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# Recent problems solved by 'stanbon'

stanbon answered: 57889 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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 Polynomials-and-rational-expressions/183081: Could you help me by showing how to divide this polynomial? (3x^3-9x-3)/(3x-3)1 solutions Answer 137458 by stanbon(57962)   on 2009-02-21 21:08:14 (Show Source): You can put this solution on YOUR website!divide this polynomial? (3x^3-9x-3)/(3x-3) ---------------------- Common Factor: [3(x^3-3x-1)] / [3(x-1)] Cancel the common factor of "3": [x^3- 3x -1] / [x-1] ------------------------ Use synthetic division: 1)....1....0....-3....-1 .......1....1....-2...|-3 Quotient: x^2+x-2 Remainder: -3 ========================== Cheers, Stan H.
 Graphs/183082: The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula, or model, I = 700w/H^2, where W = weight, in pound's, and H = height, in inches. Jerome is 75 inches tall. What weights will keep his body mass index between 25 and 33? Jerome's body mass index will fall between 25 and 33 for the set of all weights such that ____< W < ____. (round to the nearest whole number as needed)1 solutions Answer 137453 by stanbon(57962)   on 2009-02-21 20:10:59 (Show Source): You can put this solution on YOUR website!The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. ------------------------------ The body mass index is given by the formula, or model, I = 700w/H^2, where W = weight, in pound's, and H = height, in inches. ------------------------------ Jerome is 75 inches tall. What weights will keep his body mass index between 25 and 33? --- 25 < I < 33 25 < 700w/H^2 < 33 H = 75 so you get: 25 < 700 w/75^2 < 33 25*75^2 < 700 w < 33*75^2 (25*75^2)/700 < w < (33*75^2)/700 200.893 lbs. < weight < 265.179 lbs. ======================================== Stan H. Jerome's body mass index will fall between 25 and 33 for the set of all weights such that ____< W < ____. (round to the nearest whole number as needed)
 Proportions/183008: Darla bicycled at an average rate of 15 miles per hour in a 60 kilometer race. Determine the lenght of time in hours that it took her to complete the race.(hint: 1.6 kilometers= 1 mile) please help1 solutions Answer 137452 by stanbon(57962)   on 2009-02-21 19:59:13 (Show Source): You can put this solution on YOUR website!Darla bicycled at an average rate of 15 miles per hour in a 60 kilometer race. Determine the lenght of time in hours that it took her to complete the race.(hint: 1.6 kilometers= 1 mile) ----------------------------------- DATA: rate = 15 mph = (15*1.6) = 24 km/h ---------------------------------- distance = 60 km ------------------------ time = distance / rate = 60/24 = 2.5 hrs. ================================================ Cheers, Stan H.
 Sequences-and-series/183079: inductive reasoning to determine the next three numbers in the pattern: 3, 12, 26, 45, 1 solutions Answer 137451 by stanbon(57962)   on 2009-02-21 19:45:42 (Show Source): You can put this solution on YOUR website!inductive reasoning to determine the next three numbers in the pattern: 3, 12, 26, 45, ------------ Quadratic function: f(n) = (5/2)n^2 + (3/2)n -1 ----------------- Next three numbers f(5) = 69 f(6) = 98 f(7) = 132 ================ Cheers, Stan H.
 Probability-and-statistics/183061: bob and fred play the following game. Bob rolls a single die. if the result is the number 1,2,3,4,5 bob must pay fred the number of dollars indicated by the number rolled. if a 6 is rolled fred must pay bob \$57 dollars. find freds expectation? 1 solutions Answer 137449 by stanbon(57962)   on 2009-02-21 19:28:43 (Show Source): You can put this solution on YOUR website!bob and fred play the following game. Bob rolls a single die. if the result is the number 1,2,3,4,5 bob must pay fred the number of dollars indicated by the number rolled. if a 6 is rolled fred must pay bob \$57 dollars. find freds expectation? --------------------------------- Random variable values: 1,2,3,4,5,-57 corresponding probabilities are each 1/6 ------------------------------------------- Expected "winnings": (1/6)(1+2+3+4+5-57) = (1/6)(-42) = -\$7.00 =============================================================== Cheers, Stan H.
