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Recent problems solved by 'stanbon'

stanbon answered: 57156 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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

Rational-functions/203479: 1. Solve by substitution or elimination method: 3x – 2y = 26 -7x + 3y = -49 2. Solve by substitution or elimination method: 4x – 5y = 14 -12x + 15y = -42 3. Solve by substitution or elimination method: -2x + 6y = 19 10x – 30y = -15 Second part of problems: 1. Plot the graph of the equations 2x - 3y = 5 and 4x - 6y = 21 and interpret the result. 2. Plot the graph of the equations 4x - 6y = 12 and x - 5y = 10 and interpret the result. 3. Plot the graph of the equations 8x - 4y = 12 and -4x + 2y = -6 and interpret the result. 1 solutions Answer 153511 by stanbon(57224)   on 2009-07-18 22:19:46 (Show Source): You can put this solution on YOUR website! 1. Solve by substitution or elimination method: 3x – 2y = 26 -7x + 3y = -49 --- Multiply 1st by 3 ; Multiply thru 2nd by 2: 9x - 6y = 78 -14x + 6y = -98 --- Add the two modified equations to solve for "x": -5x = -20 x = 4 --- Substitute into the 1st original equation to solve for "Y": 3*4 - 2y = 26 -2y = 14 y = -7 ================================================= 2. Solve by substitution or elimination method: 4x – 5y = 14 -12x + 15y = -42 --- Multiply thru the 1st equation by 3: 12x -15y = 42 -12x + 15y = -42 --- Add the two equations to get: 0 = 0 --- This means the two equations are really the same. The solution is all points of the form (x,(5/4y + (7/2)) ================================================================== 3. Solve by substitution or elimination method: -2x + 6y = 19 10x – 30y = -15 I'll learve this one to you. =================================== Second part of problems: 1. Plot the graph of the equations 2x - 3y = 5 and 4x - 6y = 21 and interpret the result. Put each equation in slope-intercept form: y = (2/3)x -(5/3) y = (2/3)x -(7/2) --- Plot two points for each equation. Draw a line thru each pair of points to get the graphs of the two lines. ---- There is no solution for the system because the lines are parallel. ==================================================================== Cheers, Stan H. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2. Plot the graph of the equations 4x - 6y = 12 and x - 5y = 10 and interpret the result. 3. Plot the graph of the equations 8x - 4y = 12 and -4x + 2y = -6 and interpret the result.

Linear-systems/203481: I actually attempted the examples in my book but still do not grasp the concept if I can actually get someone to get to break this down for me i might be able to do the rest on my own: y= -3x+19 y= 2x-1 and x+3y=2 -x+y=1 thank you 1 solutions Answer 153508 by stanbon(57224)   on 2009-07-18 21:58:29 (Show Source): You can put this solution on YOUR website! y= -3x+19 y= 2x-1 --- Substitute to get: 2x-1 = -3x+19 5x = 20 x = 4 =================================== and x+3y=2 -x+y=1 --- Add the two equations to get: 4y = 3 y = 3/4 Substitute to solve for "x": -x + (3/4) = 1 -x = 1/4 x = -1/4 ------------------------- Solution: (-1/4,3/4) ====================================== Cheers, Stan H.

Miscellaneous_Word_Problems/203388: Eight pounds of feathers and two ounces of gold together cost $932. Fourteen pounds of feathers and three ounces of gold together cost $1402. What is the cost of five pounds of feathers and five ounces of gold? 1 solutions Answer 153458 by stanbon(57224)   on 2009-07-18 09:20:57 (Show Source): You can put this solution on YOUR website! Eight pounds of feathers and two ounces of gold together cost $932. Fourteen pounds of feathers and three ounces of gold together cost $1402. What is the cost of five pounds of feathers and five ounces of gold? ---------------------- Equations: 8f + 2g = 932 14f + 3g = 1402 ----------------------- Modify: 4f + g = 466 So, g = -4f + 466 ---------------------- Substitute into the 2nd original equation to solve for "f": 14f + 3(-4f+466) = 1402 14f + -12f + 1398 = 1402 2f = 4 f = $2 per pound (price of feathers) ---------------- Since g = -4f + 466 you get g = -4*2 + 466 = $458 per ounce (price of gold) ---------------- What is the cost of five pounds of feathers and five ounces of gold? 5f + 5g = 5*2 + 5*458 = $2300 ===================================== Cheers, Stan H. =====================================

