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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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 Expressions-with-variables/377853: Solve using the multiplication principle first. Then use the elimination method. 2x+y=13 4x+2y=23 I'm not sure if I multiply equation #1 by -2 to eliminate x? If I do that, then I eliminate y. I'm confused, what do I multiply? Thank you.1 solutions Answer 268468 by stanbon(57967)   on 2010-11-29 19:21:16 (Show Source): You can put this solution on YOUR website!Solve using the multiplication principle first. Then use the elimination method. 2x+y=13 4x+2y=23 ------ Multiply the 1st Eq. by -2 to get: -4x-2y = -26 ---- Add that to the 2nd equation to get: 0 = -3 ----- That is a contradictions which resulted because you assumed the x's in the two equations were the same and the y's in the two equations were the same. ---- They are not. The system of equations is said to be "inconsistent". If you graph the two equations you will see that they are parallel. There is no (x,y)point that lies on both of the lines. ================ Cheers, Stan H.
 Word_Problems_With_Coins/377812: If you have 21 more Quarters than Nickels and your total is \$15.45, how many of each coin do you have? I need the Solution and the Algebraic Equation PLEASE1 solutions Answer 268457 by stanbon(57967)   on 2010-11-29 18:52:37 (Show Source): You can put this solution on YOUR website!If you have 21 more Quarters than Nickels and your total is \$15.45, how many of each coin do you have? ---------------------------- Equations: Quantity Eq::: q = n+21 Value Eq::::::5n+25q = 1545 cents --------------------------------------- Substitute for "q" and solve for "n": 5n + 25(n+21) = 1545 30n = 1545-25*21 30n = 1020 n = 34 (# of nickels) q = n+21 = 55 (# of quarters) =============================== Cheers, Stan H.
 Equations/377815: The sum of two numbers is 57. One of the numbers is 21. Which of the following equations could be used to find the other number?1 solutions Answer 268448 by stanbon(57967)   on 2010-11-29 18:32:11 (Show Source): You can put this solution on YOUR website!Optional answers not posted.
 Polynomials-and-rational-expressions/377801: I need to understand how to get to the answer.... For all r is not equal to plus or minus 2, (r squared - 5r + 6) over (r squared - 4 = ? What does it mean "for all r is not equal to plus or minus 2"?1 solutions Answer 268446 by stanbon(57967)   on 2010-11-29 18:30:40 (Show Source): You can put this solution on YOUR website!For all r is not equal to plus or minus 2, (r squared - 5r + 6) over (r squared - 4 = ? What does it mean "for all r is not equal to plus or minus 2"? ---------------------- Problem: (r^2-5r+6)/(r^2-4) ---- Factor this rational expression: [(r-3)(r-2)]/[(r-2)(r+2)] =================================== What does it mean "for all r is not equal to plus or minus 2"? Ans: Since the denominator would be zero if r = 2 or if r = -2, those values of r are not allowed. ============================================= Cheers, Stan H.
 Age_Word_Problems/377791: Anna is 6 and her mother is #4. How long will it be before her mother is twice as old as she is?1 solutions Answer 268440 by stanbon(57967)   on 2010-11-29 18:20:55 (Show Source): You can put this solution on YOUR website!Anna is 6 and her mother is 34. How long will it be before her mother is twice as old as she is? --- The difference is 34-6 = 28 ---- Equation: Let "x" be the required difference. Solve: 34+x = 2(6+x) 34+x = 12+2x x = 22 In 22 yrs, mother will be twice as old as Anna. ---- Checking: 6+22 = 28:::::Anna's future age --- 34+22 = 56::::Mother's future age =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/377781: I don't understand how this problem is solved. I understand how to come up with the equation but not the answer.... "Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?" so, this means (2x-3)(3x+2)= 6x^2 – 5x – 6. However, I am unsure of how to get the answer... Thanks, Sharon1 solutions Answer 268438 by stanbon(57967)   on 2010-11-29 18:07:30 (Show Source): You can put this solution on YOUR website!(2x-3)(3x+2)= 6x^2 – 5x – 6. ----- Use FOIL: F means 1st times 1st O means last times last I means inside times inside L means last times last ------------------------------ F: 2x times 3x = 6x^2 O: 2x times 2 = 4x I: -3 times 3x = -9x L: -3 times 2 = -6 ---------------------------- Combine these results to get: 6x^2 -5x -6 ============================ Cheers, Stan H.
