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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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 Rational-functions/357189: how can you tell if y=9x-2 is a function?1 solutions Answer 255088 by stanbon(57377)   on 2010-10-16 19:40:37 (Show Source): You can put this solution on YOUR website! how can you tell if y=9x-2 is a function? ---- graph it and see if it passes the vertical line test. If x = 0, y = -2, giving you the point (0,-2) If x = 1, y = 7, giving you the point (1,7) Plot the two points and draw a line thru them. ---- ---- Vertical line test. If every vertical line intersects the graph only once the equation is a function. ------- Cheers, Stan H.
 Probability-and-statistics/357138: There are 9 apples in a bag; 5 are red and 4 are yellow. Two apples are selected at random, one after another with replacement, and the color of each is noted. Find the probablity that at least 1 is red?1 solutions Answer 255086 by stanbon(57377)   on 2010-10-16 19:37:05 (Show Source): You can put this solution on YOUR website!There are 9 apples in a bag; 5 are red and 4 are yellow. Two apples are selected at random, one after another with replacement, and the color of each is noted. Find the probablity that at least 1 is red? ---- P(at least one red) = 1 - P(none is red) --- = 1 -(4/9)(4/9) --- = 1 - 16/81 --- = 65/81 ============== Cheers, Stan H.
 Evaluation_Word_Problems/357188: Find four consecutive integers so that if the first is increased by 2, the second decreased by 2, the third multiplied by 2 and the fourth divided by 2, then the sum of the four resulting numbers is 200.1 solutions Answer 255085 by stanbon(57377)   on 2010-10-16 19:32:14 (Show Source): You can put this solution on YOUR website!Find four consecutive integers so that if the first is increased by 2, the second decreased by 2, the third multiplied by 2 and the fourth divided by 2, then the sum of the four resulting numbers is 200. ------ 1st: x-1 2nd: x 3rd: x+1 4th: x+2 ------------------------- Equation: x-1+2 + x-2 + 2(x+1) +(x+2)/2 = 200 ---- x +1 + x - 2 + 2x+2 + (x+2)/2 = 200 4x +1 + (x+2)/2 = 200 8x+2 + x+2 = 400 9x + 4 = 400 9x = 396 x = 44 ---- 1st: 39 2nd: 40 3rd: 41 4th: 42 =============== Cheers, Stan H.
 percentage/357186: need some help with this question please. a stadium has two sections A and B . Tickets for section A cost \$a and tickets for section B cost cost \$b. johana piad \$105 for 5 section A tickets and 3 section B tickets. raiyah paid \$63 for 4 section A tickets and 1 section B ticket i)write two equations in a and b to represent the information above. ii) calculate the values of a and b.1 solutions Answer 255083 by stanbon(57377)   on 2010-10-16 19:26:40 (Show Source): You can put this solution on YOUR website!Tickets for section A cost \$a and tickets for section B cost cost \$b. johana piad \$105 for 5 section A tickets and 3 section B tickets. raiyah paid \$63 for 4 section A tickets and 1 section B ticket i)write two equations in a and b to represent the information above. Value Eq:::: 5a + 3b = 105 dollars Value Eq:::: 4a + b = 63 dollars -------------------- ii) calculate the values of a and b. Modify the equations: Multiply thru the 1st equation by 4. Multiply thru the 2nd equation by 5. 20a + 12b = 4*105 20a + 5b = 5*63 ------------------------ Subtract the lower from the upper equation: 7b = 105 b = 17 (price of section B tickets) ---- Substitute and solve for "a": 4a + 17 = 63 4a = 46 a = 11.50 (price of section A tickets) =========================================== Cheers, Stan H.
 Functions/357176: Hi, Actually I'm in college algebra, but since the following problem has to do with range, this was the closest category I could come up with. Here's the problem: Find the range of the function: f(x)=x^2+12x+341 solutions Answer 255080 by stanbon(57377)   on 2010-10-16 19:19:46 (Show Source): You can put this solution on YOUR website!Find the range of the function: f(x)=x^2+12x+34 --- Since the parabola opens upward from the vertex, you have to find the y-value of the vertex. ----- Vertex occurs at x = -b/2a = -12/(2) = 6 ---- y-value at x = 6 is 6^2+12*6+34 = 142 ----- Range: All Real Numbers >= 142 =================================== Cheers, Stan H.
