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Recent problems solved by 'stanbon'

stanbon answered: 57259 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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 , 57210..57239 , 57240..57269, >>Next

Evaluation_Word_Problems/430326: John bought two computers, one desktop and one laptop. Before finance charges, the laptop cost more than the desktop. John paid for the computers using two different financing plans. For the desktop the interest rate was per year, and for the laptop it was per year. The total finance charges for one year were . How much did the desktop computer cost before finance charges? 1 solutions Answer 298839 by stanbon(57332)   on 2011-04-02 18:20:38 (Show Source): You can put this solution on YOUR website! Essential numbers are missing from your post.

Probability-and-statistics/430324: You play a game where you are to guess under which of 4 cups a coin has been placed. How many times would you expect to guess correctly in 20 plays of the game? Note that the coin is moved after each play. 1 solutions Answer 298838 by stanbon(57332)   on 2011-04-02 18:17:51 (Show Source): You can put this solution on YOUR website! You play a game where you are to guess under which of 4 cups a coin has been placed. How many times would you expect to guess correctly in 20 plays of the game? Note that the coin is moved after each play. ----- Binomial Problem with n = 20 and p = 1/4. ---------------- E(x) = np E(x) = 20(1/4) E(x) = 5 =========== Cheers, Stan H. ===========

Equations/430273: how many ounce of a 15% alcohol solution nmust bemixed with 4 ounces of a 20 % alcohol solution to make a 17% alcohol solution 1 solutions Answer 298806 by stanbon(57332)   on 2011-04-02 16:09:01 (Show Source): You can put this solution on YOUR website! how many ounces of a 15% alcohol solution nmust be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution. ----- Equations: alcohol + alcohol = alcohol 0.15x + 0.20*4 = 0.17(x+4) ------------------------------- Multiply thru by 100: 15x + 20*4 = 17x + 17*4 -2x = -3*4 x = 6 oz (amt. of 15% solution needed). ================= Cheers, Stan H. ============= -------

Rational-functions/430262: Solving Rational Equations. 1+(12)/(x^2-4)=(3)/(x-2) 1 solutions Answer 298798 by stanbon(57332)   on 2011-04-02 15:06:41 (Show Source): You can put this solution on YOUR website! 1+(12)/(x^2-4)=(3)/(x-2) ---- Multiply thru by (x^2-4) to get: (x^2-4) + 12 = 3(x+2) ---- x^2-3x -4+12-6 = 0 -------- x^2 - 3x +2 = 0 --- Factor: (x-2)(x-1) = 0 x = 2 or x = 1 ================== Cheers, Stan H. ==================

Probability-and-statistics/430157: Probabilities of Native-and Foreign-Born Persons: According to the Encyclopedia Britannica Almanac 2006, the 2004 U.S. population of 288,280,000 included 34,244,000 who were foreign born. Find the empirical probability that a randomly chosen person of that population would be... (a) foreign born (b)native born -My concern about this is if I am understanding this and setting up the formula correctly in order to solve it. Therefore, should I write it as (a)P(foreign born)= 34,244,000/288,280,000 and P(native born)= #/288,280,000?(I just not sure which way I am supposed to write this damn formula because this stuff always has confused the hell out of me so much, so please help me understand this best as possible and if I am doing this correctly or not at all too.) 1 solutions Answer 298796 by stanbon(57332)   on 2011-04-02 15:01:29 (Show Source): You can put this solution on YOUR website! Probabilities of Native-and Foreign-Born Persons: According to the Encyclopedia Britannica Almanac 2006, the 2004 U.S. population of 288,280,000 included 34,244,000 who were foreign born. Find the empirical probability that a randomly chosen person of that population would be... (a) foreign born P(foreign born) = 34,244,000/228,280,000 ----------------------- (b)native born P(native born) = (288,280,000-34,244,000) = 228,280,000 ===================================== Cheers, Stan H. ===================== -My concern about this is if I am understanding this and setting up the formula correctly in order to solve it. Therefore, should I write it as (a)P(foreign born)= 34,244,000/288,280,000 and P(native born)= #/288,280,000?(I just not sure which way I am supposed to write this damn formula because this stuff always has confused the hell out of me so much, so please help me understand this best as possible and if I am doing this correctly or not at all too.) 0 solutions