Linear_Equations_And_Systems_Word_Problems/203373: This question is from textbook Five times a number plus 2 equals 4 less than seven times the number. To find this number, denote it by x. (A) write a formula that represents five times x plus 2. (b) write a formula that represents 4 less than seven times x. write an equation that says that the expression in (a) equals the expression in (b). solve this equation. 1 solutions Answer 153443 by stanbon(57224)   on 2009-07-17 22:26:33 (Show Source): You can put this solution on YOUR website! Five times a number plus 2 equals 4 less than seven times the number. To find this number, denote it by x. (A) write a formula that represents five times x plus 2. 5x+2 or 5(x+2) ------------------------------ (b) write a formula that represents 4 less than seven times x. 7x-4 ------------------------------ write an equation that says that the expression in (a) equals the expression in (b). 5x+2 = 7x-2 2x = 4 x = 2 OR 5(x+2)=7x-4 5x+10 = 7x-4 2x = 14 x = 7 ------------------------------- Comment: Your 1st verbal statement can be interpreted in two ways. It is a good example to show you that the English language is not always clear and that parentheses are important when it comes to writing expressions or equations. ------------------------------- Cheers, Stan H. ===============================

Polynomials-and-rational-expressions/203375: this is my last question. How is this? its like the first one. I'm trying to answer it but it makes me confused.. subtract 9x^2y^2-3x^2-5 from the sum of 9x^2y^2+11x^2+5 and 11x^2y^2-6x^2+2 please, help me.. thanks alot 1 solutions Answer 153442 by stanbon(57224)   on 2009-07-17 22:17:03 (Show Source): You can put this solution on YOUR website! subtract 9x^2y^2-3x^2-5 from the sum of 9x^2y^2+11x^2+5 and 11x^2y^2-6x^2+2 ---------------------------- The sum is 20x^2y^2+ 5x^2 + 7 --- After subtracting you get: 11x^2y^2 + 8x^2 +5 ======================================== Cheers, Stan H.

Quadratic_Equations/203369: The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height. 1 solutions Answer 153439 by stanbon(57224)   on 2009-07-17 19:49:56 (Show Source): You can put this solution on YOUR website! The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height. ----------------------- Draw a picture of a rectangle. Label the width as (x+2) meters. Label the height as (x) meters. Lsbel the diagonal as sqrt(6) meters. --------------------------------- Use Pythagoras to solve for "x". x^2 + (x+2)^2 = [sqrt(6)]^2 2x^2 + 4x + 4 = 6 2x^2 + 4x -2 = 0 x^2 + 2x -1 = 0 Use the quadratic formula to solve for "x": x = [-2 +- sqrt(4 -4*1*-1]/2 x = [-2 +- sqrt(8)]/2 x = [-1 +- sqrt(2)] Positive solution: x = sqrt(2) - 1 = 0.414 meters (this is the height of the rectangle) x+2 = 2.414 meters (this is the width of the rectangle) ============================================================ Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/203357: Please help me with this word problem. The equation y= -1777x + 27.153 can be used to predict the number y of the gun death in the United Stats X years after 2000, that is x=0 corresponds to 2000, x=2 corresponds to 2002, x=6 corresponds to 2006, and so on. Predict the number of gun deaths in 2006 and 2007. In what year will the number of gun deaths be 12,937? The predict gun deaths in 2006 will be ? The predict gun deaths in 2007 will be ? The predict number of gun deaths will be 12,937in the year ? Thank you so much!!!! 1 solutions Answer 153438 by stanbon(57224)   on 2009-07-17 19:42:44 (Show Source): You can put this solution on YOUR website! The equation y= -1777x + 27.153 can be used to predict the number y of the gun death in the United Stats X years after 2000, that is x=0 corresponds to 2000, x=2 corresponds to 2002, x=6 corresponds to 2006, and so on. ------------ Predict the number of gun deaths in 2006 and 2007. In what year will the number of gun deaths be 12,937? The predict gun deaths in 2006 will be ? f(6) = -1777*(6) + 27.153 = -10634.847 Comment: That doesn't make any sense. Check your problem statement. Cheers, Stan H. ===================================== The predict gun deaths in 2007 will be ? The predict number of gun deaths will be 12,937in the year ?