 Quadratic_Equations/377744: Solve the equation log(x+1)-log(x+2)=log(1/x)1 solutions Answer 268437 by stanbon(57967)   on 2010-11-29 17:54:25 (Show Source): You can put this solution on YOUR website!log(x+1)-log(x+2)=log(1/x) ------------ log[(x+1)/(x+2)] = log(1/x) ------ (x+1)/(x+2) = 1/x ----- x(x+1) = x+2 x^2+x-x-2 = 0 --- x^2-2 = 0 (x-sqrt(2))(x+sqrt(2)) = 0 ------------------- x = sqrt(2) ==================== Cheers, Stan H.
 Polynomials-and-rational-expressions/377743: Simplify and write the polynomial in descending order. a^8 + a^7b + a^6b^2 - a^2b^6 - ab^7 - b^81 solutions Answer 268419 by stanbon(57967)   on 2010-11-29 17:15:16 (Show Source): You can put this solution on YOUR website! Simplify and write the polynomial in descending order. a^8 + a^7b + a^6b^2 - a^2b^6 - ab^7 - b^8 -------------------- It is written in descending order. See the decending powers of "a". --------------------------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/377741: 16+8w+4w 3rd power-2w 2nd power1 solutions Answer 268417 by stanbon(57967)   on 2010-11-29 17:12:49 (Show Source): You can put this solution on YOUR website!16+8w+4w 3rd power-2w 2nd power ---- 16 + 8w + 5w^3 - 2w^2 --- Rearrange: 5w^3 - 2w^2 + 8w + 16 --------------------- Not sure what you want to do with this problem. Cheers, Stan H.
 Polynomials-and-rational-expressions/377739: 9x(x 3rd power + z+3)1 solutions Answer 268416 by stanbon(57967)   on 2010-11-29 17:07:39 (Show Source): You can put this solution on YOUR website!9x(x 3rd power + z+3) ------------------ = 9x(x^3 + z + 3) ---- = 9x^4 + 9xz + 27x ======================== Cheers, Stan H.
 logarithm/377689: i need help with this problem: 2^2x+ 2^x - 12=0 This is what i tried, but i think it's wrong: I tried to factor out: (2^x+6)(1^x-2), and now i am totally lost! pls help! Thx! Pls note: the "2x" and the "x" are exponents of the numbers 2. difficult to show that on this screen. 1 solutions Answer 268385 by stanbon(57967)   on 2010-11-29 16:01:34 (Show Source): You can put this solution on YOUR website!i need help with this problem: 2^2x+ 2^x - 12=0 ---- It's a quadratic written in 2^x. --- Let w = 2^x ---- w^2 + w -12 = 0 Factor: (w+4)(w-3) = 0 w = -4 or w = 3 ---- Solve for "x": 2^x = -4 Impossible ---- 2^x = 3 x = ln3/ln2 x = 1.4651.. ================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/377661: The sum of one-third a number and half of a second number is 7. the difference between the second number and two-thirds of the first number is 2. what is each number?1 solutions Answer 268383 by stanbon(57967)   on 2010-11-29 15:57:03 (Show Source): You can put this solution on YOUR website!The sum of one-third a number and half of a second number is 7. the difference between the second number and two-thirds of the first number is 2. what is each number? -------------- Equations: (1/3)x + (1/2)y = 7 y - (2/3)x) = 2 ---------------------------- Rearrange and simplify: 3y + 2x = 42 3y - 2x = 6 ----- 6y = 48 y = 8 ---- Substitute and solve for "x": 24 - 2x = 6 2x = 18 x = 9 =========== Cheers, Stan H.
