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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, >>Next

 Distributive-associative-commutative-properties/210953: How do I solve Q(t)=x^2-5x+1. Find and simplify Q(7+h)-Q(7)/h1 solutions Answer 159368 by stanbon(57219)   on 2009-09-04 10:39:04 (Show Source): You can put this solution on YOUR website!How do I solve Q(t)=x^2-5x+1. Find and simplify [Q(7+h)-Q(7)]/h --------------------------------------------- Q(7+h) = (7+h)^2 -5(7+h) + 1 Q(7+h) = 49 + 14h + h^2 - 35 - 5h + 1 Q(7+h) = h^2 + 9h + 15 -------------------------- Q(7) = 49-35+1 = 15 ----- Q(7+h)-Q(7) = h^2+9h ------------ Finally: [Q(7+h)-Q(7)]/h = h +9 ========================================= Cheers, Stan H.
 Percentage-and-ratio-word-problems/210951: Thirty three out of 198 students surveyed said they preferred hockey to all other sports. What fraction of students surveyed is this? In high school 25 percent of the girls and 50 percent of the boys attended a football game. If 48 percent of all the students in the school are girls, what percent of all the students went to the football game?1 solutions Answer 159361 by stanbon(57219)   on 2009-09-04 10:03:15 (Show Source): You can put this solution on YOUR website!Thirty three out of 198 students surveyed said they preferred hockey to all other sports. What fraction of students surveyed is this? --- If you are studying division, divide 33 by 198 to get the percentage. If you are studying algebra, set up a proportion as follows: x/100 = 33/198 x = 100(33/198) x = 16.67% ================================ In high school 25 percent of the girls and 50 percent of the boys attended a football game. If 48 percent of all the students in the school are girls, what percent of all the students went to the football game? Let x be the number in the school. # of girls is 0.48x # of boys is 0.52x -------------------------- # of girls that went to the game = 0.25(0.48x) = 0.12x # of boys who went to the game = 0.50(0.52x) = 0.26x -------------------------- % of all students who went to the game = (0.12x+0.26x)/x = 0.38 = 38% =========================================================================== Cheers, Stan H.
 Linear-systems/210945: In 1992 the life expectancy of males in a certain country was 69.4, it was 72.9 years. Let E repersent the life expectancy in year t and let t repersent the number of years since 1992 The linear function E(t) that fits the data is E(t)=_____t+____ Use the function to predict the life expectancy of males in 2003. E(11)=______1 solutions Answer 159358 by stanbon(57219)   on 2009-09-04 09:50:28 (Show Source): You can put this solution on YOUR website!In 1992 the life expectancy of males in a certain country was 69.4, it was 72.9 years. Let E repersent the life expectancy in year t and let t repersent the number of years since 1992 The linear function E(t) that fits the data is E(t)=_____t+____ Use the function to predict the life expectancy of males in 2003. E(11)=______ --------------------------------------- You need two points. You have (0,69.4) but are missing ? in (?,72.9). Your text has it; you didn't post it. Cheers, Stan H.
 Inverses/210950: This question is from textbook Saxon Math 8/7 a/b=4 what is b/a=1 solutions Answer 159357 by stanbon(57219)   on 2009-09-04 09:46:24 (Show Source): You can put this solution on YOUR website!a/b=4 what is b/a= -------------- b/a = 1/4 ==================== Cheers, Stan H.
 Miscellaneous_Word_Problems/210948: It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together?''.1 solutions Answer 159356 by stanbon(57219)   on 2009-09-04 09:45:08 (Show Source): You can put this solution on YOUR website!It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together? -------------------------------------- Cindy's rate is 1/x job/hr ------------- Eva's rate is 1/(x+3) job/hr ------------------------------- From 9am to 5pm they have worked 8 hrs In that time they have accomplished 8*Cindy's rate + 6*Eva's rate = 90% of the job 8(1/x)+6 = 0.90 job I get x = 24.7 ------------------------------------- Solve that for "x"; then you will know Cindy and Eva's rates which are 1/x = 1/24.7 and 1/27.7). --------------------- To get the time remaining for them to finish the job. k(1/24.7 + 1/27.7) = 0.10 of the job k(0.0766) = 0.10 k = 1.306 hrs. ============================ Cheers, Stan H.
