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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, >>Next

 Surface-area/150722: WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE OF A SQUARE IS DOUBLED?.. WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE IS TRIPLED?..1 solutions Answer 110644 by stanbon(57246)   on 2008-08-04 07:10:20 (Show Source): You can put this solution on YOUR website!WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE OF A SQUARE IS DOUBLED?.. Before change: Area = L*W After change: Area = (2L)*W = 2(L*W) So the area has doubled. --------------------------- WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE IS TRIPLED?.. Before change : Area = L*W After change: Area = (3L)*W = 3(L*W) So the area is 3 times what it was originally ======================= Cheers, Stan H.
 Mixture_Word_Problems/150721: A 100 KILOGRAM MIXTURE OF 0.69 KG. OF PINTO BEANS AND 0.89 KG. KIDNEY BEANS IS VALUED AT 81.00. HOW MANY KILOGRAMS OF EACH DOES IT CONTAIN?.1 solutions Answer 110643 by stanbon(57246)   on 2008-08-04 07:07:23 (Show Source): You can put this solution on YOUR website!A 100 KILOGRAM MIXTURE OF 0.69 KG. OF PINTO BEANS AND 0.89 KG. KIDNEY BEANS IS VALUED AT 81.00. HOW MANY KILOGRAMS OF EACH DOES IT CONTAIN?. ---------------- Quantity equation : p + k = 100 Value equation: 0.69p + 0.89k = 81 ------------------- solve by any method to get: p = 40 and k = 60 ====================== Cheers, Stan H.
 Rational-functions/150719: hi i am studying for my final and i would like to know something. this is the task: tamika invests \$3000 in a 5-yr cd that pays 5.35% interest compounded monthly. how much will she have in the acc. at the end of the 5 yr period? I used the formula A=P(1+r/n)nt so I got A = 3000(1+0.535/12)60 (that is an exponent) now, i first divided 0.535 by 12 and then +1 so I get 1.044583333... and i took that by 60 exponential. I get 13.69574101 on the answer sheet it is written like this: A=3000(1+0.535/12)60 3000(1.305916985) = 3917.75 how do i get the 1.3059...etc? how do i calculate the braces with the 60 exponential part? what i did was calculating the braces first and then take it exponential 60. 1 solutions Answer 110642 by stanbon(57246)   on 2008-08-04 07:01:55 (Show Source): You can put this solution on YOUR website!tamika invests \$3000 in a 5-yr cd that pays 5.35% interest compounded monthly. how much will she have in the acc. at the end of the 5 yr period? I used the formula A=P(1+r/n)nt so I got A = 3000(1+0.535/12)60 (that is an exponent) now, i first divided 0.535 by 12 and then +1 so I get 1.044583333... and i took that by 60 exponential. I get 13.69574101 on the answer sheet it is written like this: A=3000(1+0.535/12)60 3000(1.305916985) = 3917.75 how do i get the 1.3059...etc? how do i calculate the braces with the 60 exponential part? what i did was calculating the braces first and then take it exponential 60. ---------------------- Your mistake is changing 5.35% to 0.535. You should have 5.35% = 0.0535 ---------------------- After that your procedure is correct. ---------------------- Cheers, Stan H.
