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Recent problems solved by 'stanbon'

stanbon answered: 57158 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, >>Next

Quadratic_Equations/153479: On planet X, an object falls 18 feet in 3 seconds. Knowing the distance it falls varies directly with the square of the time of fall, how long does it take an object to fall 100 feet? Round your answer to three decimal places 1 solutions Answer 112977 by stanbon(57226)   on 2008-08-26 07:52:45 (Show Source): You can put this solution on YOUR website! On planet X, an object falls 18 feet in 3 seconds. Knowing the distance it falls varies directly with the square of the time of fall, how long does it take an object to fall 100 feet? Round your answer to three decimal places --------------- distance = k*time^2 d = kt^2 Find "k": 18 = k*3^2 k = 2 ---------- Equation for planet X: d = 2t^2 100 = 2*t^2 t^2 = 50 t = 5sqrt(2) t = 7.071 seconds ===================== Cheers, Stan H.

logarithm/153462: Expanding Logarithms: Log12 + 1/2 Log7 - Log2 1 solutions Answer 112976 by stanbon(57226)   on 2008-08-26 07:48:51 (Show Source): You can put this solution on YOUR website! Log12 + 1/2 Log7 - Log2 -------- = Log[12*(7^(1/2))/2] = Log[6*sqrt(7)] ===================== Cheers, Stan H.

Trigonometry-basics/153461: -60001000000 x 10 to the power of ten how do youy write that 1 solutions Answer 112975 by stanbon(57226)   on 2008-08-26 07:46:00 (Show Source): You can put this solution on YOUR website! -60001000000 x 10 = (-6.0001000000 x 10^10) x 10 = -6.0001000000 x 10^11 ============================= Cheers, Stan H.

Polynomials-and-rational-expressions/153471: factor completely: 9m^2-9 choices: 1) (3m-3)+(3m+3) 2) (3m+3)^2 3) (3m+3)(3m-3) 4) (3m-3)^6 ??what is the difference between option 1 and option 3? 1 solutions Answer 112974 by stanbon(57226)   on 2008-08-26 07:42:29 (Show Source): You can put this solution on YOUR website! factor completely: 9m^2-9 choices: 1) (3m-3)+(3m+3) 2) (3m+3)^2 3) (3m+3)(3m-3) 4) (3m-3)^6 ??what is the difference between option 1 and option 3? ---------------- Since these are your choices, 1 and 3 are both correct and there is no difference. ---------------- A better way to factor your problem is: = 9(m^2-1) =9(m-1)(m+1) =============== Cheers, Stan H.

Polynomials-and-rational-expressions/153474: A stone is thrown into a well with an intial speed of 8 feet per second. The well is 80 feet deep. How long will it take for the stone to hit the bottom of the well? Use the equation d=vt+16t^2. where d=depth of the well, v= initial speed, and time choices: 1) 2 2) 5/2 3) 2 or 5/2 4) none of these 1 solutions Answer 112972 by stanbon(57226)   on 2008-08-26 07:38:45 (Show Source): You can put this solution on YOUR website! A stone is thrown into a well with an intial speed of 8 feet per second. The well is 80 feet deep. How long will it take for the stone to hit the bottom of the well? Use the equation d=vt+16t^2. where d=depth of the well, v= initial speed, and time -------------------- EQUATION: d(t) = vt + 16t^2 80 = 8t + 16t^2 10 = t + 2t^2 2t^2 + t - 10 = 0 2t^2 + 5t - 4t - 10 = 0 t(2t+5) -2(2t+5) = 0 (2t+5)(t-2) = 0 Positive solution: t = 2 seconds ================== Cheers, Stan H. ================== choices: 1) 2 2) 5/2 3) 2 or 5/2 4) none of these