Probability-and-statistics/430254: Survey Results reveal that 45% of patients screened for a virus test positive. from a random sample of 35 patients, estimate the probability that more than 24 test positive 1 solutions Answer 298793 by stanbon(57332)   on 2011-04-02 14:50:57 (Show Source): You can put this solution on YOUR website! Survey Results reveal that 45% of patients screened for a virus test positive. from a random sample of 35 patients, estimate the probability that more than 24 test positive ------ Binomial Problem with n = 35 and p = 0.45 ------ P(x > 24) = 1-binomcdf(35,0.45,24) = 1-0.9986 = 0.0014 ==================================== Cheers, Stan H. ============

Probability-and-statistics/430247: assum that Z-scores are normally distrubuted with a mean of 0 and a standard deviation of 1. Find p(Z more than or equal to 1.45) 1 solutions Answer 298792 by stanbon(57332)   on 2011-04-02 14:48:17 (Show Source): You can put this solution on YOUR website! If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. - Find the probability that the mean IQ score is between 90 and 95, if 9 IQ scores are randomly selected. --- t(90) = (90-100)/[15/sqrt(100)] = -10/[1.5] = -6.6667 t(95) = (95-100)/[15/sqrt(100)] = -5/[1.5] = -3.3333 ----- P(90< x-bar <95) = P(-6.6667< t < -3.3333 when df=8) = 0.0051 ==================== Cheers, Stan H. ====================

Probability-and-statistics/430243: assum that Z-scores are normally distrubuted with a mean of 0 and a standard deviation of 1. Find the z-score that corresponds with D4. 1 solutions Answer 298789 by stanbon(57332)   on 2011-04-02 14:39:28 (Show Source): You can put this solution on YOUR website! assum that Z-scores are normally distrubuted with a mean of 0 and a standard deviation of 1. Find the z-score that corresponds with D4. ----- Find the z-score that has a left-tail of 0.4 ---- invNorm(0.4) = -0.2533 ======================== Cheers, Stan H. =============

Radicals/430242: What is the graph of y= (sqrt x + 9) + 2 This question has not been submitted and your site is saying it has been. 1 solutions Answer 298787 by stanbon(57332)   on 2011-04-02 14:37:17 (Show Source): You can put this solution on YOUR website! What is the graph of y= (sqrt x + 9) + 2 --- --- Cheers, Stan H.

Polygons/430234: What is the largest exterior angle that any regular polygon can have? 1 solutions Answer 298786 by stanbon(57332)   on 2011-04-02 14:35:35 (Show Source): You can put this solution on YOUR website! What is the largest exterior angle that any regular polygon can have? ---- The more sides there are the smaller the exterior angle. --- The fewest sides you can have is 3. --- So the smallest interior angle will be 60 degrees So the largest exterior angle must be 120 degrees. ============= Cheers, Stan H. ================

Triangles/430227: The ratios of the perimeters of two similar triangles is 1:3. If the length of a side of the smaller triangle is 3, the length of the corresponding side of the larger triangle is a. 1 b. radical 3 c. 3 radical 3 d. 9 So far, the work i have is: 1/3=3/x x=9? 1 solutions Answer 298784 by stanbon(57332)   on 2011-04-02 14:26:41 (Show Source): You can put this solution on YOUR website! The ratios of the perimeters of two similar triangles is 1:3. If the length of a side of the smaller triangle is 3, the length of the corresponding side of the larger triangle is larger/smaller = larger/smaller ------ Proportion: x/3 = 3/1 x = 9 ================ Cheers, Stan H. ================ a. 1 b. radical 3 c. 3 radical 3 d. 9

Miscellaneous_Word_Problems/430228: The sum of two numbers is 50. One number is 5 less than 4 times the other number. Find the numbers. "I get stuck right at the beginning, because I'm not sure whether I use 2 variableas or just one! I know how to set up the first sentence, but the second one confuses me. " 1 solutions Answer 298782 by stanbon(57332)   on 2011-04-02 14:18:16 (Show Source): You can put this solution on YOUR website! The sum of two numbers is 50. One number is 5 less than 4 times the other number. Find the numbers. ------ Equations: x + y = 50 x = 4y-5 ----- Substitute for "x" and solve for "y": 4y-5+y = 50 5y = 55 y = 11 ---- Solve for "x": x = 4y-5 x = 4*11-5 x = 39 ============= Cheers, Stan H.