 Graphs/377668: I'm just learning these...and am a little confused on how this would be written in an inequality equations...here it is...The height of a multistory building is 135 ft.It has 15 stories.What is the height of each story?..1 solutions Answer 268381 by stanbon(57967)   on 2010-11-29 15:52:53 (Show Source): You can put this solution on YOUR website!height of a multistory building is 135 ft.It has 15 stories.What is the height of each story?.. ----- height of each story is 135/15 = 9 ft. ============== Cheers, Stan H.
 logarithm/377680: i need help with this problem: This is the model showing the percentage of Americans with heart disease who are "x" years old: 90/1+271e^-0.122x At what age will the percentage of Americans with heart disease be 70%? I'm thinking it works like this: 0.7 = 90/1+271e^-0.122x ln 0.7= ln (90/1+271e^-0.122x) NOW I AM STUCK!!!!! WHAT NOW???!!!! THX!! 1 solutions Answer 268379 by stanbon(57967)   on 2010-11-29 15:50:50 (Show Source): You can put this solution on YOUR website!This is the model showing the percentage of Americans with heart disease who are "x" years old: 90/1+271e^-0.122x At what age will the percentage of Americans with heart disease be 70%? I'm thinking it works like this: 0.7 = 90/1+271e^-0.122x ---------------------------- Try this: 70 = 90/[1+271e^-0.122x] ---- 1 + 271e^-0.122x = 90/70 = 1.2857 --- 271e^-0.122x = 0.2857 --- e^-0.122x = 0.004744 --- Take the ln to get: -0.122x = -5.3508 --- x = 43.86 yrs old ------------------------ Cheers, Stan H.
 Equations/377682: determing whether the following trinomial is a perfect square. if it is, factor the binomial.1 solutions Answer 268373 by stanbon(57967)   on 2010-11-29 15:43:09 (Show Source): You can put this solution on YOUR website!trinomial not posted
 Equations/377681: factory completely 9x^2+4 could someoen show me how to does kind of problems thank you1 solutions Answer 268372 by stanbon(57967)   on 2010-11-29 15:42:08 (Show Source): You can put this solution on YOUR website!factor completely 9x^2+4 ---- Form: a^2 + b^2 = (a+bi)(a-bi) ------------------------------------ Your Problem: = (3x+2i)(3x-2i) ======================= Cheers, Stan H.
 logarithm/377677: 16^x=321 solutions Answer 268370 by stanbon(57967)   on 2010-11-29 15:40:15 (Show Source): You can put this solution on YOUR website!16^x=32 --- 2^(4x) = 2^5 --- 4x = 5 x = 5/4 --------------- Cheers, Stan H.
 Square-cubic-other-roots/377675: solve for x: the square root of x + 7 = x - 5.1 solutions Answer 268367 by stanbon(57967)   on 2010-11-29 15:38:48 (Show Source): You can put this solution on YOUR website! solve for x: the square root of x + 7 = x - 5. ----- sqrt(x+7) = x-5 --- Square both sides to get: --- x+7 = x^2-10x+25 --- Simplify: x^2 -11x + 18 = 0 --- (x-9)(x-2) = 0 ---- x = 9 or x = 2 ====================== Check for extraneous roots: sqrt(9+7) = 9-5 true ---- sqrt(2+7) = 2-5 false, therefore x=2 is extraneous ===================== Solution: x = 9 =========================== Cheers, Stan H.
 Numbers_Word_Problems/377670: product of a number increased by 10 and 4 equals 221 solutions Answer 268362 by stanbon(57967)   on 2010-11-29 15:33:48 (Show Source): You can put this solution on YOUR website!product of a number increased by 10 and 4 equals 22 --- Equation: 4(x+10) = 22 x+10 = 22/4 x = 11/2 - 10 x = 11/2 - 20/2 x = -9/2 =================== Cheers, Stan H.
