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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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Geometry_Word_Problems/339367: The measure of one angle of a triangle is three times the measure of the smallest angle, and the measure of the last angle is equal to the sum of the other two angles. Find the measure of the greatest angle of the triangle. 1 solutions Answer 243200 by stanbon(57967)   on 2010-09-06 07:37:13 (Show Source): You can put this solution on YOUR website! The measure of one angle of a triangle is three times the measure of the smallest angle, and the measure of the last angle is equal to the sum of the other two angles. Find the measure of the greatest angle of the triangle. ------------- Let "z" be the smallest angle: x = 3z y = x+z x+y+z = 180 ---- Substitute and solve for "x": x + (x+z) + (1/3)x = 180 x + x + (1/3)x + (1/3)x = 180 2x + (2/3)x = 180 6x + 2x = 540 8x = 540 x = 67.5 degrees z = 67.5/3 = 22.5 degrees --- y = x+z = 90 degrees ========================== Cheers, Stan H.

test/339359: help me, please... can you tell me an example for algebra operation, thats equal 2 tribe.. i'm sorry if my english was so bad, because i'm an indonesian thanks for your answer 1 solutions Answer 243197 by stanbon(57967)   on 2010-09-06 07:22:53 (Show Source): You can put this solution on YOUR website! can you tell me an example for algebra operation, thats equal 2 tribe.. ---- What do you mean by "2 tribe.." Can you give an example? =================================== Cheers, Stan H.

Quadratic_Equations/339353: It is desired to draw off a part of 10 gallons of 30% solution of alcohol and to replace it by pure alcohol so as to produce a 50% solution. How many gallons should be drawn off. 1 solutions Answer 243195 by stanbon(57967)   on 2010-09-06 07:19:33 (Show Source): You can put this solution on YOUR website! It is desired to draw off a part of 10 gallons of 30% solution of alcohol and to replace it by pure alcohol so as to produce a 50% solution. How many gallons should be drawn off. --------------------- Equation: alcohol - alcohol + alcohol = alcohol 0.30*10 - 0.30x + 1.00x = 0.50(10) Multiply thru by 100 to get: 30*10 - 30x + 100x = 50*10 70x = 20*10 x = 3/10 gallon (amt. of 30% liquid to be replaced by pure alcohol) ============== Cheers, Stan H.

Geometry_Word_Problems/339369: what rectangle have a perimeter of 52cm if both length and width are whole number? 1 solutions Answer 243194 by stanbon(57967)   on 2010-09-06 07:10:12 (Show Source): You can put this solution on YOUR website! what rectangle have a perimeter of 52cm if both length and width are whole number? ------------ Perimeter = 2(length + width) 52 = 2(L + W) 26 = L+W If L = 1, W = 25 If L = 2, W = 24 If L = 3, W = 23 etc. Cheers, Stan H.

Miscellaneous_Word_Problems/339370: Bessy has 6 times as much money as Bob, but when each earns $6, Bessy will have 3 times as much money as Bob. How much does each have before and after earning the $6? 1 solutions Answer 243193 by stanbon(57967)   on 2010-09-06 07:07:07 (Show Source): You can put this solution on YOUR website! Bessy has 6 times as much money as Bob, but when each earns $6, Bessy will have 3 times as much money as Bob. How much does each have before and after earning the $6? ------------- Equations: Bes = 6*Bo (Bes + 6) = 3(Bo+6) --- Substitute for Bes and solve for Bo. --- (6Bo + 6) = 3Bo+18 3Bo = 12 Bo = $4 (amt Bob has before earning $6; $10 after earning $6) ---------------- Bes = 6Bo = 6(4) = $24 (amt Bes has before ; she has $30 after earning $6) ================================= Cheers, Stan H.

Radicals/339277: Solve and check. √(27-3x)=x-3 1 solutions Answer 243167 by stanbon(57967)   on 2010-09-05 21:29:22 (Show Source): You can put this solution on YOUR website! Solve and check. √(27-3x)=x-3 ------------------ Square both sides to get: 27-3x = x^2-6x+9 x^2 -3x - 18 = 0 (x-6)(x+3) = 0 x = 6 or x = -3 ---- Checking in sqrt(27-3x) = x-3 Check x = 6 ? sqrt(27-18) = 6-3 sqrt(9) = 3 3 = 3 True ---------------- Check x = -3 sqrt((27+9) = -3-3 sqrt(36) = -6 6 = -6 False ----- Final solution: x = 6 ============================== Cheers, stan H.

logarithm/339276: express as a sum of logarithims I need some hep on this problem, I don't understand. Thank you in advance. 1 solutions Answer 243166 by stanbon(57967)   on 2010-09-05 21:24:19 (Show Source): You can put this solution on YOUR website! express as a sum of logarithims ------------------- = log4(7) + log4(x) ====================== Cheers, Stan H.

