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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 logarithm/549406: 2log(5)+log(2x+38)=31 solutions Answer 357725 by stanbon(57282)   on 2011-12-20 18:29:01 (Show Source): You can put this solution on YOUR website!2log(5)+log(2x+38)=3 --- log(25) + log(2x+38) = 3 --- log[25(2x+38)) = 3 --- log[50x+950] = 3 ------ 50x+950 = 10^3 ------- 50x = 50 x = 1 ----- Cheers, Stan H. ================
 Exponential-and-logarithmic-functions/549407: inverses of functions: Evaluate if F(x)=3x+7 what is f(6)?1 solutions Answer 357723 by stanbon(57282)   on 2011-12-20 18:20:48 (Show Source): You can put this solution on YOUR website!Evaluate if F(x)=3x+7 what is f(6)? ------ f(6) = 3*6+7 f(6) = 25 =============== Cheers, Stan H. ==============
 Money_Word_Problems/549399: Isabella invested \$500 at 6% annual interest, compounded quarterly. The value, A, of an investment can be calculated using the equation A=P(1+r/n)^nt where P is the initial investment, r is the interest rate, n is the number of times the interest is compounded each year, and t is time in years. Exactly how long will it take for her investment to be worth four times as much (quadruple)in value?1 solutions Answer 357721 by stanbon(57282)   on 2011-12-20 18:16:52 (Show Source): You can put this solution on YOUR website!Isabella invested \$500 at 6% annual interest, compounded quarterly. The value, A, of an investment can be calculated using the equation A=P(1+r/n)^nt where P is the initial investment, r is the interest rate, n is the number of times the interest is compounded each year, and t is time in years. Exactly how long will it take for her investment to be worth four times as much (quadruple)in value? -------------------------------- Solve for "t": 4P = P(1+(0.06/4))^(4t) (1+(0.06/4))^(4t) = 4 (1.015)^(4t) = 4 --- 4t = ln(4)/ln(1.015) t = 23.28 years ================================== Cheers, Stan H. =================
 Systems-of-equations/549378: If 27 is added to a two digit number, the result is a number with the same digits, but in reverse order. The sum of the digits is 11. What is the original number? Can you please solve this for me step by step?1 solutions Answer 357704 by stanbon(57282)   on 2011-12-20 16:33:24 (Show Source): You can put this solution on YOUR website!If 27 is added to a two digit number, the result is a number with the same digits, but in reverse order. The sum of the digits is 11. What is the original number? ---- Let the 2-digit number be 10t+u. ----- Equation: 10t+u + 27 = 10u+t t + u = 11 --------------------- 9t-9u = -27 t + u = 11 ------------ t - u = -3 t + u = 11 -------------- Add and solve for "t": 2t = 8 t = 4 ----- Solve for "u": t + u = 4 4 + u = 4 u = 0 ======= The 2-digit number: 10t + u = 40 ================== Cheers, Stan H. ==================
 Matrices-and-determiminant/549381: under what conditions it has been following matrix equality? ( x y) * (1 1) = (1 1) * (x y) ( z w) (0 1) .... (0 1) (z w) Answer: provided that z = 0 and x = w How? Thank you1 solutions Answer 357703 by stanbon(57282)   on 2011-12-20 16:28:36 (Show Source): You can put this solution on YOUR website!under what conditions it has been following matrix equality? ( x y) * (1 1) = (1 1) * (x y) ( z w) * (0 1) = (0 1) * (z w) Answer: provided that z = 0 and x = w How? --- Equations: x + 0*y = x + z x + y = y + w z + 0*w = z + w z + w = 0y + w -------------------- From the 2nd row: x = w From the 4th row: z = 0 =============================== Cheers, Stan H.
