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Recent problems solved by 'stanbon'

stanbon answered: 57281 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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Functions/120001: 2. Take a look at the table below and write out an equation for f(x). x -2 -1 0 1 2 f(x) -5 -2 1 4 7 1 solutions Answer 87949 by stanbon(57354)   on 2008-01-13 21:53:37 (Show Source): You can put this solution on YOUR website! write out an equation for f(x). x -2 -1 0 1 2 f(x) -5 -2 1 4 7 ---------- Notice that when x = 0, y = 1 so the y-intercept is 1 -------- Notice that when x increases from 0 to 1, y increases from 1 to 4 So the slope is 3 -------------------- EQUATION: y = 3x+1 ================= Cheers, Stan H.

Functions/120022: factor x^3+2x^2-5x-6 by using synthetic division. 1 solutions Answer 87948 by stanbon(57354)   on 2008-01-13 21:48:57 (Show Source): You can put this solution on YOUR website! factor x^3+2x^2-5x-6 by using synthetic division. -------------------------- f(-1) = 0, so -1 is a zero. ----------------------------- -1)....1....2....-5....-6 ........1....1....-6....|..0 Remainder = 0 Quotient = x^2+x-6 which can be factored as (x+3)(x-2) ----------------------- Factored form = (x+1)(x-2)(x+3) ================= Cheers, Stan H.

Expressions-with-variables/120021: Please help!! Been out of school 14 yrs... Directions: Solve for the indicated variable. 1. 5x + y = 8;y <--- wanting to say do what?? And this one. Directions: Tell which equation you would use to isolate a variable. Explain your reasoning. 1. 3x - y = 5 2x + y = 0 I just don't get it! 1 solutions Answer 87947 by stanbon(57354)   on 2008-01-13 21:41:40 (Show Source): You can put this solution on YOUR website! Solve for the indicated variable. 1. 5x + y = 8;y <--- wanting to say do what?? Equation: 5x+y = 8 Subtract 5x from both sides to get: y = -5x+8 ----------------------- And this one. Directions: Tell which equation you would use to isolate a variable. Explain your reasoning. 3x - y = 5 2x + y = 0 ---------------- Solve the 2nd equation for "y" to get: y = -2x The reason for using the 2nd equation is nothing more than that the result is simpler. There is no magic involved. =================== Cheers, Stan H.

Linear-systems/120020: Am I asking this correctly? The directions say: Use the substitution method to solve the linear system. Problem: 1. y = x + 2 2x + y = 8 1 solutions Answer 87945 by stanbon(57354)   on 2008-01-13 21:36:59 (Show Source): You can put this solution on YOUR website! y = x + 2 2x + y = 8 ------------- Solve both for "y": y = x+2 y = -2x+8 ------------- Substitute "x+2" in place of "y" in the 2nd equation: x+2 = -2x+8 3x = 6 x=2 --------- Substitute into y = x+2 to solve for y: y = 2+2 = 4 ============================== Cheers, Stan H.

Systems-of-equations/120012: The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number. 1 solutions Answer 87944 by stanbon(57354)   on 2008-01-13 21:30:11 (Show Source): You can put this solution on YOUR website! The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number. ------------- Let the two-digit number be 10t+u where t is the tens digit and u the units digit. ------------------- EQUATION: t+u = 11 10u+t = 10t+u + 45 ------------- Rearrange the equations: t+u = 11 9t-9u = -45 ------------- Simplify: t+u = 11 t-u = -5 --------- Add the equations to solve for "t": 2t = 6 t = 3 -------- Substitute to solve for "u": 3+u = 11 u = 8 -------------- The original number is 38 ============== Cheers, Stan H.