 Rational-functions/357185: x^2-16x+4=01 solutions Answer 255077 by stanbon(57377)   on 2010-10-16 19:14:49 (Show Source): You can put this solution on YOUR website! x^2-16x+4=0 Quadratic Formula: x = [16 +- sqrt(16^2-4*4)]/2 --- x = [16 +- sqrt(240)]/2 --- x = [16 +- 4sqrt(15)]/2 --- x = [8 +- 2sqrt(15)] =========================== Cheers, Stan H.
 Rational-functions/357181: Write the following two fractions in terms of the LCM of the denominators. q+5/q^2-4q-21 and q/q^2-11q+281 solutions Answer 255073 by stanbon(57377)   on 2010-10-16 19:08:53 (Show Source): You can put this solution on YOUR website!Write the following two fractions in terms of the LCM of the denominators. q+5/q^2-4q-21 and q/q^2-11q+28 ---- Factor the denominators: q^2-4q-21 = (q-7)(q+3) q^2-11q+28 = (q-7)(q-4) --- LCM: (q+3)(q-4)(q-7) -------------------------- Rewrite the fractions: (q+5)(q-4)/LCM --- and --- q(q+3)/LCM ================ Cheers, Stan H.
 percentage/357178: a total of 1,200 students attended top view high school the ratio of teachers to students is 1:30. i)how many teachers are there in the school? two thifths of the students own personal computers ii) how many students do not own personal computers? thirty percent of the students who own personal computers also own play stations. iii) what fractions of the students in the school own play stations?1 solutions Answer 255071 by stanbon(57377)   on 2010-10-16 18:57:55 (Show Source): You can put this solution on YOUR website!a total of 1,200 students attended top view high school the ratio of teachers to students is 1:30. i)how many teachers are there in the school? 1:30 is the same as x:30x --- Equation: x + 30x = 1200 31x = 1200 x = 1200/31 ---- # of teachers = 1200/31 is approximately 39 ------------------------ two thifths of the students own personal computers ii) how many students do not own personal computers? What are thifths? ---------------------- thirty percent of the students who own personal computers also own play stations. iii) what fractions of the students in the school own play stations? Answer depends on the answer to ii. ====================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/357172: Fences R Us wants to replace their office’s traditional computers and two-dimensional monitors with a virtual reality system. The fixed monthly cost will be \$400,000, and it will cost \$700 to produce each system. 1) Find and interpret A(1000), A(10,000) and A(100,000).1 solutions Answer 255063 by stanbon(57377)   on 2010-10-16 18:21:22 (Show Source): You can put this solution on YOUR website!Fences R Us wants to replace their office’s traditional computers and two-dimensional monitors with a virtual reality system. The fixed monthly cost will be \$400,000, and it will cost \$700 to produce each system. 1) Find and interpret A(1000), A(10,000) and A(100,000). ----- A(x) = 400,000 + 700x --- A(1000) = 400,000 + 700*1000 = 1,100,000 etc. Cheers, Stan H.
 logarithm/357168: A piece of machinery valued at \$250,000 depreciates at a fixed rate of 12% per year. After how many years will the value have depreciated to \$100,000?1 solutions Answer 255059 by stanbon(57377)   on 2010-10-16 18:05:17 (Show Source): You can put this solution on YOUR website!A piece of machinery valued at \$250,000 depreciates at a fixed rate of 12% per year. After how many years will the value have depreciated to \$100,000? ------------------------------ Each year the item retains 88% of its last-year value. --- Solve: 250,000(0.88)^x = 100,000 0.88^x = 0.4 --- x = [log0.4]/[log0.88] --- x = 7.168 years ======================= Cheers, Stan H.
