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Recent problems solved by 'stanbon'

stanbon answered: 57274 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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Probability-and-statistics/345069: from past experience, the pass rate of students has been 70%. if 8 students are randomly selected. a) what is the probability at least half will fail? b) what is the standard deviation of the distribution? c)what is the probability that no student will fail? d0 state the name given to the probability distribution being described in the question and state one of its characteristics? 1 solutions Answer 247078 by stanbon(57347)   on 2010-09-20 07:30:27 (Show Source): You can put this solution on YOUR website! from past experience, the pass rate of students has been 70%. if 8 students are randomly selected. ----- Binomial Problem with n = 8 and p = 0.7 -------- a) what is the probability at least half will fail? P(4<= x <=8) = 1-binomcdf(8,0.7,3) = 0.9420 ------------------------------------------------------- b) what is the standard deviation of the distribution? std = sqrt(npq) = sqrt(8*0.7*0.3) = 1.2961 ------------------------------------------------------- c)what is the probability that no student will fail? P(x = 0) = 0.7^8 = 0.0576 ------------------------------------------------------- d) state the name given to the probability distribution being described in the question and state one of its characteristics? binomial; n independent trials. =========================================== Cheers, Stan H.

Probability-and-statistics/345089: 1. For this lab assignment, the experiment is to roll a fair die twice. If the random variable x represents the sum of the numbers rolled, find the probability distribution for this random variable. This should be in the form of a table similar to Table 5-1 on Page 195 in the textbook. 1 solutions Answer 247075 by stanbon(57347)   on 2010-09-20 07:23:48 (Show Source): You can put this solution on YOUR website! duplicate

Probability-and-statistics/345173: In a deck of cards, five are pulled at random. What is the probabilty that exactly three of them will be spades? 1 solutions Answer 247074 by stanbon(57347)   on 2010-09-20 07:22:46 (Show Source): You can put this solution on YOUR website! In a deck of cards, five are pulled at random. What is the probabilty that exactly three of them will be spades? ----- # of ways to select 3 spades: 13C3 # of ways to select 2 non-spades: 39C2 ----- # of ways to select 5 cards randomly: 52C5 ================ P(3spades and 2 other) = [13C3*39C2)/52C5 = 0.0815 ================================ Cheers, Stan H.

Probability-and-statistics/345412: 1. For this lab assignment, the experiment is to roll a fair die twice. If the random variable x represents the sum of the numbers rolled, find the probability distribution for this random variable. 1 solutions Answer 247071 by stanbon(57347)   on 2010-09-20 07:17:37 (Show Source): You can put this solution on YOUR website! For this lab assignment, the experiment is to roll a fair die twice. If the random variable x represents the sum of the numbers rolled, find the probability distribution for this random variable. ---- Draw the sample space. Draw a 6x6 square. Put 1,2,3,4,5,6 along the left edge and along the top. Put the sum of the row and the column numbers for each box in the square. You should see something like the following: 2,3,4,5,6,7 3,4,5,6,7,8 4,5,6,7,8,9 .... .... 7,8,9,10,11,12 ========================= Note that there are 36 sum entries P(2) = 1/36 P(3) = 2/36 P(4) = 3/36 .... P(11) = 2/36 P(12) = 1/36 =================== That is the probability distribution. ========================================== Cheers, Stan H. =============

Probability-and-statistics/345319: A normal distribution has a mean of 80 and a standard deviation of 14. Determine the value above which 80 percent of the values will occur. 1 solutions Answer 247069 by stanbon(57347)   on 2010-09-20 07:11:17 (Show Source): You can put this solution on YOUR website! A normal distribution has a mean of 80 and a standard deviation of 14. Determine the value above which 80 percent of the values will occur. -------------- Find the z-value associated with a right tail of 80% --- invNorm(0.8) = 0.8416 ----- Find the corresponding raw-score value using x = zs+u x = 0.8416*14+80 = 91.78 =================================== Cheers, Stan H.