Rational-functions/203367: This question is from textbook Rational expressions with different denominators 2x/x^2-9+3x/x^2+4x+3 I am confused on how to find a common denominator. I know for the first one it could be either 3x(x-3) or (x-3)(x+3) for the second denominator i can only think of (x+3)(x+1) i just don't know which denominator is missing what. I apprecate any help you can give me thank you 1 solutions Answer 153435 by stanbon(57224)   on 2009-07-17 19:34:33 (Show Source): You can put this solution on YOUR website! Rational expressions with different denominators 2x/x^2-9 + 3x/x^2+4x+3 ---------------- You have to factor whereever you can so you can see the lcd: --- (2x)/[(x-3)(x+3)] + (3x)/[(x+3)(x+1)] ----- The lcd must contain each unique factor it its hghest power. --- lcd = (x+1)(x+3)(x-3) ---------- Write each fraction over the lcd: --- [(2x)(x+1)]/lcd + [(3x)(x+3)]/lcd -------------------------------- Combine the numerators over the lcd: --- [2x^2 + 2x + 3x^2+ 9x]/lcd --- Simplify: [5x^2 + 11x]/ [(x+1)(x+3)(x-3)] ====================================== Cheers, Stan H.

Linear-systems/203365: Could you please help me out with this problem?? Solve by elimination method 7/2x + 7/3y = 42 1/4x + 1/3y = 4 Thank you very much!! 1 solutions Answer 153434 by stanbon(57224)   on 2009-07-17 19:26:39 (Show Source): You can put this solution on YOUR website! Solve by elimination method 7/2x + 7/3y = 42 1/4x + 1/3y = 4 ------------------------- Multiply thru the 1st by 6; Multiply thru the 2nd by 12 21x + 14y = 252 3x + 4y = 48 ---------------------- Solve the 2nd for "x" x = (-4/3)y + 16 ---------------------- Substitute into the modified 1st equation: 21((-4/3)y + 16) + 14y = 252 -28y + 336 + 14y = 252 -14y = - 84 y = 6 -------------------- Substitute into x = (-4/3)y + 16 to get x = (-24/3)+16 = 8 ------------------------- Ans: (8,6) =========================================== Cheers, Stan H.

Probability-and-statistics/203364: Please help me solve the following question. It is from a former Statistics Question paper of my university and I am unable to find the solution. Question: PART A; It is observed in a student coffee lounge that only 15% students have to wait for more than five minutes to be served. Calculate the following probabilities relating to a random sample of 6 students. 1. The probability that none of the 6 students have to wait for more than five minutes. 2. The probability that fewer than 2 students wait for more than five minutes. 3. The probability that either one or two students wait for more than five minutes. PART B: If we wish to calculate probabilities relating to 100 students a new method is needed. Suggest and explain a suitable methond and explain the term 'Continuity correction.' USE your method to calculate the following; 1. The probability that exactly 15 out of 100 wait for more than 5 minutes. 2. The probability that the number of students waiting for more than 5 minutes lies between 12 and 16. 1 solutions Answer 153433 by stanbon(57224)   on 2009-07-17 19:10:41 (Show Source): You can put this solution on YOUR website! Question: PART A; It is observed in a student coffee lounge that only 15% students have to wait for more than five minutes to be served. Calculate the following probabilities relating to a random sample of 6 students. --------------------------------------------- P(wait more than 5 min) = 0.15 P(wait less than 5 min) = 0.85 --------------------------------------------- 1. The probability that none of the 6 students have to wait for more than five minutes. Ans: (0.85)^6 -------------------------------- 2. The probability that fewer than 2 students wait for more than five minutes. Ans: P(0 -------------------------------- 3. The probability that either one or two students wait for more than five minutes. Ans: P(x = 1 or x = 2)) = 0.5755 ------------------------------------- PART B: If we wish to calculate probabilities relating to 100 students a new method is needed. Suggest and explain a suitable method and explain the term 'Continuity correction.' USE your method to calculate the following; 1. The probability that exactly 15 out of 100 wait for more than 5 minutes. Using the "normal approximation" you calculate the probability that x is between 14.5 and 15.5 using a mean of np = 100*0.15 = 15 and a standard devistion of sqrt(npq)=sqrt(15*0.85) = 3.5707 Ans: P(x=15) is approx normalcdf(14.5,15.5,15,3.5707) = 0.1114 -------------------------------------------------------------------- 2. The probability that the number of students waiting for more than 5 minutes lies between 12 and 16. Ans: normalcdf(11.5,16.5,15,3.5707) = 0.4993 ======================================================= Cheers, Stan H.