Functions/120018: if f(x)=2x-7 and g(x)=x^2-4x-5, find [gof](5) 1 solutions Answer 87943 by stanbon(57354)   on 2008-01-13 21:24:36 (Show Source): You can put this solution on YOUR website! if f(x)=2x-7 and g(x)=x^2-4x-5, find [gof](5) -------------- [gof](5) = [g[f(5)] = g[2*5-7] = g[3] = 3^2-4*3-5 = -8 =================== Cheers, Stan H.

absolute-value/120013: using [x-145.045]< (or = to)3.295 where x is a baseballs weight in grams. q: a manufactured baseball weighs 147 grams. is this baseball acceptable? Q: a manufactured baseball weighs 140.8 grams. is this baseball acceptable? 1 solutions Answer 87942 by stanbon(57354)   on 2008-01-13 21:21:19 (Show Source): You can put this solution on YOUR website! using [x-145.045]< (or = to)3.295 where x is a baseballs weight in grams. q: a manufactured baseball weighs 147 grams. is this baseball acceptable? Test x=147: [147-145.045] <= 3.295 1.955 <= 3.295 True, therefore x=147 is acceptable. ------------------------------------ Q: a manufactured baseball weighs 140.8 grams. is this baseball acceptable? Test x = 140.8 [140.8-145.045] <- 3.295 --4.2450 < 3.295 True, therefore x = 140.8 is acceptable ======================== Cheers, Stan H.

Linear-systems/120011: This question is from textbook i need to find the solution to these system of equations by substition method. y=4-3x y=2x-1 1 solutions Answer 87941 by stanbon(57354)   on 2008-01-13 21:00:54 (Show Source): You can put this solution on YOUR website! find the solution to these system of equations by substition method. y=4-3x y=2x-1 --------- Substitute 2x-1 in place of "y" in the 1st equation to solve for "x": 2x-1 = 4-3x 5x = 5 x = 1 ----------- Substitute into y = 2x-1 to solve for "y": y = 2*1-1 y = 1 =============== Cheers, Stan H.

Sequences-and-series/120007: How do I find all of the possibilities to combine 56 numbers, when I can only use six at a time? (I.E. 56,55,54,53,52,51 and 1,2,3,4,5,6) Thanks much : ) 1 solutions Answer 87940 by stanbon(57354)   on 2008-01-13 20:58:24 (Show Source): You can put this solution on YOUR website! Hopefully you are trying to list all the groups of six. The number of such groups is 56C6 = 56!/[50!*6!]= 32,468,436 ----------------- Cheers, Stan H.

Linear-equations/120009: This question is from textbook algebra 2 Find an Equation for the least square line of the data below. Use the equation to predict the x-value that corresponds to a y -value of 7 X:8 4 1 5 4 4 9 8 5 2 7 1 6 3 2 4 Y:7 6 2 5 6 4 8 8 6 3 8 3 6 4 1 3 I have graphed the line but i dont know how i am supose to get the equation for the line 1 solutions Answer 87939 by stanbon(57354)   on 2008-01-13 20:54:40 (Show Source): You can put this solution on YOUR website! Using a TI Linear Regression function I find the Least Squares equation to be y = 0.798x+1.357 ------------------------------- I y = 7 the value of x is 7.07 ==================== Cheers, Stan H.

Linear-systems/120008: Please please help me with this problem! This problem is about using Point-Slope Form and asks to graph each equation. What is ? i need to know what is the slope and which is the rise and run. I think that might be like; slope= 0, and rise over run = -3 over -2. I'm really confused i think i know how to graph the equation. Thank You SO much 1 solutions Answer 87938 by stanbon(57354)   on 2008-01-13 20:46:23 (Show Source): You can put this solution on YOUR website! This problem is about using Point-Slope Form and asks to graph each equation. What is y-2=(x-3) ? i need to know what is the slope and which is the rise and run. --------- Your equation can be written as y = x-3+2 or y = x-1 ----------------- The slope is the coefficient of "x" which is 1. The rise over the run is 1/1. ------------- Cheers, Stan H.

Quadratic-relations-and-conic-sections/119346: I am having a very difficult time solving this equation for an ellipse if i could get some help i would really appreciate it: 4x^2+9y^2=1 thanks 1 solutions Answer 87891 by stanbon(57354)   on 2008-01-13 13:31:06 (Show Source): You can put this solution on YOUR website! What would you like to do with the equation? Cheers, Stan H.

Graphs/119940: This question is from textbook beginning algebra Hello, I am having a problem with finding the answer to this question. Please help. 10x-1/4=9x+3/8 Thanks, Patricia 1 solutions Answer 87890 by stanbon(57354)   on 2008-01-13 13:28:23 (Show Source): You can put this solution on YOUR website! (10x-1)/4 = (9x+3)/8 Multiply both sides by 8 to get: 2(10x-1) = 9x+3 20x - 2 = 9x + 3 11x = 5 x = 5/11 ============ Cheers, Stan H.