 Travel_Word_Problems/357158: At Johnson Middle school, 170 students buy 3 ring binders from school store. This number has been increasing at a rate of about 25 per year. The number of students buying 2 ring binders is 300 and has been decreasing at a rate of about 15 per year. At these rates, when will the number of 2 ring binders sold be half the number of 3 ring binders sold?1 solutions Answer 255056 by stanbon(57377)   on 2010-10-16 17:53:55 (Show Source): You can put this solution on YOUR website!At Johnson Middle school, 170 students buy 3 ring binders from school store. This number has been increasing at a rate of about 25 per year. --- #(3 ring) = 170+25x ------------------------------------ The number of students buying 2 ring binders is 300 and has been decreasing at a rate of about 15 per year. --- #(2 ring) = 300-15x ============================== At these rates, when will the number of 2 ring binders sold be half the number of 3 ring binders sold? --- Equation: Solve: 300-15x = (1/2)(170+25x) --- 600 - 30x = 170+25x 55x = 430 x = 7.82 years -------------------------- Cheers, Stan H.
 Rational-functions/357163: Simplify: 5p+10/2p^2-2p * p^2-4p+3/p^2-p-61 solutions Answer 255054 by stanbon(57377)   on 2010-10-16 17:38:55 (Show Source): You can put this solution on YOUR website!Simplify: 5p+10/2p^2-2p * p^2-4p+3/p^2-p-6 ---- Factor where you can: [5(p+2)]/[2p(p-1)] * [(p-3)(p-1)/(p-3)(p+2)] ---- Cancel factors common to a numerator and a denominator, such as (p+2),(p-1),(p-3), you get: ---- = [5/2p] ============================== Cheers, Stan H.
 Equations/357165: solve the following system of equations x+5y= 8 (1) x= 5-5y (2)1 solutions Answer 255050 by stanbon(57377)   on 2010-10-16 17:30:00 (Show Source): You can put this solution on YOUR website! solve the following system of equations x+5y= 8 x= 5-5y ----------- Rearrange: x + 5y = 8 x + 5y = 5 ------- Assuming those x's and y's mean the same in both equations you subtract and get: --- 0 = 3 -- The assumption was wrong. There is no (x,y) pair that satisfies both equations. --- Conclusion: No solution ============================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/357160: According to wil;dlife experts, the rate at which crickets chirp is a funtion of the temperature; specifically, C = T-40, where C is the number of chirps every 15 seconds and T is the temperature in degrees Fahrenheit. How many chirps does the cricket make per second if the temp is 70 F?1 solutions Answer 255049 by stanbon(57377)   on 2010-10-16 17:26:09 (Show Source): You can put this solution on YOUR website!C = T-40, where C is the number of chirps every 15 seconds and T is the temperature in degrees Fahrenheit. How many chirps does the cricket make per second if the temp is 70 F? ------------------------------- c = 70-40 C = 30 chirps every 15 seconds ---- C/15 = 2 chirps each second ------------------------------ Cheers, Stan H.
 Linear-systems/357159: How do I find the fourth point for a rectanlge? I can use the other three to find out with a graph, but I do not know how to set up an equation. 1 solutions Answer 255048 by stanbon(57377)   on 2010-10-16 17:19:24 (Show Source): You can put this solution on YOUR website!Please post your problem. Cheers, Stan H.