 Travel_Word_Problems/377658: a rushed traveler got on an escalator and also walked up. After 45 seconds he realized that he had left his briefcase at the bottom. He turned around and walked back down the up escalator. It took 2 minutes to reach the bottom. If he had traveled 288 feet up the escalator, find the rate of the escalator, and the unaided rate of the man in feet per second. 1 solutions Answer 268359 by stanbon(57967)   on 2010-11-29 15:30:33 (Show Source): You can put this solution on YOUR website!a rushed traveler got on an escalator and also walked up. After 45 seconds he realized that he had left his briefcase at the bottom. He turned around and walked back down the up escalator. It took 2 minutes to reach the bottom. If he had traveled 288 feet up the escalator, find the rate of the escalator, and the unaided rate of the man in feet per second. ------ Up escalator DATA: time = 45 seconds; distance = 288 feet ; rate = 288/45 ft/sec ---- Down escalator DATA: time = 120 seconds ; distance = 288 feet ; rate = 288/120 ft/sec ----- Equations: Let unaided rate of the man be "m" Let rate of the escalator be "e" ---- m + e = 288/45 m - e = 299/120 ----- 2m = [288/45] + [288/120] 2m = 8.8 ft/sec man's unaided rate is 4.4 ft/sec ---- Substitute and solve for "e": 4.4 + e = 288/45 escalator rate = 2 ft/sec ================ Cheers, Stan H.
 Angles/377648: I need to find out what is the complementary angle for 55 degrees and also what is the supplementary angle for 170?1 solutions Answer 268339 by stanbon(57967)   on 2010-11-29 14:57:13 (Show Source): You can put this solution on YOUR website! I need to find out what is the complementary angle for 55 degrees and also what is the supplementary angle for 170? ----- The complement of "x" is "90-x". The complement of 55 degrees is 90-55 = 35 degrees -------------- The supplement of "x" is 180 -x. The supplement of 170 degrees is 180-170 = 10 degrees. ------ Cheers, Stan H.
 Radicals/376277: x^2+6x-4=0 Please help me solve? x^2+6x-4=0 --- Use Quadratic Formula: x = [-6 +- sqrt(36-4*1*-4)]/2 ---- x = [-6 +- sqrt(52)]/2 --- x = [-6 +- 2sqrt(13)]/2 --- x = [-3 +- sqrt(13)]1 solutions Answer 267664 by stanbon(57967)   on 2010-11-26 15:38:58 (Show Source): You can put this solution on YOUR website! x^2+6x-4=0 --- Use Quadratic Formula: x = [-6 +- sqrt(36-4*1*-4)]/2 ---- x = [-6 +- sqrt(52)]/2 --- x = [-6 +- 2sqrt(13)]/2 --- x = [-3 +- sqrt(13)] ============================ Cheers, Stan H.
 Polynomials-and-rational-expressions/376273: Please help me? Use rational exponents to write x^(1/4)*y^(1/2)*z^(1/3) as a single radical expression. 1 solutions Answer 267662 by stanbon(57967)   on 2010-11-26 15:31:09 (Show Source): You can put this solution on YOUR website!Use rational exponents to write x^(1/4)*y^(1/2)*z^(1/3) as a single radical expression. ---- Use the least common multiple of 4,2,3. lcm = 12 ------- = x^(3/12)*y^(6/12)*z^(4/12) --- = [x^3*y^6*z^4]^(1/12) ----------------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/376268: I was hoping to get some help with the following problem: Use the FOIL method to find the product (4x^2-8)(x^5-9)1 solutions Answer 267660 by stanbon(57967)   on 2010-11-26 15:25:56 (Show Source): You can put this solution on YOUR website!Use the FOIL method to find the product (4x^2-8)(x^5-9) --------- 4x^2(x^5-9)-8(x^5-9) ------------ = 4x^7 - 36x^2 - 8x^5 + 72 ------- Cheers, Stan H.
