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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>Next

 Linear-systems/371700: when we graph the inequality 4x-3y greater than or equal to 0 why can't we use (0,0) as a test point? if we test the point (6,-5), do we obtain a false statement or a true one?1 solutions Answer 264753 by stanbon(57250)   on 2010-11-15 21:10:42 (Show Source): You can put this solution on YOUR website!when we graph the inequality 4x-3y greater than or equal to 0 why can't we use (0,0) as a test point? if we test the point (6,-5), do we obtain a false statement or a true one? ---- That inequality simplifies to: 4x-3y >=0 y <= (4/3)x -------- The boundary of the inequality is y = (4/3)x ---- (0,0) is on the boundary line. It satisfies the equality but cannot be used to test the inequality because it is on the boundary line. You have to use a test point that is not on the boundary. ------------------ Using (6,-5) you get -5 < (4/3)(6) -5 < 8 That is true so the half-plane containing (6,-5) is the solution set for the inequality. ============================================== Cheers, Stan H. ========
 Divisibility_and_Prime_Numbers/371695: Translate the following phrase into an algebraic expression: “One ninth of the difference of a number and fourteen 1 solutions Answer 264748 by stanbon(57250)   on 2010-11-15 21:01:10 (Show Source): You can put this solution on YOUR website!Translate the following phrase into an algebraic expression: “One ninth of the difference of a number and fourteen". --- (1/9)(x-14) ================= Cheers, Stan H. ==========
 Polynomials-and-rational-expressions/371685: factor 12r^2 - 4r - 51 solutions Answer 264742 by stanbon(57250)   on 2010-11-15 20:58:04 (Show Source): You can put this solution on YOUR website!factor 12r^2 - 4r - 5 ---- 12r^2 -10r+6r -5 --- Factor: 2r(6r-5)+6r-5 --- Factor: (6r-5)(2r+1) ================ Cheers, Stan H.
 Probability-and-statistics/371603: JOhn is taking a true/false quiz. There are 6 questions. How many ways can the quiz be answered?1 solutions Answer 264737 by stanbon(57250)   on 2010-11-15 20:51:18 (Show Source): You can put this solution on YOUR website!JOhn is taking a true/false quiz. There are 6 questions. How many ways can the quiz be answered? ------- Each of the 6 questions can be answered in 2 ways. --- Ans: 2^6 = 64 ways ======================= Cheers, Stan H.
 Quadratic_Equations/371648: Factor completely: x^2 - 2x + y^2 + 2y - 2xy - 151 solutions Answer 264714 by stanbon(57250)   on 2010-11-15 20:06:12 (Show Source): You can put this solution on YOUR website!Factor completely: x^2 - 2x + y^2 + 2y - 2xy - 15 ------------------------- Rearrange: x^2-2xy+y^2 -2(x-y) - 15 --------------------- (x-y)^2 -2(x-y) - 15 This is a quadratic with variable (x-y) Factor: [(x-y)-5][(x-y)+3] ===================== Cheers, Stan H.
 Expressions-with-variables/371647: what is the answer to the following equation using the substitution: x=3y-1, x+2y=9 please show work!!1 solutions Answer 264705 by stanbon(57250)   on 2010-11-15 19:50:41 (Show Source): You can put this solution on YOUR website!): what is the answer to the following equation using the substitution: x=3y-1, x+2y=9 ---- Substitute for "x" and solve for "y": 3y-1 + 2y = 9 5y =10 y = 2 ------------- Since x = 3y-1, x = 3*2-1 = 5 --------------------- Cheers, Stan H.
 Age_Word_Problems/371633: Jack is 5 years older than his sister Mary. The sum of their ages is 37. How old is Jack. Show your work.1 solutions Answer 264701 by stanbon(57250)   on 2010-11-15 19:47:54 (Show Source): You can put this solution on YOUR website!Jack is 5 years older than his sister Mary. The sum of their ages is 37. How old is Jack. Show your work. ------------------- Equations: j = m+5 j+m = 37 ----- Substitute for "j" and solve for "m": m+5 + m = 37 2m = 32 m = 16 (Mary's age now) ------ Since j = m+5, j = 21 (Jack's age now) ========== Cheers, Stan H.