 Expressions-with-variables/357092: Hi, i need help with those questions am practicing but i dont understand how to work out the rearrangement etc. please show your working out clearly many thanks, 1. The speed of a car after t seconds is given by the formula v= u + at where u is the starting speed in metres per second (m s-¹) and a is the acceleration in metres per second per second (ms-2). a) A car joins a motorway at a speed of 25 ms-1 and accelerates at 0.65 ms -² for 12 seconds. Find its speed at the end of this time. b) Rearrange this formula to make the subject (i) u (ii) t 2. if a ball is thrown up in the air at a velocity of v, the height it reaches is given by h = V2/2g Where g is the acceleration due to gravity. a) Find the height reached by a ball thrown up at a velocity of 15 ms-1. b) B) Rearrange this formula to make the subject v. 3. A formula for converting temperature is C=5/9(F- 32) Where C is the temperature in degree Celsius and F is the temperature in degrees Fahrenheit a)An old recipe gives the oven temperature 375° F. Covert this temperature to Celsius. b)Rearrange this formula to make the subject F.1 solutions Answer 255005 by stanbon(57377)   on 2010-10-16 14:21:29 (Show Source): You can put this solution on YOUR website!1. The speed of a car after t seconds is given by the formula v= u + at where u is the starting speed in metres per second (m s-¹) and a is the acceleration in metres per second per second (ms-2). a) A car joins a motorway at a speed of 25 ms-1 and accelerates at 0.65 ms -² for 12 seconds. Find its speed at the end of this time. --------------------------- v = u + at v = 25 m/s + 0.65/s^2(12) v = 25 + 7.8 velocity = 32.8 meters/sec ================================ b) Rearrange this formula to make the subject (i) u = v - at ---- (ii) t = (v-u)/a ================================ 2. if a ball is thrown up in the air at a velocity of v, the height it reaches is given by h = V^2/2g Where g is the acceleration due to gravity. a) Find the height reached by a ball thrown up at a velocity of 15 ms-1. h(v) = 15^2/(2g) --------- b) B) Rearrange this formula to make the subject v. V = sqrt(2gh) ----------------------- 3. A formula for converting temperature is C=(5/9)(F)- 32 Where C is the temperature in degree Celsius and F is the temperature in degrees Fahrenheit a)An old recipe gives the oven temperature 375° F. Covert this temperature to Celsius. C(375) = (5/9)(375) - 32 = 176 1/3 ------------------------------------------------------------------- b)Rearrange this formula to make the subject F. C+32 = (5/9)F F = (9/5)(C+32) ===================== Cheers, Stan H.
 Probability-and-statistics/357090: Following are the American College Test (ACT) scores attained by the 25 members of a local high school graduating class. 21 24 23 17 31 19 19 20 19 25 17 23 16 21 20 28 25 25 21 14 19 17 18 28 20 Find P5, P10, and P20 for the ACT scores. 1 solutions Answer 255000 by stanbon(57377)   on 2010-10-16 14:03:19 (Show Source): You can put this solution on YOUR website!Following are the American College Test (ACT) scores attained by the 25 members of a local high school graduating class. 21 24 23 17 31 19 19 20 19 25 17 23 16 21 20 28 25 25 21 14 19 17 18 28 20 Find P5, P10, and P20 for the ACT scores. --------------------- I'll find P5. --- 1st: Put the data in ascending order from minimum to maximum 2nd: Find the locator for P5: 5%(25) = (5/100)25 = 5/4 = 1.25 Round up to the next whole number: locator = 2 --- 3rd Find P(5) which is the 2nd data element starting at the min. ---- P(5) = 16 =================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/357088: Johnny has paid \$58 for his phone and for going 30 minutes over what his cell phone plan allows, and he has paid \$62.50 for his bill and being \$48 minutes over his plan. A. What is an equation that will show how much he will pay depending on how many minutes he goes over. B. What does the slope stand for in this problem. C. What does the y intercept stand for in this problem.1 solutions Answer 254997 by stanbon(57377)   on 2010-10-16 13:53:02 (Show Source): You can put this solution on YOUR website!Johnny has paid \$58 for his phone and for going 30 minutes over what his cell phone plan allows, and he has paid \$62.50 for his bill and being \$48 minutes over his plan. Let "a"be normal rate and "b" be overtime rate. A. What is an equation that will show how much he will pay depending on how many minutes he goes over. (30,58) and (48,62.50) ------------------------------- slope = (62.50-58)/(48-30) = 4.5/18 = 1/4 c(x) = mx + b 58 = (1/4)(30) = b b = 50.50 ------ B. What does the slope stand for in this problem. 0.25 cents per additional minute of calling ------ C. What does the y intercept stand for in this problem. \$50.50 is the basic cost for the service with a set number of minutes of calling. ================= Cheers, Stan H.
 Systems-of-equations/357089: how do u work to find the axis of sysemtry? 1 solutions Answer 254996 by stanbon(57377)   on 2010-10-16 13:40:08 (Show Source): You can put this solution on YOUR website!how do u work to find the axis of symmetry? --------------------------------- If you have an up or down parabola with coefficients a,b,c, the axis of symmetry is x = -b/(2a) ---------------------- Cheers, Stan H.