Angles/339275: solve. (y^2-5y)^2-20(y^2-5y)-96=0 1 solutions Answer 243165 by stanbon(57967)   on 2010-09-05 21:22:47 (Show Source): You can put this solution on YOUR website! solve. (y^2-5y)^2-20(y^2-5y)-96=0 --------------------------------- [(y^2-5y)-24][(y^2-5y)-4] = 0 ---- y^2-5y = 24 or y^2-5y=4 ---- y^2-5y-24 = 0 or y^2-5y-4 = 0 (y-8)(y+3)=0 or y = [5+-sqrt(25+16)]/2 y = 8 or y = -3 or y = [5+-sqrt(41)]/2 ====================================================== Cheers, Stan H.

Miscellaneous_Word_Problems/339271: Three times the complement of an angle is 18 more than its supplement. Find the angle 1 solutions Answer 243164 by stanbon(57967)   on 2010-09-05 21:17:41 (Show Source): You can put this solution on YOUR website! Three times the complement of an angle is 18 more than its supplement. Find the angle ----------------- Let the angle be "x". Its supplement is "180-x". Its complement is "90-x". ---------------------------------- Equation: 3(90-x) = 180-x+18 270-3x = 198-x 72 = 2x x = 36 degrees. =================== Cheers, Stan H.

Numbers_Word_Problems/339269: one number is 10 times larger than another. the difference of their reciprocal is 1. what are the 2 numbers? 1 solutions Answer 243163 by stanbon(57967)   on 2010-09-05 21:14:48 (Show Source): You can put this solution on YOUR website! one number is 10 times larger than another. the difference of their reciprocal is 1. what are the 2 numbers? ----------------- Let the numbers be x and y. Equations: x = y + 10 ----- 1/x - 1/y = 1 ------------------------ Substitute for "x" and solve for "y": 1/(y+10) - (1/y) = 1 Multiply thru by y(y+10) to get: y - (y+10) = y(y+10) 10 = y^2+10y --- y^2+10y-10 = 0 y = [-10 +- sqrt(100-4*-10)]/2 y = [-10 +- sqrt(140)]/2 y = [-10 +-2sqrt(35)]/2 y = [-5 +- sqrt(35)] --- Substitute for "y" and solve for "x": x = y+10 x = 5+-sqrt(35) ======================= Cheers, Stan H.

Quadratic_Equations/339268: • When solving a linear inequality, do you always need to solve for y? Why or why not? 1 solutions Answer 243162 by stanbon(57967)   on 2010-09-05 21:07:50 (Show Source): You can put this solution on YOUR website! When solving a linear inequality, do you always need to solve for y? Why or why not? --- No. It often makes the problem easier to solve and/or to graph. But you don't always have to solve for "y". ==================== Cheers, Stan H.

Quadratic_Equations/339264: • What are the necessary and sufficient conditions for inequalities to represent an area in the first quadrant? 1 solutions Answer 243160 by stanbon(57967)   on 2010-09-05 21:02:57 (Show Source): You can put this solution on YOUR website! What are the necessary and sufficient conditions for inequalities to represent an area in the first quadrant? x>0; y>0 ============== Cheers, Stan H.

Angles/339253: Solve for x. 1+ 10 over x + 26 over x^2 = 0 i could not write this out so i had to spell it out, i hope you can understand this. 1 solutions Answer 243159 by stanbon(57967)   on 2010-09-05 21:01:35 (Show Source): You can put this solution on YOUR website! 1+ 10 over x + 26 over x^2 = 0 ------ 1 + (10/x) + (26/x^2) = 0 ------- Multiply thru by x^2 to get: x^2 + 10x + 26 = 0 x = [-10 +- sqrt(100-4*26)]/2 ---- x = [-10 +- sqrt(-4)]/2 x = [-10 +- 2i]/2 ---- x = -5+i or x = -5-i ========================== Cheers, Stan H.

Systems-of-equations/339260: please factor compeletly. x^2+24x+144 1 solutions Answer 243158 by stanbon(57967)   on 2010-09-05 20:57:28 (Show Source): You can put this solution on YOUR website! please factor compeletly. x^2+24x+144 ---- (x+12)^2 ============ Cheers, Stan H.

Polynomials-and-rational-expressions/339255: Find the value of 4x^3 + 3x^2 for x= -2 1 solutions Answer 243157 by stanbon(57967)   on 2010-09-05 20:56:22 (Show Source): You can put this solution on YOUR website! Find the value of 4x^3 + 3x^2 for x= -2 ----- 4(-2)^3 + 3(-2)^2 = 4*(-8) + 3(4) --- = -32+12 = -20 ============= Cheers, Stan H.