 Probability-and-statistics/375884: A normal distribution consist of 100 scores with a mean of 65 and a standard deviation of 5. How many scores are above 70 and how many scores are below 55? Please break it down step by step, because I am not understanding. I think I got the 2nd half right, but I cannot come up with the 1st part with scores being above 70. Thanks Kerry 1 solutions Answer 267380 by stanbon(57967)   on 2010-11-24 20:07:58 (Show Source): You can put this solution on YOUR website!A normal distribution consist of 100 scores with a mean of 65 and a standard deviation of 5. How many scores are above 70 and how many scores are below 55? Please break it down step by step, because I am not understanding. I think I got the 2nd half right, but I cannot come up with the 1st part with scores being above 70. ------ Find the z-score of 70. Find the probaility of z being greater than that z-score. Cheers, Stan H.
 Equations/375952: A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week? 1 solutions Answer 267369 by stanbon(57967)   on 2010-11-24 19:51:52 (Show Source): You can put this solution on YOUR website!A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week? ------- Equation: 1st car DATA: rate = 40 mi/gal ; # of gallons = x gal ; distance = 40x miles ----- 2nd car DATA: 30 mi/gal ; # of gallons = 45-x gal ; distance = 30(45-x) miles ---- Equation: 40x + 30*45-30x = 1650 ----- 10x = -1350+1650 --- x = 30 gallons (gas consumed by 1st car) 45-x = 15 gallons (gas consumed by 2nd car) ------------------ Cheers, Stan H.
 Probability-and-statistics/375951: in a poll conducted in 2007, 2000 adults ages 18 yr and older were asked how frequently they are in touch with their parents by phone the results of the poll are as follows answer monthly weekly daily dont know less respondents % 11 47 32 2 8 if a person who participated in the poll is selected at random what is the probability that the person said he or she kept in touch with his or her parents A) once a week B) at least once a week1 solutions Answer 267364 by stanbon(57967)   on 2010-11-24 19:36:13 (Show Source): You can put this solution on YOUR website!in a poll conducted in 2007, 2000 adults ages 18 yr and older were asked how frequently they are in touch with their parents by phone the results of the poll are as follows answer monthly weekly daily dont know less respondents % 11 47 32 2 8 if a person who participated in the poll is selected at random what is the probability that the person said he or she kept in touch with his or her parents A) once a week:::::0.47 -------------------------------- B) at least once a week::::: 0.47+0.32 = 0.79 ================== Cheers, Stan H.
 Systems-of-equations/372373: How do you solve for y in the following equations: -3/4x+y/3=5/12 x/5-y=4/51 solutions Answer 265245 by stanbon(57967)   on 2010-11-16 21:42:43 (Show Source): You can put this solution on YOUR website!-3/4x+y/3=5/12 x/5-y=4/5 --- Get rid of the fractions: -9x+4y = 5 x - 5y = 4 -------- Solve the 2nd equation for "x": x = 5y+4 Substitute and solve for "y": -9(5y+4) + 4y = 5 -45y-36 +4y = 5 ------------- -41y = 41 y = -1 =================== Substitute into x = 5y+4 to solve for "x": x = 5(-1)+4 x = -1 ---------------- Cheers, Stan H.
 Exponential-and-logarithmic-functions/372368: Factoring to solve equations Solve: 1 solutions Answer 265235 by stanbon(57967)   on 2010-11-16 21:23:03 (Show Source): You can put this solution on YOUR website! (1/2)x^2+x-(7/2)=4 --- Multiply thru by 2 to get: x^2 + 2x - 7 = 8 --- Rearrange: x^2 + 2x - 15 = 0 Factor: (x+5)(x-3) = 0 x = -5 or x = 3 ================== Cheers, Stan H.
 Inequalities/372365: my son is in tenth grade and is having trouble with his algebra i never had this in school here is a sample could you explain how to do this? first sample –z – 3 < -4 second sample 4x < x + 6 1 solutions Answer 265233 by stanbon(57967)   on 2010-11-16 21:20:10 (Show Source): You can put this solution on YOUR website!first sample –z – 3 < -4 --- Add z to both sides to get: -3 < z-4 Add 4 to both sides to get: z > 1 ============= second sample 4x < x + 6 Subtract x from both sides to get: 3x < 6 Divide both sides by 3 to get: x < 2 ========== Cheers, Stan H.