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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 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>Next

 Exponents-negative-and-fractional/175869: How do you simplify expression.All varibles represent positive and real numbers. -(8a^3b^6)-2/31 solutions Answer 130973 by stanbon(57967)   on 2009-01-10 07:30:08 (Show Source): You can put this solution on YOUR website!-(8a^3b^6)^(-2/3) --------- The exponent is -2/3 The negative means "invert" the 2 means "square" the 3 means "take the cube root" You may perform the instructions in any order to get: -------------------------- 1st: take the cube root to get: (2ab^2)^-2 --- 2nd: square to get: (4a^2b^4)^-1 ------ #rd: invert to get: 1/(4a^2b^4) ==================== Cheers, Stan H.
 expressions/175862: 54.) simplify...(x+2)(x²+x+5)...just need help with this one. please1 solutions Answer 130970 by stanbon(57967)   on 2009-01-09 22:40:52 (Show Source): You can put this solution on YOUR website!simplify...(x+2)(x²+x+5) = x(x^2+x+5) + 2(x^2+x+5) = x^3 + x^2 + 5x + 2x^2 + 2x + 10 = x^3 + 3x^2 + 7x + 10 =========================== Cheers, Stan H.
 Distributive-associative-commutative-properties/175861: 9) (5z-2)(5z+2)....use foil....need some help here...thanks1 solutions Answer 130969 by stanbon(57967)   on 2009-01-09 22:36:51 (Show Source): You can put this solution on YOUR website!(5z-2)(5z+2)....use foil ----- F: 5z*5z = 25z^2 O: 5z*2 = 10z I: 5z*-2 =-10z L: -2*2 = -4 --------------------------- Combine the four results to get: 25z^2 - 4 =============== Cheers, Stan H.
 Expressions-with-variables/175858: solve each of the following for the indicated variable d=rt for r1 solutions Answer 130967 by stanbon(57967)   on 2009-01-09 22:33:09 (Show Source): You can put this solution on YOUR website!r = d/t ========== Cheers, Stan H.
 percentage/175820: The teacher gives a test. The results are as follows: 10 A's, 42 B's, 15 C's, 8 D's and 2 F's. What percentage of the class received B's? Stuck on this problem? Thank you.1 solutions Answer 130930 by stanbon(57967)   on 2009-01-09 15:20:33 (Show Source): You can put this solution on YOUR website!The teacher gives a test. The results are as follows: 10 A's, 42 B's, 15 C's, 8 D's and 2 F's. What percentage of the class received B's? --------- x/100 = 42/87 x = 100(42/87) x = 48.27 Ans 48.27% Cheers, Stan H.
 expressions/175819: Use multiplying by 1 to find an expression equivalent to 5/17 with a denominator of 119x1 solutions Answer 130929 by stanbon(57967)   on 2009-01-09 15:17:46 (Show Source): You can put this solution on YOUR website!Use multiplying by 1 to find an expression equivalent to 5/17 with a denominator of 119x ------------------------ (5/17)(7x/7x) = 35x/119x ============================ Cheers, Stan H.
 Average/175814: A mountian with a base 5,914 feet below sea level rises 19,287 feet. What is the elevation above sea level of its peak? What is the elevation of mountain's Peak?1 solutions Answer 130921 by stanbon(57967)   on 2009-01-09 14:16:39 (Show Source): You can put this solution on YOUR website!A mountian with a base 5,914 feet below sea level rises 19,287 feet. What is the elevation above sea level of its peak? What is the elevation of mountain's Peak? -------------- Draw the picture. Height of the mountain above sea level = 19,287-5914 = 13,373 ft. Same answer for both questions. --------------------------------- Cheers, Stan H.
