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# Recent problems solved by 'stanbon'

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 , 57180..57209, >>Next

 Circles/335956: What does the "circumference" of a circle mean?1 solutions Answer 240940 by stanbon(57250)   on 2010-08-28 17:27:16 (Show Source): You can put this solution on YOUR website!the distance around the circle. ================================ Cheers, Stan H.
 Trigonometry-basics/335955: what is the domain and range of this function: ln(x+3.14159)-5 1 solutions Answer 240937 by stanbon(57250)   on 2010-08-28 17:18:55 (Show Source): You can put this solution on YOUR website!what is the domain and range of this function: ln(x+3.14159)-5 ---- x+3.14159 must be positive ----- Solve x + 3.14159 > 0 --- x > -3.14159 is the domain ================================ Cheers, Stan H.
 Miscellaneous_Word_Problems/335954: A group of math teachers went to a restaurant. They agreed to split the bill equally. When the bill arrived, two of them discovered they had forgotten their money. The others agreed to make up the difference by paying an extra \$1.30 each. If the total bill was \$78, how many teachers were in the group? I figured out the answer is 12 teachers but i can't figure out the equation.1 solutions Answer 240935 by stanbon(57250)   on 2010-08-28 17:16:48 (Show Source): You can put this solution on YOUR website!A group of math teachers went to a restaurant. They agreed to split the bill equally. When the bill arrived, two of them discovered they had forgotten their money. The others agreed to make up the difference by paying an extra \$1.30 each. If the total bill was \$78, how many teachers were in the group? ---- Let x be the expected number payers. Average charge would be 78/x. ----------------------------------- x-2 actually shared the bill. Average charge would be 78/(x-2) ----------------------------------- Equation: New average - old average = 1.30 78/(x-2) - 78/x = 1.30 Multiply thru by x(x-2) to get: 78x -78(x-2) = 1.3x(x-2) 78*2 = 1.3x^2 - 2.6x -------------------------- Multiply thru by 10 to get rid of the decimals: 13x^2 - 26x - 1560 = 0 --- x^2 - 2x - 120 = 0 (x-12)(x+10) = 0 Positive solution: x = 12 (original number of payers before 2 reneged) ====================================================== Cheers, Stan H. ============
 Exponents/335953: what is -2 squared? is it the same as (-2) squared?? 1 solutions Answer 240933 by stanbon(57250)   on 2010-08-28 17:06:54 (Show Source): You can put this solution on YOUR website!what is -2 squared? is it the same as (-2) squared?? ------------------ No --------- (-2)^2 = 4 --- -2^2 = -4 =============== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/335935: A caterer is planning a party for 64 people. The customer has \$150 to spend. A \$39 pan of pasta feeds 14 people and a \$12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make?1 solutions Answer 240931 by stanbon(57250)   on 2010-08-28 16:52:48 (Show Source): You can put this solution on YOUR website!A caterer is planning a party for 64 people. The customer has \$150 to spend. A \$39 pan of pasta feeds 14 people and a \$12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make? ---------------------------- People Equation: 14p + 6t = 64 people Value Equation: 39p + 12t = 150 dollars --------------------------------------------- Multiply thru the 1st equation by 12. Multiply thru the 2nd equation by 6. ----------------------------------------- 12*14p + 12*6t = 12*64 6*39p + 6*12t = 6*150 ------------------------------ Subtract 1st from 2nd and solve for "p": 66p = 132 p = 2 (# of pans of pasta needed) ----- Substitute into 14p+6t = 64 and solve for "t": 28 + 6t = 64 6t = 36 t = 6 (# of sandwich trays needed) =================================== Cheers, Stan H.
 Functions/335903: Find the domain of 1 solutions Answer 240923 by stanbon(57250)   on 2010-08-28 15:52:42 (Show Source): You can put this solution on YOUR website!Find the domain of h(x)= 4th root(x^2-5x) x^2-5x >= 0 x(x-5) >= 0 --- Solve the equality: x = 0 or x = 5 ------------------------ To solve the inequality: 1st: Draw a number line and plot x = 0 and x = 5 2nd: Check a test-value from each of the three resulting intervals to determine where the solutions for the inequality lie. ------------- x(x-5) > 0 Check x = -10: -*->0 ; true, so solutions in (-inf,0) Check x = 2: +*->0 ; false, so no solutions in (0,5) Check x = 10: +*+>0 ; true, so solutions in (5,+inf) ======================================================== Final solution: [0,5] or 0<= x <=5 ================= Cheers, Stan H.