 Trigonometry-basics/183067: This question is from textbook Find all solutions to the equation. Use a lowercase n to denote an arbitrary integer; separate your answers with commas; use the most compact expressions possible. -sqrt(3) + 2 sin (x) = 0 Any help is greatly appreciated! I am really struggling just to start these problems. I received 4Pi/3 + n*Pi as an answer but the system said it was wrong.1 solutions Answer 137447 by stanbon(57962)   on 2009-02-21 18:45:53 (Show Source): You can put this solution on YOUR website!-sqrt(3) + 2 sin (x) = 0 ------------------- 2sin(x) = sqrt(3) sin(x) = (1/2)sqrt(3) Take the inverse sin to get x = pi/3 or x = (2/3)pi ============================= Cheers, Stan H.
 Vectors/183074: When is it not appropriate to use the Product Rule? Give Examples please. 1 solutions Answer 137446 by stanbon(57962)   on 2009-02-21 18:33:15 (Show Source): You can put this solution on YOUR website!For what? =========================== Cheers, Stan H.
 Trigonometry-basics/183065: This question is from textbook Find all solutions to the equation. Use a lower-case n to denote an arbitrary integer; separate your answers with commas; use the most compact expressions possible. sin(4x - Pi/3) = sqrt(3)/2 Any help is greatly appreciated! I am really struggling just to get these problems started. The answer I received for this one is 2Pi/3 + 3+Pi*n but the system said that answer was wrong.1 solutions Answer 137445 by stanbon(57962)   on 2009-02-21 18:31:52 (Show Source): You can put this solution on YOUR website!sin(4x - Pi/3) = sqrt(3)/2 ------------------------- Take the inverse sin of both sides to get: 4x-(pi/3) = pi/3 4x = (2/3)pi x = (1/6)pi or (5/6)pi ======================== Cheers, Stan H.
 Money_Word_Problems/183070: This question is from textbook College Algebra a Graphing Approach 1.6 #84 Consumre Awareness. The suggested trtail price of a new car is p dollars. The dealership advertised a factory rebate of \$1200 and an 8% discount. a. Write a function R in terms of p giving the cost of the car after receiving the rebate from the factory. b. Write a function S in terms of p giving the cost of the car after receiving the dealership discount. c. Form the composite functions (R o S)(p) and (S o R)(p) and intercept each. d. Find (R o S)(18,400) and (S o R)(18,400. Which yields the lower cost for the car? Explain1 solutions Answer 137444 by stanbon(57962)   on 2009-02-21 18:22:51 (Show Source): You can put this solution on YOUR website!The suggested trtail price of a new car is p dollars. The dealership advertised a factory rebate of \$1200 and an 8% dealership discount. ------------------------------------- a. Write a function R in terms of p giving the cost of the car after receiving the rebate from the factory. --- R(p) = p - 1200 ============================================ b. Write a function S in terms of p giving the cost of the car after receiving the dealership discount. --- S(p) = p - 0.08p = 0.92p ============================================= c. Form the composite functions (R o S)(p) and (S o R)(p) and interpret each. RoS = R[S(p)] = R[0.92p] = (0.92p)-1200 Interpretation: The 8% discount is applied 1st, then the 1200 rebate. -------------------------------------------------- d. Find (R o S)(18,400) and (S o R)(18,400. Which yields the lower cost for the car? Explain --- Don't recognize that notation. ================================== Cheers, Stan H.
 Trigonometry-basics/183068: This question is from textbook Find all solutions to the equation. Use a lower-case n to denote an arbitrary integer; separate your answers with commas; use the most compact expressions possible. (cos(x) - 1) sin(x) = 0 Any help is greatly appreciated! I am really struggling just to start these problems. I received 0 + 2Pi as an answer for this but the system said it was wrong.1 solutions Answer 137440 by stanbon(57962)   on 2009-02-21 18:03:20 (Show Source): You can put this solution on YOUR website!(cos(x) - 1) sin(x) = 0 ------- You are given the factors. One of them must be zero since the product is zero. -------------- cos(x)-1 = 0 or sin(x) = 0 cos(x) = 1 or sin(x) = 0 x = pi/2 or (3/2)pi or x = 0 or pi ======================================= Cheers, Stan H.
