------------------ # of ways to succeed: 14C2 = 91 ---- # of random pairs: 21C2 = 210 ================================= Cheers, Stan H. =======
 Probability-and-statistics/545422: One half of all U.S. households pay bills electronically. If seven U.S. households are randomly selected, what is the probability that exactly two pay bills electronically? 1 solutions Answer 355588 by stanbon(57307)   on 2011-12-11 15:44:33 (Show Source): You can put this solution on YOUR website!One half of all U.S. households pay bills electronically. If seven U.S. households are randomly selected, what is the probability that exactly two pay bills electronically? ------------------------------------- Binomial Problem with n = 7 and p(pay) = 1/2 -------------- P(x = 2) = 7C2(1/2)^7 = 21/2^7 = 21/128 =================== Cheers, Stan H.
 Probability-and-statistics/545371: how many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athetic footwear? We want 99% confidence that the sample means is within \$200 of the population , and the population standard devation is known to be \$11001 solutions Answer 355586 by stanbon(57307)   on 2011-12-11 15:38:27 (Show Source): You can put this solution on YOUR website!how many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athetic footwear? We want 99% confidence that the sample means is within \$200 of the population , and the population standard devation is known to be \$1100 ----------------------------- n = [z*s/E]^2 = [2.3263*1100/200]^2 = 164 when rounded up ==================================== Cheers, Stan H. ===============
 Probability-and-statistics/545383: I can't figure out how to get the p-value. Question: 400 people are asked a question in a poll and 80 said yes. What is the P-value? I will be grateful for help, thank you.1 solutions Answer 355575 by stanbon(57307)   on 2011-12-11 14:30:53 (Show Source): You can put this solution on YOUR website!400 people are asked a question in a poll and 80 said yes. ------- sample proportion = p-hat = 80/400 = 1/5 test statistic = ((1/5)-p)/sqrt[p*q/n] = ? ------- What is the P-value? The p-value is the probability that z is less than (or greater than) the test statistic. You don't have enough information to calculate a p-value ------ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/545095: 0=y^2-8x+4y-20 ive tried everything but i can't get the answer. its asking for the equation in standard form,vertex,focus,directrix,and the functions in terms of y.please help i need to know this to pass my math class.1 solutions Answer 355441 by stanbon(57307)   on 2011-12-10 18:49:53 (Show Source): You can put this solution on YOUR website!its asking for the equation in standard form, vertex, focus, directrix,and the functions in terms of y. ---------------- y^2-8x+4y-20 = 0 ------------- y^2+4y+? = 8x-20 + ? ------ y^2+4y+4 = 3x-20+4 (y+2)^2 = 3x-16 3x = (y+2)^2+16 x = (1/3)(y+2)^2 + (16/3) ------ vertex: (-2,16/3) --- 4p = 1/3 p = 1/12 directrix: x = -2-(1/12) ; x = -25/12 focus: -2+1/12 = 23/12 :::Ans: (23/12 , 16/3) ------------- Cheers, Stan H. ===============
 Probability-and-statistics/545072: The average hourly wage of employees in a large nationwide industry is \$12.96. Assume the variable is normally distributed, with a standard deviation of \$4.46. In a randomly selected sample of 10,000 such employees, how many of them (correct to the nearest hundred) would you expect to be earning between \$9.00 and \$17.00 per hour?1 solutions Answer 355423 by stanbon(57307)   on 2011-12-10 18:38:31 (Show Source): You can put this solution on YOUR website!The average hourly wage of employees in a large nationwide industry is \$12.96. Assume the variable is normally distributed, with a standard deviation of \$4.46. In a randomly selected sample of 10,000 such employees, how many of them (correct to the nearest hundred) would you expect to be earning between \$9.00 and \$17.00 per hour? ----- z(9) = (9-12.96)/4.46 = -0.8879 ---- z(17) = (17-12.96)/4.46 = 0.9058 --------------------------------------- P(9 < x < 17) = P(-0.8879 < z < 0.9058) = 0.6302 ================ Cheers, Stan H. ================
 Probability-and-statistics/545093: Essay; show all work. A community 5K run will award \$50 to the winner. 75 people enter the race, and they each pay an entry fee of \$20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent. 1 solutions Answer 355416 by stanbon(57307)   on 2011-12-10 18:33:32 (Show Source): You can put this solution on YOUR website!Essay; show all work. A community 5K run will award \$50 to the winner. 75 people enter the race, and they each pay an entry fee of \$20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent. ---- Random winning values::::::: 50,,,,,,,-20 Corresponding probabiities::::1/75,,,,,74/75 -------- E(x) = 50(1/75) - 20(74/75) = -\$19.07 ----- You can expect to lose \$19.07 each time you play the game. ---- Fair price to play should be 20-19.07 = 93 cents ==================================================== Cheers, Stan H. ==============