 Trigonometry-basics/335928: Cos(x)=-.2 its been a while1 solutions Answer 240917 by stanbon(57250)   on 2010-08-28 15:35:30 (Show Source): You can put this solution on YOUR website!Cos(x)=-.2 ---- Take the inverse cosine of both sides to get: x = 101.54 degrees OR x = 258.46 degrees ========================== Cheers, Stan H.
 test/335924: 24x^4 - 6x find the greatest common factor of the terms in the polynomial.1 solutions Answer 240915 by stanbon(57250)   on 2010-08-28 15:31:44 (Show Source): You can put this solution on YOUR website!24x^4 - 6x find the greatest common factor --------------------------------- gcf = 6x ---- Factor: 6x(4x^3-1) ============== Cheers, Stan H.
 Numeric_Fractions/335909: Simone has 5 employees in her flower shop. Each employee works 6 4/15 hours per day. How many hours, in total, do the 5 employees work per day?1 solutions Answer 240900 by stanbon(57250)   on 2010-08-28 14:35:48 (Show Source): You can put this solution on YOUR website!duplicate
 Graphs/335916: Find the solutions to 6x^2 + 5x - 4= 0. Is the sum of your solutions equal to -b/a? Explain why the sum of the solutions to any quadratic equation is -b/a?. (Hint: Use the quadratic formula.)1 solutions Answer 240899 by stanbon(57250)   on 2010-08-28 14:33:47 (Show Source): You can put this solution on YOUR website!Find the solutions to 6x^2 + 5x - 4= 0. Is the sum of your solutions equal to -b/a? Explain why the sum of the solutions to any quadratic equation is -b/a?. (Hint: Use the quadratic formula.) --- 1st solution: x1 = (-b/2a)+(sqrt(b^2-4ac)/(2a) --- 2nd solution: x2 = (-b/2a)-(sqrt(b^2-4ac)/(2a) --- Adding you get: x1+x2 = 2(-b/2a) = -b/a ============================================ Cheers, Stan H.
 Functions/335911: f(x) = 7x squared - 4x, what is the value of f(2)? I need the steps please.1 solutions Answer 240897 by stanbon(57250)   on 2010-08-28 14:27:46 (Show Source): You can put this solution on YOUR website! f(x) = 7x squared - 4x, what is the value of f(2)? ------------- f(x) = 7x^2-4x --- f(2) = 7*(2^2)-4(2) f(2) = 7*4-8 f(2) = 20 ================== Cheers, Stan H.
 Radicals/335915: (sqrt7x-2+5)^21 solutions Answer 240896 by stanbon(57250)   on 2010-08-28 14:25:07 (Show Source): You can put this solution on YOUR website!I think a parenthesis is missing. Cheers, Stan H.
 Expressions-with-variables/335912: √48x^3 Over _______ √3xy^31 solutions Answer 240895 by stanbon(57250)   on 2010-08-28 14:23:09 (Show Source): You can put this solution on YOUR website!√48x^3 _______ √3xy^3 ================== = sqrt[16x^2/y^2]*sqrt[1/y] ===== = (4x/y)*sqrt(1/y) OR = (4x/y^2)*sqrt(y) ======================== Cheers, Stan H.
 absolute-value/335907: What is the answers to this absolute value equation, it is asking for two answers? 2|4x-5|-2=-4 I kept trying to work out the problem but all i got was negitive numbers, and none of the answers have negitives in them. Thanks 1 solutions Answer 240894 by stanbon(57250)   on 2010-08-28 14:11:44 (Show Source): You can put this solution on YOUR website!2|4x-5|-2=-4 ----------- Add 2 to both sides: --- 2|4x-5| = -2 --- Divide both sides by 2: |4x-5| = -1 ---- There are NO answers because absolute value cannot be negative. =============================== Cheers, Stan H.