Equations/203366: I need help with this algebra problem.. Solve by substitution 3x + 6y = 18 -6x + y = 16 Thank you for any help!!! 1 solutions Answer 153430 by stanbon(57224)   on 2009-07-17 18:35:28 (Show Source): You can put this solution on YOUR website! Solve by substitution 3x + 6y = 18 -6x + y = 16 ----------------------------------------- Solve the 2nd equation for "y": y = 6x+16 --- Substitute into the 1st equation: 3x + 6(6x+16) = 18 3x + 36x + 96 = 18 39x = -78 x = -2 ---------------- Since y = 6x+16, y = 6*-2+16 = 4 ---------------- Ans: (-2,4) ==================================== Cheers, Stan H.

Linear-systems/203361: Please help me finish solving problem. Solve by the substitution method. 4x+3y= -9 x=6-9y ------------ 4(6-9y) +3y= -9 24-54y+3y= -34 Y=? X=? 1 solutions Answer 153428 by stanbon(57224)   on 2009-07-17 18:07:12 (Show Source): You can put this solution on YOUR website! Solve by the substitution method. 4x+3y= -9 x=6-9y ---------- Substitute x = 6-9y into the 1st equation to solve for "y": 4(6-9y) + 3y = -9 24 - 36y + 3y = -9 -33y = -33 y = 1 ------------------- Since x = 6-9y, x = 6 -9*1 = -3 -------------- Ans: (-3,1) ======================================================

Money_Word_Problems/203359: This question is from textbook Hollis is paying off two student loans. One loan charges 7% interest per year. The other loan charges 9% interest per year. He owes $1500 more on the 7% loan than he does on the other. Last year he paid a total of $617 interest. How much does he owe on each loan? 1 solutions Answer 153427 by stanbon(57224)   on 2009-07-17 17:56:29 (Show Source): You can put this solution on YOUR website! Hollis is paying off two student loans. One loan charges 7% interest per year. The other loan charges 9% interest per year. He owes $1500 more on the 7% loan than he does on the other. Last year he paid a total of $617 interest. How much does he owe on each loan? --------------------------------------- Let the two loan amounts be "x" and "y". Equations: Interest: 0.07x + 0.09y = 617 Money owed: x - y = 1500 -------------------------------------- Rearrange: 7x + 9y = 61700 7x - 7y = 7*1500 -------------------------------------- Subtract the 2nd from the 1st to solve for "y": 16y = 51200 y=$3200 (Amt. owed on 9% loan) ---- x = y + 1500 = $4700 (Amt. owed on 7% loan) ================================================ Cheers, Stan H.

Equations/203329: What is the smallest solution of the equation x^4 − 34x^2 + 225 = 0? 1 solutions Answer 153405 by stanbon(57224)   on 2009-07-17 10:09:33 (Show Source): You can put this solution on YOUR website! What is the smallest solution of the equation x^4 − 34x^2 + 225 = 0? I graphed it to find smallest solution is x = -4.644111 ============================== Cheers, Stan H.

Permutations/203330: Six students are being grouped into three pairs to work on a science lab. How many different combinations of three pairs are possible? 1 solutions Answer 153404 by stanbon(57224)   on 2009-07-17 10:01:19 (Show Source): You can put this solution on YOUR website! 6C3 = 5*4 = 20 ==================================== Cheers, Stan H.

Miscellaneous_Word_Problems/203333: Points X, Y and Z lie on the sides of triangle ABC so that segments AX, BY and CZ, if drawn, would intersect at one interior point P. Using 3 of these 7 points at a time as vertices, how many triangles can be formed? 1 solutions Answer 153403 by stanbon(57224)   on 2009-07-17 09:58:17 (Show Source): You can put this solution on YOUR website! ): Points X, Y and Z lie on the sides of triangle ABC so that segments AX, BY and CZ, if drawn, would intersect at one interior point P. Using 3 of these 7 points at a time as vertices, how many triangles can be formed? --------------------- Draw the picture. Three points determine a triangle unless the three are collinear. There are 7C3= 25 sets of three points. 6 of those sets are collinear. Therefore 29 triangles can be formed. =============================================================== Cheers, Stan H.

