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# Recent problems solved by 'stanbon'

stanbon answered: 57314 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 , 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 Quadratic-relations-and-conic-sections/421154: the equation of the axis of the parabola x^2-4y+8=01 solutions Answer 294158 by stanbon(57387)   on 2011-03-12 07:06:33 (Show Source): You can put this solution on YOUR website!the equation of the axis of the parabola x^2-4y+8=0 --- 4y = x^2+8 y = (1/4)x^2 + 8 ---- Vertex at (0,8) Axis of symmetry: x = 0 ================================ Cheers, Stan H. ====
 Probability-and-statistics/421078: The Better Business Bureau reported that approximately 72.2% of consumer complaints in 2006 were settled. If a random sample of five consumer complaints is selected, what is the probability that at least one was not settled? At least one was settled? 1 solutions Answer 294120 by stanbon(57387)   on 2011-03-11 23:38:45 (Show Source): You can put this solution on YOUR website!The Better Business Bureau reported that approximately 72.2% of consumer complaints in 2006 were settled. ------- If a random sample of five consumer complaints is selected, --- Binomial Problem with n = 5 p(settled) = 0.722 p(not settled) = 0.278 -------- what is the probability that at least one was not settled? P(at least one was not settled) = 1 - P(all were settled of 7225) = 1 - (0.722)^5 --- = 1 - 0.1962 --- = 0.8038 ============== Cheers, Stan H. ==================== At least one was settled? P(at least one settled) = 1 - P(none settled of 5) = 1 - (0.278)^5 --- = 1 - 0.001660 = 0.99834..
 Miscellaneous_Word_Problems/421104: Mozart composed 11 less than of the number of symphonies that Haydn composed. Together they compose 145 symphonies. How many symphonies did Mozart compose? (i understand the solving part, i am just not coming up with the correct representations for each person)1 solutions Answer 294119 by stanbon(57387)   on 2011-03-11 23:14:30 (Show Source): You can put this solution on YOUR website!Mozart composed 11 less than of the number of symphonies that Haydn composed. Together they compose 145 symphonies. How many symphonies did Mozart compose? --------------------------------- Equations: M + H = 145 symphonies M = H + 11 -------------------- substitute for "M" and solved for "H": H+11+H = 145 2H = 134 H = 67 (# composed by Haydn) --- Solve for "M": M = H+11 M = 67+11 = 68 (# composed by Mozart) =========== Cheers, Stan H. ==========
 Rational-functions/421125: What numbers cannot be used for x in each rational expression? a. (3x - 1)/(x^2 - 4) b. 8/(3 + 2x) c. 5/x Can someone please explain this to me, I do not understand how or why. THanks in advance!!!!!!1 solutions Answer 294118 by stanbon(57387)   on 2011-03-11 23:05:58 (Show Source): You can put this solution on YOUR website!What numbers cannot be used for x in each rational expression? The denominators cannot be zero. ---- a. (3x - 1)/(x^2 - 4) x^2-4 cannot be zero x cannot be 2 or -2 ------------------------------ b. 8/(3 + 2x) 3+2x cannot be zero x cannot be -3/2 ----------------------- c. 5/x x cannot be zero ======================== Cheers, Stan H. ============
 Graphs/421103: in 1920, the record for a certain race was 46.9 sec. in 1940, it was 46.5 sec. Let R(t)= the record in the race and t= the number of years since 1920. fine the linear function that fit the data R(T)=1 solutions Answer 294117 by stanbon(57387)   on 2011-03-11 23:02:08 (Show Source): You can put this solution on YOUR website!in 1920, the record for a certain race was 46.9 sec. in 1940, it was 46.5 sec. Let R(t)= the record in the race and t= the number of years since 1920. fine the linear function that fit the data R(T)= ------------------------------------------ You have 2 points: (0,46.9) and (20,46.5) --- slope = 0.4/-20 = -0.02 --- Form: R(t) = mx + b R(t) = -0.02x+46.9 ================================== Cheers, Stan H. =======
