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 Probability-and-statistics/235409: I need your help in working this problem out. Thank you very much... A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9, 1, 3, and 2 grams. Assume = 0.01. · State the null and alternate hypotheses · Calculate the sample standard deviation · Determine which test statistic is appropriate (chi-square or F), and calculate its value. · Determine the critical value(s). · State your decision: Should the null hypothesis be rejected?1 solutions Answer 173654 by stanbon(57386)   on 2009-11-06 10:05:46 (Show Source): You can put this solution on YOUR website!A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9, 1, 3, and 2 grams. Assume = 0.01. · State the null and alternate hypotheses Ho: sigma^2 <= 4 (claim) Ha: sigma^2 > 4 · Calculate the sample standard deviation std of the sample = 2.667 ----------------------------------- · Determine which test statistic is appropriate (chi-square or F), and calculate its value. Chi-Sq = (n-1)*s^2/sigma^2 = 14*2.667^2/4 = 24.895 ------------------------------------- · Determine the critical value(s) Chi-Sq lower = 4.075 ; Chi-Sq upper = 31.32 -------------------------------------- State your decision: Should the null hypothesis be rejected? Since the ts is not in either rejection interval, do not reject Ho based on these test results. ====================================== Cheers, Stan H.
 Probability-and-statistics/235828: There is a 50% chance of rain on Saturday and a 50% chance of rain on Sunday. What is the probability of 2 sunny days this weekend?1 solutions Answer 173647 by stanbon(57386)   on 2009-11-06 09:36:43 (Show Source): You can put this solution on YOUR website!There is a 50% chance of rain on Saturday and a 50% chance of rain on Sunday. What is the probability of 2 sunny days this weekend? -------- The events are independent, so P(sunny and sunny) = P(sunny)*P(sunny) = 0.5*0.5 = 0.25 =========================================================== Cheers, Stan H.
 Travel_Word_Problems/235871: if a ship can travel 1000 miles in 3 hours then how fast is it traveling? 1 solutions Answer 173646 by stanbon(57386)   on 2009-11-06 09:33:30 (Show Source): You can put this solution on YOUR website!if a ship can travel 1000 miles in 3 hours then how fast is it traveling? ----------- rate = distance/time --- rate = 1000 mi/3 hrs = 333 1/3 mph ======================================= Cheers, Stan H.
 Probability-and-statistics/235846: From a bag containing 2 rupee-coins and 3 twenty paise coins, a person is asked to draw two coins at random. Find the values of his expectatioon.1 solutions Answer 173644 by stanbon(57386)   on 2009-11-06 09:31:17 (Show Source): You can put this solution on YOUR website!From a bag containing 2 rupee-coins and 3 twenty paise coins, a person is asked to draw two coins at random. Find the values of his expectatioon. ----------- Random variable values are ? ---------------- What are the relative values of rupee and paise coins? ========================= Cheers, Stan H.
 Probability-and-statistics/235847: In a college 30% students fail in Physics, 25% fail in Mathematics and 10% students fail in both. One student is chosen at random. What is the probability that a) He fails in Mathematics if he has failed in Physics b) He fails in Physics if he has failed in Mathematics. c) He fails in Physics or Mathematics. 1 solutions Answer 173636 by stanbon(57386)   on 2009-11-06 09:08:54 (Show Source): You can put this solution on YOUR website!In a college 30% students fail in Physics, 25% fail in Mathematics and 10% students fail in both. One student is chosen at random. What is the probability that a) He fails in Mathematics if he has failed in Physics P(m|p) = P(m and p)/P(p) = 0.10/0.30 = 1/3 --------------------------------------------------- b) He fails in Physics if he has failed in Mathematics. P(p|m) = P(p and m)/P(m) = 0.10/0.25 = 10/25 = 2/5 --------------------------------------------------- c) He fails in Physics or Mathematics. P(p or m) = P(p) + P(m) - P(p and m) = 0.30 + 0.25 - 0.10 = 0.45 ========================================= Cheers, Stan H.