 Linear-systems/335898: Cowling’s rule. Cowling’s rule is another method for determining the dosage of a drug to prescribe to a child. For this rule, the formula d=D(a+1) divided by 24 gives the child’s dosage d, where D is the adult dosage and a is the age of the child in years. If the adult dosage of a drug is 600 milligrams and a doctor uses this formula to determine that a child’s dosage is 200 milligrams, then how old is the child?1 solutions Answer 240893 by stanbon(57250)   on 2010-08-28 14:06:23 (Show Source): You can put this solution on YOUR website!the formula d=D(a+1) divided by 24 gives the child’s dosage d, where D is the adult dosage and a is the age of the child in years. --------------------------------------------------------- If the adult dosage of a drug is 600 milligrams and a doctor uses this formula to determine that a child’s dosage is 200 milligrams, then how old is the child? ----------------------------- d=D(a+1)/24 ----- 200 = 600(a+1)/24 ----- a+1 = 8 ------ a = 7 yrs old ========== Cheers, Stan H.
 Percentage-and-ratio-word-problems/335852: I have a chance to buy a 23 inch or 24 inch diagonal monitor for my computer system. Each monitor has a 16:10 ratio (Wide screen). What are the measurements (L, W, and Area) of each monitor? Which has the biggest area? The only thing I could think of to try would be to use the pythagorean theorem as a first step, but then that leaves out the ratio part of the question, so I think that may be wrong. We have recently studied quadratic equations, so maybe I'm supposed to put it in that form to solve? I'm really lost!1 solutions Answer 240877 by stanbon(57250)   on 2010-08-28 09:16:58 (Show Source): You can put this solution on YOUR website! I have a chance to buy a 23 inch or 24 inch diagonal monitor for my computer system. Each monitor has a 16:10 ratio (Wide screen). What are the measurements (L, W, and Area) of each monitor? -------- 24-in diagonal: (16x)^2 + (10x)^2 = 24^2 356x^2 = 576 x = 1.272 ---- width= 16x = 20.35 inches length = 10x = 12.72 inches Area = 258.88 sq. in. ------------------------------------------ Do the same for a diagonal of 23 inches. ---- Which has the biggest area? ======================================= Cheers, Stan H.
 Inequalities/335847: To be eligible financial aid, Alisa must work at least 15 hours per week in a work-study program. She wants to spend at least 5 more hours studying than working each week. What is the minimum number of hours per day (Monday through Friday) that she must study to meet this goal and be eligible for financial aid? 1 solutions Answer 240875 by stanbon(57250)   on 2010-08-28 09:02:41 (Show Source): You can put this solution on YOUR website!To be eligible for financial aid, Alisa must work at least 15 hours per week in a work-study program. She wants to spend at least 5 more hours studying than working each week. What is the minimum number of hours per day (Monday through Friday) that she must study to meet this goal and be eligible for financial aid? ---------------------------- Work >= 15 hrs. per week Study >= Work+5 hrs. per week ----------------------- Study >= 15+5 hrs per week Study >= 20 hrs per week Study >= (20/7) hrs per day ================================ Cheers, Stan H.
 Numbers_Word_Problems/335849: one third of a number is added to 4, with a result of at least 21 solutions Answer 240871 by stanbon(57250)   on 2010-08-28 08:55:11 (Show Source): You can put this solution on YOUR website!one third of a number is added to 4, with a result of at least 2 (1/3)x + 4 >= 2 --- (1/3)x >= -2 --- x >= -6 ================= Cheers, Stan H. =================
 test/335851: Jonh is tree times as old as sarah, last year jonh was four times as lod as sarah. So how old is sarah and jonh now??1 solutions Answer 240868 by stanbon(57250)   on 2010-08-28 08:52:23 (Show Source): You can put this solution on YOUR website!John is three times as old as Sarah. J = 3S Last year John was four times as oid as Sarah. (J-1) = 4(S-1) ------------------------- So how old is Sarah and John now?? --- Substitute for "J" and solve for "S": (3S-1) = 4(S-1) 3S-1 = 4S-4 S = 3 yrs. old (Sarah's age now) ------------------ Since J= 3S, J = 3*3 = 9 yrs old (John's age now) ====================================================== Cheers, Stan H. ========
 Miscellaneous_Word_Problems/335842: An airplane propeller rotates 1000 times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in 1 second. 1 solutions Answer 240865 by stanbon(57250)   on 2010-08-28 08:45:44 (Show Source): You can put this solution on YOUR website! An airplane propeller rotates 1000 times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in 1 second. -------------------- (1000*360)(degrees/minute)(1/3600)(minute/seconds) --- = (360000/3600)(degrees/second) --- = 100 degrees/second ========================== Cheers, Stan H.