 Vectors/183055: Find the point(s) where the tangent to the curve is horizontal for: y=2(x-29)(x+1) 1 solutions Answer 137429 by stanbon(57962)   on 2009-02-21 16:49:27 (Show Source): You can put this solution on YOUR website!Find the point(s) where the tangent to the curve is horizontal for: y=2(x-29)(x+1) --------------------- Take the derivative to get: y' = 2[(x-29)*1 + (x+1)*1] y' = 2[2x-28) --------- Let y' = 0 and solve for x: 2[2x-28]= 0 x = 14 ------------------- The slope is zero when x = 14 ------------------------------ f(14) = 2(14-29)(14+1) = 2(-15)(15) = -450 ================================= Ans: (14,-450) ====================== Cheers, Stan H.
 Square-cubic-other-roots/183053: This question is from textbook Algebra 2 using syntheetic substitution find f(-3) if f(x)=4x^3-3x^2-21 solutions Answer 137428 by stanbon(57962)   on 2009-02-21 16:44:50 (Show Source): You can put this solution on YOUR website!using synthetic substitution find f(-3) if f(x)=4x^3-3x^2-2 ---------------- -3)....4....-3....0....-2 .........4....-15..45...|,,-137 ====================================== f(-3) = -137 ====================================== Cheers, Stan H.
 Probability-and-statistics/183051: the odds aganist muffy beating her friend in a round of golf are 1:8 find the probability muffy will lose?1 solutions Answer 137427 by stanbon(57962)   on 2009-02-21 16:41:07 (Show Source): You can put this solution on YOUR website!the odds aganist muffy beating her friend in a round of golf are 1:8 find the probability muffy will lose? ----------------- odds against A = P(not A)/P(A) --------------------- Your Problem: odds against win = 1:8 = P(not win)/P(win) = [1/9]/[8/9] --- P(not win) = 1/9 ====================== Cheers, Stan H.
 Square-cubic-other-roots/183049: This question is from textbook Algebra 2 write (8.4x10^3)(6.5x10^5) in scientific notation1 solutions Answer 137422 by stanbon(57962)   on 2009-02-21 16:29:41 (Show Source): You can put this solution on YOUR website!write (8.4x10^3)(6.5x10^5) in scientific notation --------------------- = 8.4*6.5 *10^3*10^5 = 54.6 * 10^8 Divide the 54.6 by 10 and multiply the 10^8 by 10 = 5.46*10^9 ------------------ Cheers Stan H. ============ Cheers, Stan H.
 Equations/183045: Solve the equations for x and y or state that there is no solution. 5x - 4y = 2 4x - 5y = -1 1 solutions Answer 137421 by stanbon(57962)   on 2009-02-21 16:26:25 (Show Source): You can put this solution on YOUR website!5x - 4y = 2 4x - 5y = -1 --------------------- Multiply 1st thru by 4 and 2nd thru by 5 to get: --------------- 20x - 16y = 8 20x - 25y = -5 -------------------- Subtract 2nd from 1st to get: 9y = 13 y = 13/9 ------------ Substitute into 4x - 5y = -1 to solve for "x": 4x - 5(13/9) = -1 36x - 65 = -9 36x = 56 x = 14/9 ----------------- x = 14/9 ; y = 13/9 ========================= Cheers, Stan H.
 Probability-and-statistics/183039: a family has 5 children. the probabilty of having a girl is 1/2. what is the probabilty of having 2 girls followed by 3 boys? 1 solutions Answer 137417 by stanbon(57962)   on 2009-02-21 16:17:39 (Show Source): You can put this solution on YOUR website!a family has 5 children. the probabilty of having a girl is 1/2. what is the probabilty of having 2 girls followed by 3 boys? ---------------------- There are 2^5= 32 different boy-girl patterns for a 5 child family. --------- There is only one way to have 2 girls folled by 3 boys --------------------- The probability of having 2 girls followed by 3 boys = 1/32 ====================== Cheers, Stan H.