 Permutations/421111: There are 10 points A, B, C, …in a plane, no three on the same line. i) How many triangles are determined by these points? ii) How many of these triangles contain the point A?1 solutions Answer 294116 by stanbon(57387)   on 2011-03-11 22:53:46 (Show Source): You can put this solution on YOUR website! There are 10 points A, B, C, …in a plane, no three on the same line. i) How many triangles are determined by these points? 3 non-collinear points determine a triangle. # of triangles = 10C3 = (10*9*8)/(1*2*3) = 120 ======================================================= ii) How many of these triangles contain the point A? A plus 2 more points determine a triangle. # of triangles = 9C2 = (9*8)/(1*2) = 36 ============================================= Cheers, Stan H. =======
 test/421119: the lengths of the sides of a triangle are Xcm , (X+10)cm and(2X-5)cm.Determine the minimum value of X , if the perimeter of the triangle is greater than 85cm.1 solutions Answer 294113 by stanbon(57387)   on 2011-03-11 22:44:44 (Show Source): You can put this solution on YOUR website! the lengths of the sides of a triangle are Xcm , (X+10)cm and(2X-5)cm.Determine the minimum value of X , if the perimeter of the triangle is greater than 85cm. --------------------------- Solve: x + x+10 + 2x-5 > 85 4x + 5 > 85 4x > 80 x > 20 ----------------- Cheers, Stan H. =============
 Travel_Word_Problems/421123: A driver who drives at a speed of r mph for t hr will travel a distance d mi given by d=rt mi. how far will a driver travel at a speed of 58 for 4 hrs?1 solutions Answer 294111 by stanbon(57387)   on 2011-03-11 22:41:10 (Show Source): You can put this solution on YOUR website!how far will a driver travel at a speed of 58 for 4 hrs? ------------ distance = rt d = 58 mph*4 hr = 232 miles ============================== Cheers, Stan H. =========
 Probability-and-statistics/421121: if a single die is rolled twice in succession, what is the probability that the sum is (a) greater than 7, (b) an even number?1 solutions Answer 294109 by stanbon(57387)   on 2011-03-11 22:32:32 (Show Source): You can put this solution on YOUR website!if a single die is rolled twice in succession, what is the probability that the sum is (a) greater than 7, Greater than 7 pairs: 2/6;3/5;4/4;5/3;5/3;6/2 3/6;4/5;5/4;6/3 4/6;5/5;6/4 5/6;6/5 6/6 P(>7) = 16/36 = 4/9 ================================ (b) an even number? Ans: 18/36 = 1/2 ----------------- Cheers, Stan H. ==================
 Functions/421115: inverse of the function f(x)=-8x+4/-6x-31 solutions Answer 294106 by stanbon(57387)   on 2011-03-11 22:19:23 (Show Source): You can put this solution on YOUR website!inverse of the function f(x)=-8x+4/-6x-3 ---- Interchange x and y to get: x = (-8y+4)/(-6y-3) ---- Solve for "y": -6xy-3x = -8y+4 --- 6xy-8y = -3x-4 --- y(6x-8) = -3x-4 --- y = (-3x-4)/(6x-8) ======================= Cheers, Stan H. ==========
 Quadratic_Equations/421118: Help me solve this please w^4 -12w^2-2=01 solutions Answer 294105 by stanbon(57387)   on 2011-03-11 22:13:46 (Show Source): You can put this solution on YOUR website!Help me solve this please w^4 -12w^2-2=0 ---- w^2 = [12 +- sqrt(144-4*-2)]/2 -------- w^2 = [12 +- sqrt(152)]/2 -------- w^2 = [12 +- 2sqrt(38)]/2 --- w^2 = 6 + sqrt(38) or w^2 = 6-sqrt(38) --- Solve for "w". ================= Cheers, Stan H.