 Geometry_Word_Problems/335839: A snowman built with three spheres made of packed snow. The top sphere has half the diameter of the middle sphere. The middle sphere has half the diameter of the bottom sphere. The top sphere weighs 5 pounds. What is the total weight of the snowman? a. 30 pounds b. 65 pounds c. 125 pounds d. 250 pounds e. 365 pounds1 solutions Answer 240857 by stanbon(57250)   on 2010-08-28 07:18:03 (Show Source): You can put this solution on YOUR website!A snowman built with three spheres made of packed snow. The top sphere has half the diameter of the middle sphere. The middle sphere has half the diameter of the bottom sphere. The top sphere weighs 5 pounds. What is the total weight of the snowman? ------------------------ Let top sphere have diameter (2r) and radius = r: Then top sphere has volume (4)(pi)(r)^3 ---- Middle sphere has diameter = (4r) and radius = 2r Then middle sphere has volume (4)(pi)(2r)^3 = 8 times the volume of top sphere. -------- Bottom sphere has d = (8r) and radius = 4r Then bottom sphere has volume (4)(pi)(4r)^3 = 64 times the volume of top sphere. ------------------------------- Note: middle sphere has 8 times the volume of top sphere so weighs 8*5=40 lbs. bottom sphere has 64 times the volume of top sphere so weighs 64*5 = 320 lbs. ------------------------------- Total weight = 365 lbs. ================================== Cheers, Stan H. ================================== a. 30 pounds b. 65 pounds c. 125 pounds d. 250 pounds e. 365 pounds
 Miscellaneous_Word_Problems/335838: A function is defined as f(x) = 3x + 4. The inverse of a function “undoes” the function. Which of the following statements is true? a g(x)= (x/3)-4 is the inverse of f(x). b There is no function that is the inverse of f(x). c g(x)= (x/4)-3 is the inverse of f(x). d g(x)= (x-4)/3 is the inverse of f(x). e g(x)= (x-3)/4 is the inverse of f(x).1 solutions Answer 240856 by stanbon(57250)   on 2010-08-28 06:49:19 (Show Source): You can put this solution on YOUR website!A function is defined as f(x) = 3x + 4. The inverse of a function “undoes” the function. ------------------------ f does the following to its input: 1st: multiplies by 3 2nd: adds 4 ------------------------------ Its inverse must "undo" what f has done: 1st: it must subtract 4 2nd: it must then divide by 3 -- So the inverse looks like g(x) = (x-4)/3 ================================================ Cheers, Stan H. =============================== Which of the following statements is true? a g(x)= (x/3)-4 is the inverse of f(x). b There is no function that is the inverse of f(x). c g(x)= (x/4)-3 is the inverse of f(x). d g(x)= (x-4)/3 is the inverse of f(x). e g(x)= (x-3)/4 is the inverse of f(x).
 Percentage-and-ratio-word-problems/335840: Math Probability Question Jayne has a collectionof 50 old teapots. 27 of them have rose patterns. Some of them are covered in blue willow patterns. Some of them have striped patterns and the rest have plain colours. One teapot is chosen at random: The probability that it will have a striped pattern is 0.08 How many of Jaynes teapots are striped? The probability that it will have a blue willow pattern is 0.22. How many of Jaynes teapots have plain colours.1 solutions Answer 240854 by stanbon(57250)   on 2010-08-28 06:44:23 (Show Source): You can put this solution on YOUR website!Jayne has a collectionof 50 old teapots. 27 of them have rose patterns: 0.54 have rose patterns Some of them are covered in blue willow patterns. Some of them have striped patterns and the rest have plain colours. ----------------------------------------- One teapot is chosen at random: The probability that it will have a striped pattern is 0.08 ----------------------------------------- How many of Jaynes teapots are striped? # of striped = 0.08*50 = 4 ----------------------------------------- The probability that it will have a blue willow pattern is 0.22. How many of Jaynes teapots have plain colours. % of plain = 100%-(0.54+0.08+0.22) = 0.16 # of plain colored = 0.16*50 = 8 ================================= Cheers, Stan H.