Probability-and-statistics/153425: Can you please help me with this? Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random: a) what is the probability that the drug will be effective for 2 hours or less? b) what is the probability that the drug will be effective for 1 hour or less? c) what is the probability that the drug will be effective for 3 hours or more? I greatly appreciate all your help. Julie 1 solutions Answer 112971 by stanbon(57226)   on 2008-08-26 07:33:25 (Show Source): You can put this solution on YOUR website! Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random: ------------------------ a) what is the probability that the drug will be effective for 2 hours or less? Find the z-score for 2 hours: z(2) = (2-2)/0.3 = 0 P(x <= 2) = P(z <= 0) = 0.5 ------------------------------------ b) what is the probability that the drug will be effective for 1 hour or less? Find the z-score for 1 hour: z(1) = (1-2)/0.3 = -1/3 P(x <= 1) = P(z <= -1/3) = 0.36944.. -------------------------------------- c) what is the probability that the drug will be effective for 3 hours or more? Find the z-score for 3 hours: z(3) = (3-2)/0.3 = 1/3 P(x <= 3) = P(z <= 1/3) = 0.630559.... ============================================== Cheers, Stan H.

Permutations/153448: 1.In how many different ways can 6 classes be scheduled during a 6-period day? 2.In how many different ways can you arrange the letters of the word INTERNET? 3.In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time? 4.In how many different ways can you arrange the letters of the word TRIGONOMETRY? 5.In how many different ways can the 9 starters of a baseball team be placed in their positions? 6. How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)? 7. Of 10 candidates, the first 6 are being interviewed in the morning, and the last 4 in the afternoon. In how many ways can the interviewer arrange a schedule? 8.How many seven-digit phone numbers can be formed if the first digit cannot be 0 and a.repetition of digits is not permitted? b.if repetition of digits is permitted? 9. The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible? 10. Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if: a. the first letter must be Y b. the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first). 1 solutions Answer 112948 by stanbon(57226)   on 2008-08-25 23:05:09 (Show Source): You can put this solution on YOUR website! 1.In how many different ways can 6 classes be scheduled during a 6-period day? 6! --------------------------------- 2.In how many different ways can you arrange the letters of the word INTERNET? 8!/[2!*2!*2!*2!] --------------------------------- 3.In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time? 8P4 = 8*7*6*5 --------------------------------- 4.In how many different ways can you arrange the letters of the word TRIGONOMETRY? 12!/[2!*2!*2!] --------------------------------- 5.In how many different ways can the 9 starters of a baseball team be placed in their positions? 9! --------------------------------- 6. How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)? 4*4 --------------------------------- 7. Of 10 candidates, the first 6 are being interviewed in the morning, and the last 4 in the afternoon. In how many ways can the interviewer arrange a schedule? 10C6*6! * 4C4*4! ------------------------- 8.How many 7-digit phone numbers can be formed if the first digit cannot be 0 and a.repetition of digits is not permitted? 9*9*8*7*6*5*4 ------------------------- b.if repetition of digits is permitted? 9*10^6 ------------------------- etc. 9. The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible? 10. Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if: a. the first letter must be Y b. the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first). ============================== Cheers, Stan H.

Travel_Word_Problems/153443: a person traveling 4 hours by plane and 25 hours by ship covers 1580 miles.if the speed of the plane had been one half of the actual speed and the speed of the ship had been one fourth greater,the person would have traveled only 1315 miles in the same length of time.find the speed of the plane and the ship. 1 solutions Answer 112942 by stanbon(57226)   on 2008-08-25 22:09:51 (Show Source): You can put this solution on YOUR website! a person traveling 4 hours by plane and 25 hours by ship covers 1580 miles. if the speed of the plane had been one half of the actual speed and the speed of the ship had been one fourth greater, the person would have traveled only 1315 miles in the same length of time. find the speed of the plane and the ship. ------------------------------ Let p be the plane speed and s be the ship speed. 4p + 25s = 1580 4(p/2) + 25(5/4)s = 1315 ----------------- Rearrange: 4p + 25s = 1580 2p + (125/4)s = 1315 ----------------------- Multiply thru 2nd equation by 2 to get: 4p + 25s = 1580 4p + (125/2)s = 2630 --------------------- Subtract the 1st equation from the 2nd to get: (75/2)s = 1050 s = 28 mph (ship's speed) ----------------- Substitute s = 28 into 4p + 25s = 1580 to solve for "p" 4p + 25*28 = 1580 4p + 700 = 1580 4p = 880 p = 220 mph (plane's speed) ============================== Cheers, Stan H.