 Probability-and-statistics/235413: Two groups of ten sprinters run 100 meters. The times required by sprinters in the first group are as follows: 12.0 12.9 10.1 14.6 11.9 11.3 13.0 12.9 13.3 10.0 The times required by sprinters in the second group are as follows: 11.6 12.5 12.3 10.2 16.3 17.0 19.1 18.7 12.3 16.4 Assuming that = 0.02, test the hypothesis that the means of the two populations are equal. · State the null and alternate hypotheses · Calculate the mean and standard deviation for each group · Calculate the value of the test statistic. · Determine the critical value(s). · State your decision: Should the null hypothesis be rejected? Thank you so very much for helping with this problem. I really do appreciate all of your hard work.1 solutions Answer 173588 by stanbon(57386)   on 2009-11-05 22:16:25 (Show Source): You can put this solution on YOUR website!Two groups of ten sprinters run 100 meters. The times required by sprinters in the first group are as follows: 12.0 12.9 10.1 14.6 11.9 11.3 13.0 12.9 13.3 10.0 The times required by sprinters in the second group are as follows: 11.6 12.5 12.3 10.2 16.3 17.0 19.1 18.7 12.3 16.4 Assuming that alpha = 0.02, test the hypothesis that the means of the two populations are equal. · State the null and alternate hypotheses Ho: u(1)-u(2) = 0 Ha: u(1)-u(2) is not 0 --------------------------------- · Calculate the mean and standard deviation for each group Grp 1: mean = 12.2 ; std = 1.445 Grp 2: mean = 14.64 ; std = 3.202 ---------------------------------- · Calculate the value of the test statistic. I ran a 2-Sample Ttest and got the following: ts = t = -2.1965 -------------------------- · Determine the critical value(s). invT(0.01, with df=12.517) = -2.3266 ---------------------------------------- · State your decision: Should the null hypothesis be rejected? Since the test statistic is not in the reject interval, do not reject Ho. ---------------------------------------- Cheers, Stan H.
 Travel_Word_Problems/235770: members of a hiking club hiked to an overnight campsite at the rate of 3 mph. The following morning they returned on horseback over the same route at 10 mph. The total time spent in going and returning was 6 1/2 hrs. find the distance to the campsite. I know d= r x t, but don't know what to use for rate. 3 mph or 10 mph?1 solutions Answer 173579 by stanbon(57386)   on 2009-11-05 21:55:16 (Show Source): You can put this solution on YOUR website! members of a hiking club hiked to an overnight campsite at the rate of 3 mph. The following morning they returned on horseback over the same route at 10 mph. The total time spent in going and returning was 6 1/2 hrs. find the distance to the campsite. --------------- Hiking DATA: rate = 3 mph ; distance = x miles ; time = d/r = x/3 hrs ======================= Riding DATA: rate = 10 mph ; distance = x miles ; time = x/10 hrs ----------------------- Equation: time + time = 13/2 hrs x/3 + x/10 = 13/2 Multiply thru by 30 to get: 10x + 3x = 15*13 13x = 15*13 x = 15 miles (distance to the campsite) ======================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/235505: 5/x+3 is less than -3/x-1 solve algebraically the rational inequality1 solutions Answer 173574 by stanbon(57386)   on 2009-11-05 21:24:23 (Show Source): You can put this solution on YOUR website!5/x+3 is less than -3/x-1 --------------- Cross-multiply to get: 5(x-1) < -3(x+3) 5x-5 < -3x-9 8x < -4 x < -1/2 =============== Cheers, Stan H.
 Linear-equations/235473: I always have trouble with fractions, Im not sure why they put the 5/2 in parenthese, 3/7 x (5/2) =1 solutions Answer 173573 by stanbon(57386)   on 2009-11-05 21:22:12 (Show Source): You can put this solution on YOUR website!3/7 x (5/2) = The parentheses helps clarify the meaning of the problem (3/7)(5/2) = 15/14 ========================= Cheers, Stan H.
 Polynomials-and-rational-expressions/235756: Find the reciprocal and express it in scientific notation 6.25*10^-31 solutions Answer 173571 by stanbon(57386)   on 2009-11-05 21:19:01 (Show Source): You can put this solution on YOUR website!Find the reciprocal and express it in scientific notation 6.25*10^-3 = 6.25/1000 --- Invert to get 1000/625 = 1.6 = 1.6x10^0 ---------------- Cheers, Stan H.