 Linear-equations/183040: Solve the following by any method: {x = 9/4y + 7 {4x - 9y = 30 Is the system inconsistent, or are the equations dependent, or is the answer an ordered pair?1 solutions Answer 137411 by stanbon(57962)   on 2009-02-21 15:56:00 (Show Source): You can put this solution on YOUR website!Solve the following by any method: {x = 9/4y + 7 {4x - 9y = 30 Is the system inconsistent, or are the equations dependent, or is the answer an ordered pair? ------------------------ Multiply thru the 1st equation by 4 and leave the 2nd equation unchanged. 4x = 9y + 28 4x - 9y = 30 ------------------ Rearrange: 4x - 9y = 28 4x - 9y = 30 ------------------ Subtract: 0 = 2 ---------- No solution; lines parallel; system inconsistent ==================================================== Cheers, Stan H.
 Linear-systems/183032: HELP, I think the answer is no solution. Is that right, if not please show my how to do it. Use elimination to solve each system of equations. X=4Y+8 2X-8Y=-31 solutions Answer 137410 by stanbon(57962)   on 2009-02-21 15:52:47 (Show Source): You can put this solution on YOUR website!Use elimination to solve each system of equations. X=4Y+8 2X-8Y=-3 -------------- Rearrange: x - 4y = 8 2x-8y = -3 --------------- Multiply 1st by 2 to get: 2x - 8y = 16 2x - 8y = -3 ----------------- Subtract to get: 0 = 19 ============== That is a contradiction resulting from assuming the x and the y in one equation is the same as the x and the y in the other equation. Conclusion: There is no solution; the lines are parallel. =========================================================== Cheers, Stan H.
 Graphs/183005: This question is from textbook College Algebra A Graphing Approach 1.6 #48 given f(x) =3/8^2-1 and g(x) = x + 1 find f o g(x). Determine the domain.1 solutions Answer 137408 by stanbon(57962)   on 2009-02-21 15:47:26 (Show Source): You can put this solution on YOUR website! given f(x) =3/x^2-1 and g(x) = x + 1 find f o g(x). Determine the domain. ------------ fog(x) = f[g(x)] = f[x+1] = 3/[(x+1)^2-1] = 3/[x^2+2x+1 - 1] = 3/[x^2+2x] = 3/[x(x+2)] ----------------------- Domain: all Real Numbers except x = 0 and x = -2 ================================== Cheers, Stan H.
 Numeric_Fractions/183022: i belive the answer to 1 over 2(x+h) minus 1 over 2x with both being over h is 2h over h is that correct?1 solutions Answer 137406 by stanbon(57962)   on 2009-02-21 15:43:32 (Show Source): You can put this solution on YOUR website!i believe the answer to 1 over 2(x+h) minus 1 over 2x with both being over h is 2h over h is that correct? ---------------------------------- [1/[2(x+h)] - [1/2x]]/[h] lcd of the numerator is 2x(x+h) = [x/lcd - (x+h)/lcd] / [h] = [(x-x-h)/lcd]/ h = [-h/lcd]/h = -1/lcd = -1/[2x(x+h)] =========================== Cheers, Stan H. ===========================
 Polynomials-and-rational-expressions/183030: This question is from textbook College Algebra Help with Find all rational zeros of the polynomial (using synthetic division) 22. p(x)= What I did: multiples of 1= +-1 multiples of 4= +-1 +-4 +-2 possible zeros: +-1 +-4 +-2 (after dividing constant over leading coeficient) I used synthetic division to test which are zeros. +1 worked, +4 did not, +2 using the quotient of +1 (1 -1 -4 4) did not work gave me remainder of 8, but when I used the original coeficients (1 -2 -3 8 -4)it gave me a zero. I was told by my professor that either way it should work. Any information is much appreciated, have at test coming up. Thank you 1 solutions Answer 137400 by stanbon(57962)   on 2009-02-21 15:13:18 (Show Source): You can put this solution on YOUR website!Find all rational zeros of the polynomial (using synthetic division) 22. p(x)= What I did: multiples of 1= +-1 multiples of 4= +-1 +-4 +-2 possible zeros: +-1 +-4 +-2 (after dividing constant over leading coeficient) I used synthetic division to test which are zeros. +1 worked, +4 did not, +2 using the quotient of +1 (1 -1 -4 4) did not work gave me remainder of 8, but when I used the original coeficients (1 -2 -3 8 -4)it gave me a zero. I was told by my professor that either way it should work. --------------------------------------------------- Since the coefficients add up to zero, x = 1 is a zero. 1)....1....-2....-3....8....-4 .......1....-1....-4...4..|..0 Since the quotient coefficients add up to zero. x = 1 is AGAIN a zero. 1)....1....-1....-4....4 .......1.....0....-4...|..0 Now you have a quadratic which says x^2-4 = 0 Factor to get (x-2)(x+2)=0 x = 2 or x = -2 ------------------------- The 4 zeros are 1,1,2,-2 ============================ Cheers, Stan H.