Systems-of-equations/339258: find the largest common factor. y(y+7)-2(y+7) 1 solutions Answer 243156 by stanbon(57967)   on 2010-09-05 20:54:14 (Show Source): You can put this solution on YOUR website! find the largest common factor. y(y+7)-2(y+7) = (y+7)(y-2) ================= Cheers, Stan H.

Systems-of-equations/339256: factor completely. 5x^3+15x^2-20x 1 solutions Answer 243154 by stanbon(57967)   on 2010-09-05 20:52:02 (Show Source): You can put this solution on YOUR website! factor completely. 5x^3+15x^2-20x ------- = 5x(x^2+3x-4) --- = 5x(x+4)(x-1) ==================== Cheers, Stan H.

logarithm/339244: evaluate the exponential equation of three positive values of x, three negative values of x , and at x=0. show your work. plot the graph using the ordered pairs. state the equation of the line asymptotic to the graph. thank you in advance.. 1 solutions Answer 243151 by stanbon(57967)   on 2010-09-05 20:49:47 (Show Source): You can put this solution on YOUR website! evaluate the exponential equation of three positive values of x, three negative values of x , and at x=0. ------ y = 5^(x+3) If x = -3, y = 5^0 = 1, giving you point (-3,1) If x = -2, y = 5^1 = 5, giving you point (-2,5) If x = -1, y = 5^2 = 25,giving you point (-1,25) ------- If x = 0, y = 5^3 = 125, giving you point (0,125) If x = 1, y = 5^4 If x = 2, y = 5^6 If x = 3, y = 5^7 --------------------------------------------------------- show your work. plot the graph using the ordered pairs. --------------------------------------------------------- state the equation of the line asymptotic to the graph. y = 0 ----------------------------------------------------- Cheers, Stan H. --------------

Distributive-associative-commutative-properties/339245: i need help with inequalities 1 solutions Answer 243144 by stanbon(57967)   on 2010-09-05 20:38:40 (Show Source): You can put this solution on YOUR website! Post a couple of your problems. Cheers, Stan H.

Miscellaneous_Word_Problems/339239: A basketball player has a 70% free throw shooting average, which can be interpreted to mean that the probability of his hitting any single free throw is 0.7 or 7/10. Assume that free throws are independent events, so that what happens on one free throw doesn't affect the outcome of the next. What is the probability that in shooting five free throws he hist at least one? 1 solutions Answer 243141 by stanbon(57967)   on 2010-09-05 20:37:38 (Show Source): You can put this solution on YOUR website! A basketball player has a 70% free throw shooting average, which can be interpreted to mean that the probability of his hitting any single free throw is 0.7 or 7/10. Assume that free throws are independent events, so that what happens on one free throw doesn't affect the outcome of the next. What is the probability that in shooting five free throws he hits at least one? ----- P(hits at least one) = 1 - P(misses all five) = 1 - 0.3^5 = 1 - 0.0024 = 0.9976 ================ Cheers, Stan H. ================

logarithm/339240: Use a calculator to find an approximation to the nearest ten-thousandth. I could use some help with this problem please. Thank you in advance. 1 solutions Answer 243131 by stanbon(57967)   on 2010-09-05 20:28:24 (Show Source): You can put this solution on YOUR website! 10^e = 10^2.718281828459.... = 522.7353.. --------------- Cheers, Stan H.

Signed-numbers/339121: A number is six times another number. When the numbers are added, their sum is 49. What are the numbers? 1 solutions Answer 243065 by stanbon(57967)   on 2010-09-05 13:31:28 (Show Source): You can put this solution on YOUR website! A number is six times another number. When the numbers are added, their sum is 49. What are the numbers? ----------------- Let the numbers be x and y. --- x = 6y x + y = 49 --------------- Substitute for "x" and solve for "y": 6y+y=49 7y = 49 y = 7 --- Since x = 6y, x = 42 ------------------------ The numbers are 7 and 42 =========================== Cheers, Stan H.

Numbers_Word_Problems/339120: Bailey is thinking of a number. Nine more than four times the number is the same as fifteen less than twice the number. What is the number? 1 solutions Answer 243063 by stanbon(57967)   on 2010-09-05 13:28:26 (Show Source): You can put this solution on YOUR website! Bailey is thinking of a number. Nine more than four times the number is the same as fifteen less than twice the number. What is the number? --- Let the number be "x". Equation: 4x+9 = 2x-15 --- 2x = -24 x = -12 ============= Cheers, Stan H.