 Probability-and-statistics/235411: I submitted this question on yesterday and did not get a response. I would like to thank the tutor for helping me on this problem. A telephone survey gives 670 consumers two choices: Do they prefer Coke or Pepsi? Exactly 158 of those surveyed state that they prefer Coke. Assuming that = 0.10, test the hypothesis that the proportion of the population that prefers Coke is 50%. · State the null and alternate hypotheses · Calculate the sample proportion · Calculate the value of the test statistic. · Determine the critical value(s). · State your decision: Should the null hypothesis be rejected? 1 solutions Answer 173567 by stanbon(57386)   on 2009-11-05 21:09:48 (Show Source): You can put this solution on YOUR website!A telephone survey gives 670 consumers two choices: Do they prefer Coke or Pepsi? Exactly 158 of those surveyed state that they prefer Coke. Assuming that alpha = 0.10, test the hypothesis that the proportion of the population that prefers Coke is 50%. · State the null and alternate hypotheses Ho: p = 0.5 Ha: p is not 0.5 ----------------------- · Calculate the sample proportion p-hat = 158/670 = 0.2358 ----------------------------------- · Calculate the value of the test statistic. z(0.2358) = (0.2358-0.5000)/sqrt[.5*.5/(670)] = -13.6773 ------------- · Determine the critical value(s). invNorm(0.05) = +/-1.645 -------------- Decision: Should Ho be rejected. Yes because the test statistic is in the rejection interval to the left of -1.645. ===================================== Cheers, Stan H.
 Probability-and-statistics/235513: i have a question in the grouped data in statistics , they asking the probability that an emloyee . taken at random , earns more than 20000 pounds , total workers are 68 and they have group which interval is between 15000-24.999 . plzzzzzz help meeeeee1 solutions Answer 173561 by stanbon(57386)   on 2009-11-05 20:53:09 (Show Source): You can put this solution on YOUR website!i have a question in the grouped data in statistics , they asking the probability that an emloyee . taken at random , earns more than 20000 pounds , total workers are 68 and they have group which interval is between 15000-24.999 . ------------------ If the interval is 15000 to 24999 the range is 9999 ----------------------------- Use the median of the interval as the mean: mean = (15000+24999)/2 = 19999.5 Rounding that up the mean is 20,000 ----------- If 20,000 is the mean, the probability an employee picked at random earns more that 20,000 is 50%. ===================================================== Cheers, Stan H.
 Probability-and-statistics/235541: A car battery manufacturer introduces a new technique to increase the life of the battery. 25 batteries were tested and got a mean life of 4.6 years with a standard deviation of 0.70 years. Construct a 90% confidence interval for the mean life of the new battery. THX1 solutions Answer 173555 by stanbon(57386)   on 2009-11-05 20:44:02 (Show Source): You can put this solution on YOUR website!A car battery manufacturer introduces a new technique to increase the life of the battery. 25 batteries were tested and got a mean life of 4.6 years with a standard deviation of 0.70 years. Construct a 90% confidence interval for the mean life of the new battery. ------------------ x-bar = 4.6 yrs. standard error = E = 1.645*0.7/sqrt(25) = 0.2303 Comment: Since you want 90% confidence you build 45% on each side of the mean. That leaves 5% in each of the tails. The z-value border for that 5% tail is 1.645 as you can get using your z-chart or calculator. I used a TI calculator to get invNorm(0.95) = 1.645. ------------------- 90% CI: 4.6-0.2303 < u < 4.6+0.2303 90% CI: 4.3697 < u < 4.8303 ================================== Cheers, Stan H.
 Word_Problems_With_Coins/235732: the students want to raies \$20 total. if they have 19 pennies and the rest in quarters how many quarters would that be 1 solutions Answer 173553 by stanbon(57386)   on 2009-11-05 20:39:16 (Show Source): You can put this solution on YOUR website!the students want to raise \$20 total. if they have 19 pennies and the rest in quarters how many quarters would that be ------------------- Let the number of quarters be "x". Value of those quarters is 25x cents. -------------- Equation: 25x + 19 >= 2000 cents 25x >= 1981 x >= 79.24 Rounding up: x = 80 (# of quarters) ========================================= Cheers, Stan H.
 Human-and-algebraic-language/235733: I'm going to type the word problem. Help me with this. Mary's class took two tests last week. 80% of the class passed the math test, 90% of the class passed the English test, and 72% of the class passed both. What is the probability that a randomly selected student in Mary's class failed both tests? Express your answer as a percent rounded to the nearest tenth of a percent.1 solutions Answer 173548 by stanbon(57386)   on 2009-11-05 20:32:29 (Show Source): You can put this solution on YOUR website!Mary's class took two tests last week. 80% of the class passed the math test, 90% of the class passed the English test, and 72% of the class passed both. What is the probability that a randomly selected student in Mary's class failed both tests? Express your answer as a percent rounded to the nearest tenth of a percent. -------- P(passed M or passed E) = P(M) + P(E) - P(M and E) P(passed Math or Eng) = 0.8 + 0.9 - 0.72 = 0.98 ----- P(did not pass Math or Eng) = 1-0.98 = 0.02 ------------------------------------------------ Cheers, Stan H.