Permutations/153447: 1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected? 2.I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls? 3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery? 4. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. How many ways can 4 toppings be selected where: All the toppings are vegetables All the toppings are meat There is only cheese on the pizza There are 2 vegetables, 1 meat and 1 cheese There are 3 meats and 1 cheese. What's your favorite combo? 1 solutions Answer 112939 by stanbon(57226)   on 2008-08-25 21:50:08 (Show Source): You can put this solution on YOUR website! 1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected? 15C6 = 15!/(16-6)!6! = [15*14*13*12*11*!0] / [1*2*3*4*5*6] = 5005 -------------------------------------------- 2.I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls? 9C3 * 6C3 = 84 * 20 = 1680 -------------------------------------------- 3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery? 40C6 = 3,838,380 --------------------------------------------- 4. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. How many ways can 4 toppings be selected where: All the toppings are vegetables 8C4 = 70 ----------------------- All the toppings are meat 5C4 = 5 ----------------------- There is only cheese on the pizza 4C4 = 1 ----------------------- There are 2 vegetables, 1 meat and 1 cheese 8C2 * 5C1 * 4C1 = 28 * 5 * 4 = 560 ----------------------- There are 3 meats and 1 cheese. 5C3 * 4C1 = 10*4 = 40 ----------------------- What's your favorite combo? ----------------------- Cheers, Stan H.

Expressions-with-variables/153446: This question is from textbook algebra 1 need help please, the product of 2 and the second power of y, the answer came up with is y2 x 2. is that correct? 1 solutions Answer 112937 by stanbon(57226)   on 2008-08-25 21:38:39 (Show Source): You can put this solution on YOUR website! need help please, the product of 2 and the second power of y, the answer came up with is y2 x 2. is that correct? ------------- Correct You might write is as 2y^2 =========================== Cheers, Stan H.

Matrices-and-determiminant/153430: This question is from textbook Advanced Mathematical Concepts I need help in completing the problem. I need help on starting the problem after I set it up as an augmented matrix. It would be great if I could get it step-by-step: 2x+6y+8z=5; -2x+9y-12z=-1; 4x+6y-4z=3. Thanks a lot! 1 solutions Answer 112931 by stanbon(57226)   on 2008-08-25 21:03:50 (Show Source): You can put this solution on YOUR website! 2x+6y+8z =5 -2x+9y-12z=-1 4x+6y-4z =3 -------------------- +2...+6...+8....+5 -2...+9...-12...-1 +4...+6...-4....+3 ------------------------- Add 1st to 2nd to get: +2...+6...+8....+5 +0...+15..-4....+4 +4...+6...-4....+3 ------------------------ Add -2 times the 1st to the 3rd to get: +2...+6...+8....+5 +0...+15..-4....+4 +0...-6..-20....-7 ----------------------- Add 3rd to 1st to get: +2...+0...-12...-2 +0...+15..-4....+4 +0...-6..-20....-7 -------------------- Divide thru equation 3 by -6: +2...+0...-12...-2 +0...+15..-4....+4 +0...+1..+10/3..+7/6 -------------------- Add -15 time 3rd to the 2nd to get: +2...+0...-12...-2 +0...+0...-54...-13.5 +0...+1..+10/3..-7/6 ------------------------ Solve the 2nd equation for z: -54z = -13.5 z = 0.25 or 1/4 --------------------- Substitute z = 1/4 into the 3rd equation to solve for "y": y +(10/3)(1/4) = -7/6 y + (5/6) = -7/6 y = -2 ------------------ Substitute z = 1/4 into the 1st equation to solve for "x" 2x -12*(1/4) = -2 2x - 3 = -2 2x = 1 x = 1/2 ---------------- Final solution: x = 1/2 y = -2 z = 1/4 =============== Cheers, Stan H.