 Equations/150714: Hello E-Tutors:) Could someone lead me in the right direction with this college system of equations and inequality problem? The text book shows how to solve something similiar but it only displays an equation with two variables. Whereas this problem contains three variables. That throws me for a loop. Problem: The students from algebra class go for coffee together every day. On Monday, Jordan paid \$5.45 for three cartons of milk, four cups of coffee, and seven doughnuts. On Tuesday, Ryan paid \$5.30 for four milks, two coffees, and eight doughnuts. On Wednesday, Zack paid \$5.15 for two milks, five coffees, and six doughnuts. 1. Set up a system of equations to model this scenario. I think this is right, but have no idea how to solve three layers, with 3 different variables. m=milk c=coffee d=doughnut 3m + 4c + 7d = 5.45 4m + 2c + 8d = 5.30 2m + 5c + 6d = 5.15 2. Determine the cost of one carton milk, one coffee, and one doughnut by solving they system. 3. If on Thursday, Taylor had to pay for five milks, two coffees, and nine doughnuts how much did he spend? Think, I can get this one if I learn how to solve the second question. Thank you in advance for sharing your valuable skills with us, mishap mathematicians. :0) Grateful, Jai 1 solutions Answer 110641 by stanbon(57246)   on 2008-08-04 06:54:40 (Show Source): You can put this solution on YOUR website!3m + 4c + 7d = 5.45 4m + 2c + 8d = 5.30 2m + 5c + 6d = 5.15 ------------------------- subtract 3rd equation from 1st to get: m - c + d = 0.30 4m + 2c + 8d = 5.30 2m + 5c + 6d = 5.15 ----------------------- subtract 4 times 1st from 2nd; subtract 2 times 1st from 3rd: m - c + d = 0.30 0 + 6c + 4d = 4.10 0 + 7c + 4d = 4.55 ---------------------- interchange 2nd and 3rd to get: m - c + d = 0.30 0 + 7c + 4d = 4.55 0 + 6c + 4d = 4.10 ------------------------ subtract 3rd from 2nd to get: m - c + d = 0.30 0 + c + 0 = 0.45 0 + 6c + 4d = 4.10 ---------------------- At this point you can see that c = 0.45 ------------- Subtitute that into the 3rd equation to solve for "d": 6(0.45) + 4d = 4.10 2.7 + 4d = 4.10 4d = 1.40 d = 0.35 ---------------- Substitute the values of c and d into the 1st equation to solve for "m": m - 0.45 + 0.35 = 0.30 m - 0.10 = 0.30 m = 0.40 ----------------- one mild costs 40 cents one coffee costs 45 cents one doughnut costs 35 cents ============================ Cheers, Stan H.
 Quadratic_Equations/150686: Solve 3x^2 + 19x-14=0 using the quadratic formula 1 solutions Answer 110625 by stanbon(57246)   on 2008-08-03 21:39:27 (Show Source): You can put this solution on YOUR website!Solve 3x^2 + 19x-14=0 using the quadratic formula ------------------------ x = [-19 +- sqrt(19^2 - 4*3*-14)]/6 x = [-19 +- sqrt(529)]/6 x = [-19 +- 23]/6 x = 2/3 or x = -7 ==================== Cheers, Stan H.
 Quadratic_Equations/150687: This question is from textbook Intermediate Algebra write the rational expression Y 3/7 as a root thank you1 solutions Answer 110624 by stanbon(57246)   on 2008-08-03 21:35:38 (Show Source): You can put this solution on YOUR website!write the rational expression Y 3/7 as a root ------------------- Y^(3/7) means "the 7th root of (Y^3)" ============================== Cheers, Stan H.
 Quadratic_Equations/150656: How do you completly factor a^2 - 10ab + 3b^2, what's the answer?1 solutions Answer 110617 by stanbon(57246)   on 2008-08-03 19:50:08 (Show Source): You can put this solution on YOUR website!a^2 - 10ab + 3b^2 -------------------- Using the Quadratic formula you get: a = [10b +- sqrt(100b^2 - 4*3b^2)]/2 a = [10b +- sqrt(88b^2)/2 a = [10b +- sqrt(22)b] If these are the zeroes of the trinomial, then , by the factor Theorem, the factors are: ----------------------------- Factors: (a - [10b + sqrt(22)b]) * (a - [10b - sqrt(22)b]) =========================== Cheers, Stan H.
 Square-cubic-other-roots/150678: sqrt3 sqrt3 ----- - ----- sqrt6 -1 sqrt6 + 1 sqrt9x^2 = x + 6 I am having a hard time figuring these out. Can you help?(sqrt means square root)1 solutions Answer 110615 by stanbon(57246)   on 2008-08-03 19:30:13 (Show Source): You can put this solution on YOUR website!sqrt3 sqrt3 ----- - ----- sqrt6 -1 sqrt6 + 1 ------------------------ To subtract fractions you need to have a common denominator on the fractions. ------------- Least Common Denominator: (sqrt(6)-1)(sqrt(6)+1) = 6-1 = 5 ------------------------ Rewrite the problem with lcm = 5 [(sqrt(3)(sqrt(6)+1) - sqrt(3)(sqrt(6)-1)]/5 [(sqrt(18) + sqrt(3)) - (sqrt(18)-sqrt(3))]/5 = [2sqrt(3)] / 5 = (2/5)*sqrt(3) ===================== Cheers, Stan H.