Probability-and-statistics/345425: Component 1 has an exponential failure rate of 2X10exp-2 failures per hour. component 2 is normally distributed with a mean of 200 hours and standard deviation of 50 hurs. Assuming independence, calculate the reliability of the system after 50 hours. ------Component 1----------component 2--------------- 1 solutions Answer 247068 by stanbon(57347)   on 2010-09-20 07:05:33 (Show Source): You can put this solution on YOUR website! Component 1 has an exponential failure rate of 2X10exp-2 failures per hour. component 2 is normally distributed with a mean of 200 hours and standard deviation of 50 hrs. Assuming independence, calculate the reliability of the system after 50 hours. ------ Component 1---------- reliability rate = (1-(2x10^-2))^50 = 0.3642 --------------------- component 2---------- z(50) = (50-200)/50 = -3 reliability = 1 - P(z< -3) = 1-0.0013 = 0.9987 ================================================= Cheers, Stan H.

Probability-and-statistics/345445: A jar holds two color of marbles. The jar is composed of 60% black marbles and 40% red marbles. You select 6 marbles. What is the probability that you selected AT LEAST one of each color? 1 solutions Answer 247066 by stanbon(57347)   on 2010-09-20 06:54:12 (Show Source): You can put this solution on YOUR website! A jar holds two color of marbles. The jar is composed of 60% black marbles and 40% red marbles. You select 6 marbles. What is the probability that you selected AT LEAST one of each color? --- P(selected all black) = 0.6^6 P(selected all red) = 0.4^6 ---- P(select at least one of each) = 1-[0.6^6+0.4^6] = 0.9492 ----------------- Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/345393: Cream is about 22% butterfat and low-fat milk is about 2% butterfat. How many gallons of cream must be mixed with 18 gallons of low fat milk to make whole milk that contains 4% butterfat? 1 solutions Answer 247003 by stanbon(57347)   on 2010-09-19 22:22:26 (Show Source): You can put this solution on YOUR website! Cream is about 22% butterfat and low-fat milk is about 2% butterfat. How many gallons of cream must be mixed with 18 gallons of low fat milk to make whole milk that contains 4% butterfat? ------------- Equation: fat + fat = fat 0.22x + 0.02*18 = 0.04(x+18) --------- Multiply thru by 100. 22x + 2*18 = 4x + 4*18 18x = 2*18 x = 2 gallons (amt. of cream needed in the mixture) ================================ Cheers, Stan H.

Numbers_Word_Problems/345399: 4 divided by the sum of 3 1 solutions Answer 246995 by stanbon(57347)   on 2010-09-19 22:10:31 (Show Source): You can put this solution on YOUR website! 4 divided by the sum of 3 ---------- That is not a complete problem. Cheers, Stan H.

Inequalities/345398: 30 < - 6(x - 3) < 60 1 solutions Answer 246992 by stanbon(57347)   on 2010-09-19 22:07:46 (Show Source): You can put this solution on YOUR website! 30 < - 6(x - 3) < 60 ---- Divide thru by -6 to get: -12 < x-3 < -5 Add 3 along the line: -9 < x < -2 ============ Cheers, Stan H. ============

test/345396: 2x^2-30x=0 1 solutions Answer 246991 by stanbon(57347)   on 2010-09-19 22:04:56 (Show Source): You can put this solution on YOUR website! 2x^2-30x=0 Factor: 2x(x-15) = 0 x = 0 or x = 15 =================== Cheers, Stan H.

Probability-and-statistics/345326: An experiment consists of tossing a penny, a nickel, a dime, and a quarter. Write the probability distribubtion. 1 solutions Answer 246989 by stanbon(57347)   on 2010-09-19 22:03:13 (Show Source): You can put this solution on YOUR website! An experiment consists of tossing a penny, a nickel, a dime, and a quarter. Write the probability distribubtion. ---------------------------------------- p-----1/4 n-----1/4 d-----1/4 q-----1/4 ============== Cheers, Stan H.