 Linear-equations/183029: This question is from textbook Introductory Algebra Graph the equation and identify the y-intercept y=x+3 Thank you for your time. 1 solutions Answer 137399 by stanbon(57962)   on 2009-02-21 15:02:07 (Show Source): You can put this solution on YOUR website!Graph the equation and identify the y-intercept y=x+3 ------------------------- To graph the equation you need two points: Let x = 0, then y = 3; point (0,3) Let y = 0; then x = -3; point (-3,0) ----------------- Plot the tow points and draw a line thru them. The y-intercept is (0,3) ============================= ============================= Cheers, Stan H.
 Quadratic-relations-and-conic-sections/183003: I am having trouble finding the vertex of parabolas. I need to find the axes, roots, and the vertices of the 3 following questions. Can you please show it to me in the completing the square method. The questions are y=2x^2-x+6 y=x^2-8x+2 y=4x^2-x+1 Thanks in advance.1 solutions Answer 137379 by stanbon(57962)   on 2009-02-21 12:28:15 (Show Source): You can put this solution on YOUR website!I need to find the axes, roots, and the vertices of the 3 following questions. Can you please show it to me in the completing the square method. The questions are y=2x^2-x+6 2x^2 - x + ? = y-6+? 2(x^2 - (1/2)x + (1/4)^2 = y - 6 + 2(1/4)^2 2(x- (1/4))^2 = y - (48/8) + (1/8) 2(x-(1/4)^2 = y - (47/8) (x - (1/4)^2 = (1/2)(y -(47/8)) ------------------------------------ Vertex: (1/4 , (-47/8)) vertical axis: x = 1/4 Roots: No Real roots Use Quadratic formula to find the complex roots. ----------------------------------- y=x^2-8x+2 x^2 - 8x = y-2 x^2 - 8x + 16 = y -2 + 16 (x-4)^2 = y + 14 ---------------------- Vertex: (4 , -14) vertecal axis: x = 4 Roots: Use the quadratic formula. --------------------------- y=4x^2-x+1 4x^2 - x = y - 1 4(x^2 - (1/4)x + (1/8)^2) = y - 1 + 4*(1/8)^2 4(x - (1/8))^2 = y - 15/16 (x-(1/8))^2 = (1/4)(y - 15/16) ---- Vertex: (1/8 , 15/16) vertical axis: x = 1/8 Roots: Use the Quadratic formula ===================================== Cheers, Stan H.
 Quadratic_Equations/183004: This is my last question and I really need some help! Please I thank you. 8. The platform of the Taj Mahal in India is a rectangular prism. It is 95 m long,95 mwide and 7 m high. Find the surface area of the platform.1 solutions Answer 137377 by stanbon(57962)   on 2009-02-21 12:01:52 (Show Source): You can put this solution on YOUR website!The platform of the Taj Mahal in India is a rectangular prism. It is 95 m long,95 mwide and 7 m high. Find the surface area of the platform. ---------------------- That depends on whether you include the base area and the top area. Total surface area = side + side + side + side + base + top = 4(95*7) + 2(95)^2 = 2660 + 18050 = 20710 ============= Cheers, Stan H.
