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Recent problems solved by 'stanbon'

stanbon answered: 57214 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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Equations/100545: separate the number 78 into three parts so that the second part is twice the first part and the third part is 6 more than the first part 1 solutions Answer 73196 by stanbon(57282)   on 2007-09-26 10:34:17 (Show Source): You can put this solution on YOUR website! separate the number 78 into three parts so that the second part is twice the first part and the third part is 6 more than the first part -------------- Let the 1st part be "x" Then 2nd part is "2x" And 3rd part is "x+6" -------------- EQUATION: x + 2x + x+6 = 78 4x+6=78 x = 72/4= 18 (1st part) 2x = 36 (2nd part) x+6 = 24 (3rd part) =========== Cheers, Stan H.

Numeric_Fractions/100544: Please help me to answer this question. True or False. Explain your answer. The inequality x/x-3 > 2 is equivalent to x > 2x – 6. Thank you for your help. 1 solutions Answer 73195 by stanbon(57282)   on 2007-09-26 10:30:13 (Show Source): You can put this solution on YOUR website! False They have different domains because of the denominator in the 1st inequality. ======== Cheers, Stan H.

Probability-and-statistics/99790: a Bank has 2 tellers. customers arriving at the bank vary between 1 and 6 per minute. Each teller services 1 person per minute. What is the length of the waiting line after 5 minutes? How long will a customer wait if they arrive on the 10th minute How many times will the waiting time be reduced to zero What is the average number of people waiting in line over the 20mins 1 solutions Answer 73194 by stanbon(57282)   on 2007-09-26 10:28:25 (Show Source): You can put this solution on YOUR website! a Bank has 2 tellers. customers arriving at the bank vary between 1 and 6 per minute. Each teller services 1 person per minute. What is the length of the waiting line after 5 minutes? How long will a customer wait if they arrive on the 10th minute How many times will the waiting time be reduced to zero What is the average number of people waiting in line over the 20mins ------------- Average arrival time is (1+6)/2 = 3.5 minutes Average service time is 2*1min = 2 per minute -------------- Question: Do you have any formulas relating ave. arrival and ave. service? --------- Comment: I could see doing this with a minute by minute chart but there must be some formulas. Right!? =================== Cheers, Stan H.

Matrices-and-determiminant/100470: This question is from textbook During the 2003-2004 NBA season, Dirk Nowitzki of the Dallas Mavericks made a total of 976 shots and scored 1680 points. His shots consisted of 3-point field goals than free throws. Use an inverse matrix to find how many of each type of shot he made. 1 solutions Answer 73192 by stanbon(57282)   on 2007-09-26 10:14:04 (Show Source): You can put this solution on YOUR website! Your posting is missing information. Need to state how the number of 3-pointers, 2-pointers, and free throws relate so equations can be generated. Cheers, Stan H.

Matrices-and-determiminant/100491: heres my question Is solving systems by substitution, elimination or cramers rule which is easiest my teacher said we can use any of the three on an up coming test to solve only for 2 variables i'm not real proficient at any yet. and I want to focus on one skill / formula / to get thru this exam which one can you explain briefly (he can't) I'm frustrated because 1.) he dosent teach it out of the book and goes to quicklyin class to learn. Can you help me with a simple format I can understand THANK YOU jackie 1 solutions Answer 73191 by stanbon(57282)   on 2007-09-26 10:11:16 (Show Source): You can put this solution on YOUR website! substitution, elimination or cramers rule which is easiest --------- Try not to dispair. Anyone of these methods will get you the answer. Cramer is easy if you have a calculator and know how to use it. Substitution is a bit messy if the equations are complicated. Elimination is messy if the coefficients of x and y are big numbers or decimals or fractions. --------------- Try to look at material which is going to be presented before it is presented. That way you will have some small understanding to build on. Try also to hook up with someone who understands the math---a fellow student or worker or tutor to resolve your difficulty. ----------- Cheers, Stan H.

