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Recent problems solved by 'stanbon'

stanbon answered: 57894 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 , 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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Graphs/81440: the sophomore class at south high school raised $800 from the sale of tickets to a dance. tickets sold for $1.50 in advance, and $2.00 at the door. if a total of $475 tickets were sold, the number of tickets sold at the door was 1 solutions Answer 58330 by stanbon(57967)   on 2007-05-09 20:22:31 (Show Source): You can put this solution on YOUR website! the sophomore class at south high school raised $800 from the sale of tickets to a dance. tickets sold for $1.50 in advance, and $2.00 at the door. if a total of 475 tickets were sold, the number of tickets sold at the door was ------- Let # sold in advance = "x" ; Value of these is 1.5x dollars # sold at the door = 475-x ; value of these is 2(475-x)= 950-2x dollars ------------ EQUATION: value + value = 800 dollars 1.5x +950-2x = 800 -0.5x=-150 x=300 (# of tickets sold in advance) 475-x = 175 (# of tickets sold at the door) ============ Cheers, Stan H.

Radicals/81438: can someone please check this for me please? 7x^2+18x-9 x=-b+-sqrt/2a x=-18+-sqrt/2*7 x=(-18+24)/2*7 x=6/14=3/7 x=-42/14=-3 x=7 1 solutions Answer 58328 by stanbon(57967)   on 2007-05-09 20:16:38 (Show Source): You can put this solution on YOUR website! can someone please check this for me please? 7x^2+18x-9 x=-b+-sqrt/2a x = [-18+-sqrt18^2-4*7*-9]/14 x = [-18+-sqrt(576)]/14 x = [-18+-24]/14 x= [-18+24]/14 or x=[-18-24]/14 x= [3/7] or x= -42/14 = -3 ============= Cheers, Stan H.

Polynomials-and-rational-expressions/81442: This question is from textbook Algebra 1 CARPENTRY When building a stairway, a carpenter considers the ratio of risers to tread. If each stair being built is to have a width of 1 foot and a height of 8 inches, what will the slope of the stairway? .... _________ . l (- riser ______ tread I would be very much appreicated if you could tell me how to do this and the answer!thanx 1 solutions Answer 58324 by stanbon(57967)   on 2007-05-09 19:54:36 (Show Source): You can put this solution on YOUR website! If each stair being built is to have a width of 1 foot and a height of 8 inches, what will the slope of the stairway? ----------- slope = rise/run = 8 in/ 12 in = 2/3 ============= Cheers, Stan H.

Graphs/81465: I'd really appreciate some help with my algebra, my middle school teacher just confuses me:( Here's the equation: find the line that passes through (-5,10), (0,5), and (5,-20), find the following: what is the slope of this line? what is the y intercept of this line? what is the equation of this line? find x when y = 24 1 solutions Answer 58320 by stanbon(57967)   on 2007-05-09 19:37:22 (Show Source): You can put this solution on YOUR website! find the line that passes through (-5,10), (0,5), and (5,-20), find the following: what is the slope of this line? slope = [-20-10]/[5--5]= -30/10 = -3 what is the y intercept of this line: (0,5) what is the equation of this line?: y=-3x+5 find x when y = 24: 24=-3x+5; 19=-3x; x=-19/3 ================= Cheers, Stan H.

Rational-functions/81471: i have problems with Direct Variation, im suppose to write an equation. Here is an example: The total cost T varies with directly with the number of kilograms A of apples purchase. Apple cost $1.52per kilogram. 1 solutions Answer 58319 by stanbon(57967)   on 2007-05-09 19:29:57 (Show Source): You can put this solution on YOUR website! The total cost T varies with directly with the number of kilograms A of apples purchase. Apple cost $1.52per kilogram. -------------- T = kA T = 1.52A Total cost = (price for a kg) times (number of kg's) =========== Cheers, Stan H.