 Linear-systems/210946: Solv for the indicated letter b=3c, for c The solution is c=_____1 solutions Answer 159352 by stanbon(57219)   on 2009-09-04 09:20:24 (Show Source): You can put this solution on YOUR website!Solve for the indicated letter b=3c, for c Divide both sides by 3 to get: b/3 = c Interchange the sides. c = b/3 The solution is c = b/3 ============================ Cheers, Stan H.
 Linear-equations/210894: This question is from textbook COLLEGE ALGEBRA Pls. Help can't figure it out The law of divine proportion, according to early Egyptians and Greek, states, “the most beautiful division of a line segment into two parts is such that the ratio of the longer part to the total length is equal to the ratio of the length of the shorter part to that of the longer part” a.) If we consider the length of the line to be one unit and call t the length of the longer of the two parts, Find t. b.) What is the proportionality constant for this ratio? thank you very much1 solutions Answer 159349 by stanbon(57219)   on 2009-09-04 09:17:18 (Show Source): You can put this solution on YOUR website!The law of divine proportion, according to early Egyptians and Greek, states, “the most beautiful division of a line segment into two parts is such that the ratio of the longer part to the total length is equal to the ratio of the length of the shorter part to that of the longer part” a.) If we consider the length of the line to be one unit and call t the length of the longer of the two parts, Find t. Draw a line segment and mark a point that is not in the middle. Label the larger part as "a" and the smaller as "1-a" ---- Write the proportion as described above. a/1 = (1-a)/a Cross-multiply and solve for "a": a^2 = 1-a a^2+a-a = 0 a = [-1+-sqrt(1-4*-1)]/2 Positive solution: a = [-1+sqrt(5)]/2 = 0.618 Then b = 1-0.618 = 0.3817 ------------------------------- ======================================================================== b.) What is the proportionality constant for this ratio? a/b = 1.618 which is called the Golden Proportion. ----------------------------------------------------------------- Cheers, Stan H.
 Functions/210793: if g(x) =2 - x squared , then find g(3 + h) - g(3) over h 1 solutions Answer 159306 by stanbon(57219)   on 2009-09-03 22:04:59 (Show Source): You can put this solution on YOUR website!if g(x) =2 - x squared , then find g(3 + h) - g(3) over h ----------------- g(3) = 2-9 = -7 g(3+h) = 2-(3+h)^2 g(3+h) = 2-9-6h-h^2 g(3+h) = -7-6h-h^2 ---------------------------- Then g(3+h)-g(3) = -6h-h^2 And [g(3+h)-g(3)]/h = -6-h =============================== Cheers, Stan H.
 Rational-functions/210798: describe the relationshop between the solution set of an equation, where one side equals zero, and the value of x where the function crosses the x-axis(the x-intercepts of a graph1 solutions Answer 159303 by stanbon(57219)   on 2009-09-03 21:54:59 (Show Source): You can put this solution on YOUR website!describe the relationship between the solution set of an equation, where one side equals zero, and the value of x where the function crosses the x-axis(the x-intercepts of a graph). ---- The x-intercepts are the Real Number solutions of the equation. --- Cheers, Stan H.
 Graphs/210882: Please help me solve the following equation: (((f(x)=-x^2+4x+5))) The question does not come out of the book. I am told to find the vertex, the line of symetry, the max or min value of the quadratic function and graph the function. Thanks Missy1 solutions Answer 159302 by stanbon(57219)   on 2009-09-03 21:50:52 (Show Source): You can put this solution on YOUR website!solve the following equation: (((f(x)=-x^2+4x+5))) The question does not come out of the book. I am told to find the vertex, the line of symetry, the max or min value of the quadratic function and graph the function. ------------------------ f(x)=-x^2+4x+5 a = -1 ; b = 4 ; c = 5 -------------------------------- Max or Min value occurs when x = -b/2a = -4/(-2) = 2 f(2) = -(2)^2 + 4*2 + 5 = 9 Vertex occurs at (2,9) The vertex is a max because "a" is negative --------------------------------------------- The axis of symmetry is x = 2 because it must pass thru the vertex. ---------------- =============================================== Cheers, Stan H.