Probability-and-statistics/153427: Can somone please tell me how to do this i am so confused. Let X be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that X has an approximately normal distribution with mean U = 6.8 hours and standard deviation O=2.1 hours. Convert each of the following X intervals to standardized Z intervals: a) x is less than or equal to 7.5 b) 5 is less than or equal to X is less than or equa to 8 c) x is greater than or equal to 4 Convert each of the following z intervals to raw score X intervals d) z is greater than or equal to -2 e) 0 is less than or equal to Z is less than or equal to 2 f) Z is less than or equal to 3 Thank you for your help in advance jill 1 solutions Answer 112928 by stanbon(57226)   on 2008-08-25 20:24:57 (Show Source): You can put this solution on YOUR website! After interviewing many students, it was found that X has an approximately normal distribution with mean U = 6.8 hours and standard deviation O=2.1 hours. Convert each of the following X intervals to standardized Z intervals: a) x is less than or equal to 7.5 Find the z score of 7.5 z(7.5) = (7.5-6.8)/2.1 = 0.333333... z-interval: z <= 0.33333.... ------------------------------------------ b) 5 is less than or equal to X is less than or equal to 8 z(5) = (5-6.8)/2.1 = -0.8571... z(8) = (8-6.8)/2.1 = 0.5714... z-interval: (-0.8571 < z < 0.5714) ----------------------------------------------- c) x is greater than or equal to 4 Find z(4) then write the z-interval. ------------------------------------------ Convert each of the following z intervals to raw score X intervals d) z is greater than or equal to -2 x(z) = sigma*z + u x(-2) = 2.1*-2 + 6.8 = 2.6 x-interval: x >= 2.6 -------------------------------- e) 0 is less than or equal to Z is less than or equal to 2 x(0) = 2.1*0 + 6.8 = 6.8 x(2) = 2.1*2 + 6.8 = 11 x-interval : 6.8 <= x <= 11 -------------------------------- f) Z is less than or equal to 3 Use the same process on this problem. ============================= Cheers, Stan H.

Exponents-negative-and-fractional/153422: -4-[-(-5)]+|-6| i have no idea how to do this problem 1 solutions Answer 112927 by stanbon(57226)   on 2008-08-25 19:54:55 (Show Source): You can put this solution on YOUR website! -4-[-(-5)]+|-6| = -4 -|5| + 6 = -4 -5 + 6 = -9 + 6 = -3 ========== Cheers, Stan H.

Linear_Algebra/153419: Here is problem. I know the answer but now the operation.. Music Class has 1 freshman, 6 sophmores and 11 juniors. 1/3rd of the class are seniors. I instantly just shouted 9 but I don't know how I came up to it and need to know what the process is.. 1 solutions Answer 112925 by stanbon(57226)   on 2008-08-25 19:52:17 (Show Source): You can put this solution on YOUR website! Music Class has 1 freshman, 6 sophmores and 11 juniors. 1/3rd of the class are seniors. ---------- Let "x" be the number in the class. (2/3)rd of the class = 1 + 6 + 11 (2/3)x = 18 x = 27 ( # in the class ) # of seniors = (1/3)*27 = 9 ================================== You have it. ================================== Cheers, Stan H.

Inverses/153401: if it takes you 6 hours to run four loads with omly one washer, how long would it yake to run the same at the laudromat using 3 washers? 1 solutions Answer 112923 by stanbon(57226)   on 2008-08-25 19:46:27 (Show Source): You can put this solution on YOUR website! if it takes you 6 hours to run four loads with only one washer, Each load takes 6/4 = 3/2 hr per washer -------------------- how long would it take to run the same at the laudromat using 3 washers? ---------------------- (# of loads)/(# of washers)k = (# of hours) (4/1)k = 6 k = 3/2 -------------- EQUATION: (# of loads)/(# of washers)(3/2) = # of hours (4) /( 3) (3/2) = # of hours 4/2 = # of hours 2 = # of hours ------------------- Ans: In 2 hours, 3 washers can do 4 loads. ======================== Cheers, Stan H.

Exponents/153416: what does a problem mean when it's to the 4th power or 5th power,whatever the number is to the 4th power or whatever. how do I work this problem. example: 3 to the 4th power or -2 to the 5th power how do I do this? 1 solutions Answer 112920 by stanbon(57226)   on 2008-08-25 19:24:51 (Show Source): You can put this solution on YOUR website! example: 3 to the 4th power or -2 to the 5th power how do I do this? ---------------- 3^4 = 3*3*3*3 = 81 -------------- (-2)^5 = -2*-2*-2*-2*-2 = -32 ================= Cheers, Stan H.

