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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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 Expressions-with-variables/523293: please help solve this problem 4x-2< 9x-3 I tried by subtracting 2-4 and 3-9 to get the answer. i am not sure this is right1 solutions Answer 347285 by stanbon(57387)   on 2011-10-30 11:12:50 (Show Source): You can put this solution on YOUR website!solve this problem 4x-2< 9x-3 --- Subtract 4x from both sides to get: 5x-3 > -2 --- Add 3 to both sides to get: 5x > 1 ---- Divide by 5 to get: x > 1/5 =============== Cheers, Stan H. ===============
 Functions/523306: to convert a length in inches to centimeters c, multiply by 2.54 give the domain range & formula 1 solutions Answer 347284 by stanbon(57387)   on 2011-10-30 11:09:52 (Show Source): You can put this solution on YOUR website! to convert a length in inches to centimeters c, multiply by 2.54 give the domain range & formula ---- C = 2.54i where "i" is the length in inches and c is the lenght in centimeters. Domain: i is All Real Numbers greater than or equal to zero. Range: c is All Real Numbers greater than or equal to zero. ============================ Cheers, Stan H. =============
 Money_Word_Problems/523305: at an effective annual rate of 20%, how many years will be required to triple my initial investment to the nearest year?1 solutions Answer 347283 by stanbon(57387)   on 2011-10-30 11:06:56 (Show Source): You can put this solution on YOUR website!at an effective annual rate of 20%, how many years will be required to triple my initial investment to the nearest year? ---- A(t) = P(1 + (effective annual rate))^t ---- 3P = P(1+0.20)^t --- 1.2^t = 3 --- t*log(1.2) = log(3) t = log(3)?log(1.2) t = 6.0257 years =================== Cheers, Stan H. ===================
 logarithm/523300: Solve the equation. Logx=11 solutions Answer 347282 by stanbon(57387)   on 2011-10-30 11:05:05 (Show Source): You can put this solution on YOUR website!Solve the equation. Logx=1 --- When you have a log problem with no indicated base, it is understood to have a base of 10. ---- Your Problem: logx = 1 means log10(x) = 1 So x = 10^1 Therefore x = 10 ===================== Cheers, Stan H. =====================
 Exponents/523303: I need the answer,to this problem, I do not understand My final is due today. x^11*x^0, Multiply and simplify. Assume variables represent non zero real numbers. 1 solutions Answer 347281 by stanbon(57387)   on 2011-10-30 11:02:27 (Show Source): You can put this solution on YOUR website!x^11*x^0, Multiply and simplify. --- Adding the exponents you would get x^(11+0) = x^11 ---- OR Since you know that x^0 is "1", you would get: x^11*1 = x^11 ==================== Cheers, Stan H. =============
 Mixture_Word_Problems/523298: A chemist has 1000 g of a solution that is 40% acid. How many grams of water must be added to reduce the acidity to 25%1 solutions Answer 347280 by stanbon(57387)   on 2011-10-30 11:00:12 (Show Source): You can put this solution on YOUR website!A chemist has 1000 g of a solution that is 40% acid. How many grams of water must be added to reduce the acidity to 25% ----------------- Equation: acid + acid = acid 0.40*1000 + 0*x = 0.25(1000+x) ------ Multiply thru by 100 to get: 40*1000 + 0 = 25*1000 + 25x --- 25x = 15*1000 x = (2/5)1000 x = 400 grapm(amt. of water needed) ===================================== Cheers, Stan H. ============
 Probability-and-statistics/523258: pleaseee i really need your help for solving these two equatiooooon:(:( anad thank u very muchhhh first q;the average score on a special test of knowledge of wood refinishing has a mean of 53 and a standard deviation of 6 .using chebyshe've theorem.find the range of values in which at least 75% of the scores will lie... second q:the average of the number of trials it took a sample of mice to learn to traverse a maze was 12.the standard deviation was3.using chebyshev's theorem,find the minmum percentage of data values that will fall in range 4 to 20 trials1 solutions Answer 347276 by stanbon(57387)   on 2011-10-30 10:24:40 (Show Source): You can put this solution on YOUR website!first q;the average score on a special test of knowledge of wood refinishing has a mean of 53 and a standard deviation of 6 .using chebyshe've theorem.find the range of values in which at least 75% of the scores will lie... --- Cheb says "at least 75% of the data lies within 2 standard deviations of the mean". So 53 - 2std = 53 - 2*6 = 41 And 53 + 2std = 53 + 2*6 = 65 ---------------------------------------------------------- second q:the average of the number of trials it took a sample of mice to learn to traverse a maze was 12.the standard deviation was 3.using chebyshev's theorem,find the minmum percentage of data values that will fall in range 4 to 20 trials --- Find # of std 4 is to the left of the mean: (4-12)/3 = -8/3 = -2 2/3 --- Do the same for 20: (20-12)/3 = +8/3 = +2 2/3 ----- Cheb says "at least 75% of the data lies with 2 std's of the mean" ========================= Cheers, Stan H.