Quadratic-relations-and-conic-sections/119941: The orignal equation started like this: Eventually i simplified it to this So would my answer just be -3 and 3? What do i do with the since its unfactorable? 1 solutions Answer 87889 by stanbon(57354)   on 2008-01-13 13:25:28 (Show Source): You can put this solution on YOUR website! x^4+18=11x^2 x^4 - 11x^2 + 18 = 0 Factor to get: (x^2-9)(x^2-2)=0 x^2-9 = 0 or x^2-2 = 0 (x-3)(x+3)= 0 or (x-sqrt2)(x+sqrt2)=0 x = 3 or x=-3 or x=sqrt2 or x=-sqrt2 ====================== Cheers, Stan H.

Permutations/119877: This question is from textbook Glencoe Algebra 2 Solve for n. 35. P(n,4) = 40[P(n-1,2)] 36. P(n,4) = 3[P(n,3)] 37. n[P(5,3)] = P(7,5)] 38. 208P(n,2) = P(16,4) how exactly do you solve for n? please and thank you. 1 solutions Answer 87853 by stanbon(57354)   on 2008-01-12 22:40:59 (Show Source): You can put this solution on YOUR website! Solve for n. 35. P(n,4) = 40[P(n-1,2)] Using definition of P(n,r)= n!/(n-r)! you get: n!/(n-4)! = 40[(n-1)!/(n-3)!] Keep in mind n! = n(n-1)! and (n-3)!=(n-3)(n-4)! Cancel where you can to get: And you get: n = 40[1/(n-3)] Cross-multiply to get: n^2-3n-40=0 Factor to get: (n-8)(n+5)=0 Solve for n (Keep in mind that n must be positive). n = 8 ------------------- 36. P(n,4) = 3[P(n,3)] Use the definition of P(n,r) n!/(n-4)! = 3[n!/(n-3)!] Cancel n! of both sides. Remember (n-3)!= (n-3)(n-4)!, so cancel (n-4)! of both sides to get: 1/1 = 3/(n-3) Cross-multiply to get: 3 = n-3 Solve for n. n = 6 -------------- 37. n[P(5,3)] = P(7,5)] Apply the definition of P(n,r) to get n[5!/(2!] = 7!/(2!) Multiply both sides by 2!; Remember 7!= 7*6*5! Divide both sides by 5! to get n = 7!/5! n = 7*6 n = 42 ------------------- 38. 208P(n,2) = P(16,4) Use the definition of P(n,r) to get: 208[n!/(n-2)!] = 16!/(12!) 208[n(n-1)] = 16*15*14*13 n(n-1) = 210 n^2-n-210 = 0 (n-15)(n+14)=0 Remember, n must be positive. n = 15 =========== Cheers, Stan H. ============== Cheers, Stan H.

Equations/119879: [6x + 5]/3 = 3x/7 – 2 1 solutions Answer 87851 by stanbon(57354)   on 2008-01-12 22:23:05 (Show Source): You can put this solution on YOUR website! [6x + 5]/3 = 3x/7 – 2 Multiply thru by 21 to get: 7(6x+5) = 9x -42 42x+35 = 9x-42 33x = -77 3x = -7 x = -7/3 =============== Cheers, Stan H.

Evaluation_Word_Problems/119880: I've been trying to work this problem, but I'm stumped. I have been trying it with the variable rate equations A=RB and variable rate + fixed rate = total rate. Here is the problem: A 60watt bulb cost 50 cents to buy and 12 cents per day to use (24hrs). Another bulb cost $2.50 to buy and 2 cents per day to use. How many days of use will it take for the cost of the bulbs to be equal and what is the equivalent cost? 1 solutions Answer 87849 by stanbon(57354)   on 2008-01-12 22:19:52 (Show Source): You can put this solution on YOUR website! A 60watt bulb cost 50 cents to buy and 12 cents per day to use (24hrs). Another bulb cost $2.50 to buy and 2 cents per day to use. How many days of use will it take for the cost of the bulbs to be equal and what is the equivalent cost? ---------------------------------- 1st Bulb Cost for x days of use: A(x) = 0.50+0.12x --------------------- 2nd Bulb Cost for x days of use: B(x) = 2.50 + 0.02x --------------------- EQUATION: When does A(x) = B(x) ? 0.50+0.12x = 2.50 + 0.02x 2.00 = 0.10x x = 20 days A and B have equivalent costs for 20 days of use. ------------ The cost when x=20 days: A(20) = 0.50 + 0.12*20 = 0.50+2.40 = 2.90 B(20) = 2.50 + 0.02*20 = 2.50+40 = 2.90 ========================== Cheers, Stan H.