 Travel_Word_Problems/150665: This question is from textbook BY boat, Joseph can go 72 km upstream to a fishing hole in 4 hours. To go back he needs only 3 hours. What is his rate upstream and his rate downstream?1 solutions Answer 110605 by stanbon(57246)   on 2008-08-03 18:54:13 (Show Source): You can put this solution on YOUR website!BY boat, Joseph can go 72 km upstream to a fishing hole in 4 hours. To go back he needs only 3 hours. What is his rate upstream and his rate downstream? ---------------- Upstream DATA; distance = 72 km ; time = 4 hrs ; rate = 72/4 = 18 kph -------------- Downstream DATA: distance = 72 km ; time = 3 hrs ; rate = 72/3 = 24 kph ------------------ Let b = boat speed ; Let c = current speed EQUATIONS: b+c = 24 b-c = 18 ----------- Add to get: 2b = 42 b = 21 (boat speed in still water) Substitute into b+c = 24 to get: 21 + c = 24 c = 3 kph (current speed) ----------- Upstream speed = 18 kph Downstream speed = 24 kph
 Linear_Equations_And_Systems_Word_Problems/150668: In 1995 the life expectancy of a male in a certain country was 62.6 years In 2001 it was 64.9 years Let E represent the life expectancy in year t and let t represent the number of years since 1995 The linear function E(t) that fits the data is E(t)= t + (round to the nearest tenth) Use the function to predict the life expectancy of males in 2005 E(14)= (round to the nearest tenth) 1 solutions Answer 110598 by stanbon(57246)   on 2008-08-03 17:32:08 (Show Source): You can put this solution on YOUR website!In 1995 the life expectancy of a male in a certain country was 62.6 years In 2001 it was 64.9 years Let E represent the life expectancy in year t and let t represent the number of years since 1995 ---------- You have two points: (0,62.6) and (6,64.9), where x is the number of years after 1995. ------------------------------- slope: (64.9-62.6)/(6-0) = 2.3/6 = 23/60 ------------- intercept: when x = 0, y = 62.6 ----------------------------- Equation: E(t) = (23/60)t + 62.6 --------------------------- The linear function E(t) that fits the data is (round to the nearest tenth) Use the function to predict the life expectancy of males in 2005 E(14)= (23/60)*14 + 62.6 E(14) = 68.0 (round to the nearest tenth) --------------- Cheers, Stan H.
 Age_Word_Problems/150670: Can you please help me solve this problem: Three years ago, Rica was thrice as old as Dandy. Three years hence, she will be twice as old. Find their present ages.1 solutions Answer 110596 by stanbon(57246)   on 2008-08-03 17:00:29 (Show Source): You can put this solution on YOUR website!Three years ago, Rica was thrice as old as Dandy. Three years hence, she will be twice as old. Find their present ages. ----------------------- Let Rica's present age be "r". Let Dandy's present ate by "d". ----------------------- EQUATIONS: Three years ago: r-3 = 3(d-3) Three years hence: r+3 = 2(d+3) ----------------- Rearrange: r - 3d = -6 r - 2d = 3 -------------- Subtract 1st from 2nd to get: d = 9 (Dandy's age NOW) ----------- Substitute into r-2d = 3 r -(2*9) = 3 r = 21 (Rita's age NOW) ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/150669: Would you say a parabola would be considered a Symmetrical, second order, quadratic polynomial? I have a question asking :Parabolas are what kind of Polynomial? () Symmetrical ()Second order () Quadratic () All of the above I see all being a part of a parabola but only Quadratic is a polynomial, the second order part seems to fall under the quadratic and symmetrical seems to be just an axis that says there are two sides that mirror each other. What is your take? Shelly 1 solutions Answer 110594 by stanbon(57246)   on 2008-08-03 16:47:49 (Show Source): You can put this solution on YOUR website!Ans: All of the above. Cheers, Stan H.