 Probability-and-statistics/523260: Let be a standard normal random variable. Use the calculator provided to determine the value of such that P(0.64 less then or equal to Z less then or equal to C)= .23891 solutions Answer 347275 by stanbon(57387)   on 2011-10-30 10:16:28 (Show Source): You can put this solution on YOUR website!Use the calculator provided to determine the value of such that P(0.64 less then or equal to Z less then or equal to C)= .2389 --- Draw a standard normal curve. Mark 0.64 to the right of zero Find a z-value to the right of 0.64 with 0.2389 population between them. ---- Procedure: Find area to the left of 0.64: normalcdf(-100,0.64) = 0.7389 Add 0.7389+0.2389 = 0.9778 --- Find the z-value with a left-tail of 0.9778: invNorm(0.9778) = 2.0106 ============================================== Cheers, Stan H. ======================
 Probability-and-statistics/523276: From a standard 52-card deck, what are the odds of drawing a 10, a face card, an ace, or a spade?1 solutions Answer 347274 by stanbon(57387)   on 2011-10-30 10:08:48 (Show Source): You can put this solution on YOUR website!From a standard 52-card deck, what are the odds of drawing a 10, a face card, an ace, or a spade? --- # of 10's: 4 # of face: 12 # of ace: 4 --- # of spades: 13 -- # of ((10 or face or ace) AND spade): 3 --- # of ways to "succeed" = (4+12+4+13) - 3 = 30 ---- # of possible outcomes 52 -- P(success) = 30/52 P(failure) = 22/52 ---- Odds "in favor of success" = 30/22 = 15:11 ==================== Cheers, Stan H. ========================
 Probability-and-statistics/523261: Let Z be a standard normal random variable. Use the calculator provided to determine the value of C such that P(Z less then or equal to C)= .27431 solutions Answer 347271 by stanbon(57387)   on 2011-10-30 10:02:56 (Show Source): You can put this solution on YOUR website!Let Z be a standard normal random variable. Use the calculator provided to determine the value of C such that P(Z less then or equal to C)= .2743 ------- Find the z-value with a left-tail of 0.2743 invNOrm(0.2743) = -0.5999 --- C = -0.5999 ======================== Cheers, Stan H. ========================
 Angles/523256: A triangle has angles of x, 2x and 44 find the value of x WORKINGS OUT??? 180-44=136 136/4=34 Thank you Scarlett 1 solutions Answer 347254 by stanbon(57387)   on 2011-10-30 07:59:08 (Show Source): You can put this solution on YOUR website!A triangle has angles of x, 2x and 44 find the value of x ---- Equation: x + 2x + 44 = 180 3x = 136 x = 45 1/3 degrees 2x = 90 2/3 degrees ---------------------- Cheers, Stan H.
 Probability-and-statistics/523178: Given 8 students, 4 of which are females, if 2 students are selected at random, without replacement, what is the probability that both students are female? 1 solutions Answer 347219 by stanbon(57387)   on 2011-10-29 21:39:30 (Show Source): You can put this solution on YOUR website!Given 8 students, 4 of which are females, if 2 students are selected at random, without replacement, what is the probability that both students are female? --- # of ways to succeed: 4C2 = 6 --- # of possible pairs: 8C2 = 28 --- P(2 female) = 6/28 = 3/14 ============================ Cheers, Stan H.
 Sequences-and-series/523201: if every fourth trick-or-treater is a vampire, and every 6th, robot, how many of each will you see if seventy-five trick -or treaters come to your door?1 solutions Answer 347218 by stanbon(57387)   on 2011-10-29 21:34:52 (Show Source): You can put this solution on YOUR website!if every fourth trick-or-treater is a vampire, and every 6th, robot, how many of each will you see if seventy-five trick -or treaters come to your door? --- # of vampires: 75/4 = 18 + 3 Ans: 18 --- # of robots: 75/6 = 12 + 3 Ans: 12 ============================ Cheers, Stan H.