Probability-and-statistics/345380: This question deals with a 52 card deck. There are 2 cards of one denomination and 1 card of another denomination. How do you solve this using combination method? 1 solutions Answer 246985 by stanbon(57347)   on 2010-09-19 21:59:17 (Show Source): You can put this solution on YOUR website! This question deals with a 52 card deck. There are 2 cards of one denomination and 1 card of another denomination. How do you solve this using combination method? ---- Pick a denomination: 4 ways Pick 2 cards of that denomination: 13C2 ways Pick another denomination: 3 ways Pick one card of that denomination: 13C1 ------- # of ways to succeed in doing what was described: 4*78*3*13 = 12,168 -------------------------- # of ways to pick 3 cards randomly: 52C3 ------------------------------ Probability of performing the pattern described: 12,168/52C3 = 0.5506 ========================================== Cheers, Stan H.

Geometry_proofs/345320: If Mary goes shopping, then she will buy a new dress. What is the hypothesis of the conditional statement. 1 solutions Answer 246935 by stanbon(57347)   on 2010-09-19 19:58:54 (Show Source): You can put this solution on YOUR website! If Mary goes shopping, then she will buy a new dress. What is the hypothesis of the conditional statement. ----------------------------- Hypothesis: She will buy a new dress. Conditional: If Mary goes shopping. ================== Cheers, Stan H.

Average/345314: The sum of the high and low prices of a share of stock for Johns, inc. in 2010 is &83.50 and the difference of these two prices is $21.88. Find high and low prices. 1 solutions Answer 246933 by stanbon(57347)   on 2010-09-19 19:55:58 (Show Source): You can put this solution on YOUR website! The sum of the high and low prices of a share of stock for Johns, inc. in 2010 is &83.50 and the difference of these two prices is $21.88. Find high and low prices. ---- x + y = 83.50 x - y = 21.88 --------------- 2x = 105.38 x = $52.69 ------- Substitute and solve for "y": y = 83.50-52.69 = $30.81 =========================== Cheers, stan H.

Probability-and-statistics/345231: A student scores 62 on a geography test and 246 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 15. The mathematics test has a mean of 300 and a standard deviation of 36. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class? 1 solutions Answer 246930 by stanbon(57347)   on 2010-09-19 19:45:28 (Show Source): You can put this solution on YOUR website! A student scores 62 on a geography test and 246 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 15. The mathematics test has a mean of 300 and a standard deviation of 36. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class? ---- Geography: z(62) = (62-80)/15 = -1.2 ------------------ Mathematics: z(246) = (246- 300)/36 = -1.5 ===================================== The geography is the higher score relative to the other students. -------------- Cheers, Stan H.

Probability-and-statistics/345298: For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis? 1 solutions Answer 246927 by stanbon(57347)   on 2010-09-19 19:36:34 (Show Source): You can put this solution on YOUR website! For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation 6. Using the .01 significance level: ----- Note: You have not stated what you want to test. ======================= Cheers, Stan H. a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis?

Probability-and-statistics/345251: 1. high school dropouts. Approximately 10% of american high school students drop out of school before graduation. choose 15 students entering high school at randon. Find the probability that only 10 students will graduate. 1 solutions Answer 246923 by stanbon(57347)   on 2010-09-19 19:31:52 (Show Source): You can put this solution on YOUR website! high school dropouts. Approximately 10% of american high school students drop out of school before graduation. choose 15 students entering high school at randon. Find the probability that only 10 students will graduate. ----------------- Binomial Problem with n = 15 and p = 0.1 ------------- P(x = 10) = 15C10*0.1^10*0.9^5 = 0.00000017732... ------------- Cheers, Stan H.

Probability-and-statistics/345271: Two students are selected at random from a class of 13 males and 7 females. Find the probability that both students are males. (See Example 4. Round your answer to two decimal places.) 1 solutions Answer 246916 by stanbon(57347)   on 2010-09-19 19:25:19 (Show Source): You can put this solution on YOUR website! Two students are selected at random from a class of 13 males and 7 females. Find the probability that both students are males. ---------------------------- # of ways to pick 2 males: 13C2 = 78 ----- # of ways to pick 2 students randomly: 20C2 = 190 ----------------------------------- Probability of selecting 2 males: 78/190 = 0.4105 ====================================================== Cheers, Stan H.