Rational-functions/119878: I need your help. I am not the greatest when it comes to solving functions. x^2=1+y^2....is this a function or not is this correct? y=square root x-1 x-1>0 or x>1 domain [1,infin) range [0,infin) no function Is this correct? y=2x-3 2(1)-3=-1 2(2)-3=1 domain (2,1) range (1,-1) Please help. 1 solutions Answer 87848 by stanbon(57354)   on 2008-01-12 22:03:01 (Show Source): You can put this solution on YOUR website! I need your help. I am not the greatest when it comes to solving functions. x^2=1+y^2....is this a function or not is this correct? x^2-y^2=1 This is a hyperbola opening right and left. It is not a function because an x value has more than one corresponding y value. y = [sqrt(x^2-1)] or y = -[sqrt(x^2-1)] domain [1,infin) or (-inf,-1] range: All Real Numbers -------------- Cheers, stan H.

Money_Word_Problems/119798: Sam has $10,000 to invest. He will put the money into 2 accounts,one that earns 10% simple interest,and one that earns 12% simple interest. If he wants to have $1160.00 in interest at the end of the year,how much should he invest in each account? I need the two equations only. I do not know how to set the equations up. I can take it from there. thank you very much : ) 1 solutions Answer 87790 by stanbon(57354)   on 2008-01-12 14:20:42 (Show Source): You can put this solution on YOUR website! Sam has $10,000 to invest. He will put the money into 2 accounts,one that earns 10% simple interest,and one that earns 12% simple interest. If he wants to have $1160.00 in interest at the end of the year,how much should he invest in each account? I need the two equations only. ---------------- EQUATIONS only: x+y = 10,000 0.10x + 0.12y = 1160 =============== Cheers, Stan H.

Money_Word_Problems/119799: Kermit and Miss Piggy wish to invest $5,000 ,part at 8% simple interest,and the rest at 14% simple interest. If they must earn $610 in interest by the end of one year,how much should they invest at each rate? I need the equations. & please solve this for me if you can. thank you very much. I appreciate it. : ) 1 solutions Answer 87789 by stanbon(57354)   on 2008-01-12 14:18:12 (Show Source): You can put this solution on YOUR website! Kermit and Miss Piggy wish to invest $5,000 ,part at 8% simple interest,and the rest at 14% simple interest. If they must earn $610 in interest by the end of one year,how much should they invest at each rate? --------------- Let amt. invested at 14% be "x" ; interest on this is 0.14x dollars ------------- Amt. invested at 8% is 5000-x ; interest is 0.08(5000-x)= 400-0.08x dollars ------------ EQUATION: interest + interest = 610 dollars 0.14x + 400-0.08x = 610 0.06x = 210 x = $3500.00 (amt. to invest at 14%) 5000-x = $1500.00 (amt. to invest at 8%) ==================== Cheers, Stan H.

Polynomials-and-rational-expressions/119773: How do I solve long division of x^3-4x^2-3x-10 divided by x-5? 1 solutions Answer 87788 by stanbon(57354)   on 2008-01-12 14:11:48 (Show Source): You can put this solution on YOUR website! How do I solve long division of x^3-4x^2-3x-10 divided by x-5? ------------- Using synthetic division you get: 5)....1....-4....-3....-10 .......1.....1.....-2...|..0 Remainder: 0 Quotient: x^2+x-2 ====================== Cheers, Stan H.