 Average/523202: Suppose we have a population of scores with a mean (μ) of 200 and a standard deviation (σ) of 10. Assume that the distribution is normal. Provide answers to the following questions: What score would cut off the top 5 percent of scores? What score would cut off the bottom 5 percent of scores? What score would cut off the top 2.5 percent of scores? What score would cut off the bottom 2.5 percent of scores? 1 solutions Answer 347216 by stanbon(57387)   on 2011-10-29 21:26:18 (Show Source): You can put this solution on YOUR website!Suppose we have a population of scores with a mean (μ) of 200 and a standard deviation (σ) of 10. Assume that the distribution is normal. Provide answers to the following questions: --- I'm using a TI-84 to do the calculations: -------- What score would cut off the top 5 percent of scores? Find the z-value with a left tail of 0.95: invNorm(0.95) = 1.645 Find the corresponding score value using x = zs+u x = 1.645*10 + 200 = 216.45 ======================================================================== What score would cut off the bottom 5 percent of scores? Same procedure but z = -1.645 --------------------------------------------- What score would cut off the top 2.5 percent of scores? invNorm(0.975) = 1.96 Then find the x-score ----------------------------- What score would cut off the bottom 2.5 percent of scores? Same procedure but z = -1.96 ==================================== Cheers, Stan H. ===========================
 Money_Word_Problems/523200: find the value of \$8000 if the annual interest 4.5 compounded quarterly for 8 years1 solutions Answer 347213 by stanbon(57387)   on 2011-10-29 21:16:11 (Show Source): You can put this solution on YOUR website!find the value of \$8000 if the annual interest 4.5 compounded quarterly for 8 years ---- A(t) = P(1+(r/n))^(n*t) ----- A(8) = 4000(1+(0.045/1))^(1*8) --- A(8) = 4000(1+ 0.045)^8 ---- A(8) = 4000(1.4221) --- A(8) = \$5688.40 ===================== Cheers, Stan H. =====================
 Matrices-and-determiminant/523181: In the school's chemistry lab, a certain acid is stored in two different dilutons. One bottle contains a weaker solution that is only 25% acid, but another has a stronger solution of 65% acid. students must pour some from each container to make 60ml of a solution that is 50% acid. HOw much from each container should be used? I know i'm going to use the two variables s-stronger and w-weaker. just can't figure out what the two equations going to be.1 solutions Answer 347210 by stanbon(57387)   on 2011-10-29 21:06:09 (Show Source): You can put this solution on YOUR website! In the school's chemistry lab, a certain acid is stored in two different dilutons. One bottle contains a weaker solution that is only 25% acid, but another has a stronger solution of 65% acid. students must pour some from each container to make 60ml of a solution that is 50% acid. HOw much from each container should be used? ----- Equations: Quantity: s + w = 60 ml Acid::::0.65s+0.25w = 0.50*60 -------------------------------------- Multiply thru the Quantity equation by 65 Multiply thru the Acid equation by 100 -------------------------------------------- 65s + 65w = 65*60 65s + 25w = 50*60 --------------------- subtract and solve for "w": 40w = 15*60 w = (3/2)15 w = 22.5 ml (amt. of weaker solution needed) ------ Solve for "s": s + w = 60 s = 60-22.5 = 37.5 ml ------------------------------ Cheers, Stan H. ===========================
 Inequalities/523197: hi how do you solve inequalities like for instance -4x>8???1 solutions Answer 347207 by stanbon(57387)   on 2011-10-29 20:58:32 (Show Source): You can put this solution on YOUR website!-4x>8 ----- Divide both sides by -4. That reverses the inequality. --- x < -2 ------- Cheers, Stan H.