 Age_Word_Problems/549369: Jim is 6 more than twice Ernie's age. If Jim is 56 how old is Ernie?1 solutions Answer 357688 by stanbon(57282)   on 2011-12-20 15:06:13 (Show Source): You can put this solution on YOUR website!Jim is 6 more than twice Ernie's age. If Jim is 56 how old is Ernie? --- Equations: j = 2e+6 j = 56 ------------- Substitute for "j" and solve for "e": 56 = 2e + 6 2e = 50 Ernie = 25 yrs old ====================== Cheers, Stan H. ======================
 Matrices-and-determiminant/549368: Déterminer la valeur de K pour que la matrice suivante sois inversible: K 3 K 8 6 8 1 2 3 Thanks1 solutions Answer 357686 by stanbon(57282)   on 2011-12-20 15:03:10 (Show Source): You can put this solution on YOUR website!Déterminer la valeur de K pour que la matrice suivante sois inversible: K 3 K 8 6 8 1 2 3 --------- The determinant: (K*6*3+8*2*K+1*8*3)-(k*6*1+8*2K+3*8*3) = 0 ------------------------ 18k+16k+24-(6k+16k+72) = 0 ------------------------ (34k+24)-(22k+72) = 0 12k - 48 = 0 k = 4 -------------- The matrix is singular if k = 4; It is invertible if k is not 4. =============================== Cheers, Stan H.
 test/549322: Equation of a circle in atandered form centered at (-2,3) with radius of 31 solutions Answer 357633 by stanbon(57282)   on 2011-12-20 11:12:41 (Show Source): You can put this solution on YOUR website!Equation of a circle in atandard form centered at (-2,3) with radius of 3 ---- (x+2)^2+(y-3)^2 = 3^2 ========================== Cheers, Stan H. =================
 Surface-area/549323: An object is 81 inches long, 37 inches high and 8 inches deep. What is the square footage?1 solutions Answer 357631 by stanbon(57282)   on 2011-12-20 11:03:39 (Show Source): You can put this solution on YOUR website! An object is 81 inches long, 37 inches high and 8 inches deep. What is the square footage? ----------- Surface Area = 2(81*37+81*8+37*8) sq.ft. =================================== Cheers, Stan H.
 Rational-functions/549305: Find all zeros of g(x)=x^3+3x^2-50x+36 given that -9 is a zero. (No Decimals!)1 solutions Answer 357626 by stanbon(57282)   on 2011-12-20 10:24:49 (Show Source): You can put this solution on YOUR website!Find all zeros of g(x)=x^3+3x^2-50x+36 given that -9 is a zero. ------- Use synthetic division: -9)....1....3....-50....36 ........1....-6......4....|..0 ============================== Quotient: x^2-6x+4 Use the quadratic formula to find the 2 remaiining zeros. ==================== Cheers, Stan H.
 Functions/549306: What's the domain of f(x)=x/(x^2+2x-31 solutions Answer 357623 by stanbon(57282)   on 2011-12-20 10:12:32 (Show Source): You can put this solution on YOUR website!What's the domain of f(x)=x/(x^2+2x-3) ------ That denominator cannot be zero: x^2+2x-3 = 0 (x+3)(x-1) = 0 x = -3 ; x = 1 -------------------- Domain is "All Real Numbers except x = -3 and x = 1. ===================================================== Cheers, Stan H.
 Linear-systems/549310: write the eqaution of a line with a parallel slope tp y=2x-6 and through the point (4,2)1 solutions Answer 357619 by stanbon(57282)   on 2011-12-20 10:08:05 (Show Source): You can put this solution on YOUR website!write the eqaution of a line with a parallel slope to y=2x-6 and through the point (4,2) ---- slope = 2 Form: y = mx+b 2 = 2*4 + b b = -6 ---- Equation: y = 2x-6 ============= cheers, Stan H. =============