Numeric_Fractions/100540: Please help me with this question. Find two positive real numbers that differ by 1 and have a product of 1. Thank you 1 solutions Answer 73189 by stanbon(57282)   on 2007-09-26 09:57:51 (Show Source): You can put this solution on YOUR website! Find two positive real numbers that differ by 1 and have a product of 1 --------- 1st: x-y=1 2nd: xy=1 ---------- 1st: x = y+1 Substitute into 2nd to get: (y+1)y=1 y^2+y-1=0 y = [-1 +- sqrt(1 - 4*-1)]/2 y = [-1 +- sqrt(5)]/2 Positive answer: y = [-1+sqrt(5)]/2 = 0.618 ---------- Substitute into 2nd to get: x = 1/y = 0.618^-1 = 1.618 ============== Cheers, stan H.

Linear-systems/100541: This question is from textbook I have made many attempts to answer this equation and cannot come up with the answer - please help. The problem is -2(x-b)-(5a-x)=a+b 1 solutions Answer 73187 by stanbon(57282)   on 2007-09-26 09:52:32 (Show Source): You can put this solution on YOUR website! -2(x-b)-(5a-x)=a+b -2x+2b-5a+x = a+b -x = 6a-b x = b-6a ========= Cheers, Stan H.

Average/100539: If set A consists of three positive integers a, b, and c such that a< b< c, which of the following operations could not affect the median of set A? A) increasing the value of a B) increasing the value of b C) decreasing the value of b D) increasing the value of c E) decreasing the value of c 1 solutions Answer 73186 by stanbon(57282)   on 2007-09-26 09:50:29 (Show Source): You can put this solution on YOUR website! increasing c because the order of the elements would not change. -------- Cheers, Stan H.

Radicals/100479: Let x(1) and x(2) be the real solutions to the equation x^2-sqrt(11)x+2=0 Then the sum x(1)+x(2) is equal to ? I have the answer, but have no idea how to get to it. I think the two solutions are: 1/2(-sqrt(2) + sqrt(11); converted to decimals: 0.951206 and 1/2 (sqrt(2) + sqrt(11); converted to decimals: 2.3654 So x(1)+x(2) = 3.316627 How to work this out? Squaring? (How?), Factoring (How?) 1 solutions Answer 73185 by stanbon(57282)   on 2007-09-26 09:42:17 (Show Source): You can put this solution on YOUR website! x^2-sqrt(11)x+2=0 Use the quadratic formula to get: x = [sqrt(11) +- sqrt(11-4*2)]/2 x = [sqrt(11) +- sqrt(3)]/2 x1 = [sqrt(11) + sqrt(3)]/2 x2 = [sqrt(11) - sqrt(3)]/2 --------- x1+x2 = sqrt(11) ============== Cheers, Stan H.

Exponents/100527: how to slove -9 exponet 0? 1 solutions Answer 73184 by stanbon(57282)   on 2007-09-26 09:33:24 (Show Source): You can put this solution on YOUR website! Your question has two possible answers: (-9)^0 = 1 -9^0 = -1 ============== Parentheses make a difference ================ Cheers, Stan H.

Quadratic_Equations/100530: Science and Medicine. The equation h = -16t^2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft. 1 solutions Answer 73183 by stanbon(57282)   on 2007-09-26 09:31:01 (Show Source): You can put this solution on YOUR website! The equation h(t) = -16t^2 + 112t gives the height of an arrow, shot upward from te ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180ft. ------------ EQUATION: -16t^2+112t= 180 -16t^2+112t-180 = 0 -4t^2+28t-45=0 t = [-28 +- sqrt(28^2-4*-4*-45)]/-8 t = [-28 +- sqrt(64)]/-8 t = [-28 +- 8]/-8 Positive answer: t = [-36/-8] or t=[-20/-8] t = 4.5 seconds or t=2.5 seconds The 2.5 is the time on the way up; the 4.5 is the time on the way down. =========== Cheers, Stan H. -------------------

Average/100534: If set A consists of three positive integers, a,b and c such that a< b< c, which of the following operations could not affect the median of set A. 1 solutions Answer 73179 by stanbon(57282)   on 2007-09-26 09:21:10 (Show Source): You can put this solution on YOUR website! I think you left something out of your posting. Cheers, Stan H.