Trigonometry-basics/153413: sin of theta = 0.7586 i dont know what to do? 1 solutions Answer 112919 by stanbon(57226)   on 2008-08-25 19:22:12 (Show Source): You can put this solution on YOUR website! sin of theta = 0.7586 Solve for theta by taking the inverse sine of both sides to get: theta = sin^-1(0.7586) theta = 49.34 degrees ========================== Cheers, Stan H.

absolute-value/153405: Solve the equation |y-6|+2y=9 So far, I have: y-6=-(9-2y) y-6=-9+2y -y=-3 y=3 I tested that, and it is correct. Am I on the right track, and/or is there another answer? How do I find this additional answer? Also - Graph the equation y=|x+4| + |3-x| I know how to graph, but I am not quite sure how to start off. Many thanks if you can simplify it. 1 solutions Answer 112918 by stanbon(57226)   on 2008-08-25 19:18:11 (Show Source): You can put this solution on YOUR website! Solve the equation |y-6|+2y=9 Rearrange: |y-6| = 9-2y y-6 = 9-2y or y-6 = -(9-2y)= 2y-9 3y = 15 or y = 3 y = 5 or y = 3 ---------------- Testing: Does y = 5 ? |5-6| + 2*5 = 9 1+10 = 9 False; so y=5 is not a solution. ------------------ Testing: Does y = 3 ? |3-6| + 2*3 = 9 3 + 6 = 9 True ; so y=3 is the only solution. ------------------ Cheers, Stan H.

test/153410: Simplify the following: x^2+y^2-[x(x+y)-y(y-x)] 1 solutions Answer 112917 by stanbon(57226)   on 2008-08-25 19:05:07 (Show Source): You can put this solution on YOUR website! Simplify the following: x^2+y^2-[x(x+y)-y(y-x)] = x^2 + y^2 -[x^2+xy -y^2+xy] = x^2 + y^2 -x^2 +y^2 -2xy = 2y^2 - 2xy ============== Cheers, Stan H.

Numeric_Fractions/153411: You went trout fishing and caught 6 trout fish. The lengths are 8 5/8, 10 1/2, 9 1/4, 8 3/4, 10 2/3 and 9 5/6. What is the average length of the trout you caught? Please explain. I get 1383/144 or 9 87/144 but this is wrong, what am I doing wrong? 1 solutions Answer 112915 by stanbon(57226)   on 2008-08-25 19:00:24 (Show Source): You can put this solution on YOUR website! Add the numbers to get 309/5 Divide by 6 to get 103/10 or 10.3 =================================== Cheers, Stan H.

Polynomials-and-rational-expressions/153407: This question is from textbook Algebra I I can't figure out how to do this problem. How do I show my work on this equation: 40/a - 4 = 0 I know the answer is 10, it's obvious, but I dont know how to get that answer. Please help me! 1 solutions Answer 112914 by stanbon(57226)   on 2008-08-25 18:53:09 (Show Source): You can put this solution on YOUR website! (40/a) - 4 = 0 (40/a) = 4 Multiply both sides by a to get: 40 = 4a a = 10 ================== Cheers, Stan H.

Travel_Word_Problems/153398: a car used 14 gal. of gas an traveled a total distance of 550 mi. the car's fuel efficiency is 40 mi./gal on the highway and 35 mi/gal in the city. how many gal of gasoline were used on the highway? write linear equation and solve 1 solutions Answer 112912 by stanbon(57226)   on 2008-08-25 18:46:27 (Show Source): You can put this solution on YOUR website! a car used 14 gal. of gas and traveled a total distance of 550 mi. the car's fuel efficiency is 40 mi./gal on the highway and 35 mi/gal in the city. how many gal of gasoline were used on the highway? ------------------------ Let h be distance on highway ; Let c be distance in city. -------------- EQUATIONS: distance equation: h + c = 550 gas use equation : (h/40 + c/35) = 14 Simplifying the 2nd equation: 7h + 8c = 3920 ---------------------------------- EQUATIONS: h + c = 550 7h+8c = 3920 --------------------- Modify: 8h + 8c = 4400 7h + 8c = 3920 ----------------- h = 480 miles (distance traveled on the highway) 480/40 = 12 gallons (# of gallons of gas used in highway travel) =========================== Cheers, Stan H.