 Linear-equations/210866: This question is from textbook Intermediate Algebra Thank you in advance. A business earned \$6570 this year on an investment of \$45,000 in mutual funds made last year. The two funds invested in were a pharmaceutical fund which paid out simple interest of 13% and a biotech fund which paid out simple interest of 16% . How much was invested in each fund a year ago to earn \$6570 in combined interest?1 solutions Answer 159298 by stanbon(57219)   on 2009-09-03 21:41:01 (Show Source): You can put this solution on YOUR website!A business earned \$6570 this year on an investment of \$45,000 in mutual funds made last year. The two funds invested in were a pharmaceutical fund which paid out simple interest of 13% and a biotech fund which paid out simple interest of 16% . How much was invested in each fund a year ago to earn \$6570 in combined interest? --------------------------------------------- Simple Interest: I = Prt ------------------------ x*0.13 + (45000-x)*0.16 = 6570 --- 13x + 16*45000 - 16x = 657000 -3x = -63000 x = 21000 (amount invested at 13%) 45000-21000 = 24000 (amount invested at 16% ============================================ Cheers, Stan H.
 Probability-and-statistics/210872: This question is from textbook Holt Algebra 2 One study found that 8% of men and 0.5% of women are born color-bline. Of the study participants, 52% were men. What is the probability that a study participant is male and born color-blind? What is the probability that a study participant is male or born color-blind?1 solutions Answer 159292 by stanbon(57219)   on 2009-09-03 21:27:55 (Show Source): You can put this solution on YOUR website!One study found that 8% of men and 0.5% of women are born color-bline. Of the study participants, 52% were men. What is the probability that a study participant is male and born color-blind? -------------- P(male and color-blind) = P(color-blind|male)*P(male)= 0.08*0.52 = 0.0416 =============================================================================== What is the probability that a study participant is male or born color-blind? P(blind or male) = P(blind)+P(male)-P(blind and male) = 0.085 + 0.52 - 0.0416 = 0.5634 =============================== Cheers, Stan H.
 Probability-and-statistics/210870: EDITORIAL CORRECTION OF THE TABLE: The problem is as stated: Use the data in the following table, which summarizes blood groups and Rh types for 100 subjects. These values may vary in different regions according to the ethnicity of the population. ------------------Group -----------------A---B--AB--O Type--Rh(+)---39--35--8--4 --------Rh(-)---6---5---2--1 Blood groups and types If 2 of the 100 subjects are randomly selected find the probability that they are both group O and type Rh+. A. Assume that the selections are made with replacement. B. Assume that the selections are made without replacement.1 solutions Answer 159289 by stanbon(57219)   on 2009-09-03 21:09:47 (Show Source): You can put this solution on YOUR website!Which of the data are type O data? Cheers, Stan H.
 Probability-and-statistics/210776: This is from the textbook Statistical Techniques in Business and Economics, 13th edition, exercise #34 Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the Unites States is \$110,00. This distribution follows the normal distribution with a standard deviation of \$40,000. if we select a random sample of 50 households what is the standard error of the mean what is the expected shape of the distribution of the sample mean what is the likelihood of selecting a sample with a mean of at least \$112,000 what is the likelihood of selecting a sample with a mean of more than \$100,00 find the likelihood of selecting a sample with a mean of no more than \$100,000 but no less than \$112,000.1 solutions Answer 159253 by stanbon(57219)   on 2009-09-03 17:13:03 (Show Source): You can put this solution on YOUR website!Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the Unites States is \$110,00. This distribution follows the normal distribution with a standard deviation of \$40,000. if we select a random sample of 50 households what is the standard error of the mean? Ans: 40,000/sqrt(50) ---------------------------------- what is the expected shape of the distribution of the sample mean The mean of the sample means is \$110,000; standard deviation = 40,000/sqrt(50) ---------------------------------- what is the likelihood of selecting a sample with a mean of at least \$112,000 z(112,000) = (112,000-110,000)/[40,000/sqrt(50)] = 0.3536 P(x-bar >=112000) = P(z>=0.3536) = 0.3618... ---------------------------------- what is the likelihood of selecting a sample with a mean of more than \$100,000 Find the z value of 100,000 Find the P(z is greater than that value) ------------------------------------------------ find the likelihood of selecting a sample with a mean of no more than \$100,000 but no less than \$112,000. Use the z-value of 100,000 and the z-value of 112,000 Find the probability z is between those values. ========================================================== Cheers, Stan H.