 Linear-equations/421120: Use the five steps for problem solving to answer the following. Angle U and angle V ae complementary angles. If angle U is three less than twice angle V, what are the measures of the angles? Completely lost on this, please help1 solutions Answer 294104 by stanbon(57387)   on 2011-03-11 22:09:42 (Show Source): You can put this solution on YOUR website!Angle U and angle V ae complementary angles. If angle U is three less than twice angle V, what are the measures of the angles? ----------------- Equations: U + V = 90 U = 2V-3 ------------ Substitute for "U" and solve for "V": 2V-3+V = 90 3v = 93 V = 31 degrees ----- Solve for "U": U = 2V-3 U = 2*31-3 U = 62-3 U = 59 degrees ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/421116: i need help solving this 9a^3b^2 + 3a^2 b^21 solutions Answer 294103 by stanbon(57387)   on 2011-03-11 22:05:22 (Show Source): You can put this solution on YOUR website!i need help solving this 9a^3b^2 + 3a^2 b^2 ---- 3a^2b^2[3a+1] -------------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/421117: i need help with this 6x^3 + 3x^2 – 3x1 solutions Answer 294101 by stanbon(57387)   on 2011-03-11 21:56:55 (Show Source): You can put this solution on YOUR website!i need help with this 6x^3 + 3x^2 – 3x ---- 3x(2x^2+x-1) ---- 3x(2x-1)(x+1) ==================== Cheers, Stan H.
 logarithm/421030: Please help me! Solve for x. log 10x-log (2x-3)= log 6 (Simplify your answer. Type an integer or a fraction.)1 solutions Answer 294037 by stanbon(57387)   on 2011-03-11 16:17:27 (Show Source): You can put this solution on YOUR website!Solve for x. log 10x-log (2x-3)= log 6 ---- log[10x/(2x-3)] = log6 ---- 10x/(2x-3) = 6 10x = 12x-18 2x = 18 x = 9 ============ Cheers, Stan H. ============
 logarithm/421024: Please help me out! Write in logarithmic form. 5 to the second power=25 What is the equivalent logarithmic form? log 5_______=_______1 solutions Answer 294035 by stanbon(57387)   on 2011-03-11 16:13:55 (Show Source): You can put this solution on YOUR website!Write in logarithmic form. 5 to the second power=25 What is the equivalent logarithmic form? log5(25)= 2 ---------- Cheers, Stan H. =============
 Quadratic_Equations/420802: can you help me graph this equation x^2+2x+51 solutions Answer 293926 by stanbon(57387)   on 2011-03-10 22:59:40 (Show Source): You can put this solution on YOUR website!can you help me graph this equation x^2+2x+5 ---------- y = x^2+2x+5 ---- It is a parabola opening upward. It has a minimum at x = -b/2a = -2/2 = -1 Then f(-1) = 1-2+5 = 4 So vertex at (-1,4) --- Y-intercept = f(0) = 5 ---- Plot the vertex and the point (0,5) and draw a parabola opening upward though them to get: ================ Cheers, Stan H.
 Rational-functions/420812: List all real values of x such that f (x) = 0. If there are no such real x, type DNE in the answer blank. If there is more that one real x, give a comma separated list (e.g. 1,2). f(x)= (-3/x-7)+(-8/x+5) 1 solutions Answer 293924 by stanbon(57387)   on 2011-03-10 22:55:08 (Show Source): You can put this solution on YOUR website!(-3/x-7)+(-8/x+5) = 0 --- Multiply thru by (x-7)(x+5) to get: -3(x+5) - 8(x-7) = 0 -11x -15+56 = 0 -11x = -41 --- x = 41/11 ============== Cheers, Stan H.
 Expressions-with-variables/420813: Use a graphing calculator to solve the following equation for x. 2^x=29 What is the solution set? (Simplify your answer. Type an integer or a decimal rounded to the nearest thousandth.) 1 solutions Answer 293921 by stanbon(57387)   on 2011-03-10 22:51:35 (Show Source): You can put this solution on YOUR website!Use a graphing calculator to solve the following equation for x. 2^x=29 --- Graph Y1 = 2^x Graph Y2 = 29 --- Find the point of intersection using your calculator: x = 4.857981.. Cheers, Stan H.