 Probability-and-statistics/371621: If the hypothesis test is conducted using α = .025, this means that: a. there is a 2.5% chance that the null hypothesis is true b. there is 2.5% chance of committing a Type I error and 97.5% chance of committing a Type II error c. there is a 0.25% chance that the null hypothesis is true d. there is a maximum 2.5% chance that a false null hypothesis will be rejected e. there is a maximum 2.5% chance that a true null hypothesis will be rejected 1 solutions Answer 264693 by stanbon(57250)   on 2010-11-15 19:39:20 (Show Source): You can put this solution on YOUR website!If the hypothesis test is conducted using α = .025, this means that: a. there is a 2.5% chance that the null hypothesis is true b. there is 2.5% chance of committing a Type I error and 97.5% chance of committing a Type II error c. there is a 0.25% chance that the null hypothesis is true d. there is a maximum 2.5% chance that a false null hypothesis will be rejected e. there is a maximum 2.5% chance that a true null hypothesis will be rejected ------ Ans: b Cheers, Stan H.
 Square-cubic-other-roots/371624: What is i^101?1 solutions Answer 264687 by stanbon(57250)   on 2010-11-15 19:31:39 (Show Source): You can put this solution on YOUR website!What is i^101? ----- 101 = 4*25+1 ---- i^(101) = i^(4*25+1) = (i^4)^25 * i = 1^25*i = 1*i = i ============================= Cheers, Stan H.
 Functions/371623: find the domain of the function f(x)=3x+41 solutions Answer 264683 by stanbon(57250)   on 2010-11-15 19:29:18 (Show Source): You can put this solution on YOUR website!find the domain of the function f(x)=3x+4 ---- Domain: All Real Numbers Cheers, Stan H.
 Numeric_Fractions/371610: I have to put these fractions in order from greatest to least: 2 2/3, 2 6/11, 2 5/9, 2 1/2 Not sure how to do it. Do I need to find the LCD and if so how do I figure it out?1 solutions Answer 264682 by stanbon(57250)   on 2010-11-15 19:26:10 (Show Source): You can put this solution on YOUR website!I have to put these fractions in order from greatest to least: 2 2/3, 2 6/11, 2 5/9, 2 1/2 Not sure how to do it. Do I need to find the LCD and if so how do I figure it out? ------------ Yes, find the LCD, then reformulate each number. LCD of 3,11,9,2 --- LCD = 2*9*11 = 198 ---- 2 = 396/198 --- 2 6/11 = 28/11 = (2*9*28)/198 = 504/198 --- 2 5/9 = 23/9 = (2*11*23)/198 = 506/198 --- 2 1/2 = 5/2 = (9*11*5)/198 = 495/198 ======================================== Cheers, Stan H. ========================================
 Expressions-with-variables/371616: -1=3+4x1 solutions Answer 264677 by stanbon(57250)   on 2010-11-15 19:14:15 (Show Source): You can put this solution on YOUR website!-1=3+4x ---- 4x = -4 x = -1 ============ Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/371613: if twice an integer is the same as one-third of six times that integer, what is the integer1 solutions Answer 264676 by stanbon(57250)   on 2010-11-15 19:12:43 (Show Source): You can put this solution on YOUR website!if twice an integer is the same as one-third of six times that integer, what is the integer? ------ Equation: 2x = (1/3)(6x) 2x = 2x --- X could be any integer. ============================== Cheers, Stan H.
 Quadratic_Equations/371345: how do i find the completion of squares for the equation y2-5y+6=01 solutions Answer 264557 by stanbon(57250)   on 2010-11-15 13:36:21 (Show Source): You can put this solution on YOUR website!how do i find the completion of squares for the equation y^2-5y+6=0 ---- y^2-5y+? = -6+? ----- Complete the square: y^2-5y+(5/2)^2 = -6+(5/2)^2 --- Factor the left side: (y-(5/2))^2 = (-24/4)+(25/4) ------ (y-(5/2))^2 = = 1/4 --- y-(5/2) = 1/2 or y-(5/2) = -1/2 ---- y = 3 or y = 2 =============================== Cheers, Stan H.