Probability-and-statistics/81424: An electronic toy manufacturer uses a particular kind of quality test to check the toys. The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys. The test indicates that toy A is defective. If 5% of toys have defects, what is the probability that toy A has a defect? 1 solutions Answer 58318 by stanbon(57967)   on 2007-05-09 18:00:54 (Show Source): You can put this solution on YOUR website! An electronic toy manufacturer uses a particular kind of quality test to check the toys. The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys. The test indicates that toy A is defective. If 5% of toys have defects, what is the probability that toy A has a defect? ------------ Let D be defective and D' be non defective: The Problem is a Bayes problem. ------- P(D) = P(D and D) + P(D and D') =P(D)*P(D|D) + P(D)*P(D|D') =P(D)[P(D|D)+P(D|D')] =0.05[0.85+P(D|D')] Need to find P(D|D') --------- P(D|D') = [P(D and D')/P(D')] = [P(D'|D)P(D)/P(D')] = [0.02*0.05/0.95]=0.0010526... --------- Put that is the P(D) line up above to get: P(D)=0.05[0.85+0.0010526]= 0.05(0.8510526)=0.0426 --------- P(a randomly selected item is defective is defective )= 0.0426 ========== Cheers, Stan H.

Exponential-and-logarithmic-functions/81419: (1/4) ln 2 + ln 4 1 solutions Answer 58314 by stanbon(57967)   on 2007-05-09 16:54:24 (Show Source): You can put this solution on YOUR website! (1/4) ln 2 + ln 4 = ln2^(1/4) + ln4 = ln[2^(1/4)*4] =========== Cheers, Stan H.

Expressions-with-variables/81413: please help these are due today. solve by substitution. 5x-2y=-5 y-5x=3 4x-12y=5 -x+3y=-1 1 solutions Answer 58313 by stanbon(57967)   on 2007-05-09 16:52:26 (Show Source): You can put this solution on YOUR website! solve by substitution. 5x-2y=-5 y-5x=3 ------ Substitute into the 1st equation to get: 5x-2(5x+3)=-5 -5x=1 x=-1/5 --- Substitute that into y-5x=3 to solve for y: y-5(-1/5)=3 y+1=3 y=2 Solution: x=-1/5, y=2 ============================= 4x-12y=5 -x+3y=-1 -------- solve 2nd equation for x to get: x=3y+1 Substitute into the 1st equation to get: 4(3y+1)-12y=5 12y+4-12y=5 4=5 ------- This is a contradiction. The system in "inconsistent" There is no solution. =================== Cheers, Stan H.

Miscellaneous_Word_Problems/81408: A skeleton contains one hundredth of its original amount of its original amount of carbon-14. If carbon-14 has a half-life of 5750 years, to the nearest 1000 years, how old is the skeleton? 1 solutions Answer 58312 by stanbon(57967)   on 2007-05-09 16:46:04 (Show Source): You can put this solution on YOUR website! A skeleton contains one hundredth of its original amount of its original amount of carbon-14. If carbon-14 has a half-life of 5750 years, to the nearest 1000 years, how old is the skeleton? ----------- A(t) = A(o)(1/2)^(t/5750) 0.01A(o) = A(o)(1/2)^(t/5750) 0.01 = 0.5^(t/5750) Take the log of both sides to get: log 0.01 = (t/5750)*log0.5 t/5750 = log0.01/log0.5 =6.64385619... t = 38202 yrs ============== Cheers, Stan H.

Trigonometry-basics/81409: This question is from textbook Precalculus the frog population in a small pond grows exponentially. The current population is 85 frogs, and the relative growth rate is 18% per year. a. find function that models the population after t years. b. find the projected population after 3 years. c. find the number of years required for the frog population to reach 600. 1 solutions Answer 58310 by stanbon(57967)   on 2007-05-09 16:40:05 (Show Source): You can put this solution on YOUR website! the frog population in a small pond grows exponentially. The current population is 85 frogs, and the relative growth rate is 18% per year. a. find function that models the population after t years. A(t) = A(0)(1.18)^t A(t) = 85(1.18)^t ---------- b. find the projected population after 3 years. A(3) = 85(1.18)^3 A(3)= 139.65 frogs Rounding down: 139 frogs -------------------- c. find the number of years required for the frog population to reach 600. 600 = 85(1.18)^t 7.0588=1.18^t Take the log of both sides to ge: t=[log7.0588]/[log1.18] t=11.81 years ================ Cheers, Stan H.

real-numbers/81411: What's the difference between Real And irrational numbers and how can i tell the difference? 1 solutions Answer 58309 by stanbon(57967)   on 2007-05-09 16:32:47 (Show Source): You can put this solution on YOUR website! Irrational numbers are included in the set of Real Numbers. Iffational numbers have a non-repeating decimal form like pi or e or sqrt3 or cube root of 5; all of these have a non-repeating decimal form. Rean numbers comprise all the irrational and all the rational numbers. ================== Cheers, Stan H.