 Complex_Numbers/545012: Find the reciprocal of 3-4i/101 solutions Answer 355379 by stanbon(57307)   on 2011-12-10 13:48:29 (Show Source): You can put this solution on YOUR website! Find the reciprocal of 3-4i/10 ----- [(3-4i)/10]^-1 = 10/(3-4i) ---- Multiply numerator and denominator by 3+4i to get: ---- = [10(3+4i)]/[9+16] ---- = (10/25)(3+4i) ---- = (2/5)(3+4i) ================= Cheers, Stan H. =================
 logarithm/544991: I have a big problem with this equation. 5^(x-2) = 3^(2x) That is, I know the answer but I don't know what's the method to have it. The answer is: log 25 / log 5/9 Help me please Thank you1 solutions Answer 355377 by stanbon(57307)   on 2011-12-10 13:22:19 (Show Source): You can put this solution on YOUR website!5^(x-2) = 3^(2x) --------------- (x-2)log(5) = (2x)log(3) --- xlog(5) - log(25) = x(log(9)) ---- x[log(5)-log(9)] = log(25) --- x = log(25)/(log(5/9)) ------ x = -5.4763 ================ Cheers, Stan H. ================
 Exponential-and-logarithmic-functions/544976: log10 x + log10 (x+21)=2 1og10[x(x+21)=2 x^2+21x=2 x^2+21x-2=01 solutions Answer 355367 by stanbon(57307)   on 2011-12-10 12:05:01 (Show Source): You can put this solution on YOUR website!log10 x + log10 (x+21)=2 1og10[x(x+21)=2 That means x(x+21) = 10^2 ------- x^2+21x-100 = 0 ----- x^2+25x-4x-100 = 0 x(x+25)-4(x+25) = 0 (x+25)(x-4) = 0 Acceptable answer: x = 4 ============================= Cheers, Stan H. ===================
 Exponential-and-logarithmic-functions/544975: hello!. I need a solution for logarithmic function 3/5**log5 by using method of base change. Thank you. 1 solutions Answer 355366 by stanbon(57307)   on 2011-12-10 12:00:54 (Show Source): You can put this solution on YOUR website!3/5**log5 ---- You don't need "base change" to find this answer: --- = log(5^(3/5)) --- = log(2.6265) --- = 0.4194 =============== Cheers, Stan H. ===============
 Polynomials-and-rational-expressions/544914: Completely factor the expression 216x2 – 384y2 1 solutions Answer 355364 by stanbon(57307)   on 2011-12-10 11:53:11 (Show Source): You can put this solution on YOUR website!216x2 – 384y2 --- 216 = 6^3 = 2^3*3^3 --- 384 = 8^2*6 = 2^7*3 --- 24(9x^2-16y^2) ---- = 24(3x-4y)(3x+4y) ===================== Cheers, Stan H. ================
 Linear-equations/544909: The value of stock ABC Corporation has been increasing by the same fixed dollar amount each year. the pattern is expected to continue. Let 1980 be the base year corresponding to X=0, with x=1,2,3....corresponding to later years. ABC stock was selling at \$37.50 in 1985, and \$45.00 in 1988. If y represents the price of ABC stock, find the equation y=mx+b that relates x and y, and predict the price in the year 2000. 1 solutions Answer 355334 by stanbon(57307)   on 2011-12-10 07:44:36 (Show Source): You can put this solution on YOUR website!The value of stock ABC Corporation has been increasing by the same fixed dollar amount each year. the pattern is expected to continue. ------------------------------ Let 1980 be the base year corresponding to X=0, with x=1,2,3....corresponding to later years. ABC stock was selling at \$37.50 in 1985. --- That tells you the "y" intercept is 37.50 ------------------------------------------------------ ABC stock was selling at \$37.50 in 1985, and \$45.00 in 1988. That gives you 2 points (0,37.50) and (3,45.00) ---- So the slope is (45-37.5)/3 = 7.5/3 = 2.5 -------------------------- If y represents the price of ABC stock, find the equation y=mx+b that relates x and y, --- Answer: y = 2.5x+37.5 ------------------------------- and predict the price in the year 2000. f(5) = 2.5*5+37.5 = \$50.00 ================================ Cheers, Stan H. ================
 Polynomials-and-rational-expressions/544913: Andrew factored the expression -30x^3-9x^2-3x as -5x(6x^2-2x-1) . But when Melissa applied the distributive law and multiplied out -5x(6x^2-2x1) , she got -30x^3+10x^2+5x; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state. 1 solutions Answer 355333 by stanbon(57307)   on 2011-12-10 07:37:03 (Show Source): You can put this solution on YOUR website!Andrew factored the expression -30x^3-9x^2-3x as -5x(6x^2-2x-1) . But when Melissa applied the distributive law and multiplied out -5x(6x^2-2x1) , she got -30x^3+10x^2+5x; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state. ------------------------------ -30x^3-9x^2-3x as -5x(6x^2-2x-1) --- Dividing -30x^3-9x^2-3x by -5x you should get: 6x^2+(9/5)x+(3/5) ======================== Cheers, Stan H.