 Miscellaneous_Word_Problems/371335: A train left a railroad station in N.Y. at 9:00 AM bound for Washington, D.C. traveling at a uniform speed. At 10:30 AM another train left the same station bound for Washington D.C. (on a different track) averaging 20 mph more than the first train and passed the first train 180 miles from N.Y. Find the speed of each train. 1 solutions Answer 264528 by stanbon(57250)   on 2010-11-15 12:16:49 (Show Source): You can put this solution on YOUR website!A train left a railroad station in N.Y. at 9:00 AM bound for Washington, D.C. traveling at a uniform speed. At 10:30 AM another train left the same station bound for Washington D.C. (on a different track) averaging 20 mph more than the first train and passed the first train 180 miles from N.Y. Find the speed of each train. ----- 1st train DATA: distance = 180 mi ; time = x hrs ; rate = 180/x mph --- 2nd train DATA: distance = 180 mi ; time = (x-(3/2)) hrs ; rate = 180/(x-(3/2)) mph ---- Equation: 2nd train rate - 1st train rate = 20 mph 180/(x-(3/2)) - 180/x = 20 ----- 2/(2x-3) - 1/x = 1/9 ----- Multiply thru by 9x(2x-3) to get: 18x - 9(2x-3) = x(2x-3) 27 = 2x^2-3x 2x^2 - 3x - 27 = 0 --- x = 4.5 hrs --- 1st train rate = 180/4.5 = 40 mph --- 2nd train rate = 180/(4.5-1.5) = 180/3 = 60 mph ====================== Cheers, Stan H.
 Functions/371329: 1. Determine the constant of variation for the direct variation given. R varies directly with S. When S is 16, R is 80. 1/5 5 16 2 Tomar's paycheck varies directly with the hours he works. When Tomar works 5 hours, he gets paid \$60.00. How much does Tomar make in 8 hours? \$75 \$80 \$96 \$120 3. Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____. equal to zero less than 2 equal to 6 greater than 11 4. Determine the constant of variation for the direct variation given. (0, 0), (3, 12), (9, 36) 3 4 12 5. Select all of the following that are a direct variation. Songs are 99 cents each to download. Tickets for rides at the fair are \$1 each. Arcade games are 50 cents or \$1. To go tubing it is \$5 to rent the tube and \$7 for each hour. 6. Determine the constant of variation for the direct variation given. Fat calories varies directly with the grams of fat. There are 27 calories for each 3 grams of fat. 1/9 3 91 solutions Answer 264526 by stanbon(57250)   on 2010-11-15 12:03:33 (Show Source): You can put this solution on YOUR website!1. Determine the constant of variation for the direct variation given. R varies directly with S. ---- R = kS ---- When S is 16, R is 80. 80 = k*16 k = 5 -------- ------------------- 2 Tomar's paycheck varies directly with the hours he works. p =kh ---- When Tomar works 5 hours, he gets paid \$60.00. 60 = k*5 k = 12 --- Equation: p - 12h ----- How much does Tomar make in 8 hours? p = 12*8 p = 96 ------- 3. Y varies directly with X and has a constant rate of change of 6. y = 6x --- When the value of Y is 11, then the value of X could be _____. 11 = 6x x = 11/6 -------- less than 2 -------------------- 4. Determine the constant of variation for the direct variation given. (0, 0), (3, 12), (9, 36) k = (12-0)/(3-0) = 4 ------ 5. Select all of the following that are a direct variation. Songs are 99 cents each to download. yes ------ Tickets for rides at the fair are \$1 each. yes ----- Arcade games are 50 cents or \$1. no ----- To go tubing it is \$5 to rent the tube and \$7 for each hour. yes ----- 6. Determine the constant of variation for the direct variation given. Fat calories varies directly with the grams of fat. c = kf --- There are 27 calories for each 3 grams of fat. 27 = k*3 k = 9 ------- Cheers, Stan H. ==========
 Complex_Numbers/371328: (6-7i)+(-4+3i)1 solutions Answer 264525 by stanbon(57250)   on 2010-11-15 11:52:49 (Show Source): You can put this solution on YOUR website!(6-7i)+(-4+3i) ----- = 2 -4i =============== cheers, Stan H.