 Volume/420807: A sphere has a volume of 32 in. If the diameter is halved, find the new volume. help..!!! 1 solutions Answer 293918 by stanbon(57387)   on 2011-03-10 22:48:30 (Show Source): You can put this solution on YOUR website!A sphere has a volume of 32 in^3. If the diameter is halved, find the new volume. ---- Vol = (4/3)pi*r^3 --- 32 = (4/3)pi*r^3 24 = pi*r^3 --- r = (24/pi)^(1/3) ------ If the diameter is halved, the radius is halved --- New radius = (1/2)(24/pi)^(1/3) New radius = (1/8)^(1/3)*(24/pi)^(1/3) New radius = (3/pi)^(1/3) --- New volume = (4/3)pi^3 --- New volume = 4 cu in. ======================= Cheers, Stan H. =======================
 Probability-and-statistics/420772: a bag contains 6 orange, 6 balck, and 7 red marbles. Find the probablility of picking 3 orange marbles if each marble is NOT returned to the bag before the next marble is picked1 solutions Answer 293914 by stanbon(57387)   on 2011-03-10 22:13:56 (Show Source): You can put this solution on YOUR website!a bag contains 6 orange, 6 black, and 7 red marbles. Find the probablility of picking 3 orange marbles if each marble is NOT returned to the bag before the next marble is picked ---------------------------- P(pick 3 orange) = 6C3/19C3 = 20/969 ====================== Cheers, Stan H. ==============
 Probability-and-statistics/420775: Drawing: Arrows hitting a target. Target has two possible scores: 5 and 10. Problem: "If three arrows are shot, and all the arrows hit the target, how many different total scores are possible?" I'm trying to help my kid here. We can come up with 4 possible scores. 5-5-5, 5-5-10, 5-10-10, 10-10-10, 10-10-5, 10-5-5, 5-5-5, so you have four possible scores: 15, 20, 25 and 30. 4 answers are provided for multiple choice: 6, 9, 10 and 12. He was told by his teacher that the correct answer is 10. 10 possible different total scores. HELP!!!! Thank you!1 solutions Answer 293913 by stanbon(57387)   on 2011-03-10 22:10:16 (Show Source): You can put this solution on YOUR website! Drawing: Arrows hitting a target. Target has two possible scores: 5 and 10. Problem: "If three arrows are shot, and all the arrows hit the target, how many different total scores are possible?" I'm trying to help my kid here. We can come up with 4 possible scores. 5-5-5, 5-5-10, 5-10-10, 10-10-10, 10-10-5, 10-5-5, 5-5-5, so you have four possible scores: 15, 20, 25 and 30. 4 answers are provided for multiple choice: 6, 9, 10 and 12. He was told by his teacher that the correct answer is 10. 10 possible different total scores. 3 5s: 555 sum = 15 2 5s: 5,5,10 sum = 20 1 5s: 5,10,10 sum = 25 3 10s: 10,10,10 sum = 30 ------ Comment: The problem may have had a picture of the target. There may have been a part of the target that had no points associated with it. ----- You would then also have 5,0,0 sum = 5 5,5,0 sum = 10 ------- But I don't see how there would be 10 different total scores. ================ Cheers, Stan H.
 Proportions/420790: how do I figure out what % 9 is of 241 solutions Answer 293911 by stanbon(57387)   on 2011-03-10 21:55:29 (Show Source): You can put this solution on YOUR website!figure out what % 9 is of 24 ---- 9/24 = x/100 --- x = 100(9/24) --- x = 37.5% =============== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/420793: I need to write this equation in standard form. y^2=-3x I know it's a parabola, but do you complete the square to get in standard form? 1 solutions Answer 293909 by stanbon(57387)   on 2011-03-10 21:52:50 (Show Source): You can put this solution on YOUR website!I need to write this equation in standard form. y^2=-3x I know it's a parabola, but do you complete the square to get in standard form? -------------------- x = (-1/3)y^2 is the standard form ======================================== cheers, Stan H.