 Trigonometry-basics/210770: This question is from textbook Single Variable Calculus Simplify the given function by referring to the appropriate triangle or trigonometric identity. 1 solutions Answer 159241 by stanbon(57219)   on 2009-09-03 15:55:35 (Show Source): You can put this solution on YOUR website!Simplify the given function by referring to the appropriate triangle or trigonometric identity. -------- Draw a right triangle. Let "a" be one of the small angles. Let a = tan^-1(x) Then the tan(a) = x/1 Lebel the side opposite "a" as "x", and the adjacent side as one. Then, using Pythagoras", the hypotenuse is sqrt(1+x^2) --------------- Then cos(a) = 1/sqrt(1+x^2) ---------------------------------- Cheers, Stan H.
 Expressions-with-variables/210774: f 0f g {3} when f=2x and g = 5x-11 solutions Answer 159236 by stanbon(57219)   on 2009-09-03 15:49:49 (Show Source): You can put this solution on YOUR website!f 0f g {3} when f=2x and g = 5x-1 -------------- fog(3) = f[g(3)] = f[5*3-1] = f[14] = 2*14 = 28 ===================================================== Cheers, Stan H.
 Linear-equations/210772: Hi,I need some help solving this equation please The ordered pair (3,2) is a solution of the equation 2x-5y=?1 solutions Answer 159235 by stanbon(57219)   on 2009-09-03 15:47:53 (Show Source): You can put this solution on YOUR website!Hi,I need some help solving this equation please The ordered pair (3,2) is a solution of the equation 2x-5y=? ----------------------------- Since 2x-5y = ?, --- ? = 2*3 - 5*2 ? = 6-10 ? = -4 ============= Cheers, Stan H.
 Probability-and-statistics/210766: Please help me in this question:(Hypothesis Testing on Two Samples) A sample of 14 cans of Coke diet soda gave the mean number of calories of 23 per can with a standard deviation of 3 calories. Another sample of 16 cans of Pepsi diet soda gave the mean number of calories of 25 per can with standard deviation of 4 calories. at the 1% significance level, can you conclude that the mean numbers of calories per can are different for these two brands of diet soda? Assume that the calories per can of diet soda are normally distributed for each of the two brands and that the standard deviations for the two population are equal.1 solutions Answer 159234 by stanbon(57219)   on 2009-09-03 15:45:37 (Show Source): You can put this solution on YOUR website!Please help me in this question:(Hypothesis Testing on Two Samples) A sample of 14 cans of Coke diet soda gave the mean number of calories of 23 per can with a standard deviation of 3 calories. Another sample of 16 cans of Pepsi diet soda gave the mean number of calories of 25 per can with standard deviation of 4 calories. at the 1% significance level, can you conclude that the mean numbers of calories per can are different for these two brands of diet soda? Assume that the calories per can of diet soda are normally distributed for each of the two brands and that the standard deviations for the two population are equal. -------------------------------- Ho: u(coke)-u(pepsi) = 0 Ha: u(coke)-u(pepsi) is not 0 -------------------------------- I ran a 2-Sample T-test and got the following: t = -1.56.. p-value = 0.130.... ------------ Conclusion: Since the p-value is greater than 1%, do not reject Ho. There is no statistical difference in the number of calories. ====================================================== Cheers, Stan H.