Probability-and-statistics/339056: If a clever history teacher gives a quiz on the first day of class and asks students to write 10 historical events in order of occurrence, what is the probability that a student wil do this correctly(without prior knowledge)? 1 solutions Answer 243062 by stanbon(57967)   on 2010-09-05 13:26:47 (Show Source): You can put this solution on YOUR website! If a clever history teacher gives a quiz on the first day of class and asks students to write 10 historical events in order of occurrence, what is the probability that a student wil do this correctly(without prior knowledge)? ----------- There are 10! arrangements. --- Probability of getting the correct arrangement = 1/10! ========================================================= Cheers, Stan H.

Probability-and-statistics/339119: there are eight balloons in a box 6 green and 2 red. what is the probability that you pick a red 1 solutions Answer 243061 by stanbon(57967)   on 2010-09-05 13:22:34 (Show Source): You can put this solution on YOUR website! there are eight balloons in a box 6 green and 2 red. what is the probability that you pick a red --------------- Ans: 2/8 = 1/4 ================== Cheers, Stan H.

Exponents/339046: 8^n/3 = 1/4 then what is the value of n^n ? a -4 b -1/2 c - 1/4 d 1/4 e 1/2 1 solutions Answer 243042 by stanbon(57967)   on 2010-09-05 09:52:27 (Show Source): You can put this solution on YOUR website! 8^n/3 = 1/4 then what is the value of n^n ? --------------------- Raise both sides to the 3rd power to get: 8^n = 1/64 --- 8^n = 8^-2 --- n = -2 --- Then (n^n) = (-2)^(-2) = 4^-1 = 1/4 ========================================= Cheers, Stan H. ============ a -4 b -1/2 c - 1/4 d 1/4 e 1/2

expressions/339053: If 2-x(1/x + 2) =19-4x then x = (A)-3 (B)3 (C)4 (D)5 (E)9 The answer is E but i am getting 3. Thanks 1 solutions Answer 243040 by stanbon(57967)   on 2010-09-05 09:46:51 (Show Source): You can put this solution on YOUR website! If 2-x(1/x + 2) =19-4x then x = ? ------------------- Using the distributive law you get: 2-x(1/x)-x(2) = 19-4x ----------- 2-1-2x = 19-4x 1-2x = 19-4x Add 4x to each side Subtract 1 from each side 2x = 18 x = 9 =================== Cheers, Stan H. =================== (A)-3 (B)3 (C)4 (D)5 (E)9

Quadratic_Equations/339048: If x = 2 is one solution of x^2 + 8x - c = 0, then the other solution is… (A)20 (B) 10 (C) - 2 (D) - 10 (E) - 20 1 solutions Answer 243039 by stanbon(57967)   on 2010-09-05 09:43:44 (Show Source): You can put this solution on YOUR website! If x = 2 is one solution of x^2 + 8x - c = 0, then the other solution is… (A)20 (B) 10 (C) - 2 (D) - 10 (E) - 20 ------------------ Use synthetic division: 2)....1....8....-c .......1....10...|..-c+20 Solve -c+20 = 0 c = 20 ----- Now solve x^2+8x-20 = 0 Factor: (x+10)(x-2)=0 x = -10 or x = 2 ================== Cheers, Stan H.

Trigonometry-basics/339049: subtract straght down to see the answer y=2/5x-7 y=2/5x+4 1 solutions Answer 243037 by stanbon(57967)   on 2010-09-05 09:38:14 (Show Source): You can put this solution on YOUR website! subtract straght down to see the answer y=2/5x-7 y=2/5x+4 -------------- 0 = 0 -11 0 = -11 ----- That is a contradiction. It tells you the "y" and the "x" in the two equations never have the same defined value. That tells you the lines are parallel; they do not share an (x,y) point. ===================================== Cheers, Stan H.

Average/339050: how can i find out what average is? 1 solutions Answer 243035 by stanbon(57967)   on 2010-09-05 09:34:36 (Show Source): You can put this solution on YOUR website! how can i find out what average is? --------- You could Google "average". --- The average of a set of numbers is the sum of the numbers divided by the number of numbers in the set. --- {1, 5, 7, 13} The average is (1+5+7+13)/4 = 26/4 = 6.5 ============== Cheers, Stan H.

Distributive-associative-commutative-properties/339052: i need help to solve the commutative or distrbutive to find equivalent expression for the following: (x+y)x + (x+y)y 1 solutions Answer 243034 by stanbon(57967)   on 2010-09-05 09:30:49 (Show Source): You can put this solution on YOUR website! (x+y)x + (x+y)y --- Using the distributive law you get: = x^2+xy + xy+y^2 Combine "like" terms: = x^2+2xy+y^2 Factor = (x+y)(x+y) --------------------------- OR (x+y)x+(x+y)y The common factor is (x+y): = (x+y)(x+y) ==================== Cheers, Stan H.