Expressions-with-variables/81416: can you help me factor completely? 5x^2-2xy+5x-2y 1 solutions Answer 58308 by stanbon(57967)   on 2007-05-09 16:29:15 (Show Source): You can put this solution on YOUR website! 5x^2-2xy+5x-2y Factor the 1st two and the last two terms separately: x(5x-2y) + (5x-2y) Factor out the common factor: (5x-2y)(x+1) ================ Cheers, Stan H.

Expressions-with-variables/81417: can someone please please help me simplify? 1+3/7 over 3-1/3 1 solutions Answer 58307 by stanbon(57967)   on 2007-05-09 16:26:28 (Show Source): You can put this solution on YOUR website! 1+3/7 over 3-1/3 ---------- [1+(3/7)]/[3-(1/3)] =[(7/7)+(3/7)]/[(9/3)-(1/3)] =[(10/3)]/[(8/3)] =(10/3)*(3/8) Cancel the 3 factors to get: =10/8 Reduce to get: =5/4 ============= Cheers, Stan H.

Expressions-with-variables/81415: Can you help me solve please? x/x-3+2=3/x-3 I don't see a solution but i am not sure 1 solutions Answer 58306 by stanbon(57967)   on 2007-05-09 16:22:31 (Show Source): You can put this solution on YOUR website! Can you help me solve please? x/(x-3) + 2 = 3/(x-3) Multiply thru by (x-3) to get: x + 2(x-3) = 3 x + 2x -6 = 3 3x=9 x=3 But x cannot be 3 because the original problem has x-3 in the denominator and letting x=3 would cause the denoinator to be zero. So, no solution for your problem. =============== Cheers, Stan H.

Polynomials-and-rational-expressions/81412: a passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passanger train is 25 mi/phr faster than the speed fo the freight train, find the speed of each. 1 solutions Answer 58305 by stanbon(57967)   on 2007-05-09 16:18:07 (Show Source): You can put this solution on YOUR website! a passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passanger train is 25 mi/phr faster than the speed fo the freight train, find the speed of each. ---------- Passenger train DATA: distance=25 mi ; rate = x mph ; time = d/r = 325/x hrs ----------------- Freight train DATA: distance = 200 m ; rate = x-25 mph ; time = d/r = 200/(x-25) hr ------------------- EQUATION: time = time 325/x = 200/(x-25 Crsoo- multiply to get: 325(x-25) = 200x 325x-8125 = 200x 125x = 8125 x = 65 mph ( speed of passenger train) x-25 = 40mph(speed of freight train) ===================== Cheers, Stan H.

Expressions-with-variables/81346: A biologist catches and marks 20 perch from a lake. A week later she catches 50 fish, of which 12 are marked. Write the equation he can use to get a good estimate of the perch. 1 solutions Answer 58290 by stanbon(57967)   on 2007-05-09 09:21:11 (Show Source): You can put this solution on YOUR website! A biologist catches and marks 20 perch from a lake. A week later she catches 50 fish, of which 12 are marked. Write the equation he can use to get a good estimate of the perch. ----------------- Let "x" be the total number of perch in the lake. Use a proportion: total #/number caught = sample total/sample # caught x/50= 50/12 =========== Cheers, Stan H.

Radicals/81359: Please show me how to solve a square root. I don't understand. Thanks My homework problem was: (3square root of 3)(square root of 7) the choices were: A.) 6 square root of 1323 (I chose this one) B.) 6 square root of 3087 c.) 6 square root of 441 D.) 6 square root of 1029 1 solutions Answer 58289 by stanbon(57967)   on 2007-05-09 09:15:34 (Show Source): You can put this solution on YOUR website! (3square root of 3)(square root of 7) =3sqrt21 ========= Cheers, Stan H.