 Evaluation_Word_Problems/549302: A theatre sells 200 tickets one day. The tickets are sold for \$33. and \$18. The total dollar amount collected for the one day is \$4,800. How do a write the equation for this problem and steps to solve? x= \$33. tickets y= \$18. tickets x + y = 200 tickets 33x + 18y = 4,800. I do not know how to continue Thank you, Karen1 solutions Answer 357609 by stanbon(57282)   on 2011-12-20 09:34:54 (Show Source): You can put this solution on YOUR website!A theatre sells 200 tickets one day. The tickets are sold for \$33. and \$18. The total dollar amount collected for the one day is \$4,800. How do a write the equation for this problem and steps to solve? x= \$33. tickets y= \$18. tickets x + y = 200 tickets 33x + 18y = 4,800. ---------------------- Multiply thru the 1st equation by 33: 33x + 33y = 33*200 33x + 18y = 4800 ------- Subtract and solve for "y": 15y = 1800 y = 120 (# of \$18 tickets sold) ---- Solve for "x": x + y = 200 x + 120 = 200 x = 80 (# of \$33 tickets sold) =================================== Cheers, Stan H. ===============
 Mixture_Word_Problems/549304: a man mixes 100 lbs of 90% copper alloy with 150 lbs of 60% copper alloy what is his percentage of the total copper alloy?1 solutions Answer 357607 by stanbon(57282)   on 2011-12-20 09:30:10 (Show Source): You can put this solution on YOUR website!a man mixes 100 lbs of 90% copper alloy with 150 lbs of 60% copper alloy what is his percentage of the total copper alloy? ------------------ Equation: copper + copper = copper 0.90*100 + 0.60*150 = x(100+150) Multiply thru by 100 to get: 90*100 + 60*150 = x(25000) 25000x = 9000+9000 x = 0.72 = 72% ==================== Cheers, Stan H. ====================
 Average/549303: My boyfriend has a 66% in his class. What will his grade be if he makes a 93% on a final worth 25% of his grade?1 solutions Answer 357604 by stanbon(57282)   on 2011-12-20 09:25:15 (Show Source): You can put this solution on YOUR website!My boyfriend has a 66% in his class. What will his grade be if he makes a 93% on a final worth 25% of his grade? --- So far he has 66% of 75 = 50 points: If he gets 93% of 25 he will get 23.25 points. --- He will have (50+23.25) points out of 100 = 73.25% =================================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/549299: Find the equation for the right bisector of the line segment joining the points A(1,0) and B(2,3).1 solutions Answer 357602 by stanbon(57282)   on 2011-12-20 09:20:23 (Show Source): You can put this solution on YOUR website!Find the equation for the right bisector of the line segment joining the points A(1,0) and B(2,3). ------ The mid-point is ((1+2)/2,(0+3)/2) = (3/2 , 3/2) ---- The line thru AB is 3/1 = 3 ----- The slope of the bisector must be -1/3 ------------------------------------------ Form: y = mx+b 0 = (-1/3)1+b b = 1/3 --- Equation of perpendicular bisector is y = (-1/3)x+(1/3) ======================================================== Cheers, Stan H. ============
 Graphs/549263: The number y of passengers riding an elevator can be no greater than the elevator's maximum weight capacity x (in pounds) divided by 150. Write and graph an inequality that relates the number of passengers to the maximum weight capacity. Identify and interpret one of the solutions. For the inequality, I was thinking it would be y is greater than or equal to x/150, but I wasn't sure how to graph it.1 solutions Answer 357600 by stanbon(57282)   on 2011-12-20 09:06:43 (Show Source): You can put this solution on YOUR website!The number y of passengers riding an elevator can be no greater than the elevator's maximum weight capacity x (in pounds) divided by 150. Write and graph an inequality that relates the number of passengers to the maximum weight capacity. Identify and interpret one of the solutions. ---------------- "Can be no greater than" means 'is less than or equal to'. --------------- Inequality: y <= x/150 ----- =========== Example y = x/150 If max weight capacity is 900 lbs. y = 900/150 = 6 passenger capacity is 6 persons. --------------------------------------- Cheers, Stan H.