Quadratic_Equations/430231: I need help with a few Algebra problems, please. If the discriminant in the quadratic formula is a perfect square, then the quadratic equatio will have _____________solution(s). Solve the quadratic formula. Simplify the answer. x^2 - 3x - 1 = 0 4x^2 + x - 1 =0 Thank you for your help! 1 solutions Answer 298781 by stanbon(57332)   on 2011-04-02 14:15:12 (Show Source): You can put this solution on YOUR website! I need help with a few Algebra problems, please. If the discriminant in the quadratic formula is a perfect square, then the quadratic equation will have _____________solution(s).e dis If the discriminant is negative there are 2 complex unequal solutions. If the discriminant is zero there are 2 Real equal solutions. If the discriminant is positive there are 2 Real unequal solutions. ========================================================================= Solve the quadratic formula. Simplify the answer. x^2 - 3x - 1 = 0 x = [3 +- sqrt(9-4*-1)]/2 x = [3 +- sqrt(13)]/2 ----------------------------- 4x^2 + x - 1 =0 x = [-1 +- sqrt(1-4*4*-1)]/8 x = [-1 +- sqrt(17)]/8 =============================== Cheers, Stan H.

Numeric_Fractions/430230: 9/11 divided by 3/4 has to be inthe simplest form 1 solutions Answer 298779 by stanbon(57332)   on 2011-04-02 14:10:01 (Show Source): You can put this solution on YOUR website! 9/11 divided by 3/4 ------------- (9/11)/(3/4) ---- = (9/11)*(4/3) ---- = (3/11)*(4/1) ---- = 12/11 ============ Cheers, Stan H. ============

Probability-and-statistics/430159: Using Spinner to Generate Numbers: (KEEP IN MIND-that the SPINNER has just 3 sides to it using the numbers 1, 2, 3) Suppose the spinner here is spun twice in succession to determine a two-digit number. Giving each of the following. (a) the sample space _______________ (b) the probability of an odd number ___________ (c) the probability of an number with repeated digits ____________ (d) the total number of a greater than 30 ___________ (e) the probability of a prime number ___________ -My concern about this is if I am understanding this and setting up the formula correctly in order to solve it. Therefore, should I write it as the (a)3/6 (1st spun 1 or 2 or 3, 2nd spun 1 or 2 or 3) (b) 2/6 (odd numbers 1,3) (c)? (d)? (e) 2/6 (prime numbers 2, 3) (I just not sure which way I am supposed to write this damn formula because this stuff always has confused the hell out of me so much, so please help me understand this best as possible and if I am doing this correctly or not at all too.) 1 solutions Answer 298734 by stanbon(57332)   on 2011-04-02 07:06:57 (Show Source): You can put this solution on YOUR website! Using Spinner to Generate Numbers: (KEEP IN MIND-that the SPINNER has just 3 sides to it using the numbers 1, 2, 3) Suppose the spinner here is spun twice in succession to determine a two-digit number. Giving each of the following. (a) the sample space 11,12,13,21,22,23,31,32,33 -------- (b) the probability of an odd number :: 6/8 = 3/4 --------- (c) the probability of an number with repeated digits ::3/8 (d) the total number of a greater than 30 ::3/8 (e) the probability of a prime number :: 4/8 = 1/2 ============== Cheers, Stan H. ==============

Age_Word_Problems/430160: The sum of ages of father and a son is 45 years.5 years ago the product of their ages was 4 times the fathers age at that time.Find the present ages of father and son? 1 solutions Answer 298733 by stanbon(57332)   on 2011-04-02 07:02:57 (Show Source): You can put this solution on YOUR website! The sum of ages of father and a son is 45 years.5 years ago the product of their ages was 4 times the fathers age at that time.Find the present ages of father and son? --- Equations: f + s = 45 (f-5)(s-5)=4(f-5) ---- Substitute for "f" and solve for "s": f = 45-s (45-s-5)(s-5) = 4(45-s-5) --- Divide both sides by 45-s-5 to get: s-5 = 4 s = 9 (son's age now) ---- Solve for "f": f+9 = 45 f = 36 (father's age now) ============================ Cheers, Stan H.