 Systems-of-equations/183002: This question is from textbook Intermediate Algebra Hello, I need help Please with the following problem. Solve the system: 2x + y + Z + w = 3 x - 2y - z + w = -3 x - y - 2z - w = -3 x + y - z + 2w = 4 I have tried adding 1 & 2 getting 3x - y + 2w = 0 Then taking 1 & multiplying it by 2 and then adding it to 3 and getting 5x+y=w=3 Then taking 4 & mutliplying it by -2 then adding it to 1 getting 3x+2y+3w=1 Then I am stuck because I don't know what to do next. I know I have to get rid of the same 2 variables. Any help would be greatly appreciated. Thanks, Jen 1 solutions Answer 137375 by stanbon(57962)   on 2009-02-21 11:56:43 (Show Source): You can put this solution on YOUR website!2x + y + Z + w = 3 x - 2y - z + w = -3 x - y - 2z - w = -3 x + y - z + 2w = 4 ----------------------- Interchange 1st and 2nd to get: x - 2y - z + w = -3 2x + y + Z + w = 3 x - y - 2z - w = -3 x + y - z + 2w = 4 ---------------------- Subtract two times the 1st equation from the 2nd; subtract the 1st equation from the 3rd; subtract the 1st equation from the 4th equation to get: x - 2y - z + w = -3 0 + 5y + 3Z - w = 9 0 + y - z - 2w = 0 0 + 3y + 0 + w = 7 --------------------------- Interchange the 2nd equation and the 3rd equation to get: x - 2y - z + w = -3 0 + y - z - 2w = 0 0 + 5y + 3Z - w = 9 0 + 3y + 0 + w = 7 ---------------------------- Subtract 5 times the 2nd equation from the 3rd ; subtract 3 times the 2nd equation from the 4th to get: x - 2y - z + w = -3 0 + y - z - 2w = 0 0 + 0 + 8Z + 9w = 9 0 + 0 + +3z + 7w = 7 ------------------------ Solve 3rd and 4th as a systme: 8Z + 9w = 9 3z + 7w = 7 ----------------- Multiply 1st equation by 3 and the 2nd equation by 8 to get: 24z + 27w = 27 24z + 56w = 56 ------------------- Subtract the 1st equation from the 2nd equation to get: 29w = 29 w = 1 --- Substitute to solve for "z": 3z + 56 = 56 z = 0 ---------------- Substitute those values in the following equations to solve for x and for y. x - 2y - z + w = -3 0 + y - z - 2w = 0 ------------------------- x -2y - 0 + 1 = -3 0 + y - 0 - 2 = 0 ------------------------ x-2y = -4 y = 2 ------------ Therefore x - 2*2 = -4 x = 0 ================== Ans: x = 0 ; y = 2 ; z = 0 ; w = 1 ==================================== Cheers, Stan H.
 Equations/182995: 5. The sum of the page numbers on facing pages of a book is 157; what are the page numbers?1 solutions Answer 137374 by stanbon(57962)   on 2009-02-21 11:16:56 (Show Source): You can put this solution on YOUR website!The sum of the page numbers on facing pages of a book is 157; what are the page numbers? ----------------- Those would be consecutive page numbers. ------------ Equation: x + (x+1) = 157 2x = 156 x = 78 (1st page) x+1 = 79 (next page) ========================== Cheers, Stan H.