 Evaluation_Word_Problems/523196: Tom sells shoes part time at a department store. He can earn either \$500 per month plus 4% commission of his total sales, or \$400 per month plus 5% commission on his total sales. What is the total price of the shoes Tom needs to sell to earn the same income from each pay scale? Which is the better offer? 1 solutions Answer 347206 by stanbon(57387)   on 2011-10-29 20:56:01 (Show Source): You can put this solution on YOUR website!Tom sells shoes part time at a department store. He can earn either \$500 per month plus 4% commission of his total sales S(x) = 500 + 0.04x where x is his sales for the month. ----------------------------- Or \$400 per month plus 5% commission on his total sales. T(x) = 400 + 0.05x ---------- What is the total price of the shoes Tom needs to sell to earn the same income from each pay scale? Solve: S(x) = T(x) 500+0.04x = 400 + 0.05x 100 = 0.01x x = \$1000 ---------------------- Which is the better offer? 500 + 0.04x R 400+0.5x 100 R 0.01x -- S is better than T if sales are less than \$1000 T is better than S if sales are greater than \$1000 ================= Cheers, Stan H. ========================
 Word_Problems_With_Coins/523187: Danika has \$0.78 in nickels and pennies. The number of pennies that she has is one more than twice the number of nickels. Find how many of each type of coin she has.1 solutions Answer 347204 by stanbon(57387)   on 2011-10-29 20:46:10 (Show Source): You can put this solution on YOUR website!Danika has \$0.78 in nickels and pennies. The number of pennies that she has is one more than twice the number of nickels. Find how many of each type of coin she has. ------ Value Equation: p + 5n = 78 cents Quantity Eq::: p = 2n+1 coins ---------------------------------- Substitute for "p" and solve for "n": 2n+1 + 5n = 78 7n = 77 n = 11 (# of nickels) ---- solve for "p": p = 2n + 1 p = 2*11+1 = 23 (# of pennies) ======================================= Cheers, Stan H. ==============
 Probability-and-statistics/523192: 8. Playtime Toys has fifty employees of whom forty are members of the union. Five employees are selected at random to form a committee to meet with management to negotiate shift starting times. a. What kind of probability distribution will you use to solve this problem? b. What is the probability that four of the committee members will be union members? c. What is the probability that four of the committee members with non union members? 1 solutions Answer 347202 by stanbon(57387)   on 2011-10-29 20:40:57 (Show Source): You can put this solution on YOUR website!Playtime Toys has fifty employees of whom forty are members of the union. Five employees are selected at random to form a committee to meet with management to negotiate shift starting times. --- Binomial Problem with n = 5 ; p(union) = 4/5 ---------------------------------------------------- a. What kind of probability distribution will you use to solve this problem? Binomial -------------------- b. What is the probability that four of the committee members will be union members? P(x = 4) = 5C4*(4/5)^4(1/5) = 0.4096 -------------------------------------------------------- c. What is the probability that four of the committee members with non union members? P(x = 1) = 5C1(4/5)(1/5)^4 = 0.0064 ======================== Cheers, Stan H.
 Functions/523189: given the function f(x)=x+3/2x-1, find f(0)1 solutions Answer 347199 by stanbon(57387)   on 2011-10-29 20:31:57 (Show Source): You can put this solution on YOUR website!given the function f(x)= (x+3)/(2x-1), find f(0) ----------- f(0) = (0+3)/(2*0-1) = 3/-1 = -3 ------- Cheers, Stan H. ========
 Human-and-algebraic-language/523186: Please help in solving. Need to see how it is solved. David has 10 pets. All his pets are either fish or hamsters. He has two more fish than hamsters. How many hamsters does David have?1 solutions Answer 347198 by stanbon(57387)   on 2011-10-29 20:26:32 (Show Source): You can put this solution on YOUR website!David has 10 pets. All his pets are either fish or hamsters. He has two more fish than hamsters. How many hamsters does David have? --------- Let # of hamsters be "x". Then # of fish is "x+2" ----- Equation: x + (x+2) = 10 2x + 2 = 10 2x = 8 x = 4 (# of hamsters) x+2 = 6 (# of fish) ===================== Cheers, Stan H. ===========
 Polynomials-and-rational-expressions/523160: Factor completely: 63c^2+294cp+343p^2 Please show work. Thank you!1 solutions Answer 347191 by stanbon(57387)   on 2011-10-29 18:50:51 (Show Source): You can put this solution on YOUR website!Factor completely: 63c^2+294cp+343p^2 ----- Divide thru by 7: = 7[9c^2 + 42cp + 49p^2] ------ = 7[9c^2 + 21cp + 21cp +49p^2) ---- = 7[3c(3c+7p) + 7p(3c+7p)] ---- = 7[(3c+7p)(3c+7p)] ----------- = 7(3c+7p)^2 ================ Cheers, Stan H. ================