 Probability-and-statistics/175812: I'm stumped on 2 word problems dealing with probability. Can someone please help me???? Here they are: 1. Suppose a contest offers \$1,000 to the person who can guess the winning four digit number. How many possibilities are there? 2. There are 10 women and 8 men in a club. How many different committees of 6 people can be selected from the group if equal numbers of men and women are to be on the committee? TIA for your help! Andrew1 solutions Answer 130919 by stanbon(57967)   on 2009-01-09 14:13:35 (Show Source): You can put this solution on YOUR website!1. Suppose a contest offers \$1,000 to the person who can guess the winning four digit number. How many possibilities are there? ---------- # of four-digit numbers: 1000-9999= 8999+1 = 9000 ------------------------------------------------------- 2. There are 10 women and 8 men in a club. How many different committees of 6 people can be selected from the group if equal numbers of men and women are to be on the committee? ---- 6 on the committe requires 3 men and 3 women. # of groups of 3 women: 10C3 = [10*9*8]/[1*2*3] = 120 # of groups of 3 men : 8C3 = 8*7*6/1*2*3 = 56 ------------------ # of possible committees: 120*56 = 6720 ============================================ Cheers, Stan H.
 Inequalities/175708: The attendence at home basketball games has ranged between 820 and 1540 spectators. Write an absolute value inequality descibing the possible attendance at home basketball games.1 solutions Answer 130909 by stanbon(57967)   on 2009-01-09 12:13:48 (Show Source): You can put this solution on YOUR website!The attendence at home basketball games has ranged between 820 and 1540 spectators. Write an absolute value inequality descibing the possible attendance at home basketball games. ------------ Find the average attendance figure: (820+1540)/2 = 1180 ------------ Find the difference between average and max (or min). 1540-1180 = 360 ---------------------------- Equation: |x-1180| <= 360 x is the possible attendance at home basketball games. ====================== Cheers, Stan H.
 Rational-functions/175772: Well I am pretty sure this is the topic we are doing. The one i selected above. Well anyways, this is the problem I have just been stuck on for EVER. it has 3 part, A, B, and C. and you cant get B or C if you dont get A. and ive been stuck on A. but even if i get past A, Im stil not quite sure if i know what to do with B and C. Let p(x)=x(x-3)^2(x+1) A) Sketch this graph of p(x). Label all intercepts. <-- I'm not even sure i know how to graph this at all. could you walk me through it? b)Find another polynomial funtcion, q(x), that has the same zeroes as p(x) and goes throught the point (-1,16). <--- once i get the first graph I'm not sure How i would MAKE it go through (-1,16), How would i go upon doing that? c) Explain how to determine the end behavior of a polynomial function. <--- what does it mean by determine if we already solved it above?1 solutions Answer 130856 by stanbon(57967)   on 2009-01-08 23:18:29 (Show Source): You can put this solution on YOUR website!Let p(x)=x(x-3)^2(x+1) A) Sketch this graph of p(x). Label all intercepts. <-- x-intercepts: x = 0, x= 3 with multiplicity 2, x= -1 y-intercept: P(0) = 0(0-3)^2(0+1) = 0 -------------------------------------------------------- b)Find another polynomial funtcion, q(x), that has the same zeroes as p(x) and goes throught the point (-1,16). <--- once i get the first graph I'm not sure How i would MAKE it go through (-1,16), How would i go upon doing that? Consider q(x) = x(x-3)^2(x+1)+16 This has the same zeroes as p(x) and q(-1) = 16 ------------------------------------------------------ c) Explain how to determine the end behavior of a polynomial function. <--- what does it mean by determine if we already solved it above? "end behavior" refers to the y-values as x gets increasingly large Since the highest power term determines that y value look at x(x-3)^2(x+1) = x^4+.... As x gets larger x^4 gets larger so y gets larger and the end behavior is "y gets increasingly larger". ================================================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/175771: point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of line AB? 1 solutions Answer 130855 by stanbon(57967)   on 2009-01-08 22:51:23 (Show Source): You can put this solution on YOUR website!point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of line AB? ---------------- Draw the picture. The line x = 2 passes thru the point (2,1) (2,1) is the midpoint of AB A is 6 units to the left of (2,1), so B must be 6 units to the right of (2,1) -------------------- B is (8,1) ================= Cheers, Stan H.