 Rational-functions/235603: help me solve this problem : X1/2 -(X-5)1/2 =21 solutions Answer 173540 by stanbon(57386)   on 2009-11-05 19:47:02 (Show Source): You can put this solution on YOUR website!help me solve this problem : X^(1/2) -(X-5)^(1/2) = 2 ---- Square both sides to get: x -2sqrt[x(x-5)] + x-5 = 4 2x-5-4 = 2[sqrt(x^2-5x)] Simplify: 2x-9 = 2[sqrt(x^2-5x)] --- Square both sides to get: 4x^2 - 36x + 81 = 4(x^2-5x) 4x^2 - 36x + 81 = 4x^2 - 20x 16x = 81 x = 81/16 ============================= Cheers, Stan H.
 Numbers_Word_Problems/235689: I am desperately trying to expain how to predict and test problem solving,is only a third grader and has not been taught algebra so not able to explain that way. problems are as such... Peter delievers 110 newspapers on the weekend. He delivers 20 more papers on Sunday than on Saturday. How many papers does he deliver each day?1 solutions Answer 173533 by stanbon(57386)   on 2009-11-05 19:22:18 (Show Source): You can put this solution on YOUR website!Peter delivers 110 newspapers on the weekend. He delivers 20 more papers on Sunday than on Saturday. How many papers does he deliver each day? ----------------------------- Let number delivered on Saturday be "x". Then number delivered on Sunday is "x+20". ----------------- Equation: x + x+20 = 110 2x + 20 = 110 2x = 90 x = 45 (# he delivers on Saturday) x+20 = 65 (# he delivers on Sunday) ====================================== Cheers, Stan H.
 Graphs/235686: Please find the vertex, y intercept and x intercept and graph the following equation: x^2 + 8x + 7 =1 solutions Answer 173532 by stanbon(57386)   on 2009-11-05 19:19:00 (Show Source): You can put this solution on YOUR website!Please find the vertex, y intercept and x intercept and graph the following equation: x^2 + 8x + 7 = y ------------------- Vertex occurs where x = -b/2a = -8/2 = -4 f(-4) = (-4)^2+8(-4)+7 = 16-32+7 = -9 So vertex is (-4,-9) ---------------------------- y-intercept at f(0) = 7 --- x-intercepts when y = 0: x^2+8x+7 = 0 (x+7)(x+1) = 0 x = -7 or x = -1 Those are the x-intercepts. ================================ ================================ Cheers, Stan H.
 Expressions-with-variables/235614: Rewrite the equation so that x is a function of y and then use the result to find x when y =-2 4(5-y)=14x+31 solutions Answer 173530 by stanbon(57386)   on 2009-11-05 19:13:07 (Show Source): You can put this solution on YOUR website!Rewrite the equation so that x is a function of y and then use the result to find x when y =-2 4(5-y)=14x+3 20-4y = 14x + 3 -4y = 14x - 17 y = (-14/4)x + (17/4) ----------------------------- If y = -2 solve for "x": 4(5-y) = 14x+3 4(7) = 14x+3 25 = 14x x = 25/14 --------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/235617: I am supposed to evaluate the polynomial when x = -4: 2x^2-2x+9 -16-(-16)+9= -16+16+9=9 The answer is 9? The negative 16 at the beginning confused me, I wasn't sure if it becomes paoitive or not.1 solutions Answer 173526 by stanbon(57386)   on 2009-11-05 19:07:31 (Show Source): You can put this solution on YOUR website!I am supposed to evaluate the polynomial when x = -4: 2x^2-2x+9 -------------- 2(-4)^2 - 2(-4) + 9 --- 2(16) + 8 + 9 --- 49 ======================== Cheers, Stan H.