 Money_Word_Problems/210740: Solve the problem. Suppose that \$7000 is invested in an account where interest is compounded continuously at 3.2% per year. What is the doubling time? A)4.6 yr B)21.7 yr C)2.2 yr D)0.2 yr 1 solutions Answer 159231 by stanbon(57219)   on 2009-09-03 15:23:56 (Show Source): You can put this solution on YOUR website!Solve the problem. Suppose that \$7000 is invested in an account where interest is compounded continuously at 3.2% per year. What is the doubling time? ------------------------ A(t) = P*e^(rt) For doubling time: 2P = P*e^(rt) e^rt = 2 ----- Your problem: e^(0.032t) = 2 Take the natural log of both sides to get: 0.032t = ln(2) t = [ln(2)]/0.032 t = 21.66 years =========================== Cheers, Stan H. A)4.6 yr B)21.7 yr C)2.2 yr D)0.2 yr
 Numeric_Fractions/210765: x 1 - - - = 2 8 4 On the equation above what is my first step?1 solutions Answer 159229 by stanbon(57219)   on 2009-09-03 15:19:47 (Show Source): You can put this solution on YOUR website!x 1 - - - = 2 8 4 ---------------------- In general, when you have an equation with fractions, multiply both sides by the least common multiple of the denominators. ---------------------- Your Problem: lcm = 8 Multiply thru by 8 --- x - 2 = 16 x = 18 =============== Cheers, Stan H.
 logarithm/210767: This question is from textbook Single Variable Calculus I need help with the problem The question says to solve for the missing variable. SO what i did was made both sides in terms of e and then set the exponents equal to each other and i get 8/11 which i am told is not correct. help please?1 solutions Answer 159228 by stanbon(57219)   on 2009-09-03 15:16:35 (Show Source): You can put this solution on YOUR website!e^(2x+1)=9e^(1-x) ------------------------ Take the natural log of both sides: --- 2x+1 = ln(9) + (1-x) 3x = ln(9) x = [ln(9)]/3 x = 0.7324.. Cheers, Stan H.
 Mixture_Word_Problems/210742: Solve the problem. In 1998, the population of a given country was 37 million, and the exponential growth rate was 5% per year. Find the exponential growth function. A)P(t) = 370.05t , where P(t) is in millions and t is the number of years after 1998. B)P(t) = 37e0.05t, where P(t) is in millions and t is the number of years after 1998. C)P(t) = 37e5t, where P(t) is in millions and t is the number of years after 1998. D)P(t) = 37e0.05, where P(t) is in millions and t is the number of years after 19981 solutions Answer 159226 by stanbon(57219)   on 2009-09-03 15:12:24 (Show Source): You can put this solution on YOUR website!In 1998, the population of a given country was 37 million, and the exponential growth rate was 5% per year. Find the exponential growth function. P(t) = 37e^(0.05t) ==================== Cheers, Stan H. ================ A)P(t) = 370.05t , where P(t) is in millions and t is the number of years after 1998. B)P(t) = 37e0.05t, where P(t) is in millions and t is the number of years after 1998. C)P(t) = 37e5t, where P(t) is in millions and t is the number of years after 1998. D)P(t) = 37e0.05, where P(t) is in millions and t is the number of years after 1998
 Polynomials-and-rational-expressions/210751: This question is from textbook intermediate algebra Divide Using synthetic division. 16. (3x^4 + 8x - 10)/ (x+2)1 solutions Answer 159225 by stanbon(57219)   on 2009-09-03 15:06:22 (Show Source): You can put this solution on YOUR website!Divide Using synthetic division. 16. (3x^4 + 8x - 10)/ (x+2) ------------------------- -2)....3....0....8....-10 ........3....-6...20..|..-70 ================================== Quotient: 3x^2-6x+20 Remainder: -70 ============================== Cheers, Stan H.
 Linear-systems/210758: find the domain of the function g(x)=2/7-3x1 solutions Answer 159223 by stanbon(57219)   on 2009-09-03 15:03:33 (Show Source): You can put this solution on YOUR website!find the domain of the function g(x)=2/7-3x --- 7-3x cannot zero. ------------------- If 7-3x=0 3x = 7 x = 7/3 --------------- So domain is All Real Numbers except x = 7/3 ================================================ Cheers, Stan H.
 Quadratic_Equations/210762: (6x-5)^2/3 = x^1/3 I have no idea what to do.1 solutions Answer 159221 by stanbon(57219)   on 2009-09-03 15:01:02 (Show Source): You can put this solution on YOUR website!(6x-5)^2/3 = x^1/3 --- Raise both sides to the 3rd power to get: (6x-5)^2 = x Expand: 36x^2 - 60x + 25 = x 36x^2 - 61x + 25 = 0 -------------------------- Solve using the quadratic formula. Then check your answers and eliminate extraneous zeroes. ----------------------------------- Cheers, Stan H.