 Complex_Numbers/175769: If is a solution for , where m and n are real numbers, what is the value of m?1 solutions Answer 130854 by stanbon(57967)   on 2009-01-08 22:40:53 (Show Source): You can put this solution on YOUR website!If is a solution for , where m and n are real numbers, what is the value of m? --------------- If 3+2i is a solution then 3-2i is a solution. Then (x-3+2i)(x-3+2i) is the form of the quadratic Then (x-3)^2-(2i)^2 is the form of the quadratic. Then x^2 -6x + 9 + 4 is the form of the quadratic Then x^2 -6x + 13 = x^2 + mx + n m=-6 n = 13 ======================== Cheers, Stan H.
 Probability-and-statistics/175765: 1. Find the number of permutations in the word GEOMETRY. 2. In how many ways can 12 books be displayed on a shelf if 12 books are available. 1 solutions Answer 130853 by stanbon(57967)   on 2009-01-08 22:31:59 (Show Source): You can put this solution on YOUR website!1. Find the number of permutations in the word GEOMETRY. 8!/2! = 20160 arrangements ------------------------------------- 2. In how many ways can 12 books be displayed on a shelf if 12 books are available. 12! = 479,001,600 ways ============================= Cheers, Stan H. ===============================
 Proportions/175753: if 4% of a number is z, then what is 50% of the number?1 solutions Answer 130838 by stanbon(57967)   on 2009-01-08 21:18:09 (Show Source): You can put this solution on YOUR website!if 4% of a number is z, then what is 50% of the number? - Let the number be "x" 0.04x = z x = 100z/4 = 25z ------------------- Then 0.50x = 0.50*25z = 12.5z ===================================== Cheers, Stan H.
 Rational-functions/175739: For a certain time period the ratio of the dollar value of exports to the dollar value of imports for the United States was 2 to 3. If the value of exports during that time period was 48 billion dollars, then what was the value of imports?1 solutions Answer 130829 by stanbon(57967)   on 2009-01-08 20:32:01 (Show Source): You can put this solution on YOUR website!For a certain time period the ratio of the dollar value of exports to the dollar value of imports for the United States was 2 to 3. If the value of exports during that time period was 48 billion dollars, then what was the value of imports? ----------------- 2 to 3 is the same as 2x to 3x where 2x is exports and 3x is imports. ---------------- Equation: 2x + 3x = 48 B 5x = 48 B x = 9.6 B -------------------- imports = 3x = 3*9.6 = 28.8 Billion ======================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/175736: Find the real-number solutions of the equation. x^3+2x^2-25x-50=01 solutions Answer 130826 by stanbon(57967)   on 2009-01-08 20:26:09 (Show Source): You can put this solution on YOUR website!Find the real-number solutions of the equation. x^3+2x^2-25x-50=0 ---------- I graphed it to find x=-5 is a root. ------- Using synthetic division find the other roots: -5)....1....2....-25...-50 ........1....-3....-10..|..0 -2).....1-----5....|..0 5)......1....|0 ========================= x = -5 or -2 or 5 ========================= Cheers, Stan H.
 Polynomials-and-rational-expressions/175733: factor the polynomials by grouping. 9m^3+18m^2-4m-8 1 solutions Answer 130824 by stanbon(57967)   on 2009-01-08 20:14:32 (Show Source): You can put this solution on YOUR website! factor the polynomials by grouping. 9m^3+18m^2-4m-8 ---------------------- 9m^2(m+2) - 4(m+2) = (m+2)(9m^2-4) = (m+2)((3m-2)(3m+2) ====================== Cheers, Stan H.
 Probability-and-statistics/175705: The records of a casualty insurance company show that, in the past, its clients have had a mean of auto accidents per day with a variance of 1.8 . The actuaries of the company claim that the variance of 0.0016 the number of accidents per day is no longer equal to 0.0016 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis Ho and the alternative hypothesis Hi that we would use for this test. 1 solutions Answer 130822 by stanbon(57967)   on 2009-01-08 20:09:55 (Show Source): You can put this solution on YOUR website!The records of a casualty insurance company show that, in the past, its clients have had a mean of auto accidents per day with a variance of 1.8 . The actuaries of the company claim that the variance of 0.0016 the number of accidents per day is no longer equal to 0.0016 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis Ho and the alternative hypothesis Hi that we would use for this test. ----------- Ho: sigma^2 = 1.8 Ha: sigma^2 is not equal to 1.8 ===================================== Cheers, Stan H.