Probability-and-statistics/203204: A corporate executive officer is attempting to arrange a meeting of his three presidents for tomorrow morning. He believes that each of these three busy individuals, independently has a 60% chance of being able to attend the meeting: a. Find the probability distribution of x, the number of vice presidents who can attend the meeting b. What is the probability that none of the three vice presidents can attend the meeting? c. If the meeting will be held tomorrow morning only if everyone can attend, what is the probability that the meeting will take place at this time? d. How many of the vice presidents should the CEO expect to be available for tomorrow morning’s meeting? 1 solutions Answer 153402 by stanbon(57224)   on 2009-07-17 09:48:47 (Show Source): You can put this solution on YOUR website! A corporate executive officer is attempting to arrange a meeting of his three presidents for tomorrow morning. He believes that each of these three busy individuals, independently has a 60% chance of being able to attend the meeting: a. Find the probability distribution of x, the number of vice presidents who can attend the meeting It's binomial with n=3 and p=0.6 ---------------------------------------------- b. What is the probability that none of the three vice presidents can attend the meeting? P(x=0) = (0.4)^3 ------------------------------------------------ c. If the meeting will be held tomorrow morning only if everyone can attend, what is the probability that the meeting will take place at this time? P(x=3) = (0.6)^3 ------------------------------------------------ d. How many of the vice presidents should the CEO expect to be available for tomorrow morning’s meeting? E(x) = 0*P(x=0) + 1*P(x=1) + 2*P(x=2) + 3*P(x=3) ================================================= Cheers, Stan H.

Expressions-with-variables/203310: Please help me to solve by substitution or elimination method: (1). 3x-2y=26 -7x+3y=-49 (2). 4x-5y=14 -12x+15y=-42 (3). -2x+6y=19 10x-30y=-15 1 solutions Answer 153386 by stanbon(57224)   on 2009-07-16 22:03:22 (Show Source): You can put this solution on YOUR website! Please help me to solve by substitution or elimination method: (1). 3x-2y=26 -7x+3y=-49 --- Multiply 1st equation by 3; Multiply 2nd equation by 2. 9x - 6y = 78 -14x + 6y = -98 -- Add the results to get rid of the y-terms: -5x = -20 x = 4 --- Substitute into one of the equations to solve for "y": 3*4 - 2y = 26 -2y = 14 y = -7 ----------------------------------------------------------- (2). 4x -5y = 14 -12x +15y=-42 --- Multiply thru the 1st by 3: 12x - 15y = 42 --- Add that equation to the 2nd (above) to get: 0 = 0 --- That means the equations are really just one equation. The solution for the "system" is (x,(4/5)x - (14/5)) ========================================================= (3). -2x+6y=19 10x-30y=-15 -------- Multiply thru the 1st equation by 5 to get: -10x + 30y = 95 --- Add that to the 2nd equation to get: 0 = 80 That is a contradiction and means there is no solution. The graphs would be parallel. ==================================================== Cheers, Stan H.

Coordinate-system/203309: 1. How do we write the equation of a horizontal line? What would be an example? 2. How do we write the equation of a vertical line? What would be an example? 3. The points (1, 3), (2, 5), (8, 17), (50, 101), and (1000, 2001) all lie on line M. The points (1, -1), (2, -3), (8, -15), (50, -99), and (1000, -1999) all lie on line N. a. Form the equations of both the lines. Show your work. b. What are the co-ordinates of the point of intersection of lines M and N? c. Write the co-ordinates of the intersections of lines M and N with the x-axis. d. Write the co-ordinates of the intersection of lines M and N with the y-axis. 1 solutions Answer 153382 by stanbon(57224)   on 2009-07-16 21:48:03 (Show Source): You can put this solution on YOUR website! 1. How do we write the equation of a horizontal line? If the line is horizontal all the points have the same y value. Form: y = k --- What would be an example? Ex: y = 8 -------------------------------------------------------------------------------- 2. How do we write the equation of a vertical line? All the points will have the same x value. Form: x = k What would be an example? Ex: x = 4 ============================================================================ 3. The points (1, 3), (2, 5), (8, 17), (50, 101), and (1000, 2001) all lie on line M. The points (1, -1), (2, -3), (8, -15), (50, -99), and (1000, -1999) all lie on line N. a. Form the equations of both the lines. Show your work. b. What are the co-ordinates of the point of intersection of lines M and N? c. Write the co-ordinates of the intersections of lines M and N with the x-axis. d. Write the co-ordinates of the intersection of lines M and N with the y-axis. These four questions were answered yesterday. ==================================================== Cheers, Stan H.