 Probability-and-statistics/150654: A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge? 1 solutions Answer 110593 by stanbon(57246)   on 2008-08-03 16:46:27 (Show Source): You can put this solution on YOUR website!A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge? ----------------- Ho: u = 3.5 Ha: u > 3.5 --------------- x-bar of the data = 3.76 --------------- Comment: The decision rule depends on whether you use a "t" or a "z" critical value. If "t" the decision rule is "reject Ho if t is above 2.821". If "z" the decision rule is "reject Ho if z is above 2.326". --------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/150602: Please help me find x. -12x^3 + 52x^2 + 54x + 12 = 0 I don't know where to go from here? Please show work so I know how to do problems like this from now on, Thanks! My work that I think is wrong... -12(x^3 - (13/3)x^2 - (27/6)x - 1) = 0 Thanks again for your help!1 solutions Answer 110548 by stanbon(57246)   on 2008-08-03 08:19:07 (Show Source): You can put this solution on YOUR website!Please help me find x. -12x^3 + 52x^2 + 54x + 12 = 0 x = -0.5481009, -0.3488316, or 5.2302657 ------------- I used a graphing calculator to find these zeroes. ------------- Cheers, Stan H.
 Quadratic_Equations/150609: (4 / x^6) ^3 I need to simplify it and I am pulling my hair out. Maybe I am too old for this! Can you possibly show me a detailed explanation?1 solutions Answer 110547 by stanbon(57246)   on 2008-08-03 08:08:16 (Show Source): You can put this solution on YOUR website!(4 / x^6) ^3 I need to simplify it ---------------------- = (4/x^6)(4/x^6)(4/x^6) multiply the coefficients and add the exponents to get = 64/x^18 ================ Another way to do it: (4/x^6)^3 = [4^3/x^(3*6)] = 64/x^18 ===================== Cheers, Stan H.
 Probability-and-statistics/150569: Find the value for the correlation coefficient r: x 5, 1, 4, 2, 3 ------------------------- y 5, 10, 12, 4, 8 Can anyone help?1 solutions Answer 110533 by stanbon(57246)   on 2008-08-02 22:20:07 (Show Source): You can put this solution on YOUR website!Find the value for the correlation coefficient r: x 5, 1, 4, 2, 3 ------------------------- y 5, 10, 12, 4, 8 ================================== I used a TI calculator on the data to get: r = -0.09449... Cheers, Stan H.
 Inequalities/150576: You are taking a history course in which there will be four tests, each worth 100 poins. You have scores of 95, 99 and 100 on the first three tests. You must make a total of 360 in order to get an A. What scores on the last test will give you an A. The solution is {s|s>___} Simplify your answer.1 solutions Answer 110531 by stanbon(57246)   on 2008-08-02 22:13:28 (Show Source): You can put this solution on YOUR website!You are taking a history course in which there will be four tests, each worth 100 poins. You have scores of 95, 99 and 100 on the first three tests. You must make a total of 360 in order to get an A. What scores on the last test will give you an A. -------------------- Let x be the 4th test score. ---------------------- EQUATION: 95 + 99 + 100 + x > 360 x + 294 > 360 x > 66 ========== Cheers, Stan H.
 Inequalities/150575: Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of its blue book value. Michelle's care had 9600 in repairs after an accident. What can be concluded about its blue book value? The blue book value of Michelle's car ___,\$___ Type an inequality symbol and then an integer.1 solutions Answer 110527 by stanbon(57246)   on 2008-08-02 22:09:24 (Show Source): You can put this solution on YOUR website!Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of its blue book value. Michelle's car had 9600 in repairs after an accident. What can be concluded about its blue book value? Let the blue book value be "x". 9600 < 0.80x x > \$12000 -------------------------- The blue book value of Michelle's car ___,\$___ Type an inequality symbol and then an integer. Cheers, Stan H.
 Inequalities/150574: 5(r-6) + 4 > 6(r + 3)- 28 The solution set is {r|r ___, ___ Type an inequality symbol, then and integer or fraction1 solutions Answer 110526 by stanbon(57246)   on 2008-08-02 22:05:14 (Show Source): You can put this solution on YOUR website! 5(r-6) + 4 > 6(r + 3)- 28 5r-30 + 4 > 6r+18-28 5r - 26 > 6r -10 r < -16 The solution set is {r|r < -16)} Type an inequality symbol, then and integer or fraction -------------------------------- Cheers, Stan H.