 Probability-and-statistics/549289: The weight of a new-born baby follows a normal distribution with mean 3.44 kg and standard deviation 1.31 kg. The probability of the average weight of n new- born babies being greater than 3.13 kg is 0.937. Find the value of n 1 solutions Answer 357594 by stanbon(57282)   on 2011-12-20 08:30:34 (Show Source): You can put this solution on YOUR website!The weight of a new-born baby follows a normal distribution with mean 3.44 kg and standard deviation 1.31 kg. The probability of the average weight of n new- born babies being greater than 3.13 kg is 0.937. Find the value of n ------ x-bar = 3.13 AND z(3.13) = (3.13-3.44)/(1.31/sqrt(n) Find the z-score with a left-tail of 1-0.937 = 0.0630: invNorm(0.0630) = -1.5301 --- So (3.13-3.44)/[1.31/sqrt(n)] = -1.5301 -0.31/(1.31/sqrt(n)) = -1.5301 1.31/sqrt(n) = -0.31/-1.5301 = 0.2026 sqrt(n) = 1.31/0.2026 = 6.4658 n = 41.8 rounding up to 49 ================================ Cheers, Stan H. ================
 Complex_Numbers/549291: what is the polynomial of least degree that includes the zeroes -5, 1+3i, 1-3i?1 solutions Answer 357592 by stanbon(57282)   on 2011-12-20 08:14:30 (Show Source): You can put this solution on YOUR website!what is the polynomial of least degree that includes the zeroes -5, 1+3i, 1-3i? f(x) = (x+5)(x-1-5i)(x-1+5i) ---- f(x) = (x+5)((x-1)^2+25) --- f(x) = (x+5)(x^2-2x+26) ---- f(x) = x^3+3x^2+16x+130 ============================ Cheers, Stan H.
 Probability-and-statistics/549244: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02 What is the probability that (a) both will fail? (b)neither will fail? (c) one of the other will fail? show all steps carefully.1 solutions Answer 357554 by stanbon(57282)   on 2011-12-19 23:03:03 (Show Source): You can put this solution on YOUR website! A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02 What is the probability that (a) both will fail?;;(0.02)^2 --------------------------------- (b)neither will fail?:: (0.98)^2 -------- (c) one of the other will fail?::: 1-[0.02^2+0.98^2] =================== Cheers, Stan H. ===================
 Probability-and-statistics/549032: A person scores a 81 on a test of verbal ability and a 6.4 on a tesat of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is the persons stronger ability: verbal of quatitative? explain your answer to a person who has never hada course in statistics.1 solutions Answer 357530 by stanbon(57282)   on 2011-12-19 21:11:54 (Show Source): You can put this solution on YOUR website!A person scores a 81 on a test of verbal ability and a 6.4 on a test of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Verbal: z(81) = (81-50)/20 = 31/20 = 1.55 ---- Quantitative: z(6.4) = (6.4-0)/5 = 1.28 ----- Which is the persons stronger ability: verbal of quatitative? --- Ans: verbal ========================= Cheers, Stan H. ====================
 Probability-and-statistics/549160: The following are all 6 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale. 10,6,7,6,5,8 Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places1 solutions Answer 357528 by stanbon(57282)   on 2011-12-19 20:51:51 (Show Source): You can put this solution on YOUR website!The following are all 6 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale. 10,6,7,6,5,8 Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places Ans: 1.63 ====================== Cheers, Stan H. ==============
 Surface-area/549146: Hi there i hope you can help. i need to work out the price of grass seeding. i have worked out that need 122m squared of grass seed spread. The price is spread (75g/ m squared) at £8.75 per 2.5kg box I have completely lost all sense on this. can you help please.1 solutions Answer 357504 by stanbon(57282)   on 2011-12-19 18:40:53 (Show Source): You can put this solution on YOUR website!i need to work out the price of grass seeding. i have worked out that need 122m squared of grass seed spread. The price is spread (75g/ m squared) at £8.75 per 2.5kg box ------ Each square meter requires 75 grams of seed --- You need 122*75 = 9150 grams of seed ---- 9150 grams = 9.15 kg --- Price will be 9.15*8.75 = 80.0625 pounds ========================================== Cheers, Stan H.