 Exponents/210763: 1=.5^n1 solutions Answer 159219 by stanbon(57219)   on 2009-09-03 14:56:30 (Show Source): You can put this solution on YOUR website!1=.5^n ------------- "n" must be zero; let's see why. ------------- Take the log of both sides: nlog(0.5) = log1 n = log(1)/log(0.5) n = 0/log(0.5) n = 0 ================= Cheers, Stan H.
 Rate-of-work-word-problems/210711: Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will john complete the work?1 solutions Answer 159203 by stanbon(57219)   on 2009-09-03 13:01:08 (Show Source): You can put this solution on YOUR website! Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will john complete the work? ---------------------------------- John DATA: time = x day/job ; rate = 1/x job/day ------------ Sam DATA: time = x-6 days/job ; rate = 1/(x-6) job/day ---------------- Together DATA: time = 4 days/job ; rate = 1/4 job/day ========================================= Equation: rate + rate = together rate 1/x + 1/(x-6) = 1/4 4(x-6) + 4x = x(x-6) 4x - 24 + 4x = x^2 - 6x x^2 - 14x +24 = 0 x^2 - 12x - 2x + 24 = 0 x(x-12)-2(x-12) = 0 (x-12)(x-2) = 0 To get a positive solution for Sam and John: x = 12 days (John time) x-6 = 6 days (Sam time) ======================= Cheers, Stan H.
 Graphs/210738: Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph.. State the equation of the line asymptotic to the graph (if any). y = 3(x - 4)1 solutions Answer 159201 by stanbon(57219)   on 2009-09-03 12:52:49 (Show Source): You can put this solution on YOUR website!Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph.. State the equation of the line asymptotic to the graph (if any). y = 3^(x - 4) ------------------ ----------------------------------------- Asymptote: y = 0 ======================== Cheers, Stan H.
 Travel_Word_Problems/210731: As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles per hour. Find the amount of time she runs at each speeds if her total running time is 2 hours and 20 minutes.1 solutions Answer 159199 by stanbon(57219)   on 2009-09-03 12:48:23 (Show Source): You can put this solution on YOUR website!As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles per hour. Find the amount of time she runs at each speeds if her total running time is 2 hours and 20 minutes. --------------- Level DATA: rate = 8 mph ; distance = x miles ; time = d/r = x/8 hrs. ---------------------- Hilly DATA: rate = 4 mph ; distance = (12-x) miles ; time = (12-x)/4 hrs ----------------------- Equation: time + time = 2 1/3 hrs x/8 + (12-x)/4 = 7/3 ---- 3x + 6(12-x) = 8*7 3x + 72 - 6x = 56 -3x = -16 x = 16/3 miles (distance run on the level) --- Time on level ground: (16/3)/8 = 2/3 hr. Time on hilly ground: (7/3)-(2/3) = 4/3 hr. =========================================== Cheers, Stan H.
 Equations/210733: Describe a situation when solving a system of two equations in two variables using the Graphical Method may not be appropriate for finding the precise numerical solution. 1 solutions Answer 159197 by stanbon(57219)   on 2009-09-03 12:41:11 (Show Source): You can put this solution on YOUR website!Describe a situation when solving a system of two equations in two variables using the Graphical Method may not be appropriate for finding the precise numerical solution. ------------------------------------------ 0.0000331x - 0.0000000042 = 0.1 -23x + 57 y = 0.0000000000001 --------------------------------- This would be a bit difficult to work with the graphical method. =================================== Cheers, Stan H.
 Equations/210734: Describe a situation when solving a system of two equations in two variables using the Substitution Method would be preferred over the Graphical or Addition Methods? Specifically, how would the system of equation be presented before solving it? 1 solutions Answer 159195 by stanbon(57219)   on 2009-09-03 12:38:21 (Show Source): You can put this solution on YOUR website!One of the two equations would already be solved for one of the variables. Example: 2x + 3y = 6 x = -y+1 ================= Cheers, Stan H.