Probability-and-statistics/81325: Please Help! This will be greatly appreciated. (Show Step by step solutions to these problems I got incorrect on my test)Thank You. Question 1 A local bank says that the standard deviation for bank account balances is less than or equal to $2150.91. A random sample of size n=16 bank accounts reveals a standard deviation of s=$2129.61. Assume that the bank balances are normally distributed. Test the hypothesis that the standard deviation for bank accounts is less than or equal to $2150.91 at the a=0.05 significance level. Question 2 The following represents the mean scores on the same set of 5 statistics exams given in Spring 2004 and Fall 2004. Test the claim that the mean scores for the Spring 2004 semester were not equal to the mean scores for Fall 2004 semester. Use a=0.05. Spring 2004- Test 1= 48.7, Test 2= 68.9,Test 3= 75.2, Test 4= 94.3, Test 5= 98.7 Fall 2004- Test 1= 49.0, Test 2= 68.8, Test 3= 75.5, Test 4= 95.1, Test 5= 100.6 Question 3 An instructor wanted to test the effectiveness of a CALS (Computer Aided Learning System). Two classes were offered in Statistics I. One class used a CALS and the other used traditional methods. At the end of the two courses both classes were given the same final exam. The CALS class had 117 students and 19 of the class receives a grade of B or higher. The class taught using traditional methods had 143 students and 39 of the class receives a grade of B or higher. At a=0.05 can you conclude that the CALS produced a smaller proportion of students with a grade of B or higher. Question 4 Test the claim that the difference between the mean salary for computer programmers and the mean salary for photographers in Wisconsin is not equal to 28,000. The results of a survey of randomly selected computer programmers and photographers in Wisconsin are shown in the figure below. Use alpha= 0.01 and Rejection Region test. Testing a Difference other than zero. Photographers and Computer Programmer Salaries Computer programmers x1= $52,400 s1= $8,290 n1= $31 Photographers x2= $24,200 s2= $3,490 n2= $32 1 solutions Answer 58287 by stanbon(57967)   on 2007-05-09 09:06:42 (Show Source): You can put this solution on YOUR website! Question 1 A local bank says that the standard deviation for bank account balances is less than or equal to $2150.91. A random sample of size n=16 bank accounts reveals a standard deviation of s=$2129.61. Assume that the bank balances are normally distributed. Test the hypothesis that the standard deviation for bank accounts is less than or equal to $2150.91 at the a=0.05 significance level. --------- Ho: sigma <= 2150.91 Ha: sigma > 2150.91 Critical Value Chi-Sq = 32.801 Test Statistic: Chi-Sq = (16-1)2139.61^2/2150.1^2 = 14.84 Conclusion: Fail to Reject Ho The standard deviation for bank accounts is less than or equal to $2150.91 -------------------- Question 2 The following represents the mean scores on the same set of 5 statistics exams given in Spring 2004 and Fall 2004. Test the claim that the mean scores for the Spring 2004 semester were not equal to the mean scores for Fall 2004 semester. Use a=0.05. Spring 2004- Test 1= 48.7, Test 2= 68.9,Test 3= 75.2, Test 4= 94.3, Test 5= 98.7 Fall 2004- Test 1= 49.0, Test 2= 68.8, Test 3= 75.5, Test 4= 95.1, Test 5= 100.6 Ho: mu(spring)-mu(fall)=0 Ha: mu(spring)-to mu(fall) is not equal to zero Critical Value: t=2.776 mu(spring)=77.16 s(spring)=20.25 mu(fall)=77.8 s(fall)=20.83 s(mu(s)-mu(f))= sqrt[20.25^2/5 + 20.83^2/5]=12.99 Test Statistic: t(mu(f)-mu(s))= [77.8-77.16]/12.99 = 0.049 Fail to Reject Ho Test results in spring and fall have the same average. ============= Question 3 An instructor wanted to test the effectiveness of a CALS (Computer Aided Learning System). Two classes were offered in Statistics I. One class used a CALS and the other used traditional methods. At the end of the two courses both classes were given the same final exam. The CALS class had 117 students and 19 of the class receives a grade of B or higher. The class taught using traditional methods had 143 students and 39 of the class receives a grade of B or higher. At a=0.05 can you conclude that the CALS produced a smaller proportion of students with a grade of B or higher. Ho: p(cals)-p(tm)>=0 Ha: p(cals)-p(tm)<0 Critical value: z=-1.645 Test Stat: z(19/117-39/143)=0.11033/sqrt[(19/117)(98/117)/117+(39/143)(104/143)/143] = -2.185 Conclusion: Reject Ho CALS results fall below Traditional Methods results --------------------- Question 4 Test the claim that the difference between the mean salary for computer programmers and the mean salary for photographers in Wisconsin is not equal to 28,000. The results of a survey of randomly selected computer programmers and photographers in Wisconsin are shown in the figure below. Use alpha= 0.01 and Rejection Region test. Testing a Difference other than zero. Photographers and Computer Programmer Salaries Computer programmers x1= $52,400 s1= $8,290 n1= $31 Photographers x2= $24,200 s2= $3,490 n2= $32 -------- I'll leave this one to you; I may look at it later or you might want to post it separately. Cheers, Stan H.