 Quadratic_Equations/235622: 6. Solve the equation by factoring. z2 + 3z + 2 = 0 (1 point) * z = –2 or z = –1 * z = –2 or z = 1 * z = 2 or z = –1 * z = 2 or z = 11 solutions Answer 173524 by stanbon(57386)   on 2009-11-05 19:04:52 (Show Source): You can put this solution on YOUR website!Solve the equation by factoring. z^2 + 3z + 2 = 0 Factor: (z+2)(z+1) = 0 z = -2 or z = -1 ====================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/235628: If a chart that lists a census of people (175,104,000) who believe in "Look before you leap" and is approximently 7/10ths of the population. What is the total population?1 solutions Answer 173522 by stanbon(57386)   on 2009-11-05 19:02:29 (Show Source): You can put this solution on YOUR website!If a chart that lists a census of people (175,104,000) who believe in "Look before you leap" and is approximently 7/10ths of the population. What is the total population? ------------------------- Let the total population be "x". --- Equation: (7/10)x = 175,104,000 x = (10/7)(175,104,000) x = 250148571.4 Round down to a whole number. ===================================== Cheers, Stan H.
 Rectangles/235662: the width of a rectangular poster is one half of its length. the area of the poster is 128sq ft what is the width of the poster?1 solutions Answer 173519 by stanbon(57386)   on 2009-11-05 18:58:08 (Show Source): You can put this solution on YOUR website!the width of a rectangular poster is one half of its length. the area of the poster is 128sq ft what is the width of the poster? --------------------------------- Let the length be x : Then the width is x/2: ------------------------- Equation: Area = length * width 128 = x*(x/2) x^2 = 256 x^2-256 = 0 x^2-2^8 = 0 (x-2^4)(x+2^4) = 0 Positive Solution: x = 16 ft. ------------------ x/2 = 8 ft. (width) ========================= Cheers, Stan H.
 Miscellaneous_Word_Problems/235674: I need help with this problem: Two numbers; one is ten times greater than the other; their sum is equal to their product. I have used trial and error and am just not getting it. Thanks, Cathy1 solutions Answer 173516 by stanbon(57386)   on 2009-11-05 18:53:24 (Show Source): You can put this solution on YOUR website!Two numbers; one is ten times greater than the other; their sum is equal to their product. ----------------------- Let one of the numbers be "x". The other number is "10x". ------------------------------ Equations: x + 10x = x(10x) 11x = 10x^2 --- 10x^2-11x = 0 x(10x-11) = 0 Positive solution: 10x-11 = 0 x = 11/10 = 1.1 (1st number) 10x = 11 (2nd number) ============================== Cheers, Stan H.
 Probability-and-statistics/235546: a manufacture of tv tubes has for many years used a process giving a mean tube life of 4900 hrs and a standard deviation of 1200 hours. A new process is tried to see if it will increase the life significantly. A sample of 100 new tubes gave a mean life of 5000 hrs. Is the new process better than the old process at 1% level of significant? Construct hypotheses test it and interpret the result.1 solutions Answer 173515 by stanbon(57386)   on 2009-11-05 18:49:56 (Show Source): You can put this solution on YOUR website!a manufacture of tv tubes has for many years used a process giving a mean tube life of 4900 hrs and a standard deviation of 1200 hours. -------------------------------------------------------------------- A new process is tried to see if it will increase the life significantly. A sample of 100 new tubes gave a mean life of 5000 hrs. -------------------------------------------------------------------- Is the new process better than the old process at 1% level of significant? Construct hypotheses test it and interpret the result. --------------------- Ho: u = 4900 Ha: u > 4900 (claim) ------------------------- Test statistic: t(5000) = (5000-4900)/[1200/Sqrt(100)] =1000/1200= 0.8333.. ------------------------------- p-value: P(t>0.8333 with df=99) = 0.2033 --------------------------------- Since the p-value is greater than 1% do not reject Ho. The new process is not an improvement over the old process. ============================================================ Cheers, Stan H.
 Probability-and-statistics/235577: a miniature golf course offers a free game to golfers who make a hole-in-one on the last hole.Last week, 56 out of 270 golfers made a hole-in-one on the last hole.Find the experimental probability that a golfer makes a hole-in-one on the last hole.please round your answer to two decmial places.1 solutions Answer 173506 by stanbon(57386)   on 2009-11-05 18:33:47 (Show Source): You can put this solution on YOUR website!a miniature golf course offers a free game to golfers who make a hole-in-one on the last hole.Last week, 56 out of 270 golfers made a hole-in-one on the last hole.Find the experimental probability that a golfer makes a hole-in-one on the last hole.please round your answer to two decmial places. -------------------- Based on one week's data the probability is 56/270 = 0.2074.. Cheers, Stan H.