Probability-and-statistics/345025: A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level. H0: u1 < u2 H1: u1 >u2 a. Is this a one-tailed or a two-tailed test? b. State the decision rule. c. Compute the value of the test statistic. d. What is your decision regarding H0? e. What is the p-value? 1 solutions Answer 246842 by stanbon(57347)   on 2010-09-19 10:03:06 (Show Source): You can put this solution on YOUR website! A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. ====================================== A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. ================ Conduct the following test of hypothesis using the .08 significance level. H0: u1 <= u2 H1: u1 >u2 --- Note: Equality MUST be part of Ho in every hypothesis test. ----------- a. Is this a one-tailed or a two-tailed test? Right-tailed H1 ALWAYS tells you the type of test. ========================================== b. State the decision rule. If the p-value is greater than 8%, fail to reject Ho. ========================================== c. Compute the value of the test statistic. t = (2.57-2.69)/sqrt[s1^2/n1 + s2^2/n2] = 0.6071 ------------------------------------------ d. What is your decision regarding H0? e. What is the p-value? Note: The p-value is 0.2725, so fail to reject Ho. ============================ Comment: I used a 2-Sample T test on a TI-84 to get the test statistic and the p-value.l ======================================== Cheers, Stan H.

Exponential-and-logarithmic-functions/345033: 3e^x-1=17 1 solutions Answer 246841 by stanbon(57347)   on 2010-09-19 09:48:23 (Show Source): You can put this solution on YOUR website! 3e^x-1=17 --- 3e^x = 18 e^x = 6 --- x = ln(6) =============== Cheers, Stan H.

test/345029: X/b-a=x/a-b find x 1 solutions Answer 246840 by stanbon(57347)   on 2010-09-19 09:46:11 (Show Source): You can put this solution on YOUR website! x/b-a=x/a-b find x ================= x/(b-a) = x(a-b) --- x/(b-a) = -x(b-a) --- x = -x 2x = 0 x = 0 ============== Cheers, Stan H.

Angles/345031: An angle is 12 degrees more than its complement. Find the measure of the complement. 1 solutions Answer 246839 by stanbon(57347)   on 2010-09-19 09:43:55 (Show Source): You can put this solution on YOUR website! An angle is 12 degrees more than its complement. Find the measure of the complement. ------ Angle: x Complement: 90-x --------------------- Equation: x = 90-x+12 2x = 102 x = 51 degrees 90-x = 39 degrees ==================== Cheers, Stan H.

Probability-and-statistics/344944: Please answer this question. I am having difficulty understanding this course my Professor does not speak English well, and has problems explaining the steps to the class. Thank you The following frequency distribution reports the electricity cost for a sample of 50 two-bedroom apartments in Albuquerque, New Mexico during the month of May last year. Electricity Cost Frequency $80 up to $100 3 100 up to 20 8 120 up to 140 12 140 up to 160 16 160 up to 180 7 180 up to 200 4 - Total 50 a. Estimate the mean cost. b. Estimate the standard deviation. c. Use the Empirical Rule to estimate the proportion of costs within two standard deviations of the mean. Waht are these limits? 1 solutions Answer 246838 by stanbon(57347)   on 2010-09-19 09:41:43 (Show Source): You can put this solution on YOUR website! The following frequency distribution reports the electricity cost for a sample of 50 two-bedroom apartments in Albuquerque, New Mexico during the month of May last year. Comment: When you are given a frequency distribution, you have to use the "Mark" of each category as the representative value for the numbers in that category. --------------------- Electricity Cost Frequency $80 up to $100 3 ::::: Mark = (100+80)/2 = 90 100 up to 120 8 ::::: Mark = (120+100)/2 = 110 120 up to 140 12 ::::: Mark = (120+140)/2 = 130 140 up to 160 16 ::::: Mark = 150 160 up to 180 7 ::::: Mark = 170 180 up to 200 4 ::::: Mark = 190 - Total 50 a. Estimate the mean cost. mean = [3*90+8*110+12*130+16*150+7*170+4*190)/(sum of the freqs) = 141.2 Note: I used a TI-84 to get that mean value. ------------------ b. Estimate the standard deviation. S = 26.236 -------------------------- c. Use the Empirical Rule to estimate the proportion of costs within two standard deviations of the mean. What are these limits? mean - 2*S = 141.2-2*26.236 = 87.728 mean + 2*S = 141.2+2*26.236 = 192.672 ========================================== Cheers, Stan H.