Numbers_Word_Problems/203306: What is the value of the sum –1 + 2 – 3 + 4 – 5 + 6 – 7 +10,000? 1 solutions Answer 153379 by stanbon(57224)   on 2009-07-16 21:13:16 (Show Source): You can put this solution on YOUR website! What is the value of the sum –1 + 2 – 3 + 4 – 5 + 6 – 7 +10,000? ------------ Each successive pair sums to "1" There are 5000 pairs The total sum is 5000 ----------------------------- OR Add the positive terms: 2+4+6+...+10000 S(5000) = (5000/2)(2+10000) = 5000*5001 -------------------------------- Add the negative terms: 1+3+5+...+9999 S(5000) = (5000/2)(1+9999) = 2500*10000 --------------------------------- Subtract the sum of the negatives from the sum of the positives to get: 5000*5001 - 2500*10000 = 5000 =============================================== Cheers, Stan H. ===============================================

Polynomials-and-rational-expressions/203298: Hi I am very confused about all of this: Solve the following: 1. 2x=-3x+9 2. 3x/5=-6 3.y/4+2=7 5.16= -2x/3 6. Find f(1) for f(x) =2x^3-3x^2+x-21 7. Afunction gives the value of C as 2x(22/7)xr . Find C when r=7cm and r=91cm 1 solutions Answer 153376 by stanbon(57224)   on 2009-07-16 20:54:57 (Show Source): You can put this solution on YOUR website! Solve the following: 1. 2x=-3x+9 Add 3x to both sides to get: 5x = 9 Divide both sides by 5 to get: x = 9/5 ====================================== 2. 3x/5=-6 Multiply both sides by 5 to get: 3x = -30 Divide both sides by 3 to get: x = -10 ====================================== 3.y/4+2=7 Subtract 2 from both sides to get: y/4 = 5 Multiply both sides by 4 to get: y = 20 ====================================== 5.16= -2x/3 Multiply both sides by 3 -2x = 48 Divide both sides by -2 to get: x = -24 ====================================== 6. Find f(1) for f(x) =2x^3-3x^2+x-21 f(1) = 2 - 3 + 1 -21 f(1) = -21 ====================================== 7. A function gives the value of C as 2x(22/7)xr . Find C when r=7cm and r=91cm C = 2(22/7)r If r = 7 cm, C = 2*(22/7)*7 = 44 ---- If r = 91 cm, C = 2(22/7)*91 = 2*22*13 = 572 ===================================================== Cheers, Stan H.

Evaluation_Word_Problems/203307: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase in fare of $1. Find the fare that yields the greatest income. 1 solutions Answer 153373 by stanbon(57224)   on 2009-07-16 20:41:27 (Show Source): You can put this solution on YOUR website! A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase in fare of $1. Find the fare that yields the greatest income. ----------------------------------- Income = (fare)(# of passengers) ------------------------------- I(x) = (10 +1x)(300-15x) I(x) = 3000 - 150x + 300x - 15x^2 I(x) = -15x^2 + 150x + 3000 --------------------- Maximum "I" occurs when x = -b/2a = -150/(2*-15) = $5 ---------------------- Fare = (10-x) = $5.00 will give maximum Income. =================================================== Cheers, Stan H.