 Probability-and-statistics/335831: The unemployment rate in a city is 12%. Find the probability that at most 2 out of 10 people from this city sampled at random are unemployed. Round your answer to four decimal places..1 solutions Answer 240851 by stanbon(57250)   on 2010-08-28 06:31:26 (Show Source): You can put this solution on YOUR website!The unemployment rate in a city is 12%. Find the probability that at most 2 out of 10 people from this city sampled at random are unemployed. Round your answer to four decimal places.. ----- Binomial Problem with n= 10 and p = 0.12 --------------------- P(0<= x <=2) = binomcdf(10,0.12,2) = 0.8913 =================================================== Cheers, Stan H.
 Probability-and-statistics/335835: HISTORY TEST RESULTS Score 100 95 90 85 80 75 70 65 60 Number of 1 2 4 1 3 2 2 0 1 Students The scores on Tuesday’s history test for 16 students are shown in the table above. Sam, who was the only student absent on Tuesday, will take the test next week. If Sam receives a score of 95 on the test, what will be the median score for the test? (A) 90 (B) 87.5 (C) 85 (D) 82.5 (E) 801 solutions Answer 240850 by stanbon(57250)   on 2010-08-28 06:28:16 (Show Source): You can put this solution on YOUR website!85 will be the middle score, or median. Cheers, Stan H.
 Travel_Word_Problems/335791: How do you write this problem? Tow sailboats 400 meters apart are sailing toward each other. one is moving at a rate of 10m per sec and the other is moving at a rate of 15m per sec. in how many seconds will the boats pass each other? and in how may second will the boats be 400 meters apart again? I think you write the problem like this 400=10m+15m and 400=10m-15m1 solutions Answer 240814 by stanbon(57250)   on 2010-08-27 21:49:21 (Show Source): You can put this solution on YOUR website!How do you write this problem? Two sailboats 400 meters apart are sailing toward each other. one is moving at a rate of 10m per sec and the other is moving at a rate of 15m per sec. in how many seconds will the boats pass each other? --- Their closing speed is (10+15) meter/second 400 meters/25 meter per second = 16 seconds ---------------------------------------------------- And in how may seconds will the boats be 400 meters apart again? There separation speed is also 25 meters/second 400 meters/25 meters /er second = 16 seconds ================================================ Cheers, Stan H.
 Equations/335780: I am having some problem with find the lowest terms for these two I don't know how to convert each rational expression into an equivalent rational expression with the LCD as the denominator. Please help. 5x/x^2-1 and -4/x^2-2x+11 solutions Answer 240809 by stanbon(57250)   on 2010-08-27 21:44:28 (Show Source): You can put this solution on YOUR website!convert each rational expression into an equivalent rational expression with the LCD as the denominator. Please help. 5x/x^2-1 and -4/x^2-2x+1 ---- You have to factor each denominator: (5x)/[(x-1)(x+1)] and (-4)/[(x-1)^2] ----- The LCD = (x+1)(x-1)^2 ------ Rewrite each fraction with the LCD as its denominator: [(5x)(x-1)]/LCD and [-4(x+1)]/LCD ================================== Cheers, Stan H. ==================================
 Miscellaneous_Word_Problems/335790: driving from town A to town D, you pass thru town B then town C. town A to town B is 10 miles farther than from town B to town C. town B to town C is 10 miles farther than from town C to town D. if town A is 390 miles from town D, how many mile is town A to town B?? A-------B-------C-------D .-------------------------.=390 390/3=130 answer is 140 mi; just can't explain or show method; could you help?1 solutions Answer 240805 by stanbon(57250)   on 2010-08-27 21:39:00 (Show Source): You can put this solution on YOUR website! driving from town A to town D, you pass thru town B then town C. ------------------------ town A to town B is 10 miles farther than from town B to town C. town B to town C is 10 miles farther than from town C to town D. --------------------------- if town A is 390 miles from town D, how many mile is town A to town B?? A-------B-------C-------D .-------------------------.=390 ========================================= Let dist. from B to C be "x" miles. Then dist. from A to B is "x+10" miles. And dist. from C to D is "x -10" miles =========================================== Equation: x+10 + x + x-10 = 390 3x = 390 x = 130 miles ---- A to B = x+10 = 140 B to C = x = 130 C to D = x-10 = 120 ========================= Cheers, Stan H. =========================