Probability-and-statistics/153265: This question is from textbook Trevor wants to buy a local restaurant. 60% of the business days it's open, the restaurant makes a $850 profit. Estimate the probability that the store will make p$850 profit more than 17 out of the next 20 business days. If this actually happened, might you suspect that p is greater than 0.60? High school seniors in SAT math had a mean score of 500 with a standard deviation 100. In an ACT, the mean was 18 and a standard deviation of 6. Both scores are normally distributed. a) An engineering school only accepts SAT and ACT scores in the top 10%. What's the minimum SAT and ACT scores for this program b) Suppose the school accepts SAT and ACT scores in the top 20%. What are the minimum SAT and ACT scores for this program? c) IF the school accepts the top 60% scores, what are the minimum SAT and ACT scores? 1 solutions Answer 112907 by stanbon(57226)   on 2008-08-25 18:07:44 (Show Source): You can put this solution on YOUR website! Trevor wants to buy a local restaurant. 60% of the business days it's open, the restaurant makes a $850 profit. Estimate the probability that the store will make p$850 profit more than 17 out of the next 20 business days. If this actually happened, might you suspect that p is greater than 0.60? Comment: Your problem does not make sense as posted. -------------------------------------------------------------- High school seniors in SAT math had a mean score of 500 with a standard deviation 100. In an ACT, the mean was 18 and a standard deviation of 6. Both scores are normally distributed. -------------------------------------------------- a) An engineering school only accepts SAT and ACT scores in the top 10%. What's the minimum SAT and ACT scores for this program Find the z-score that separates the top 10% of the standard normal curve area from the bottom 90%: That value is 1.2816 Now find the raw ACT and SAT scores that correspond using z=(x-u)/sigma. ACT: 1.2816 = (x-18)/6; x = 6*1.2816+18 = 25.689.. SAT: 1.2816 = (x-500)/100; x = 100*1.2816+500 = 628.16 ------------------------------------------------------- b) Suppose the school accepts SAT and ACT scores in the top 20%. What are the minimum SAT and ACT scores for this program? Follow the same procedure with z = 0.8416 ----------------------- c) IF the school accepts the top 60% scores, what are the minimum SAT and ACT scores? Follow the same procedure with z = -0.2533 ====================== Chers, Stan H.

Graphs/153363: Please help. I am having trouble with a few problems. Thanks for listening. evaluate the function: g(x)=3.2x+2.8 when x=3, x=0 and x=-4 graph the line that has the given intercepts: x intercept: -1/2 y intercept: -3 sketch graph of the inequality: 7y-2x=3<17 1 solutions Answer 112886 by stanbon(57226)   on 2008-08-25 15:53:03 (Show Source): You can put this solution on YOUR website! evaluate the function: g(x)=3.2x+2.8 when x=3, x=0 and x=-4 g(3) = 3.2*3 + 2.8 = 9.6+2.8 = 12.4 g(0) = 3*0 + 2.8 = 2.8 g(-4) = 3*-4+2.8 = -12 + 2.8 = 9.2 ======================================= graph the line that has the given intercepts: x intercept: (-1/2,0) y intercept: (0,-3) slope = -3/(1/2) = -6 intercept: -3 EQUATION: y = -6x - 3 --------------------------- ================================================== sketch graph of the inequality: 7y-2x+3<17 ---------------- 1st: Graph the EQUALITY as a dashed line; it is the boundary of the INEQUALITY: 7y - 2x -14 < 0 7y = 2x + 14 y = (2/7)x +2 ---------------- 2nd: Since you want y to be LESS THAN (2/7)x + 2, shade the half-plane BELOW the boundary. That is the graph of the INEQUALITY. ===================================== Cheers, Stan H.