Human-and-algebraic-language/203302: A plane travels at a speed of 220mph in still air. Flying with a tailwind, the plane is clocked over a distance of 975 miles. Flying against a headwind it takes 1 hour more time to complete the return trip. What was the wind velocity. Round to nearest tenth. 1 solutions Answer 153372 by stanbon(57224)   on 2009-07-16 20:33:00 (Show Source): You can put this solution on YOUR website! A plane travels at a speed of 220mph in still air. Flying with a tailwind, the plane is clocked over a distance of 975 miles. Flying against a headwind it takes 1 hour more time to complete the return trip. What was the wind velocity. Round to nearest tenth. ----------------------------------------- With-the-wind DATA: distance = 975 miles ; rate = (220+w) mph ; time = d/r = 975/(220+w) hrs ------------------------------------------------- Against-the-wind DATA: distance = 975 miles ; rate = (220-w) mph ; time = d/r = 975/(220-w) hrs -------------------------------------------------- Equation: time against - time with = 1 hr 975/(220-w) - 975/(220+w) = 1 --- 975(220+w) - 975(220-w) = (220+w)(220-w) 2(975w) = 220^2 - w^2 w^2 + 1950w - 46450 = 0 Positive solution: w = 24.512 mph (rate of the wind) =========================================== Cheers, Stan H. ===========================================

Travel_Word_Problems/203303: This question is from textbook Mathematics For Technical trades The brightest star in our sky is Sirius, which is 51,700,000,000,000 miles away from earth. The speed of light is approximately 299,329.8 kilometers per second. Determine how long it will take light leaving earth to reach Sirius. round your answer to the nearest tenth of a year. Use 365 days = 1 Year. Here is a story problem we have and I cannot figure this out can you? Thanks janet 1 solutions Answer 153369 by stanbon(57224)   on 2009-07-16 18:57:50 (Show Source): You can put this solution on YOUR website! The brightest star in our sky is Sirius, which is 51,700,000,000,000 miles away from earth. The speed of light is approximately 299,329.8 kilometers per second. Determine how long it will take light leaving earth to reach Sirius. round your answer to the nearest tenth of a year. Use 365 days = 1 Year. --------------------------------- Change the kilometers per second to miles per second by dividing be 1.6 to get 187981.125 miles per second: ---- Divide the distance Sirius is from the earth by 187981.125 to get 276350700.8 seconds --------------- Calculate the number of seconds in a year as follows: 60*60*24*(365) = 31536000 seconds in a year --------------- Divide that bigger number of seconds by the smaller number to get 870.63..years ---------------------- Comment: You should check all these calculations. You need to be accurate ----------------------- Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/203304: Please I need help with word problem! In 1994, the life expectancy of males in a certain country was 61.5 years. In 2001, it was 65.1 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994. The liner function E(t) that fits the date is E(t)=? +? Use th e function to predict the life expectancy of males in 2009. E(15)=? First point (0, 65.1) Second point (7, 65.1) M= 65.1-65.1 ------------------ 0-7 E(t)=0.7-65.1 E(15)=0.5(t)+65.1 E(15)=72.6 Thank you! 1 solutions Answer 153367 by stanbon(57224)   on 2009-07-16 18:28:11 (Show Source): You can put this solution on YOUR website! In 1994, the life expectancy of males in a certain country was 61.5 years. In 2001, it was 65.1 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994. The linear function E(t) that fits the date is E(t)=? +? Use the function to predict the life expectancy of males in 2009. E(15)=? First point (0, 61.5) Second point (7, 65.1) M= (61.5-65.1)/(0-7) = -3.6/-7 = 0.5143 E-intercept = 61.5 E(t) = 0.5143t + 61.5 ------------------ E(15)=0.5143(t)+61.5 E(15)=69.2142 ========================= Cheers, Stan H.