 Quadratic-relations-and-conic-sections/420795: I need to put this in standard form: x^2+y^2-16=0 I know its a circle. That's about it.1 solutions Answer 293907 by stanbon(57387)   on 2011-03-10 21:51:12 (Show Source): You can put this solution on YOUR website! I need to put this in standard form: x^2+y^2-16=0 I know its a circle. That's about it. --- Standard form: x^2 + y^2 = 16 ================= Cheers, Stan H. ==========
 Linear-equations/420785: i'm having problems with my algebra for the life me i just can not get it like this question here -3 is a solution of - x + 2y = -7 1 solutions Answer 293905 by stanbon(57387)   on 2011-03-10 21:49:37 (Show Source): You can put this solution on YOUR website! -3 is a solution of - x + 2y = -7 ------------------- The solution is an infinite set of ordered pairs. ----- y = (x-7)/2 --- If x = -3, y = (-3-7)/2 = -5 -------------------------------- Cheers, Stan H. ===========
 Linear-systems/420788: I really need help. I have only 1 question. here is is the info. You are driving from Grand Rapids, to Detroit, MI. You leave Grand Rapid at 4:00pm. At 5:10pm you pass through Lansing, MI a distance of 65miles. I have to write a linear equation that gives the distance in miles, d, in terms of time, t. Let t represents the number of the minutes since 4:00pm. Then, what time will you arrive in Detroit if it is 150 miles from Grand Rapidsm MI. Okay, I think: d = 65 miles, and t = 70 minutes. 65 divided by 70 = 0.928 miles per minute. 0.928 x 150 minutes = 2.33 hours (arrival time would be at 6 hours and 33 minutes. Thank you for any help that you can give me. 1 solutions Answer 293904 by stanbon(57387)   on 2011-03-10 21:44:57 (Show Source): You can put this solution on YOUR website!You are driving from Grand Rapids, to Detroit, MI. You leave Grand Rapid at 4:00pm. At 5:10pm you pass through Lansing, MI a distance of 65miles. --- d = rt --- t = 70 min = 7/6 hr d = 65 Rate = 65/(70) miles/min --- distance = 0.928571t I have to write a linear equation that gives the distance in miles, d, in terms of time, t. ------ Let t represents the number of the minutes since 4:00pm. Then, what time will you arrive in Detroit if it is 150 miles from Grand Rapidsm MI. --- 150 = 0.028571t t = 161.54 minutes = (161.54) = (120 + 41.54)min = 2 hr 41.54 min --- time of arrival at Grand Rapids = 6:54 PM =============================== Cheers, Stan H. ========
 Reduction-of-unit-multipliers/420780: Jemma is having an outdoor party for 96 guests.She plans to have enough lemonade so that each guest have 2 1|2 cups.She has a punch bowl that holds 3 gallons.How many times will Jemma have to fill the punch bowl ?1 solutions Answer 293903 by stanbon(57387)   on 2011-03-10 21:28:29 (Show Source): You can put this solution on YOUR website!Jemma is having an outdoor party for 96 guests.She plans to have enough lemonade so that each guest have 2 1|2 cups.She has a punch bowl that holds 3 gallons.How many times will Jemma have to fill the punch bowl ? ------------------------- Amt of lemonade: 96*2.5 = 240 cups --- # of punch bowls full: 240/3 = 80 bowls ========================================== Cheers, Stan H. =================
 Graphs/420761: Make a graph that shows when fahrenheit and celsius meet. I don't know what the x-axis or the y-axis should be. From the functions... *C=(F-32)* 5/9 *F= C* 9/5 + 32 , I solved them and found out that on a graph, -40 is when the celsius and fahrenheit will meet. So, can you help me figure out what the graph would look like? What are the units of the y-axis and x-axis? Would they be in degrees... or what? Thanks! 1 solutions Answer 293902 by stanbon(57387)   on 2011-03-10 21:24:19 (Show Source): You can put this solution on YOUR website!Make a graph that shows when fahrenheit and celsius meet. I don't know what the x-axis or the y-axis should be. From the functions... *C=(F-32)*(5/9) *F= C*(9/5) + 32 ----- y = (5/9)(x-32) y = (9/5)x + 32 ---- ------------------------- Cheers, Stan H. ==================
 Equations/420762: SOLVE FOR N 2N-3=9-N1 solutions Answer 293899 by stanbon(57387)   on 2011-03-10 21:01:11 (Show Source): You can put this solution on YOUR website!SOLVE FOR N 2N-3=9-N 3N = 12 N = 4 ------------------ Cheers, Stan H. =============
 Rational-functions/420759: The domain of the function f(x) =49/15x-12 is all real numbers x except for x where x equals______1 solutions Answer 293898 by stanbon(57387)   on 2011-03-10 20:59:52 (Show Source): You can put this solution on YOUR website!The domain of the function f(x) =49/15x-12 is all real numbers x except for x where x equals 12/15 = 4/5 ==== Cheers, Stan H.