 Probability-and-statistics/150572: Find Q1, Q2, and Q3 for the data set below: 5.4 2.0 6.8 3.1 2.9 4.7 2.1 5.0 1.9 3.4 Can anyone help?1 solutions Answer 110525 by stanbon(57246)   on 2008-08-02 22:00:18 (Show Source): You can put this solution on YOUR website!Find Q1, Q2, and Q3 for the data set below: 5.4 2.0 6.8 3.1 2.9 4.7 2.1 5.0 1.9 3.4 --------------------- I ran the data using a TI calculator: Q1: 2.1 Q2: 3.25 Q3: 5 -------------- Cheers, Stan H.
 Rational-functions/150537: a bird species in danger of extinction has a population that is decreasing (A=A(base0)e^kt). five years ago the population was at 1400 and today only 1000 are still alive. once the population drops below 100, the situation is irreversible. When will this happen?1 solutions Answer 110500 by stanbon(57246)   on 2008-08-02 15:10:37 (Show Source): You can put this solution on YOUR website!a bird species in danger of extinction has a population that is decreasing (A=A(base0)e^kt). five years ago the population was at 1400 and today only 1000 are still alive. once the population drops below 100, the situation is irreversible. When will this happen? ---------------------------- A(t) = A(o) e^(kt) Find "k": 1000 = 1400 e^(k*5) (5/7) = e^(5k) Take the ln to get: 5k = ln (5/7) 5k = -0.3365 k = -0.06729 --------------- Equation: A(t) = A(o) e^(-0.06729t) ---------- When will the population be 100? 100 = 1000 e^(-0.06729t) 0.10 = e^(-0.06729t) -0.06729t = ln(0.10) t = 31.22 years from 5 yrs. ago OR 26.22 years from NOW ======================= Cheers, Stan H.
 Rational-functions/150535: After 50 times at bat, a major league baseball player has a batting average of 0.160. How many consecutive hits must the player get to raise his batting average to 0.250? i tried solving this problem this way: 0.250 - 0.160 = 0.09 50/0.09 = 555.555....1 solutions Answer 110498 by stanbon(57246)   on 2008-08-02 14:59:08 (Show Source): You can put this solution on YOUR website!After 50 times at bat, a major league baseball player has a batting average of 0.160. How many consecutive hits must the player get to raise his batting average to 0.250? ----------------------- After 50 times at bat he has 0.16*50 = 8 hits ----------------- Let x be the number of hits he needs to be batting 0.250 EQUATION: # hits/# at bat = (x + 8)/(50+x) = 0.250 x + 8 = (1/4)(50+x) 4x + 32 = 50 + x 3x = 18 x = 6 (# of consecutive hits he needs to be batting 0.250) ============================ Cheers, Stan H.
 Miscellaneous_Word_Problems/150534: How many pounds of hamburger that \$1.60 per pound must be mixed with 70 pounds of hamburger that costs \$2.10 per pound to make a mixture that costs \$1.70 per pound?1 solutions Answer 110497 by stanbon(57246)   on 2008-08-02 14:50:51 (Show Source): You can put this solution on YOUR website!How many pounds of hamburger that costs \$1.60 per pound must be mixed with 70 pounds of hamburger that costs \$2.10 per pound to make a mixture that costs \$1.70 per pound? --------------------- Value Equation: 160x + 210*70 = 170(x+70) 160x + 210*70 = 170x + 170*70 10x = 40*70 x = 280 lbs. (Amt of 1.60 hamburger that must be added) ===================== Cheers, Stan H.
 Rational-functions/150528: Using the formula I=PRT to find simple interest on an account, find the ammount earned in 3 years if you deposited \$500 into a saving account earning 6% per year.1 solutions Answer 110491 by stanbon(57246)   on 2008-08-02 14:32:52 (Show Source): You can put this solution on YOUR website!Using the formula I=PRT to find simple interest on an account, find the amount earned in 3 years if you deposited \$500 into a saving account earning 6% per year. ------------------ I = 500*0.06*3 = \$90 ==================== Cheers, Stan H.