Rate-of-work-word-problems/119789: Julianne and Angel are having a party. It would take Angel 6 hours to call everyone she wants to invite. If Julianne helps, it will take only 4 hours. How long woule it take only Julianne to invite everyone? 1 solutions Answer 87786 by stanbon(57354)   on 2008-01-12 14:01:41 (Show Source): You can put this solution on YOUR website! Julianne and Angel are having a party. It would take Angel 6 hours to call everyone she wants to invite. If Julianne helps, it will take only 4 hours. How long woule it take only Julianne to invite everyone? ----------- Angel DATA: Time = 6 hrs./job : Rate = 1/6 job/hr -------------- Together DATA: Time = 4 hrs/job ; Rate = 1/4 job/hr --------------- Julianne DATA: Time = x hrs/job ; Rate = 1/x job/hr -------------- EQUATION: rate = rate = together rate 1/6 + 1/x = 1/4 Multiply thru by 12x to get: 2x + 12 = 3x x = 12 (# of hrs. it would take Julianne alone) Cheers, Stan H.

Graphs/119747: graph the inequalitie you have atleast $30.00 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. 1 solutions Answer 87739 by stanbon(57354)   on 2008-01-11 21:52:45 (Show Source): You can put this solution on YOUR website! you have atleast $30.00 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. --------- Let the number of quarters be "q"; Value is 25q cents ----------- Let the number of dimes be "d" ; Value is 10d cents ------------- EQUATION: 25q + 10d >= 3000 ==================== Cheers, StanH.

Finance/119672: A club treasurer has $28.45 consisting of nickles, dimes, and quarters. She has 9 more nickles than dimes and three times as many dimes as quarters. How many does she have of each coin? She has ____ nickles, ____ dimes, and ____ quarters. 1 solutions Answer 87722 by stanbon(57354)   on 2008-01-11 18:29:31 (Show Source): You can put this solution on YOUR website! A club treasurer has $28.45 consisting of nickles, dimes, and quarters. She has 9 more nickles than dimes and three times as many dimes as quarters. How many does she have of each coin? --------------------------- Let # of quarters be "x"; Value is 25x cents # of dimes is "3x"; Value is 10*3x = 30x cents # of nickels is "3x+9" ; Value is 5(3x+9) = 15x+45 cents -------------------------------- EQUATION: value + value + value = 2845 cents 25x + 30x + 15x+45 = 2845 70x = 2800 x = 40 (# of quarters) 3x = 120 (# of dimes) 3x+9 = 129 (# of nickels) ================= Cheers, Stan H.

expressions/119706: Can someone show me how to solve this problem by factoring 4x^2+8xy-6y 1 solutions Answer 87716 by stanbon(57354)   on 2008-01-11 16:40:42 (Show Source): You can put this solution on YOUR website! Can someone show me how to solve this problem by factoring 4x^2+8xy-6y ---------------- 2(x^2+4xy-3) ============== Cheers, Stan H.

Polynomials-and-rational-expressions/119715: Help! I have looked at your examples for finding the degree of a polynomial expression but still do not understand. Please help with finding the degree for x^2-x-x^5. Thank you. 1 solutions Answer 87715 by stanbon(57354)   on 2008-01-11 16:38:17 (Show Source): You can put this solution on YOUR website! It's 5 because the highest power term has x^5 as a factor. --------------- Cheers, Stan H.

Polynomials-and-rational-expressions/119712: Find three consecutive integers such that the sum of their squares is 77. 1 solutions Answer 87714 by stanbon(57354)   on 2008-01-11 16:36:38 (Show Source): You can put this solution on YOUR website! Find three consecutive integers such that the sum of their squares is 77. 1st: x 2nd: x+1 3rd: x+2 ---------- EQUATION: x^2 + (x+1)^2 + (x+2)^2 = 77 3x^2 +6x +5 = 77 3x^2+6x-72=0 x^2+2x-24=0 (x+6)(x-4)=0 x = -6 or x=4 ----------- If x = -6, then x+1 = -5, and x+2 = -4 If x = 4, then x+1 = 5, and x+2 = 6 =================== Cheers, Stan H.