Quadratic_Equations/100528: I am guessing this is a quadratic equation. (x+y-z)(x-y+z) How do I solve it? What is the name of this equation? What are the steps to solve it? I am an exchange student in Japan and I don't understand completly when the teacher is teaching. Thank you very much. 1 solutions Answer 73178 by stanbon(57282)   on 2007-09-26 09:18:05 (Show Source): You can put this solution on YOUR website! (x+y-z)(x-y+z) Put it in the form (a+b)(a-b) =(x+(y-z))(x-(y-z)) = (x^2 - (y-z)^2) ---------------- That might be the answer you want, or you may want to expand it to: =x^2-(y^2-2yz+z^2) =x^2-y^2-z^2+2yz ===================== Enjoy your stay. ===================== Cheers, Stan H.

Probability-and-statistics/100533: There are 5 nickels, 3 dimes, and 2 quarters. What is the probability of selecting 1 nickel, 1 dime, and 1 quarter in any order with replacement? 1 solutions Answer 73177 by stanbon(57282)   on 2007-09-26 09:12:43 (Show Source): You can put this solution on YOUR website! There are 5 nickels, 3 dimes, and 2 quarters. What is the probability of selecting 1 nickel, 1 dime, and 1 quarter in any order with replacement? ---------------- "With replacement" makes all your selections independent. P(nickel)=5/10= 1/2 P(dime)=3/10 P(quarter)=2/10= 1/5 -------------- So, Prob(nickel dime quarter in any order) = 3!(30/1000) = 6(3/100)= 0.18 ------------ Cheers, Stan H.

Linear-equations/100529: I've worked these problems over and over and can't seem to find the proper answer. 1. Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible. (-1, 3) and (4, -2) I got m = - 2 - (-3)/4 - (- 1 = -5/5 = -1 m = -1, (x1 – y1)= (-1, 3) y - 3 = -1 (x -(-1)) y = -x + 1 + 3 y = -x + 4 Is this right??? 2. 1. Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible. (-2, -3) and (2, 0) I got m = 0 - (-3)/2-(-2) = 3/4 m = 3/4, (x1, x2) = (-2, -3) y - (-3) = 3/4 (x-(-2) y = 3/4x + 2 - 3 y = 3/4 x -1 I know the answer is supposed to be y = 3/4 x - 3/2, but I can't get it... What am I doing wrong??? 1 solutions Answer 73175 by stanbon(57282)   on 2007-09-26 08:56:18 (Show Source): You can put this solution on YOUR website! 1. Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible. (-1, 3) and (4, -2) I got m = [- 2 - (3)]/[4 - (- 1)] = -5/5 = -1 That is correct. ---------- You know the form of the line is y=mx+b You know m=-1, and y=3 when x=-1, so substitute into the form and solve for "b". 3 = -1*-1+b b=2 --------- Therefore the equation is y = -x + 2 ======================= 2. 1. Write the equation of the line passing through each of the given pairs of points. Write your result in slope-intercept form, where possible. (-2, -3) and (2, 0) I got m = [0 - (-3)]/[2-(-2)] = 3/4 That is correct. ------------ m = 3/4, (x1, x2) = (-2, -3) y - (-3) = (3/4) (x-(-2)) y + 3 = (3/4)x + (3/4)2 y + 3 = (3/4)x + (3/2) y = (3/4)x +(3/2)-3 y = (3/4)x - (3/2) ------------------------- Cheers, Stan H. ================== I know the answer is supposed to be y = 3/4 x - 3/2, but I can't get it... What am I doing wrong???

Coordinate-system/100429: In which quadrant does P(x,y) lie? 1 solutions Answer 73103 by stanbon(57282)   on 2007-09-25 19:42:11 (Show Source): You can put this solution on YOUR website! There is no way to answer that without more information. Cheers, Stan H.

Distributive-associative-commutative-properties/100425: I NEED TO KNOW THE ANSWER TO THIS 1*87=87 AND3(6A)-(3*6) AND 2B+0=2B 1 solutions Answer 73102 by stanbon(57282)   on 2007-09-25 19:39:19 (Show Source): You can put this solution on YOUR website! 1*87=87 because "1" is the multiplicative identity. ----------------------- AND3(6A)-(3*6)A because of the associative pricipal of multiplication. ---------------------------------- AND 2B+0=2B because "0" is the additive identity. ---------------- Cheers, Stan H.