 Functions/175721: 27^3 - 8Y^31 solutions Answer 130818 by stanbon(57967)   on 2009-01-08 19:56:54 (Show Source): You can put this solution on YOUR website!27^3 - 8Y^3 = (3)^3 - (2y)^3 = (3 - y)(3^2 + 3y + y^2) =============================== Cheers, Stan H.
 Linear-equations/175725: My question says you had 132 dolars after 6 weeks and 240 dolarsv after 12 weeks. you saved the same amount each week. do you think that you can generilize this problem situation by using a linear equation? use complete sentences and explain yor reasoning.1 solutions Answer 130817 by stanbon(57967)   on 2009-01-08 19:53:36 (Show Source): You can put this solution on YOUR website!you had 132 dolars after 6 weeks and 240 dollars after 12 weeks. you saved the same amount each week. do you think that you can generilize this problem situation by using a linear equation? use complete sentences and explain yor reasoning. ----------------------------------- You have two points: (6,132) and (12,240) ------------------ linear if you assume the money increases a fixed amount each month. ----------- Cheers, Stan H.
 Linear-equations/175722: This question is from textbook What it the slope of the line that passes through each pair (1,2),(4,3) m= y2-y1 x2-x11 solutions Answer 130815 by stanbon(57967)   on 2009-01-08 19:47:06 (Show Source): You can put this solution on YOUR website!slope of the line that passes through each pair (1,2),(4,3) ------------------ m = (3-2)/(4-1) = 1/3 ------------------------- Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/175723: A car purchased for \$20,000 depreciates annually at a rate of 13% a)write an equation that models the value of the car V(t) = 20000*0.87^t -------------------------- b)predict the value of the car after 6 years V(6) = 20000*0.87^6 = \$8672.52 ==================================== Cheers, Stan H. 1 solutions Answer 130812 by stanbon(57967)   on 2009-01-08 19:43:32 (Show Source): You can put this solution on YOUR website!A car purchased for \$20,000 depreciates annually at a rate of 13% a)write an equation that models the value of the car V(t) = 20000*0.87^t -------------------------- b)predict the value of the car after 6 years V(6) = 20000*0.87^6 = \$8672.52 ==================================== Cheers, Stan H.
 expressions/175596: this expression <2+(5*33)/6+1e-2> is supposed to have an answer of 29.51. How do you get this answer, please show work.1 solutions Answer 130811 by stanbon(57967)   on 2009-01-08 19:38:40 (Show Source): You can put this solution on YOUR website!2+(5*33)/6+1e-2 ------- Note: e = 2.71281828.... e^-2 = 0.135 ---------- 2 + (165/6) + 0.135 = 29.635 ============== Cheers, Stan H.
 Inequalities/175503: A tool and die shop makes a metal pull tab for a pop can. The length of the tab is 1.2 inches. The measurement may have an error of as much as 0.002 inches. Write an absolute value inequality that shows the range of the possible lengths of the tabs. Solve the inequality.1 solutions Answer 130808 by stanbon(57967)   on 2009-01-08 19:22:08 (Show Source): You can put this solution on YOUR website!A tool and die shop makes a metal pull tab for a pop can. The length of the tab is 1.2 inches. The measurement may have an error of as much as 0.002 inches. Write an absolute value inequality that shows the range of the possible lengths of the tabs. Solve the inequality ---------------------- |x - 1.2| <= 0.002 -0.002 + 1.2 <= x <= 0.002 + 1.2 1.198 <= x <= 1.202 ========================= Cheers, Stan H.