Mixture_Word_Problems/119685: 36 gallons of 25% alchol solution means : 25%, or one quarter, of the solution is pure alchol. one quarter of 36 is 9. That solution contains 9 gallons of pure alchol. how many gallons of 30% alchol solution and how many of 60% alchol solution must be mixed to produce 18 gallons of 50% solution 1 solutions Answer 87671 by stanbon(57354)   on 2008-01-11 11:54:32 (Show Source): You can put this solution on YOUR website! -------------- how many gallons of 30% alchol solution and how many of 60% alchol solution must be mixed to produce 18 gallons of 50% solution Let "x" be the amount of 30% alcohol; active ingredient = 0.3x gallons -------- Then "18-x" is amt. of 60% alcohol ; act. ingre. =0.6(18-x)=10.8-0.6x gals. -------------- Amt. of mixture is 18 gals; act. ingre. = 0.5*18 = 9 gallons ---------------- EQUATION: active = active = active 0.3x + 10.8-0.6x = 9 -0.3x = -1 x = 10/3 = 3 1/3 gallons (Amount of 30% alcohol needed for the mixture.) ============== Cheers, Stan H.

Linear-systems/119639: Please show me how to solve this problem: 2t + 4s = 10 3t + 3d = 9 1t + 3d + 2s = 8 1 solutions Answer 87635 by stanbon(57354)   on 2008-01-10 22:35:26 (Show Source): You can put this solution on YOUR website! 2t + 0d + 4s = 10 3t + 3d + 0s = 9 1t + 3d + 2s = 8 ------------------- Using the Matrix function of a TI caluculator I get: t = 2 d = 1 s = 3/2 ================= Cheers, Stan H.

Probability-and-statistics/119565: This is not out of a book this is homework - any help is greatly appreciated. A machine is set to fill a small bottle with 9.0 grams of medicine. A sample of eight bottles revealed the following amounts (grams) in each bottle. 9.2 8.7 8.9 8.6 8.8 8.5 8.7 9.0 At the .01 significance level, can we conclude that the mean weight is less than 9.0 grams? a. State the null hypothesis and the alternate hypothesis. b. How many degrees of freedom are there? c. Give the decision rule. d. Compute the value of t. What is your decision regarding the null hypothesis? e. Estimate the p-value. 1 solutions Answer 87634 by stanbon(57354)   on 2008-01-10 22:29:04 (Show Source): You can put this solution on YOUR website! A machine is set to fill a small bottle with 9.0 grams of medicine. A sample of eight bottles revealed the following amounts (grams) in each bottle. 9.2 8.7 8.9 8.6 8.8 8.5 8.7 9.0 At the .01 significance level, can we conclude that the mean weight is less than 9.0 grams? a. State the null hypothesis and the alternate hypothesis. Ho: mu=9 grams Ha: mu<9 ----------------------- b. How many degrees of freedom are there? n-1 = 7 -------------- c. Give the decision rule. ????? d. Compute the value of t. What is your decision regarding the null hypothesis? x-bar = 8.8 grams ; df = 7; Alpha = 1%; Test Statistic = (8.8-9)/[0.2268/sqrt(8))] = -.2/0.0802 = -2.4942 e. Estimate the p-value. p-value = 0.0207 --------------------- Conclusion: Since p-value is greater than 1% there is insufficient evidence to reject Ho. ========================= Cheers, Stan H.

Probability-and-statistics/119633: This question is from textbook In the carnival game "chuck-a-luck," you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all 3 times, you win $3; if your number comes up twice, you win $2; if it comes up once, you win $1; otherwise you lose $1. What is your expected gain or loss? 1 solutions Answer 87633 by stanbon(57354)   on 2008-01-10 22:01:55 (Show Source): You can put this solution on YOUR website! In the carnival game "chuck-a-luck," you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all 3 times, you win $3; if your number comes up twice, you win $2; if it comes up once, you win $1; otherwise you lose $1. What is your expected gain or loss? ------------------ The random variable is "gain" with values 3,2,1,-1 The corresponding Probabilities are: P(3) = (1/6)^3 P(2) = 3*(1/6)^3 P(1) = 3*(1/6)^3 P(-1) = 1 - 7(1/3)^3 ------------------ Expected gain is: 3*(1/6)^3+2*3(1/6)^3+1*3(1/6)^3-1*(1-7(1/3)^3) Expected gain is (1/3)^3[3+6+3-(0.7407)]= (1/3)^3[11.2593] = 0.4170 Rounding to the nearest cent, expected gain is 42 cents =========================== Cheers, Stan H.