Linear-systems/81320: This question is from textbook College Algebra Greetings Tutors! Please help. I've been going around and around on this problem: Find an equation of the line containing the centers of the two circles x^2 + y^2 - 4x + 6y + 4 = 0 and x^2 + y^2 + 6x + 4y + 9 = 0 I'm not even sure where to begin. Thanks in advance. 1 solutions Answer 58265 by stanbon(57967)   on 2007-05-08 23:24:34 (Show Source): You can put this solution on YOUR website! Find an equation of the line containing the centers of the two circles x^2 + y^2 - 4x + 6y + 4 = 0 complete the square to find the center: x^2-4x+4 +y^2+6y+9 = 9 (x-2)^2 + (y+3)^2 = 3^2 Center at (2,-3) -------------------- and x^2 + y^2 + 6x + 4y + 9 = 0 Complete the square to find the center: x^2+6x+9 + y^2+4y+4 = 4 (x+3)^2 + (y+2)^2 = 262 Center at (-3,-2) ------------------ Find the equation of the line thru (2,-3) and (-3,-2) slope = [-2--3]/[-3-2]= 1/-5 = -1/5 Form is y=mx+b where y=-3 when x=2 and where m=-1/5 -3=(-1/5)*2 + b b= -3+2/5 b=-13/5 ----------- EQUATION you want: y=(-1/5)x-(13/5) ======================= Cheers, Stan H.

Quadratic_Equations/81322: Please helllllppp! The price p and the quantity x sold of a certain product obey the demand equation: x = -20p + 500 0 less than or equal to p which is less than or equal to 25 a) express the revenue R as a function of x b) what is the revenue if 20 units are sold? c) what quantity x maximizes revenue? what is the maximum revenue? d) what price should the company charge to maximize revenue? Thank you thank you 1 solutions Answer 58264 by stanbon(57967)   on 2007-05-08 23:11:50 (Show Source): You can put this solution on YOUR website! The price p and the quantity x sold of a certain product obey the demand equation: x = -20p + 500 p(x)=(500-x)/20 = 25-(1/20)x 0 less than or equal to p which is less than or equal to 25 a) express the revenue R as a function of x Revenue(x) = (price)*(quantity) Rev(x) = (25-(1/20)x)(x Rev(x) = 25x-(1/20)x^2 b) what is the revenue if 20 units are sold? Rev(20) = 25*20-(1/20)20^2 Rev(20) = 500-20 Rev(20) = $480 ----------------- c) what quantity x maximizes revenue? what is the maximum revenue? Rev(x) is a quadratic with a=-1/20, b=25 max occurs at x=-b/2a = [-25/(-2/20)] = [250] =------------------------- d) what price should the company charge to maximize revenue? p(x) = 25-(1/20)x p(250) = 25-(1/20)(250) p(250) = 25-25/2 p(250) = $12.50 ======================== Cheers, Stan H.

Human-and-algebraic-language/81239: In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000? 1 solutions Answer 58263 by stanbon(57967)   on 2007-05-08 21:55:15 (Show Source): You can put this solution on YOUR website! In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000? ----------- Let "x" be the total amount of prize money. 1st place received (1/2)x = 6000 so total amount = 12000 But you said 2nd place received (1/4)(6000)=1500 ---------- Comment These are contradictory conditions. Check your problem statement. ========= Cheers, Stan H.