 Linear_Equations_And_Systems_Word_Problems/335785: Set up and Calculate. The first programmer,Sammy,grossed \$535 in 1 week by working 48 hours. The second programmer, Matin, grossed \$587 in 1 week by working 52 hours. Time-and-a-half is paid for all hours worked in excess of 40 hours. Which programmer earns more per hour. I have to use a linear equation to do this problem. Sammy takes 5 hours longer to complete 300 lines of code than Martin. Toghether, Sammy and Martin can complete the code in 6 hours. Clearly explain the results showing the calculations of how long it takes each programmer to complete the code if he programs on his own. (hint:quadratic equation) and at what speed he is programming lines per hour1 solutions Answer 240802 by stanbon(57250)   on 2010-08-27 21:31:29 (Show Source): You can put this solution on YOUR website!The first programmer,Sammy,grossed \$535 in 1 week by working 48 hours. The second programmer, Matin, grossed \$587 in 1 week by working 52 hours. Time-and-a-half is paid for all hours worked in excess of 40 hours. Which programmer earns more per hour. I have to use a linear equation to do this problem. ----------------- Let Sammy's hourly rate be "S" Let Martin's hourly rate = "M" ----- Equations: Sammy Eq: 40S + (S/2)8 = 535 dollars 40S+4S = 535 44S = 535 S = \$12.16 per hour (Sammy's hourly rate) ----------------------------------------------- Martin Eq;40M + (M/2)12 = 587 40M + 6M = 587 46M = 587 M = \$12.76 per hour (Martin's hourly rate) ============================================== Sammy takes 5 hours longer to complete 300 lines of code than Martin. Toghether, Sammy and Martin can complete the code in 6 hours. Sammy DATA: time = x+5 hr/job ; rate = 1/(x+5) job/hr --- Martin DATA: time = x hr/job ; rate = 1/x job/hr ---- Together DATA: time = 6 hr/job ; rate = 1/6 job/hr ======================= Equation: rate + rate = together rate 1/(x+5) + 1/x = 1/6 --- Multiply thru by 6x(x+5) 6x + 6(x+5) = x(x+5) 6x + 6x+30 = x^2+5x 12x + 30 = x^2+5x x^2 - 7x - 30 = 0 Factor: (x-10)(x+3) = 0 Positive solution: x = 10 hrs (time required by Martin to do the job alone) Martin's rate is 1/10 job/hr. ------------------------------------ x+5 = 15 hrs (time required by Sammy to do the job alone) Sammy's rate is 1/15 job/hr. ===================================== Cheers, Stan H. ===================================== Clearly explain the results showing the calculations of how long it takes each programmer to complete the code if he programs on his own. (hint:quadratic equation) and at what speed he is programming lines per hour
 Equations/335786: If Don subtracts 24 from one-half of his number he gets 0. What is Don's number? I don't know how to set it up in equation form.1 solutions Answer 240793 by stanbon(57250)   on 2010-08-27 21:10:41 (Show Source): You can put this solution on YOUR website!If Don subtracts 24 from one-half of his number he gets 0. What is Don's number? ------------------- Let the number be "x": Equation: (1/2)x - 24 = 0 (1/2)x = 24 x = 48 =========== Cheers, Stan H. ==========
 Equations/335787: Three consecutive integers have a sum of -33. What are the integers? I have the answer.. But I need to know how to set it up in equation form. 1 solutions Answer 240790 by stanbon(57250)   on 2010-08-27 21:09:03 (Show Source): You can put this solution on YOUR website!Three consecutive integers have a sum of -33. What are the integers? --- 1st: x 2nd: x+1 3rd: x+2 ---------- Equation: x + x+1 + x+2 = -33 3x+3 = -33 3x = -36 x = -12 x+1 = -11 x+2 = -10 --------------------- Cheers, Stan H.