Equations/100419: I don't understand how to solve this equation: (2a^2b^3)^2 1 solutions Answer 73098 by stanbon(57282)   on 2007-09-25 19:29:57 (Show Source): You can put this solution on YOUR website! (2a^2b^3)^2 = 4a^4 b^6 ============= Cheers, Stan H.

Equations/100414: -3(y-1)=9 1 solutions Answer 73094 by stanbon(57282)   on 2007-09-25 19:14:33 (Show Source): You can put this solution on YOUR website! -3(y-1)=9 y-1 = -3 y = -2 =================== Cheers, Stan H.

Inequalities/100402: Please help me solve this problem by identifing the inequality represented by the sentence: When a number is divided by 3, and the quotient is increased by 5, the result is more than 2. 1 solutions Answer 73089 by stanbon(57282)   on 2007-09-25 19:07:51 (Show Source): You can put this solution on YOUR website! identifing the inequality represented by the sentence: When a number is divided by 3, and the quotient is increased by 5, the result is more than 2. ---------- Let "the number" be x. ---------------- INEQUALITY: (x/3) + 5 > 2 --------------- Cheers, Stan H.

Radicals/100331: In the coordinate plane, the points F(-2,1), G(1,4), and H(4,1) lie on a circle with center P. What are the coordinates of point P? Choices: (A) (0,0) (B) (1,1) (C) (1,2) (D) (1,-2) (E) (2.5, 2.5) Please show me how to solve this equation. Thank You very much! 1 solutions Answer 73080 by stanbon(57282)   on 2007-09-25 17:55:20 (Show Source): You can put this solution on YOUR website! In the coordinate plane, the points F(-2,1), G(1,4), and H(4,1) lie on a circle with center P. What are the coordinates of point P? ---------------- Procedure: Find the equation of the perpendicular-bisector of line segment FG. Find the equation of the perpendicular-bisector of line segment GH. ----------- Find the intersection of those two equations. That is the center of the circle. ------------ Cheers, Stan H.

Angles/100346: find the measure of each angle- m of angle 11 = 4x m of angle 12 = 2x-6 (there's a picture of two lines intersecting) 1 solutions Answer 73079 by stanbon(57282)   on 2007-09-25 17:46:23 (Show Source): You can put this solution on YOUR website! find the measure of each angle- m of angle 11 = 4x m of angle 12 = 2x-6 (there's a picture of two lines intersecting) --------------- The angles are vertical angles. ---------------------- Since they are vertical angles they are equal. EQUATION: 4x = 2x-6 2x=-6 x=-3, so angle 11 = 4x = -12 ----------- Comment: That does not make any sense; I am sure you do not have a picture having a negative angle. --------------------- Are you sure the angles are vertical? Cheers, stan H. Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/75231: If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers? 1 solutions Answer 73078 by stanbon(57282)   on 2007-09-25 17:43:54 (Show Source): You can put this solution on YOUR website! If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers? ---------------------- Let x and x+1 be the consecutive integers. EQUATION: (3/5)(x+1) -(1/2)x = -3 Multiply thru by 10 to get: 6(x+1) - 5x = -30 6x+6-5x = -30 x = -36 (1st integer) x+1= -35 (next consecutive integer) ============== Cheers, stan H.

Angles/100348: the complement of an angle is five times the measure of the angle itself. find the angle and its complement. 1 solutions Answer 73076 by stanbon(57282)   on 2007-09-25 17:35:24 (Show Source): You can put this solution on YOUR website! the complement of an angle is five times the measure of the angle itself. find the angle and its complement. --------------- Let the angle be x; then its complement = "90-x". EQUATION: 90-x = 5x 6x = 90 x = 15 (the angle) 90-x = 75 (the complement) ============= Cheers, Stan H.

Equations/100347: This question is from textbook Pre-Alg What is y+3y+8y+2 and I got to show my work. 1 solutions Answer 73075 by stanbon(57282)   on 2007-09-25 17:32:31 (Show Source): You can put this solution on YOUR website! What is y+3y+8y+2 = 12y + 2 =============== Cheers, Stan H.