 Probability-and-statistics/523155: Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the .10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flaŽvor excellent? (a) State the null hypothesis and the alternate hypothesis. (b) What is the probability of a Type I error? (c) Is this a one-tailed or a two-tailed test? (d) What is the decision rule? (e) What is the value of the test statistic? (f) What is your decision regarding the null hypothesis? (g) What is the p-value? Explain what it means in terms of this problem. 1 solutions Answer 347189 by stanbon(57387)   on 2011-10-29 18:37:31 (Show Source): You can put this solution on YOUR website!Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent.:: pa-hat = 87/150 = 0.580 ------------------------ Of 200 children sampled, 123 rated it excellent.:: pc=hat = 123/200 = 0.615 ------------------------ Using the .10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flaŽvor excellent? ---------- (a) State the null hypothesis and the alternate hypothesis. Ho: pa-pc = 0 Ha: pa-pc is not 0 ------------------------------ (b) What is the probability of a Type I error?::P(Type I) = alpha = 10% ---------------------------------- (c) Is this a one-tailed or a two-tailed test?:::: 2-tail ----------------------------------- (d) What is the decision rule?:: Reject Ho is test stat <-1.645 or >+1.645 ----------------------------------- (e) What is the value of the test statistic?::: ts = (0.580-0.615)/sqrt[(.58*0.42/150)+(0.615*0.385/200)] = -0.6605 ------------------------------------------------------------------ (f) What is your decision regarding the null hypothesis? Since the ts is not in a reject interval, fail to reject Ho. ------------ (g) What is the p-value? Explain what it means in terms of this problem. p-valu = 2*P(z < -0.6605) = 2*0.25 = 0.50 ------- There is a 50% probability that the test results could have provided stronger evidence for rejecting Ho. ======================================== Cheers, Stan H. ============
 Mixture_Word_Problems/523018: please help me answer this question a computer operator types 3600 words in an hour.How many words does she type in a minutes1 solutions Answer 347156 by stanbon(57387)   on 2011-10-29 09:14:27 (Show Source): You can put this solution on YOUR website! please help me answer this question a computer operator types 3600 words in an hour.How many words does she type in a minutes --- 3600(wds/hour)(1 hr/60 min) = (3600*1)/(1*60)(wds/min) = 60 wds/min =========== Cheers, Stan H.
 Quadratic_Equations/523017: Please help me, I need to get through this test to finish school. 1. Multiply and Simplify 4y^2/5y^2-40y+80 * 5y-20/2y = (Type and Exponential notation with positive exponents) 2. Multiply (8x+6)(5x^2+5x+8) 3. Evaluate the Polynomial for x=6 2x^2-5x+7= 4. Solve. (x+19)(x-2)(x+10)>0 Select the correct choice below and if necessary, fill in the answer box to complete your choice. A. The solution set is {|x| } B. The solution is all real numbers C. There is no solution. 1 solutions Answer 347155 by stanbon(57387)   on 2011-10-29 09:10:52 (Show Source): You can put this solution on YOUR website!1. Multiply and Simplify 4y^2/(5y^2-40y+80) * (5y-20)/2y ------------- = (4y^2)/[5(y-4)^2] * (5(y-4))/(2y) ---- Cancel where you can to get: = (2y)/(y-4) ====================================== 2. Multiply (8x+6)(5x^2+5x+8) ---- = (8x)(5x^2+5x+8) + 6(5x^2+5x+8) ---- = 40x^3+40x^2+64x + 30x^2+30x+48 ---- = 40x^3+70x^2+94x+48 ====================================== 3. Evaluate the Polynomial for x=6 2x^2-5x+7= 2(36)-5(6)+7 = 72-30+7 = 49 =========================================== 4. Solve. (x+19)(x-2)(x+10)>0 Draw a number line. Plot x = -19 ; x = -10 ; x = 2 Test a value in each of the 4 intervals to see where the solutions are. (x+19)(x-2)(x+10)>0 -- Test x = -25 to get: -*-*- > 0; false Test x = -15 to get: +*-*- > 0; true so solutions in(-19,-10) Test x = 0 to get:: +*-*+ > 0; false Test x = 5 to get:: +*+*+ > 0; true so solutions in (2,+oo) --- Solution: {x | -19< x < -10 or 2< x <+oo} ============================================== Cheers, Stan H. ============== ============= Select the correct choice below and if necessary, fill in the answer box to complete your choice. A. The solution set is {|x| } B. The solution is all real numbers C. There is no solution.
 Polynomials-and-rational-expressions/523014: Use the rational zero theorem to find all real zero of each polynomial function. Use the zeros to factor if the over the real numbers... f(x)=-3x^3+6x^2-15x-301 solutions Answer 347154 by stanbon(57387)   on 2011-10-29 09:01:21 (Show Source): You can put this solution on YOUR website!Use the rational zero theorem to find all real zero of each polynomial function. Use the zeros to factor if the over the real numbers... f(x)=-3x^3+6x^2-15x-30 ------------ = -3[x^3-2x^2+5x+10] --- There is only one rational zero around x = -1.1562.. ============================= Cheers, Stan H.