Miscellaneous_Word_Problems/81310: Katrina can mow the lawn in 2 hours. It takes her brother 3 hours to mow the lawn. When they borrow a neighbor's lawn mower and work together, how long does it take them to mow the lawn? 1 solutions Answer 58259 by stanbon(57967)   on 2007-05-08 21:49:18 (Show Source): You can put this solution on YOUR website! Katrina can mow the lawn in 2 hours. It takes her brother 3 hours to mow the lawn. When they borrow a neighbor's lawn mower and work together, how long does it take them to mow the lawn? ----------- Katrina DATA: Time to mow the lawn = 2 hrs/job ; Rate = 1/2 job/hr -------- Brother DATA: Time to mow the lawn = 3 hrs/job ; Rate = 1/3 job/hr ------------- Together DATA: Time to mow the lawn = x hrs/job ; Rate = 1/x job/hr ================ EQUATION: rate + rate = rate together 1/2 + 1/3 = 1/x 3x+2x = 6 5x=6 x=6/5 of an hour or 1 hr and 12 minutes ================= Cheers, Stan H.

Miscellaneous_Word_Problems/81311: The Nut House sells mixed nots that are 20% cashews. The owner wants to prepare 4 punds of mixed nuts that are 25% cashews as a special promotion. How many pounds of cashews and how many pounds of the 20% mixture should she combine to get the 25% micture? 1 solutions Answer 58258 by stanbon(57967)   on 2007-05-08 21:45:34 (Show Source): You can put this solution on YOUR website! The Nut House sells mixed nots that are 20% cashews. The owner wants to prepare 4 punds of mixed nuts that are 25% cashews as a special promotion. How many pounds of cashews and how many pounds of the 20% mixture should she combine to get the 25% micture? ---------------- 20% Mixture Data: Let he amt be "x" lbs ; Amt of cashews = 0.20x lbs Amt of 100% cashews is "4-x" lbs ; =============== 25% Mixture Dats: Amt = 4 lbs ; Amt of cashews = 0.25*4 lbs = 1 lb =================== EQUATION: cashews + cashews = cashews 0.20x + 4-x = 1 lb -0.80x = -3 x= 3.75 lbs (this is the # of lbs of the 20% mixture she should use) =========== Cheers, Stan H.

Polynomials-and-rational-expressions/81313: Solve the equation for A: (A^2 - 4)/(A - 2) = A + 3 So far I tried to find the lowest common denominator, and multiplied it by the numerator on each side. I'm having trouble finishing it though. I get to a point where my numbers can't be factored any further. I'm not sure if I'm even on the right track or not. I'd appreciate any help. Thanks. 1 solutions Answer 58254 by stanbon(57967)   on 2007-05-08 21:38:45 (Show Source): You can put this solution on YOUR website! (A^2 - 4)/(A - 2) = A + 3 Factor to simplify the equation: [(A-2)(A+2)/(A-2)]=A+3 Cancel the A-2 factors to get: A+2 = A+3 Subtract A from both sides: 2=3 -------- This tells yu the equation is a contrdiction. There is no solution. ========= chees, Stan H.

Linear-equations/81300: I needed to create a linear equation or inequality for my math class. I created c=pg(52) Where c=$4664.40 (cost of gas for the year) p=$2.99 (price of gas per gallon) g= 30 (number of gallons used) (52) Weeks for the year My teacher asked me to graph my equation by doing the following: Vary either the price of gas or the number of gallons. How do I graph this equation by doing what my instructor suggested? I am confused ;0/ PLEASE HELP!!! 1 solutions Answer 58253 by stanbon(57967)   on 2007-05-08 21:35:51 (Show Source): You can put this solution on YOUR website! You can't; you have two many variables. ------------- Let's say you want to vary the price of gas but want to purchase no more than 12 gallons of gas per week to help conserve fuel. Then Cost = 12p where p is the price per gallon for gas. Then you have a graph that looks like: On this you can read the cost of your gas as it changes from $0 per gallon to $5 per gallon. Cheers, Stan H.

Sequences-and-series/81308: "Find the sum of the first 50 terms of the arithmetic series with first term = -1 and fifth term 9." So far I tried to find d. Then I tried to plug it into a(sub n) = a(sub 1) + (n - 1)d, so that I could find a(sub n). Then I plugged everything into the formula S(sub n) = n/2(a(sub 1) + a(sub n). But I got a number that doesn't look right. If anyone could help me with this, I would very much appreciate it. Thanks. 1 solutions Answer 58247 by stanbon(57967)   on 2007-05-08 21:20:51 (Show Source): You can put this solution on YOUR website! "Find the sum of the first 50 terms of the arithmetic series with first term = -1 and fifth term 9." ------------ a(1) = -1 a(5) = -1 + 4d = 9 4d=9+1 d=5/2=2.5 ----------------- a(50) = -1+49d=-1+49*2.5= 121.5 ------------- S(50) = (50/2)(-1+121.5) =25(120.5) =3012.5 ========== Cheers, Stan H.