 Travel_Word_Problems/357081: The fastest moving insect is the large tropical cockroach. It scurries at speeds of up to 2.3 feet per second. Now write an equation that represents how many miles a roach can travel in 1.5 hours. 1 solutions Answer 254994 by stanbon(57377)   on 2010-10-16 12:49:36 (Show Source): You can put this solution on YOUR website!The fastest moving insect is the large tropical cockroach. It scurries at speeds of up to 2.3 feet per second. Now write an equation that represents how many miles a roach can travel in 1.5 hours. ----------------------------------------------- distance = [2.3 ft/sec][1 mile/5280 ft][5400 sec/1.5 hr] ---- distance = [2.3*1*5400]/[1*5280*1] [miles/1.5 hrs] ---- distance = [12420/5280] miles/1.5 hrs --- distance = 2.35 miles/1.5 hrs ================================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/357079: how can i solve for this equation: g(x)=2x+3 f(x)=3x^2-3x Find -4g(-4x)+4f(-4x)1 solutions Answer 254993 by stanbon(57377)   on 2010-10-16 12:40:54 (Show Source): You can put this solution on YOUR website!how can i solve for this equation: g(x)=2x+3 f(x)=3x^2-3x ---------------------- Find -4g(-4x)+4f(-4x) --- = -4[2(-4x)+3] + 4[3(4x)^2-3(-4x)] ---- = -4[-8x+3] + 4[48x^2+12x] --- = 32x-12 + 192x^2+48x --- = 192x^2 + 80x - 12 =========================== Cheers, Stan H.
 Probability-and-statistics/357070: a box contains 17 large and 16 small marbles each marble is either green or white 6 large marbles are green, 8 small marbles are white if a marble is selected from the box what is the probability that it is large or green1 solutions Answer 254992 by stanbon(57377)   on 2010-10-16 12:35:36 (Show Source): You can put this solution on YOUR website! a box contains 17 large and 16 small marbles each marble is either green or white 6 large marbles are green, 8 small marbles are white 11 large marbles are white, 3 small marbles are green ------------------------------------------------- if a marble is selected from the box what is the probability that it is large or green -------------------- P(large or green) = P(large) + P(green) - P(large and green) --- = [17+9-6]/33 = 20/33 ==================== Cheers, Stan H.
 Human-and-algebraic-language/357071: The sum of two numbers is 22. Using q as the smaller number, translate "five less than the larger number" into a variable expression and simplify.1 solutions Answer 254991 by stanbon(57377)   on 2010-10-16 12:24:41 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 22. Using q as the smaller number, translate "five less than the larger number" into a variable expression and simplify. Equations: smaller: q larger: p p + q = 22 q = p-5 ----- Substitute for "q" and solve for "p": p + p-5 = 22 2p = 27 p = 13.5 q = p-5 = 8.5 =================== Cheers, Stan H.
 Quadratic_Equations/357073: Solve 36x2 -12ax + (a2 – b2) = 0 1 solutions Answer 254990 by stanbon(57377)   on 2010-10-16 12:19:51 (Show Source): You can put this solution on YOUR website!Solve 36x2 -12ax + (a2 – b2) = 0 ------------ [36x2 -12ax + a2] – b2 = 0 ---- (6x-a)^2 - b^2 = 0 ----- Factor: [6x-a-b][6x-a+b] = 0 ---- x = (a+b)/6 or x = (a-b)/6 ------------------------------ Cheers, Stan H.
 Polynomials-and-rational-expressions/357072: factor(3-x)^3-x^3 1 solutions Answer 254989 by stanbon(57377)   on 2010-10-16 12:12:43 (Show Source): You can put this solution on YOUR website!factor(3-x)^3-x^3 --------------------- = [(3-x)-x][(3-x)^2 + (3-x)(x) + x^2] ------------- Cheers, Stan H.
 Probability-and-statistics/357045: Vacation Sites A U.S. Travel Data Center's survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations1 solutions Answer 254988 by stanbon(57377)   on 2010-10-16 12:07:19 (Show Source): You can put this solution on YOUR website!Vacation Sites A U.S. Travel Data Center's survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations ---- p-hat: 0.42 ME = 1.96*sqrt[0.42*0.58/sqrt(1500)] = 0.0250 ----- 95% CI: 0.42-0.0250 < p < 0.42+0.0250 ======================================== Cheers, Stan H.