Inverses/100336: I kind of understand how to do these f◦g and g◦f problems, but I dont know how to do this one because the fraction throws me off. Please help me!!! Thank you!!!! The problem is: For and , show that f ◦ g ( x ) = x and g ◦ f ( x) = x. 1 solutions Answer 73074 by stanbon(57282)   on 2007-09-25 17:31:01 (Show Source): You can put this solution on YOUR website! f(x)=2x+1 and g(x)=(x-1)/2 show that f ◦ g ( x ) = x and g ◦ f ( x) = x. -------------- fog(x)= f[g(x)] = f[(x-1)/2] = 2[(x-1)/2]+1 = (x-1)+1 = x --------- gof(x) = g[f(x)] = g[2x+1] = ((2x+1)-1)/2 = 2x/2 = x ============== Cheers, Stan H.

Coordinate-system/100344: This question is from textbook cpm Complete the table below for the equation y=2x-1 and draw a graph. b)Estimate the x-value snd corresponding to y=2 c)find the x intercept. d)find the y intercept. 1 solutions Answer 73073 by stanbon(57282)   on 2007-09-25 17:23:11 (Show Source): You can put this solution on YOUR website! Complete the table below for the equation y=2x-1 and draw a graph. b)Estimate the x-value snd corresponding to y=2 2= 2x-1; 2x = 3; x =3/2 ----------------------- c)find the x intercept. If y=0, 2x-1=0 ; x = 1/2 is the x-intercept ------------------------ d)find the y intercept. If x=0, y = -1 is the y-intercept =============== Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/100342: Find two consecutive odd intergers whose sum is 176. 1 solutions Answer 73070 by stanbon(57282)   on 2007-09-25 17:18:06 (Show Source): You can put this solution on YOUR website! Find two consecutive odd intergers whose sum is 176. 1st odd integer : 2x+1 2nd odd integer ; 2x+3 --------------- EQUATION: 2x+1+2x+3 = 176 4x+4= 176 4x = 172 x = 43 2x+1 = 87 (1st odd integer) 2x+3 = 89 (2nd odd integer) =============== Cheers, Stan H.

Inverses/100338: I have no idea how to solve this problem: If y is inversely proportional to the square of x, and y=1 when x=4, find y when x=8. 1 solutions Answer 73069 by stanbon(57282)   on 2007-09-25 17:13:48 (Show Source): You can put this solution on YOUR website! If y is inversely proportional to the square of x y = k/x^2 ------- and y=1 when x=4 1 = k/4^2 k= 16 ------------------- find y when x=8. y = 16/x^2 y = 16/8^2 y = 1/4 ============ Cheers, Stan H.

Probability-and-statistics/99789: If i drive through 3 sets of traffic lights and the probablity of any one being green is 0.3 and the probability of one not being green is 0.7 how do i find what the probability of all being green and the probability that at least one light will not be green? Also how do i calculate the theoretical probability that all three sets of lights will be green. 1 solutions Answer 73057 by stanbon(57282)   on 2007-09-25 16:18:15 (Show Source): You can put this solution on YOUR website! If i drive through 3 sets of traffic lights and the probablity of any one being green is 0.3 and the probability of one not being green is 0.7 -------------------------------------- how do i find what the probability of all being green? = 0.3^3 = 0.027 --------------------- and the probability that at least one light will not be green? = 1 - P(all are green) = 1-0.027 = 0.973 ----------------------- Also how do i calculate the theoretical probability that all three sets of lights will be green. You multiply 0.3*0.3*0.3 to get 0,027 ============== Cheers, Stan H.

Linear-systems/100310: This is my question... Answer the following information about this line: y = 2x-3 m=_______ b=_______ Find the x or y for the following points on the above line: (0,__) , (___, 0) , (1,___0 , (____, 9) I am clueless how to anwser this...HELP!!!!!! 1 solutions Answer 73049 by stanbon(57282)   on 2007-09-25 15:31:39 (Show Source): You can put this solution on YOUR website! Answer the following information about this line: y = 2x-3 m=2______ b=-3_______ Find the x or y for the following points on the above line: (0,-3__) , (3/2___, 0) , (1,-1___) , (6____, 9) ------------------ Cheers, Stan H.