Functions/81305: If f(x)=5x-1, find the following f(a-2)... I have no idea of how to go about doing this, I am new to this kind of math, I would really appreciate someone's help. 1 solutions Answer 58244 by stanbon(57967)   on 2007-05-08 21:09:39 (Show Source): You can put this solution on YOUR website! If f(x)=5x-1, find the following f(a-2)... ---------- Comment: f(a-2) tells you to substitute a-2 in place of x: Your Problem: f(a-2) = 5(a-2)-1 f(a-2) = 5a-10-1 f(a-2) = 5a-11 ========= Cheers, Stan H.

Graphs/81244: This question is from textbook Can you graph the inequality. y≥1-3x 1 solutions Answer 58241 by stanbon(57967)   on 2007-05-08 21:01:47 (Show Source): You can put this solution on YOUR website! Can you graph the inequality. y≥1-3x ------------ You have to graph the boundary: y=1-3x Plot two points: (If x=0, y=1; If x=1,y=-2) Plot those points and draw a line thru them. That takes care of the EQUALITY. -------- To graph the INEQUALITY pick a test point like (0,0) Substitute those values into the inequality: 0>1-3*0 0>1 That is wrong so that side of the boundary is NOT the solution set of the INEQUALITY; tho other side is so darken the other side. -------- The line and the darkened side (half-plane) is the graph you want. =========== Cheers, Stan H.

Radicals/81247: please check this for me? I have to factor completely. 49x^2-25 -25+79x^2=0 -25+25+49x^2=0+25 0+49x^2=0+25 49x^2=0+25 49x^2=25 1 solutions Answer 58240 by stanbon(57967)   on 2007-05-08 20:56:01 (Show Source): You can put this solution on YOUR website! I have to factor completely. 49x^2-25 = (7x-5)(7x+5) ------------ -25+79x^2=0 79x^2-25=0 (sqrt(79)x -5)(sqrt(79)x+5)=0 --------------- -25+25+49x^2=0+25 Simplify to get 49x^2-25=0 (7x-5)(7x+5)=0 x=5/7 or x=-5/7 ============= 0+49x^2=0+25 Simplify to get: 49x^2-25=0 same result ------------------ 49x^2=0+25 49x^2=25 same result ===================== Cheers, Stan H.

Expressions-with-variables/81230: Could you please help me out with this problem. Math is so hard and confusing to me. 4x-12y=5 -x+3y=-1 1 solutions Answer 58239 by stanbon(57967)   on 2007-05-08 20:50:34 (Show Source): You can put this solution on YOUR website! 4x-12y=5 -x+3y=-1 ----------- You can solve the system by elimination, as follows: Multiply thru the 2nd equation by 4 to get: -4x+12y = -4 ----------- Add that to the 1st equation to get rid of the x terms: You get 0x+0y = 1 This says 0 = 1 which is incorrect. Comment: Why did this happen? You assumed the x's and the y's in both equations meant the same number. That assumption led to the contradiction. You have to conclude the x's and the y's do not mean the same number in these two equations. The systme is called "inconsistent" and has no solution. ============= Cheers, Stan H.

Radicals/81232: Please show me how to get the square root. Thanks (5 square root of 6-4)(3square root of 6-1) 1 solutions Answer 58238 by stanbon(57967)   on 2007-05-08 20:45:35 (Show Source): You can put this solution on YOUR website! (5 square root of 6-4)(3square root of 6-1) -------- (5sqrt6 -4 )(3sqrt6 -1) Use FOIL to get this product: F: (5sqrt6*3sqrt6)= 15*6=90 O: (5sqrt6 *-1) = -5sqrt6 I: (-4*3sqrt6) = -4sqrt6 L: -4*-1 = 4 --------------- Add the "like" terms to get = 94 - 9sqrt6 =========== Cheers, Stan H.