Probability-and-statistics/430161: Question:study of long distance phone calls made from the corporate office revealed the length of calls in minutes and follows a normal distribution. Mean is 4.2 minutes and standard deviation is 0.60 minutes. a) what fraction of the calls last between 4.2 and 5 minutes? b) what fraction of the calls last more than 5 minutes? c) what fraction of the calls last between 5 and 6 minutes? d) what fraction of the calls last between 4 and 6 minutes? For A I took Z=4.2-4.2/.6 and got 0 with a p score of 0.0000 and then Z=5-4.2/.6 and got 1.333 with a p score of 0.4082 So is the final answer the 0.4082 because both Zscore land on one side of the curve or do I need to take the .5000 for the other side and subtract the 0.4082? For B I took Z= 5-4.2/0.6 and got 1.333 with a p score of 0.4082 and then I .5000 minus 0.4082 and got 0.0918 and then took 1-0.0918 and got a final answer of 0.9082 For C I took the z score for 5 and got 1.333 with probability of 0.4082 and z score for 6 and got 3.0 and probability of 0.4987. My question on C is what do I do next with the 2 probabilities, they are both on the same side of the curve so do I add them, or do I subtract them, and do I subtract anything from 1? Any help is greatly appreciated, I am taking this class online in a different time zone, so getting help from the instructor is difficult. Thank you:) 1 solutions Answer 298732 by stanbon(57332)   on 2011-04-02 06:58:26 (Show Source): You can put this solution on YOUR website! Question:study of long distance phone calls made from the corporate office revealed the length of calls in minutes and follows a normal distribution. Mean is 4.2 minutes and standard deviation is 0.60 minutes. a) what fraction of the calls last between 4.2 and 5 minutes? For A I took Z=(4.2-4.2)/.6 and got 0 with a p score of 0.0000 and then Z=5-4.2/.6 and got 1.333 with a p score of 0.4082 So is the final answer the 0.4082 because both Z score land on one side of the curve or do I need to take the .5000 for the other side and subtract the 0.4082? ---- Response: The p-value for z = 0 is 0.5000 Once you have the z-values you get P(4.2< x < 5) = P(0< z < 1.333) = 0.4082 So you are correct. =================================== b) what fraction of the calls last more than 5 minutes? For B I took Z= (5-4.2)/0.6 and got 1.333 with a p score of 0.4082 and then I .5000 minus 0.4082 and got 0.0918 and then took 1-0.0918 and got a final answer of 0.9082 ---- Response: P(x> 5) = P(z > 1.333) = the p-value of 1.333 = 0.0913 ============================================================ c) what fraction of the calls last between 5 and 6 minutes? For C I took the z score for 5 and got 1.333 with probability of 0.4082 and z core for 6 and got 3.0 and probability of 0.4987. My question on C is what do I do next with the 2 probabilities, they are both on the same side of the curve so do I add them, or do I subtract them, and do I subtract anything from 1? --- Response: P(5< x < 6) = P(1.333 < z < 3) = 0.0899 ============================================================ d) what fraction of the calls last between 4 and 6 minutes? Response: z(4) = (4-4.2)/0.6 = -0.3333 Z(6) = (6-4.2)/0.6 = 3 --- P(4< x < 6) = P(-0.3333 < z < 3) = 0.6292 ================ If you do not have a TI-83 or better calculator, you should try to get one. Otherwise you will get bogged down with the arithmetic of these stat problems. ==================== Cheers, Stan H. ======

Polynomials-and-rational-expressions/430027: • Simplify each expression. Show all the steps of your simplification. a. (n2 – 5n + 3)(n2 + n – 1) b. (4a3b2)3 (3ab4)2 I have half of the first one done but i know i am missing the explination of some steps, i forget how to do the steps in depth i just do the problem without showing most of my work, pelase help! 1 solutions Answer 298712 by stanbon(57332)   on 2011-04-01 22:26:36 (Show Source): You can put this solution on YOUR website! a. (n2 – 5n + 3)(n2 + n – 1) --- = n^2(n^2+n-1) -5n(n^2+n-1) + 3(n^2+n-1) ----- = n^4+n^3+n^2 - 5n^3-5n^2+5n + 3n^2+3n-3 ---- = n^4+n^3-n^2+8n-3 ================================= b. (4a3b2)^3 (3ab4)^2 ---- = (64a^12b^6)(9a^2b^8) --- = 576a^14b^14 =================== Cheers, Stan H. ===================

Linear-systems/430119: ok here is the question graph 4x-y=1 by finding ordered pairs to satisfy the equation im studying the thea study guide i see this in the book and gives me values to replace x but i dont understand how you get the values. have not done this stuff in years please help, thanks 1 solutions Answer 298704 by stanbon(57332)   on 2011-04-01 21:26:00 (Show Source): You can put this solution on YOUR website! graph 4x-y=1 by finding ordered pairs to satisfy the equation --- y = 4x-1 --- If x = 0, y = -1 If x = 2, y = 7 --- Plot the two points (0,-1) and (2,7) and draw a line thru them: ---------------- Cheers, Stan H.