 Travel_Word_Problems/235562: How many minutes will it take an airplane flying at 370mph to intercept another airplane that is 95 miles away if the second airplane is heading toward the first at 200mph?1 solutions Answer 173469 by stanbon(57386)   on 2009-11-05 15:37:18 (Show Source): You can put this solution on YOUR website!How many minutes will it take an airplane flying at 370mph to intercept another airplane that is 95 miles away if the second airplane is heading toward the first at 200mph? ---------------------------- The rate difference = 370-200 = 170 mph ------------------------- The time to close a 95 mile gap is 95/170 = 0.5588 hrs. 0.5588 hrs = (0.5588*60 min) = 33.53 minutes ================================================== Cheers, Stan H.
 Probability-and-statistics/235550: The apollo space craft program lasted from 1967 to 1972 and incl 13 missions. The missions lasted from as little as 7 hrs to as long as 301 hrs. The duration of each flight is listed below: 9-195-241-301-216-260-7-244-192-147-10-295-142- Is this dataset a sample or a population? find the mmean and median of the flight time? Find the range and quartile range of the flight times.1 solutions Answer 173468 by stanbon(57386)   on 2009-11-05 15:33:24 (Show Source): You can put this solution on YOUR website!The apollo space craft program lasted from 1967 to 1972 and incl 13 missions. The missions lasted from as little as 7 hrs to as long as 301 hrs. The duration of each flight is listed below: 9-195-241-301-216-260-7-244-192-147-10-295-142- Is this dataset a sample or a population? It is the population of the set of flights described. It is a sample from the set of all space flights. --------------------------------------------------------- find the mmean and median of the flight time? mean: add the numbers and divide by 13 to get 166.08 median is the middle number after putting the numbers in order: 195 Find the range and quartile range of the flight times. range = max-min = 301-7 = 294 ----------------- I'll leave quartile range to you. ==================================== Cheers, Stan H.
 Probability-and-statistics/235547: Tthe mean amount purchased by each customer at a casino is 23.50 euros. The population is positively skewed and the standard deviation is not known. A MARKETING REseARCHER TOOK A sample of 50 customers. If the standard deviation of the sample is 5 euros, what is the likelihood that the sample mean is greater than 22.5 but less then 25 euros1 solutions Answer 173467 by stanbon(57386)   on 2009-11-05 15:26:57 (Show Source): You can put this solution on YOUR website!The mean amount purchased by each customer at a casino is 23.50 euros. The population is positively skewed and the standard deviation is not known. A MARKETING REseARCHER TOOK A sample of 50 customers. If the standard deviation of the sample is 5 euros, what is the likelihood that the sample mean is greater than 22.5 but less then 25 euros -------------- Although the population is not normally distributed, the sample means will tend toward normality as n gets larger. ----------------- Mean of the sample means: 23.50 If 5 euros is the std of the population, 5/Sqrt(50) is std of sample means: t(25) = (25-23.5)/[5/sqrt(50)] = 2.1213 t(22.5) = (22.5-23.5)/[5/sqrt(50)] = -1.4142 -------------------------------------------------- P(22.5 < x < 25) = P(-1.4142 < t < 2.1213 with df=49) = 0.8987 =================================================================== Cheers, Stan H.
 Mixture_Word_Problems/235504: outline the steps you would use to prepare a 10% salt solution from a 25% salt solution for a 100 ml.1 solutions Answer 173455 by stanbon(57386)   on 2009-11-05 13:00:58 (Show Source): You can put this solution on YOUR website!outline the steps you would use to prepare a 10% salt solution from a 25% salt solution for a 100 ml. ------------------ Equation: salt + salt = salt 0.25x + 0(100-x) = 0.10(100 ml) Multiply both sides by 100 to get: 25x = 10(100) x = 1000/25 = 40 ml (amount of 10% solution you need in the mix) 100-x = 60 ml (amount of water you need in the mix) ======================================================= Cheers, Stan H.
 Quadratic_Equations/235508: For these problems I need use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions. 2x^2 + 5x + 5 = 01 solutions Answer 173454 by stanbon(57386)   on 2009-11-05 12:55:08 (Show Source): You can put this solution on YOUR website!just determine the number and types of solutions. 2x^2 + 5x + 5 = 0 --- a = 2 ; b = 5 ; c = 5 --- discriminant = b^2-4ac = 25 -4*2*5 = -15 ================================================= Since the discriminant is negative the quadratic has two unequal Complex Number solutions. ================================================= Cheers, Stan H