 Inequalities/175711: In woodshop class, you must cut a piece of wood within 3/16 inch of the teacher's specification of 5 1/8 inches. Write an absolute value inequality that describes the acceptable lengths for this piece of wood. Solve the inequality.1 solutions Answer 130806 by stanbon(57967)   on 2009-01-08 19:14:51 (Show Source): You can put this solution on YOUR website! woodshop class, you must cut a piece of wood within 3/16 inch of the teacher's specification of 5 1/8 inches. Write an absolute value inequality that describes the acceptable lengths for this piece of wood. Solve the inequality. --------------------------------- |x - 5 1/8| <= 3/16 |x - (41/8)| <= 3/16 -3/16 <= x - (41/8) <= 3/16 -3/16 + 41/8 <= x <= 3/16 +41/8 -3/16 + 82/16 <= x <= 3/16 + 82/16 79/16 <= x <= 85/16 =========================================================== Cheers, Stan H.
 Expressions-with-variables/175690: Do you minus the exponents in a division problem?1 solutions Answer 130794 by stanbon(57967)   on 2009-01-08 18:26:00 (Show Source): You can put this solution on YOUR website!Yes: a^2/a^3 = 1/a^(3-2) = 1/a Or a^2/a^3 = a^(2-3) = a^-1 ================================ Cheers, Stan H.
 Rate-of-work-word-problems/175691: a 6 passenger plane cruises at 180 mph in calm air. if the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed? i know that r= d/t1 solutions Answer 130790 by stanbon(57967)   on 2009-01-08 18:22:29 (Show Source): You can put this solution on YOUR website!a 6 passenger plane cruises at 180 mph in calm air. if the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed? ----------------------- Withwind DATA: rate = 180+c ; distance = 7 mi ; time = d/r = 7/(180+c) hrs. ------------------ againstwind DATA: rate = 180-c ; distance = 5 mi ; time = d/r = 5/(180-c) hrs. ---------------- EQUATION: time = time = 7/(180+c) = 5/(180-c) Cross-multiply 7(180-c) = 5(180+c) 7*180 - 7c = 5*180+5c 12c = 2*180 c = 2*15 c = 30 mph (speed of the wind) =================================== Cheers, Stan H.
 Graphs/175688: i am supposed to get the formula y-y1=m(x-x1) into the formula y=mx+b. the problem is: y-2=7(x-1). i have an idea how to do this, but i'm still lost.1 solutions Answer 130787 by stanbon(57967)   on 2009-01-08 18:16:08 (Show Source): You can put this solution on YOUR website!i am supposed to get the formula y-y1=m(x-x1) into the formula y=mx+b. the problem is: y-2=7(x-1) y = 7x - 7 + 2 y = 7x -5 ================= Cheers, Stan H.
 Linear_Algebra/175686: How do I find the possible values of r in the inequality 5>r-3?1 solutions Answer 130786 by stanbon(57967)   on 2009-01-08 18:13:38 (Show Source): You can put this solution on YOUR website!find the possible values of r in the inequality 5>r-3? r-3 < 5 Add 3 to both sides to get: r < 8 ====================== Cheers, Stan H.
 expressions/175680: 11) Simplify -24a3b5 + 36a2b2 – 12ab2 divided by –4ab. can you show the work please.1 solutions Answer 130785 by stanbon(57967)   on 2009-01-08 18:11:37 (Show Source): You can put this solution on YOUR website!Simplify: [-24a3b5 + 36a2b2 – 12ab2] / [–4ab] That -4ab is a common denominator: = 6a^2b^4 - 9ab + 3b = 3[2a^2b^4 -3ab + b] ======================== Cheers, Stan H.
 Radicals/175682: mini 3 square root 32x^5y^101 solutions Answer 130784 by stanbon(57967)   on 2009-01-08 18:06:10 (Show Source): You can put this solution on YOUR website!mini 3 square root 32x^5y^10 ---- That mini 3 means "cube root". ------------- = cbrt(8x^3y^9)*cbrt(4x^2y) = 2xy^3*curt(4x^2y) ========================= Cheers, Stan H.