Probability-and-statistics/203268: The New York Times reported (Laurie J. Flynn, “Tax Surfing,” The New York Times, March 25, 2002, C10) that the mean time to download the homepage from the internal revenue service web site www.irs.gov was 0.8 second. Suppose that the download time was normally distributed with a standard deviation of 0.2 second. If you selected at random sample of 30 download times, a) What is the probability that the sample mean is less than 0.75 second? b) What is the probability that the sample mean is between than 0.70 and 0.90 second? c) The probability is 80% that the sample mean is between what two values symmetrically distributed around the population mean? d) The probability is 80% that the sample mean is less than what value? 1 solutions Answer 153366 by stanbon(57224)   on 2009-07-16 18:14:12 (Show Source): You can put this solution on YOUR website! The New York Times, March 25, 2002, C10) that the mean time to download the homepage from the internal revenue service web site www.irs.gov was 0.8 second. Suppose that the download time was normally distributed with a standard deviation of 0.2 second. If you selected at random sample of 30 download times, ------------------------------------------------------ a) What is the probability that the sample mean is less than 0.75 second? Find the z-value of 0.75. z(0.75) = (0.75-0.8)/0.2 = -0.05/0.2 = -0.05/0.2 = -.25 P(x<0.75) = P(z<-0.25) = normalcdf(-100,-0.25) = 0.4013 ----------------------------------------------------------------- b) What is the probability that the sample mean is between than 0.70 and 0.90 second? Find the z-scores of 0.7 and of 0.9 P(0.7 ------------------------------------------ c) The probability is 80% that the sample mean is between what two values symmetrically distributed around the population mean? Find the z-values allociated with 10%ile and 90%ile z for 10%ile is InvNorm(0.1) = -1.2816 z for 90%ile is InvNorm(0.9) = 1.2816 --- Find the corresponding x-values using x = zs + u: x(-1.2816) = -1.2816*0.2 + 0.8 = 0.5437 x(1.2816) = 1.05632 ----------------------------------------------------------- d) The probability is 80% that the sample mean is less than what value? Draw a normal curve and mark the mean position. Put a point at the 80%ile position. Find the z-value of that 80%ile position = InvNorm 0.8416 Find the corresponding x-value: x = 0.8416*0.2 + 0.8 = 0.9683 ================================================================= Cheers, Stan H.

Probability-and-statistics/203231: Need Help with Standard Normal Probabilities Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places. P(Z> - 1.44) = P(Z ≤ - 1.55 = P(0.631 solutions Answer 153347 by stanbon(57224)   on 2009-07-16 09:23:07 (Show Source): You can put this solution on YOUR website! Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places. P(Z> - 1.44) = 0.9251 P(Z ≤ - 1.55 = 0.0606 P(0.63) = 0 ----------- Cheers, Stan H.

Expressions-with-variables/203184: solving systems by the addition method: x+ y = 10 2y=20-2x 1 solutions Answer 153307 by stanbon(57224)   on 2009-07-15 18:11:22 (Show Source): You can put this solution on YOUR website! solving systems by the addition method: x+ y = 10 2y=20-2x ---------------- Rewrite: x + y = 10 y = 10 - x ------------------------ Rearrange: x + y = 10 x + y = 10 ------------------- Obviously, the two equations are the same. ---------------------- Solution: All points of the form (x,10-x) ============================================== Cheers, Stan H.

Geometry_Word_Problems/203194: Do you think that it would be easier or more difficult to visualize solids as compared to objects in one or two-dimensional planes? Are there obvious examples that you can come up with of solids that appear or are being used in our daily lives and the environment that surrounds us? I know that it is very difficult to not be able to see all sides of a solid but I could not think of any examples. Can someone please help me. 1 solutions Answer 153306 by stanbon(57224)   on 2009-07-15 18:06:53 (Show Source): You can put this solution on YOUR website! Do you think that it would be easier or more difficult to visualize solids as compared to objects in one or two-dimensional planes? Are there obvious examples that you can come up with of solids that appear or are being used in our daily lives and the environment that surrounds us? -------------------- Consider the difficulty involved in seeing the back of your head. ------------- Consider trying to see if your brake lights are burned out while you are seated in the driver's seat. ------------- Cheers, Stan H.

Miscellaneous_Word_Problems/203196: Eric bought 300 shares. If he sells them for $4500, he can earn a profit of $1500. Set up an algebraic equation and find the price he paid for a share? (Hint: Assume the price of a share is x dollars) Thank you, Lara Carlson 1 solutions Answer 153305 by stanbon(57224)   on 2009-07-15 18:01:28 (Show Source): You can put this solution on YOUR website! ): Eric bought 300 shares. If he sells them for $4500, he can earn a profit of $1500. Set up an algebraic equation and find the price he paid for a share? ------------------------ Use a proportion: x/1 = (4500-1500)/300 = 3000/300 = 10 x = $10 (price he paid for one share) =========================================== Cheers, Stan H.

Number-Line/203197: Locate 3/5 on a number line 1 solutions Answer 153304 by stanbon(57224)   on 2009-07-15 17:58:45 (Show Source): You can put this solution on YOUR website! Locate 3/5 on a number line ------------------------------------ Draw a line and mark some point "0". Mark a point to the right of it as "1". -------------- Mark off 4 equal segments between 0 and 1. The 3rd marker to the right of 0 is 3/5 ------------------------------------------------- Cheers, Stan H.