Rectangles/430114: Hi there! I have a rectangle with an area of 1150 units. What is the height and width of this rectangle if the height and width are only whole numbers? Please note that this rectangle is as close to a square as possible (the only reason it is not a perfect square is because the square root of 1150 is not a whole number) I have tried to find the answer to this by taking the square root of 1150 and multiplying integers close to it together (e.g. 34*34, 34*34, 34*33, 35*33 etc) but still come up with nothing. If you could also show me a way to solve this kind of problem I would be very grateful, as I have a few other rectangle problems like this I need solving. Thanks so much! 1 solutions Answer 298697 by stanbon(57332)   on 2011-04-01 21:16:34 (Show Source): You can put this solution on YOUR website! I have a rectangle with an area of 1150 units. What is the height and width of this rectangle if the height and width are only whole numbers? Please note that this rectangle is as close to a square as possible (the only reason it is not a perfect square is because the square root of 1150 is not a whole number) ---- The prime factored form of 1150 = 2*5^2*23 ----- The closest you can come to a square using whole numbers is 23*2(25) = = 46*25 So one dimension is 46; the other is 25 The alternative answer would be 2*25 (23) giving you dimensions 50 and 23. --- The 46*25 is closer to a square than 50*23 ================ Cheers, Stan H.

Probability-and-statistics/430113: one colored chip- red,blue, or green- is selected at random and a die is rolled. 1 solutions Answer 298690 by stanbon(57332)   on 2011-04-01 20:57:20 (Show Source): You can put this solution on YOUR website! What is the question? Cheers, Stan H.

Travel_Word_Problems/430084: On monday Ben drove to work in 35 minutes,On friday he average 9 miles per hour more, and it took him 7 minutes less to get to work. how far in miles does he travel to work. 1 solutions Answer 298689 by stanbon(57332)   on 2011-04-01 20:55:51 (Show Source): You can put this solution on YOUR website! On monday Ben drove to work in 35 minutes,On friday he average 9 miles per hour more, and it took him 7 minutes less to get to work. how far in miles does he travel to work. ------------------------ Monday DATA: time = 35/60 hr ; rate = x mph ; distance = 35x/60 miles ---- Friday DATA: time = 18/60 hr ; rate = x+9 mph ; distance = rt = (x+9)(18/60) miles ----------------- Equation: distance = distance 35x/60 = (x+9)(18/60) 35x = 18x + 9*18 7x = 9*18 x = 23.142857 ----- Distance = 35*23.142857/60 = 13.5 miles ============================================ Cheers, Stan H.

Rational-functions/430102: x2-6x+5 graph the function 1 solutions Answer 298684 by stanbon(57332)   on 2011-04-01 20:45:59 (Show Source): You can put this solution on YOUR website! y = x^2-6x+5 -------------------- graph the function --- Solve x^2-6x+5 = 0 (x-5)(x-1) = 0 --- x = 5 or x = 1 --- Plot two points: (5,0) and (1,0) ---- y-intercept = ? Let x = 0, then y = 5 Plot the point: (0,5) ---- Draw a parabola opening upward thru those three points. ================================================ cheers, Stan H.

Radicals/430101: how would i begin to solve a problem that is T= 2pie the square root l/g to solve for g. 1 solutions Answer 298683 by stanbon(57332)   on 2011-04-01 20:42:17 (Show Source): You can put this solution on YOUR website! solve a problem that is T= 2pie the square root l/g to solve for g ------------------- T = 2(pi)sqrt(1/g) ---- sqrt(1/g) = T/[2(pi)] --- 1/g = [T/(2pi)]^2 ---- g = [2pi/T)^2 =================

Linear_Equations_And_Systems_Word_Problems/430098: I need to see how to solve this word problem: A boy was offered a bonus if he sold 100 subscriptions to a magazine. Each day he sold 3 subscriptions more than he had on the previous day, and on the 8th day he reached his 100 quota. How many subscriptions did he sell each day? 1 solutions Answer 298676 by stanbon(57332)   on 2011-04-01 20:27:00 (Show Source): You can put this solution on YOUR website! A boy was offered a bonus if he sold 100 subscriptions to a magazine. Each day he sold 3 subscriptions more than he had on the previous day, and on the 8th day he reached his 100 quota. How many subscriptions did he sell each day? ----- Arithmetic Sequence with common difference = 3 and S(8) = 100 ---- Solve: S(8) = (8/2)(1st + last) 100 = 4(1st + last) 1st + last = 25 ---- a(n) = 1st+(n-1)d last = a(8) = 1st+7*3 --- Solve: 1st+ [1st+21] = 25 2*1st + 21 = 25 1st = 2 ---- 1st day: 2 2nd: 5 3rd: 8 4th: 11 5th: 14 6th: 17 7th: 20 8th: 23 --- Sum = 100 ================= Cheers, Stan H.