 Probability-and-statistics/371232: In a random sample of 500 people of a ctty, it was found that 160 preferred seafood. Find a 95% confidence interval for the actual proportion of people who preferred seafood.1 solutions Answer 264516 by stanbon(57250)   on 2010-11-15 10:17:50 (Show Source): You can put this solution on YOUR website!In a random sample of 500 people of a city, it was found that 160 preferred seafood. Find a 95% confidence interval for the actual proportion of people who preferred seafood. ----- p-hat = 160/500 = 0.32 --- ME = 1.96*sqrt(0.32*0.68/500) = 0.0410 ---- 95% CI: 0.32-0.0410 < p < 0.32+0.0410 ----- Cheers, Stan H.
 Probability-and-statistics/371298: Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right of z = 1.25.1 solutions Answer 264515 by stanbon(57250)   on 2010-11-15 10:11:42 (Show Source): You can put this solution on YOUR website!Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right of z = 1.25. --------- left of z= -1.25: 0.1060 --- right of 1.25: 0.1060 ---- Add them up ================== Cheers, Stan H.
 Probability-and-statistics/371297: find the area under the standard normal curve between z -1.5 and z 2.51 solutions Answer 264514 by stanbon(57250)   on 2010-11-15 10:09:31 (Show Source): You can put this solution on YOUR website!find the area under the standard normal curve between z -1.5 and z 2.5 --- If you do not have a calculator that can do this for you, you need to learn how to read your z-chart. This is basic to learning stats. --- Ans P(-1.5 < z < 2.5) = 0.9270 ===================== Cheers, Stan H.
 Functions/371286: Which of the following functions represents a cell phone bill if there is a monthly charge of 20 dollars plus 6 cents for each minute of use? f(x) = 20 + 6x f(x) = 20.06x f(x) = 20 + 0.06x1 solutions Answer 264513 by stanbon(57250)   on 2010-11-15 10:04:05 (Show Source): You can put this solution on YOUR website!Which of the following functions represents a cell phone bill if there is a monthly charge of 20 dollars plus 6 cents for each minute of use? --------- The 20 is dollars Change 6 cents to 0.06 dollars ------ Let "x" be # of minutes of use. ---- Equation: Cost = 20 + 0.06x dollars Cost = 20.06x dollars -------------------------- Cheers, Stan H. -------------------------- f(x) = 20 + 6x f(x) = 20.06x f(x) = 20 + 0.06x
 Linear_Equations_And_Systems_Word_Problems/371292: Can you show me the correct way to work this problem through systems of linear equations? Thanks: Problem: Joe has \$1.15 in dimes and nickles. The number of nickels is one less than twice the number of dimes. How many nickles and how many dimes does he have? 1 solutions Answer 264512 by stanbon(57250)   on 2010-11-15 10:01:03 (Show Source): You can put this solution on YOUR website!Problem: Joe has \$1.15 in dimes and nickles. The number of nickels is one less than twice the number of dimes. How many nickles and how many dimes does he have? ----- Method using two variable: --- Quantity Equation: n = 2d-1 Value Equation::: 5n + 10d = 115 cents -------------------------------------------- Substitute for "n" and solve for "d": 5(2d-1) + 10d = 115 10d-5 + 10d = 115 20d = 120 d = 6 (# of dimes) --- Since n = 2d-1, n = 2*6-1 = 11 (# of nickels) ============================================== Cheers, Stan H. ===========
 Linear_Equations_And_Systems_Word_Problems/371293: Can you show the correct way to work this system of linear equations word problem out? Thanks! Problem: Water and bleach are to be mixed in a ration of 50 to 1. How many milliliters of each are needed to make 800ml of the mix? 1 solutions Answer 264511 by stanbon(57250)   on 2010-11-15 09:57:24 (Show Source): You can put this solution on YOUR website!Problem: Water and bleach are to be mixed in a ration of 50 to 1. How many milliliters of each are needed to make 800ml of the mix? --------------- 50 to 1 is the same as 50x to x where 50x is water and x is bleach. ---- Equation: water + bleach = 800ml 50x + x = 800 51x = 800 x = 800/51 ---- Water = 50(800/51) = 784 ml (amt. of water Bleach = 800/51 = 15.69 ml (amt. of bleach) ============================================== Cheers, Stan H.