 Complex_Numbers/549143: Can you please help me solve this 15-5i^2+3i^321 solutions Answer 357503 by stanbon(57282)   on 2011-12-19 18:31:23 (Show Source): You can put this solution on YOUR website!Can you please help me solve this 15-5i^2+3i^32 --- = 15-5(-1)+3(1) --- = 15+5+3 --- = 23 ============ Cheers, Stan H. ============
 test/549142: y=3x-7; (0,4) Write equation in slope-intercept form for the line that is parallel through the given point.1 solutions Answer 357502 by stanbon(57282)   on 2011-12-19 18:29:25 (Show Source): You can put this solution on YOUR website!y=3x-7; (0,4) Write equation in slope-intercept form for the line that is parallel through the given point. ---- The given line has slope = 3 --- Form: Y = mx+b Solve for "b": 4 = 3*0 + b b = 4 ------ Equation: y = 3x+4 ============= Cheers, Stan H. =============
 Polynomials-and-rational-expressions/549141: how do you solve 8x2-50=01 solutions Answer 357501 by stanbon(57282)   on 2011-12-19 18:27:06 (Show Source): You can put this solution on YOUR website!how do you solve 8x^2-50=0 -------------- 8x^2 = 50 x^2 = 25/4 x = +-(5/2) =============== Cheers, Stan H. ===============
 Probability-and-statistics/549048: In a class of 15 people exactly 3 got A's. If two people are randomly chosen from this class, what is the probability that at least one of these two people got and A?1 solutions Answer 357500 by stanbon(57282)   on 2011-12-19 18:24:48 (Show Source): You can put this solution on YOUR website!In a class of 15 people exactly 3 got A's. If two people are randomly chosen from this class, what is the probability that at least one of these two people got and A? ----- P(at least 1 got A) = 1 - P(none got A) ----- P(none got A) = 12C2/15C2 = 0.6286 ----------------- P(at least 1 got A) = 1 - 0.6286 = 0.3714 =============================================== Cheers, Stan H. ===============
 Numbers_Word_Problems/549117: 2)The lager of two numbers is 1 more than 3 times the smaller. The difference between 8 times the smaller and 2 times the lager is 10. Find the numbers1 solutions Answer 357486 by stanbon(57282)   on 2011-12-19 17:53:25 (Show Source): You can put this solution on YOUR website!Let larger be "y" Let smaller be "x" ----------------------------- The larger of two numbers is 1 more than 3 times the smaller. The difference between 8 times the smaller and 2 times the larger is 10. Find the numbers --- Equations: y = 3x + 1 8x - 2y = 10 ------------------- Substitute for "y" and solve for "x": 8x - 2(3x+1) = 10 8x - 6x-2 = 10 2x = 12 x = 6 ---- Solve for "y": y = 3x+1 y = 3*6+1 y = 19 ================ Cheers, Stan H.
 Mixture_Word_Problems/549129: How many gallons of 80% antifreeze must be added to 90 gallons of 20% antifreeze to get a mixture of 70% antifreeze?1 solutions Answer 357482 by stanbon(57282)   on 2011-12-19 17:48:51 (Show Source): You can put this solution on YOUR website!How many gallons of 80% antifreeze must be added to 90 gallons of 20% antifreeze to get a mixture of 70% antifreeze? ------ alcohol + alcohol = alcohol 0.20*90 + 0.80x = 0.70(90+x) --- Multiply thru by 100 to get: 20*90 + 80x = 70*90 + 70x 10x = 50*90 x = 450 gallong (amt. of 80% solution needed) ====================== Cheers, Stan H. ======================
 Complex_Numbers/549122: Perform the indicated operation (6+3i)+(2-8i) is the answer 8-5i? Then i dont understand -3(4+3i)-(-9+3i)1 solutions Answer 357479 by stanbon(57282)   on 2011-12-19 17:44:53 (Show Source): You can put this solution on YOUR website!Perform the indicated operation (6+3i)+(2-8i) is the answer 8-5i?;;;;Yes ---------------------------------------- Then i dont understand -3(4+3i)-(-9+3i) --- = -12-9i +9-3i ----- = -3 -12i ================ Cheers, Stan H. ===========
 Travel_Word_Problems/549126: you are traveling for the holidays to go visit your family. You know that you live 876 miles from your relatives. you can travel on the interstate the whole way so your parents are abe to drive an average of 76 miles per hour. Is this a linear representation? What is an equation to represent your miles traveled in realationship to the hours you will travel?1 solutions Answer 357476 by stanbon(57282)   on 2011-12-19 17:41:11 (Show Source): You can put this solution on YOUR website!you are traveling for the holidays to go visit your family. You know that you live 876 miles from your relatives. you can travel on the interstate the whole way so your parents are abe to drive an average of 76 miles per hour. -------------------------- Is this a linear representation?:::Yes ------------------ What is an equation to represent your miles traveled in relationship to the hours you will travel? ----------------------- miles = time*rate 876 miles = time*76 mph ================================= Cheers, Stan H. =============