 Complex_Numbers/523015: find the value of | 40 + 9i |. a 40 + 9i b 40 - 9i c -40 - 9i d -40 + 9i e not given1 solutions Answer 347152 by stanbon(57387)   on 2011-10-29 08:55:32 (Show Source): You can put this solution on YOUR website!find the value of | 40 + 9i | ---- = sqrt[40^2+9^2] = 41 ----------------------- Answer: e ============== Cheers, Stan H. ============== a 40 + 9i b 40 - 9i c -40 - 9i d -40 + 9i e not given
 Probability-and-statistics/523005: Hi, I am having problems with a chi-square related question. Here is the question: (a) Write the null and alternative hypothesis for a one-sided test to determine whether men are, on average, heavier than men from 20 years ago. These are the hypotheses I have come up with: Null Hypothesis  There is no difference between the average weight of men now and 20 years ago. Alternative Hypothesis  Men, on average, are heavier than men from 20 years ago. (b) Carry out a test of the hypothesis in (a) at the 5% significance level, i.e. calculate the: - Test statistic - Critical value of the Normal Distribution for a one-sided test at the 5% significance level This is where I am having problems. I know how to do chi-square (I'm assuming we have to use chi-square as that's what we have been using in the other questions) when I have the data, ie. observed and expected. What I am unsure about is what data to use as this is all I have been provided with: From data collected 20 years ago, the average weight of an adult male was 71 kilograms and the standard deviation 7.2 kilograms. Table: Weights (in kilograms) of a new random sample of 29 adult males 59 79 61 81 62 82 66 68 83 69 84 70 73 77 84 74 88 76 78 91 78 74 86 59 66 73 74 75 76 So far I have been using the averaging weight of the new sample of men which is 74.7 and the average weight from 20 years ago which is 71 and trying to use a one-way chi-square method. So basically my table looks like this: Today 20 Years Ago Weight 74.7 71 First of all is this the correct way of doing it? If so, my next dilemma is trying to figure out the expected frequency from the observed. I know how to calculate the expected from a contingency table of 2 or more rows, but when i try to apply the same formula to just one row, the expected ends up the same as the observed, which surely cant be right? If I am going about it totally the wrong way, any advice would be appreciated. I am not a mathematician or even studying it ,so apologies for my lack of knowledge. Hopefully someone can help me out. Ryan1 solutions Answer 347150 by stanbon(57387)   on 2011-10-29 08:34:33 (Show Source): You can put this solution on YOUR website!That is not a Chi-Sq problem. It is a 2-sample Z or T test problem. --- Also, a strict rule for hypothesist testing requires that equality ALWAYS appears in the Null Hypothesis. ---- I think if you use Google you will be able to find examples online of a 2-Sample test. Cheers, Stan H.
 Radicals/522953: I am having a very hard time with understanding how to come up with an answer to this word problem. During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?1 solutions Answer 347115 by stanbon(57387)   on 2011-10-28 22:23:00 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip? -------------------- 1st part DATA: distance = 91 miles ; rate = r mph ; time = d/r = 91/r hrs --------------------------- 2nd part DATA: distance = 21 miles ; rate = r-5 mph ; time = d/r = 21/(r-5) hrs ---------------- Equation: time + time = 5 hrs 91/r + 21/(r-5) = 5 ---- 91(r-5) + 21r = 5r(r-5) 112r - 455 = 5r^2-25r --- Rearrange: 5r^2 - 137r + 455 = 0 Positive solution: r = 23.5331 mph (1st part speed) r-5 = 18.5331 mph (2nd part speed) ==================================== Cheers, stan H. ==============
 Polygons/522948: The sum of the interior angles of a polygon is 8y. If Y is 15 greater than the number of sides of the polygon, how many sides does the polygon have?1 solutions Answer 347114 by stanbon(57387)   on 2011-10-28 22:15:28 (Show Source): You can put this solution on YOUR website!The sum of the interior angles of a polygon is 8y. If Y is 15 greater than the number of sides of the polygon, how many sides does the polygon have? --- Let number of sides be "n": sum of interior angles = (n-2)180 = 8Y y = n+15 --- Substitute for "y" and solve for "n" ----------------------- (n-2)180 = 8(n+15) ---- (n-2)180 = 8n+120 180n-360 = 8n+120 172n = 480 ----- That does not turn out to be a whole number. Please check the wording of your problem. I have some suspicion about that "8Y". ---- Cheers, Stan H. ==============