 Probability-and-statistics/371295: 3. A two-digit number is written at random. Determine the probability that the number will be: a) an odd number.? b) larger than 75.? c) a multiple of 5.? d) an even number smaller than 40.? 1 solutions Answer 264510 by stanbon(57250)   on 2010-11-15 09:53:29 (Show Source): You can put this solution on YOUR website! A two-digit number is written at random. Determine the probability that the number will be: a) an odd number.::: 1/2 b) larger than 75.:::(99-76+1)/(100-9) = 24/91 c) a multiple of 5.:::: (count them)/91 d) an even number smaller than 40.::::(count them)/91 ----------- Cheers, Stan H.
 Linear-systems/371296: 0.12(2x-5)+3x=811 solutions Answer 264508 by stanbon(57250)   on 2010-11-15 09:47:53 (Show Source): You can put this solution on YOUR website!0.12(2x-5)+3x=81 --- 0.24x-0.60 + 3x = 81 --- 3.24x = 81.60 ---- x = 25.19.. Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/371294: Can you explain the correct way to work this systems of linear equations word problem out? Thanks! Problem: A bricklayer begins work at 7 a.m., laying 170 bricks per hour. Two hours later his apprentice joins him and lays 80 bricks per hour. At what time will they have laid 965 bricks? 1 solutions Answer 264507 by stanbon(57250)   on 2010-11-15 09:45:29 (Show Source): You can put this solution on YOUR website!Problem: A bricklayer begins work at 7 a.m., laying 170 bricks per hour. Two hours later his apprentice joins him and lays 80 bricks per hour. At what time will they have laid 965 bricks? ---- Apprentice DATA: rate = 80 b/h ; time = x hrs ; work done = 80x bricks ---------------------------------- Bricklayer DATA: rate = 170 b/h ; time = x+2; ; work done = 170(x+2) bricks ------------------------- Equation: bricks + bricks = 965 bricks 80x + 170(x+2) = 965 80x + 170x + 340 = 965 250x = 625 x = 2.5 hrs ---- x+2 = 4.5 hrs ---------------- Time: 7 am + 4.5 hrs = 11:30 am (time they finish the work) ====================================== Cheers, Stan H.
 test/371257: I want to know if you know how to simplify rational expressions by using negative 1 as a factor?1 solutions Answer 264490 by stanbon(57250)   on 2010-11-15 08:01:30 (Show Source): You can put this solution on YOUR website!Example: f(x) = (x-3)[(x+5)/(3-x)] ---- f(x) = [(x-3)/(3-x)](x+5) --- f(x) = (-1)(x+5) --- f(x) = -x-5 ================ Cheers, Stan H.
 logarithm/371259: solve ln(5-X)-ln(5+X)=-ln9 my sol. 5-ln5=-ln91 solutions Answer 264489 by stanbon(57250)   on 2010-11-15 07:58:23 (Show Source): You can put this solution on YOUR website!solve ln(5-X)-ln(5+X)=-ln9 ===== ln[(5-x)/(5+x) = -ln(9 ====== ln[(5-x)/(5+x)] = ln(1/9) --- (5-x)/(5+x) = 1/9 Cross multiply to get: 9(5-x)= 5+x 45-9x = 5+x 10x = 40 x = 10 ==================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/371146: 150=[900X]^0.51 solutions Answer 264424 by stanbon(57250)   on 2010-11-14 22:28:25 (Show Source): You can put this solution on YOUR website!150 = [900X]^0.5 ------- Square both sides to get: 900x = 150^2 x = 150^2/900 --- x = 25 ======== Cheers, Stan H.
 logarithm/371151: log5(2x-)+1=log 5x1 solutions Answer 264423 by stanbon(57250)   on 2010-11-14 22:24:53 (Show Source): You can put this solution on YOUR website!log5(2x-)+1=log 5x ----- log5(2x-?) ---- Something is missing from your post. Cheers, Stan H.
 Probability-and-statistics/371155: Classify the following as an example of a nominal, ordinal, interval, or ratio level of measurement, and state why it represents this level: gender of employees at a local warehouse 1 solutions Answer 264420 by stanbon(57250)   on 2010-11-14 22:22:17 (Show Source): You can put this solution on YOUR website!Ans: nominal Why? The data is a series of words: male, female, male...etc. ==== cheers, Stan H.