 absolute-value/182991: A.) |2x + 2| = 14 x= B.) |x| = 6 x= C.) -5|x + 1| = -10, the isolated absolute value equation would be |x + 1| = -15. I think its true...can you help me out? D.) 2|x + 4| = 8, the isolated absolute value equation would be |x + 4| = 4. I think its false...What do you think? E.)|x – 2| + 10 = 12 X= F.)|2x + 6| - 4 = 20 x = G.)6 – 3|2x + 6| = 0 X= H.) Solve for x. 10 - |x + 2| = 12 I.) Solve for x. -5|x + 1| = -10 1 solutions Answer 137372 by stanbon(57962)   on 2009-02-21 11:08:28 (Show Source): You can put this solution on YOUR website!A.) |2x + 2| = 14 2x+2 = 14 or 2x+2 = -14 x+1 = 7 or x+1 = -7 x = 6 or x = -8 ------------------------- B.) |x| = 6 x=6 or x = -6 ------------------------- C.) -5|x + 1| = -10 |x+1| = 2 x+1 = 2 or x+1 = -2 x = 1 or x = -3 -------------------------- D.) 2|x + 4| = 8 |x+4| = 4 x+4 = 4 or x+4=-4 x = 0 or x = -8 ----------------------------- E.)|x – 2| + 10 = 12 |x-2| = 2 x-2= 2 or x-2=-2 x = 4 or x = 0 -------------------------- F.)|2x + 6| - 4 = 20 |2x+6| = 24 2x+6 = 24 or 2x+6 = -24 2x = 18 or 2x = -30 x = 9 or x = -15 -------------------------- G.)6 – 3|2x + 6| = 0 3|2x+6| = 6 2x + 6 = 2 or 2x+6 = -2 2x = -4 or 2x = -8 x = -2 or x = -4 ------------------------- H.) 10 - |x + 2| = 12 |x+2} = -2 No solution as absolute cannot equal a negative value. ========================================================== I.) -5|x + 1| = -10 |x+1| = 2 x+1 = 2 or x+1 = -2 x = 1 or x = -3 ====================== Cheers, Stan H.
 Probability-and-statistics/182826: High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels), or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase Noise level climb cruise descent row total low 6 2 6 14 medium 18 3 8 29 high 1 3 14 18 col total 25 8 28 611 solutions Answer 137371 by stanbon(57962)   on 2009-02-21 10:31:14 (Show Source): You can put this solution on YOUR website!High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels), or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase Noise level climb cruise descent row total low 6 2 6 14 medium 18 3 8 29 high 1 3 14 18 col total 25 8 28 61 ------------------------- Ho: row and column factors are independent Ha: they are dependent ---- I ran a Chi-Sq. Test on the 3 by 3 array of data. Test Statistic: Chi-Sq. = 15.160 p-value: 0.004 df: (3-1)(3-1) = 4 ------- Conclusion: Since p-value is less than 5%, Reject Ho. The row and column factors are dependent. ============================================= Cheers, Stan H.
 Probability-and-statistics/182969: In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p? 1 solutions Answer 137360 by stanbon(57962)   on 2009-02-21 07:17:15 (Show Source): You can put this solution on YOUR website! In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. ----- p-hat = 1143/86991 = 0.013 -- E = 1.96*sqrt[0.013*0.087/86991] = 2.89x10^-7 ---------------- 95% CI: 0.013-2.89x10^-7 < p < 0.013+2.89x10^7 ---------------- (b) Why is the normality assumption not a problem, despite the very small value of p? I'll leave that to you. Cheers, Stan H.
 Miscellaneous_Word_Problems/182945: In north high school the ratio of the number of women teachers to men teachers is 11 to 10 if the average age of the women is 34 and the average age of the men is 32 detemine the average age in years of all the teachers1 solutions Answer 137350 by stanbon(57962)   on 2009-02-20 22:10:35 (Show Source): You can put this solution on YOUR website! In north high school the ratio of the number of women teachers to men teachers is 11 to 10 if the average age of the women is 34 and the average age of the men is 32 detemine the average age in years of all the teachers ------------------------------------ # of women = 11x # of men = 10x ----------------------- Total years of women = 34*11x = 374x yrs. Total years of men = 32*10x = 320x yrs. ----------------------------- Average age of all teachers: (374x + 320x)/(11x+10x) = 694x/21x = 33.048 years =============================================================================== Cheers, Stan H.
 Linear-equations/182952: The perimeter of a rectangle is 112 inches. The length exceeds the width by 8 inches. Find the length and the width. The length is ________ inches. (type an intreger or decimal.) The width is ________ inches. (type an intreger or decimal)1 solutions Answer 137349 by stanbon(57962)   on 2009-02-20 22:04:36 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 112 inches. The length exceeds the width by 8 inches. Find the length and the width. ---------------------------------------- Perimeter = 2(L + W) 112 = 2((x+8) + x) 56 = 2x + 8 2x = 48 x = 24 in (width of the rectangle) x+8 = 32 in (length of the rectangle) ========================================= Cheers, Stan H.