 Age_Word_Problems/357043: please help me answer this question: a flare is launched from a life raft with an initial velocity of 80 meters per second. how many seconds will it take for the flare to return the sea?1 solutions Answer 254969 by stanbon(57377)   on 2010-10-16 09:38:51 (Show Source): You can put this solution on YOUR website!a flare is launched from a life raft with an initial velocity of 80 meters per second. how many seconds will it take for the flare to return the sea? -------------- h(t) = -9.8t^2 + 80t ---- When the flare is at sea level, it height is zero. --- Solve -9.8t^2+80t = 0 t(-9.8t+80) = 0 t= 0 when the flare leaves the raft. -9.8t+80 = 0 when the flare hits the water. 9.8t = 80 t = 8.16 seconds ========================== Cheers, Stan H.
 test/356951: What value of the variable x us associated with: a. Y=0 b. y=1 c. Y=-8 the equation is y=x cubed1 solutions Answer 254893 by stanbon(57377)   on 2010-10-15 20:27:29 (Show Source): You can put this solution on YOUR website!What value of the variable x us associated with: a. Y=0 Solve x^3 = 0 Ans: x = 0 ----------------- b. y=1 Solve x^3 = 1 x = 1 ------------------- c. Y=-8 Solve x^3 = -8 x = -2 =================================== the equation is y=x cubed Cheers, Stan H.
 Travel_Word_Problems/356938: Rachael runs 2 kilometers to a bus stop, and then rides 4.5 km to school. On average the bus is 45 km/hr faster than Rachael's average running speed. If the entire trip takes 25 minutes, how fast does Rachael run?1 solutions Answer 254891 by stanbon(57377)   on 2010-10-15 20:23:47 (Show Source): You can put this solution on YOUR website!Rachael runs 2 kilometers to a bus stop, and then rides 4.5 km to school. On average the bus is 45 km/hr faster than Rachael's average running speed. If the entire trip takes 25 minutes, how fast does Rachael run? ------- Running DATA: distance: 2 km ; rate = x km/h ; time = 2/x hrs ------- Bus DATA: distance: 4.5 km ; rate = x+45 km/h ; time = 4.5/(x+45) hrs. ---------------------- Equation: time + time = 25/60 hr ---- 2/x + 4.5/(x+45) = 5/12 ---- Multiply thru by 12x(x+45) to get: 24(x+45) + 12*4.5x = 5x(x+45) --------------- 24x + 1080 + 54x = 5x^2 + 225x ============================= 78x + 1080 = 5x^2 + 225x 5x^2 + 147x - 1080 = 0 ----------------------- Positive solution: x = 6.0868 km/h (running rate) ================= Cheers, Stan H.
 Miscellaneous_Word_Problems/356939: I'm having problems solving this algebra word problem. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank? 1 solutions Answer 254886 by stanbon(57377)   on 2010-10-15 20:04:57 (Show Source): You can put this solution on YOUR website!A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank? ------ Emptying pipe: time = 1/2 hr/job ; rate = 2 jobs/hr ------ Filling pipe: time = 3/4 hrs/job ; rate = 4/3 job/hr ------------------------------------------- Together DATA: time = x hr/job rate = 1/x job/hr ===================================== Equation: empty rate - fill rate = together rate 2 - 4/3 = 1/x --- 2/3 = 1/x x = 3/2 hrs (time to fill the tank) ========================== Cheers, stan H.
 Length-and-distance/356948: j is the midpoint of hk, h has coordinates (6,-2) and j has coordinates (9,3). fin d the coordinates of k. Hint use the midpoint formula 1 solutions Answer 254880 by stanbon(57377)   on 2010-10-15 19:54:26 (Show Source): You can put this solution on YOUR website!j is the midpoint of hk, h has coordinates (6,-2) and j has coordinates (9,3). find the coordinates of k. Hint use the midpoint formula ----- Let the coordinates of k be (x,y) --- (x+6)/2 = 9 x+6 = 18 x = 12 ----------------- (y-2)/2 = 3 y-2 = 6 y = 8 ----- K has coordinates (12,8) ============================= Cheers, Stan H.