Rational-functions/344937: Use the quadratic formula to solve x^2-x=-9 1 solutions Answer 246791 by stanbon(57347)   on 2010-09-18 22:54:25 (Show Source): You can put this solution on YOUR website! Use the quadratic formula to solve x^2-x=-9 --- x^2-x+9 = 0 a = 1 ; b = -1 ; c = 9 ------- x = [1 +- sqrt(1-4*9)]/2 --- x = [1 +- sqrt(-35)]/2 ---- x = [1 +- isqrt(35)]/2 ========================== Cheers, Stan H.

test/344931: How much pure acid should be mixed with 5 gallons of a 40% acid solution in order to get a 90% acid solution? 1 solutions Answer 246790 by stanbon(57347)   on 2010-09-18 22:48:21 (Show Source): You can put this solution on YOUR website! How much pure acid should be mixed with 5 gallons of a 40% acid solution in order to get a 90% acid solution? ---- Equation: acid + acid = acid x + 0.40*5 = 0.90(x+5) ---------------------------- Multiply thru by 100 to get: 100x + 40*5 = 90x + 90*5 10x = 50*5 x = 25 gallons (amt. of pure acid needed for the mixture) ============================================ Cheers, Stan H.

Functions/344932: Solve the equation and check the solution if there is no solution say so 4-8x/x+1+8/x+1 1 solutions Answer 246788 by stanbon(57347)   on 2010-09-18 22:43:33 (Show Source): You can put this solution on YOUR website! Where is the equal sign?

Functions/344927: Solve the equation and check the solution if there is no solution say so 5/4x+2=1/x 1 solutions Answer 246787 by stanbon(57347)   on 2010-09-18 22:41:47 (Show Source): You can put this solution on YOUR website! 5/(4x+2) = 1/x -------------------- Cross multiply to get: 5x = 4x+2 x = 2 -------------- Cheers, Stan H.

Rate-of-work-word-problems/344915: andrew can paint the neighbor's house 3 times as fast as bailey. the year they worked together it took them 2 days. how long would it take for each one to paint hte house alone? 1 solutions Answer 246786 by stanbon(57347)   on 2010-09-18 22:39:05 (Show Source): You can put this solution on YOUR website! andrew can paint the neighbor's house 3 times as fast as bailey. --- Let bailey's time be 3x days/job ;then his rate is 1/3x job/day ---------------------------- Andrew's time is x days/job ; andrew's rate is 1d/x job/day -------------------------------------- the year they worked together it took them 2 days. Together time = 2 days/job ; together rate = 1/2 job/day ------ how long would it take for each one to paint the house alone? Equation: rate + rate = together rate 1/3x + 1/x = 1/2 ---- Multiply thru by 6x to get: 2 + 6 = 3x x = 8/3 days (time for andrew to do the job alone). 3x = 8 days (time for bailey to do the job alone). ======== Cheers, Stan H.

Square-cubic-other-roots/344906: ± (square root of 81) 1 solutions Answer 246785 by stanbon(57347)   on 2010-09-18 22:11:37 (Show Source): You can put this solution on YOUR website! ± (square root of 81) ----- +/-9 ========== Cheers, Stan H.

Functions/344907: Perform the indicated operation. When no operation is indicated, simplify the rational expression completely. 10m^4/9a^2*3a^2b 1 solutions Answer 246782 by stanbon(57347)   on 2010-09-18 22:09:32 (Show Source): You can put this solution on YOUR website! Perform the indicated operation. 3x^2-5x/18x-30 ------ Factor: [x(3x-5)] / [6(3x-5)] ----- Cancel the factor common to the numerator and denominator: 3x-5 ---- = x/6 ========== Cheers, Stan H.