Linear-systems/430099: Solve the system by elimination or substitution.Show all steps. -15x+3y=6 y=2+5x 1 solutions Answer 298669 by stanbon(57332)   on 2011-04-01 20:11:10 (Show Source): You can put this solution on YOUR website! -15x+3y=6 y=2+5x ---- Substitute for "y" and solve for "x": --- -15x + 3(2+5x) = 6 -15x+6+15x = 6 6 = 6 ----- That means x can take any value. The solution is the set of points (x, 2+5x) --- It means the two equations are really the same equation. It means the system of equations is dependent. It means the graph of the two equations only gives you one line. ================== Cheers, Stan H.

Percentage-and-ratio-word-problems/430092: how many gallons of a 90% antifreeze solution must be mixed with 60 gallons of 10% antifreeze to get a mixture that is 80% antifreeze? 1 solutions Answer 298668 by stanbon(57332)   on 2011-04-01 20:07:08 (Show Source): You can put this solution on YOUR website! how many gallons of a 90% antifreeze solution must be mixed with 60 gallons of 10% antifreeze to get a mixture that is 80% antifreeze? ------------- Equation: alcohol + alcohol = alcohol 0.90x + 0.10*60 = 0.80*(x+60) ---- Multiply thru by 100: --- 90x + 10*60 = 80x+80*60 10x = 70*60 x = 420 gallons (amt. of 90% solution needed) ============================ Cheers, Stan H. ============

Numeric_Fractions/430097: solve a - 7/10 = 4 3/5 1 solutions Answer 298667 by stanbon(57332)   on 2011-04-01 20:03:27 (Show Source): You can put this solution on YOUR website! solve a - 7/10 = 4 3/5 -------------------- a - (7/10) = (23/5) ----- Multiply thru by 10: 10a - 7 = 46 10a = 53 a = 5 3/10 ============= Cheers, Stan H. ===========

Numeric_Fractions/430096: solve f - 3 1/3 = 12 1/4 1 solutions Answer 298666 by stanbon(57332)   on 2011-04-01 20:01:24 (Show Source): You can put this solution on YOUR website! solve f - 3 1/3 = 12 1/4 ------------ f - (10/3) = (49/4) --- Multiply thru by 12: ---- 12f - 40 = 3*49 --- 12f = 187 --- f = 15 29/50 ================= Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/430080: Let Q represent the mass of a quantity of carbon 14, whose half-life is 5437 years. The quantity present after t years is given by Q = 9 (1/2)t/5437 Sketch the graph of the function over the interval t = 0 to t = 10000. a) Find the initial quantity. b) Find the quantity present after 2171 years. 1 solutions Answer 298660 by stanbon(57332)   on 2011-04-01 19:41:59 (Show Source): You can put this solution on YOUR website! Let Q represent the mass of a quantity of carbon 14, whose half-life is 5437 years. The quantity present after t years is given by Q(t) = 9 (1/2)^(t/5437) -------------------------------- Sketch the graph of the function over the interval t = 0 to t = 10000 Note: This site's graphing cannot handle that large a domain. It does not provide a true picture of what is happening to the function values as they decrease over 10,000 years. -----------------------------------. a) Find the initial quantity. Q(0) = 9*(1/2)^0 = 9 units of wt. ===================================== b) Find the quantity present after 2171 years. Q(2171) = 9(1/2)^(2171/5437) = 6.82403.. units of wt. ==== Cheers, Stan H.

Evaluation_Word_Problems/430086: Which of the following expressions is equal to (x+2)+(x-2)(2x+1)? A 2x^2-2x B 2x^2-4x C 2x^2+x D 4x^2+2x 1 solutions Answer 298658 by stanbon(57332)   on 2011-04-01 19:27:52 (Show Source): You can put this solution on YOUR website! (x+2)+(x-2)(2x+1) ----- = (x+2) + 2x^2+x-4x-2 --- = 2x^2-2x ============ Cheers, Stan H.