Complex_Numbers/153359: Cn you please help me solve this system of equations? 3x-y=5 2x-3y=-6 1 solutions Answer 112884 by stanbon(57226)   on 2008-08-25 15:35:36 (Show Source): You can put this solution on YOUR website! 3x-y=5 2x-3y=-6 -------------- Multiply thru the 1st equation by 3 to get: 9x - 3y = 15 2x - 3y = -6 ---------------- Subtract the 2nd equation from the 1st to get: 7x = 21 x = 3 ----------------- Substitute into 3x-y = 5 to solve for Y: 3*3 -y = 5 y = 4 ------------ Final solution: x =3; y = 4 ================ Cheers, Stan H.

Sequences-and-series/153362: Can you please help me expand this set of numbers? (3x-5)(2x+7) 1 solutions Answer 112883 by stanbon(57226)   on 2008-08-25 15:30:32 (Show Source): You can put this solution on YOUR website! expand this set of numbers? (3x-5)(2x+7) Use FOIL: F: 3x * 2x = 6x^2 O: 3x * 7 = 21x I: -5*2x = -10x L: -5*7 = -35 ----------------- Combine those four terms to get: 6x^2 + 11x -35 ================== Cheers, Stan H.

Expressions-with-variables/153340: I am asking for help,please. simplify: (5x^-7x+2)-(8-4x) the 5x^ means 5x square solve: 12/x+4 = 2+ x/x+4 the / represents the fraction line 1 solutions Answer 112869 by stanbon(57226)   on 2008-08-25 12:04:34 (Show Source): You can put this solution on YOUR website! simplify: (5x^2-7x+2)-(8-4x) = 5x^2 - 7x + 2 - 8 + 4x = 5x^2 - 3x - 6 ========================== solve: 12/x+4 = 2+ x/x+4 12/(x+4) = x/(x+4) Since the denominators are the same, the numerators are equal. x = 12 ============ Cheers, Stan H.

Polynomials-and-rational-expressions/153337: 9x^2y^3-3x^3y^2-15xy 1 solutions Answer 112865 by stanbon(57226)   on 2008-08-25 12:00:10 (Show Source): You can put this solution on YOUR website! 9x^2y^3-3x^3y^2-15xy Assuming you want to factor this: = 3xy(3xy^2 - x^y^2 - 5) ========================== Cheers, Stan H.

Human-and-algebraic-language/153325: An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train. 1 solutions Answer 112864 by stanbon(57226)   on 2008-08-25 11:57:18 (Show Source): You can put this solution on YOUR website! An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train. -------------------------------- Local train DATA: rate = x mph ; distance = 50 miles ; time = 50/x hrs ---------------- Express train DATA: rate = 2x mph ; distance = 50 miles ; time = 50/2x hrs ---------------- EQUATION: local train time - express train time = 1 hr 50/x - 50/2x = 1 Multiply thru by 2x to get: 100 - 50 = 2x 2x = 50 x = 25 mph (local train speed) 2x = 50 mph (express train speed) =================== Cheers, Stan H.

Polynomials-and-rational-expressions/153334: (x-4)^3 I got this answer: x^3-12x^2+48x-64 Is that correct? 1 solutions Answer 112859 by stanbon(57226)   on 2008-08-25 11:45:52 (Show Source): You can put this solution on YOUR website! That looks good. Cheers, Stan H.

logarithm/153275: solve for x: log5x(x-1)=2 1 solutions Answer 112837 by stanbon(57226)   on 2008-08-25 09:18:49 (Show Source): You can put this solution on YOUR website! solve for x: log5x(x-1)=2 ---------- This says "when the exponent of 10 is 2 then 10^2 = 5x(x-1)" --------------- EQUATION: 5x(x-1) = 10^2 5x^2 - 5x - 100 = 0 x^2 -x -20 = 0 (x-5)(x+4) = 0 x = 5 or x= -4 ----------- Checking in the original problem: Can x = 5 ? log[5*5(5-1) = 2 log[100] = 2 true ------------- Can x = -4 log5(-4)(-4-1) = 2 log(100) = 2 true ---------------- Cheers, Stan H.