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Recent problems solved by 'stanbon'

stanbon answered: 57894 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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logarithm/328542: Find the logarithm using the change of base formula : log 7 15 1 solutions Answer 235340 by stanbon(57967)   on 2010-08-03 16:23:55 (Show Source): You can put this solution on YOUR website! Find the logarithm using the change of base formula : -------------- log 7 (15) = [log(15)]/[log(7)] = 1.3917 ============================================= Cheers, Stan H. ===========

logarithm/328540: Find the indicated value of the log function: log6 (1/1296) 1 solutions Answer 235338 by stanbon(57967)   on 2010-08-03 16:21:34 (Show Source): You can put this solution on YOUR website! Find the indicated value of the log function: log6 (1/1296) = log6(1) - log6(1296) ---- = 0 - log6(6^4) --- = 0 - 4 --- = -4 =============== Cheers, Stan H.

Trigonometry-basics/328508: Sonia harvested 39 bushels of beans per acre from 46 acres in May and 31 bushels of beans per care from 43 acres in June. How many bushels of beans did Sonia harvest? Thank you for your time. 1 solutions Answer 235336 by stanbon(57967)   on 2010-08-03 16:18:20 (Show Source): You can put this solution on YOUR website! Sonia harvested 39 bushels of beans per acre from 46 acres in May and 31 bushels of beans per acre from 43 acres in June. How many bushels of beans did Sonia harvest? Thank you for your time. ---- That depends on how many acres Sonia harvested. ================ Cheers, Stan H.

Trigonometry-basics/328512: Find an angle between -2pi and 0 that is coterminal with 5/12pi. Explain your answer in radians in terms of pi. 1 solutions Answer 235333 by stanbon(57967)   on 2010-08-03 16:15:14 (Show Source): You can put this solution on YOUR website! Find an angle between -2pi and 0 that is coterminal with 5/12pi. Explain your answer in radians in terms of pi. ---- (5/12)pi - (2pi) --- = (5/12) - (24/12)pi --- = (-19/12)pi ============== Cheers, Stan H.

Finance/328537: A total of $10, 126 was invested into two saving accounts. One account yields 8.5% simple interest and the other 9% simple interest. The person would like to find the amount placed in each account if a total of $901.66 in interest is received after one year. Write a system of linear equations to express this problem. I tried 901.66 = 10126 - (8.5x+9y) But that looks really wrong to me. 1 solutions Answer 235332 by stanbon(57967)   on 2010-08-03 16:11:50 (Show Source): You can put this solution on YOUR website! A total of $10, 126 was invested into two saving accounts. One account yields 8.5% simple interest and the other 9% simple interest. The person would like to find the amount placed in each account if a total of $901.66 in interest is received after one year. Write a system of linear equations to express this problem. ----------------- Quantity Equation: x + y = 10,126 Interest Equation:0.085x + 0.09y = 901.66 ------- Multiply thru Quantity by 85 Multiply thru Interest by 1000 ------------------------------------ 85x + 85y = 85*10126 85x + 90y = 901660 --------------------- Subtract 1st from 2nd and solve for "y": 5y = 40950 --- y = $8190 (amt invested at 9%) ----- Since x+y = 10126, x = $1936 (amt invested at 8.5% ===================================================== Cheers, Stan H. ================

logarithm/328535: solve: 4 log x = -8 1 solutions Answer 235327 by stanbon(57967)   on 2010-08-03 16:06:14 (Show Source): You can put this solution on YOUR website! 4 log x = -8 ---------- log(x) = -2 --- base = 10, exponent = -2 result = x ------------- x = 10^-2 x = 1/100 ================ Cheers, Stan H.

Linear-equations/328534: y=-1/2x+5 state the x intercept and y intercept, then graph using intercepts and a third point 1 solutions Answer 235325 by stanbon(57967)   on 2010-08-03 16:04:26 (Show Source): You can put this solution on YOUR website! y=-1/2x+5 state the x intercept and y intercept, then graph using intercepts and a third point ------------------- x-intercept = ? Let y = 0, then x = 10 ---- y-intercept = ? let x = 0, then y = 5 --------------------------- 3rd point = ? Let x = 2, then y = 4 ------- Plot: (10,0),(0,5),(2,4) and draw a line thru them. ===================== Cheers, Stan H.

Numbers_Word_Problems/328524: Question (1)Divide x4 + x2 -80 by ( x + 3) Question (2)Simplify using positive exponents(–3x) -2 1 solutions Answer 235322 by stanbon(57967)   on 2010-08-03 16:00:41 (Show Source): You can put this solution on YOUR website! Question (1)Divide x4 + x2 -80 by ( x + 3) --- Using synthetic division: -3)....1....0....1....0....-80 .........1....-3...10...-30..|..10 Quotient: x^3 - 3x^2 + 10x -30 Remainder: 10 =================================== Question (2)Simplify using positive exponents(–3x)^-2 = 1/(9x^2) ============== Cheers, Stan H. ==============

logarithm/328531: Solve where appropriate log2 square root x^2-4=1 1 solutions Answer 235319 by stanbon(57967)   on 2010-08-03 15:55:24 (Show Source): You can put this solution on YOUR website! Solve where appropriate log2 (square root x^2-4) = 1 ----- sqrt(x^2-4) = 2^1 ------ Square both sides: x^2-4 = 2 --- x^2 = 6 --- x = sqrt(6) or x = -sqrt(6) ----- Cheers, Stan H.

Equations/328521: write the equation of a line perpendicular to the y-axis and passing through the point (5,-3) 1 solutions Answer 235310 by stanbon(57967)   on 2010-08-03 15:44:42 (Show Source): You can put this solution on YOUR website! write the equation of a line perpendicular to the y-axis and passing through the point (5,-3) -------------------- Plot the point and draw the line. Equation: x = 5 ====================== Cheers, Stan H.

Probability-and-statistics/328522: A single die is rolled one time. Find the probability of rolling an even number or a number less than 3. 1 solutions Answer 235300 by stanbon(57967)   on 2010-08-03 15:21:58 (Show Source): You can put this solution on YOUR website! A single die is rolled one time. Find the probability of rolling an even number or a number less than 3. ------ P(even or < 3) = P(even) + P(<3) - P(even AND <3) ------ = (3/6) + (2/6) = (1/6) --- = 4/6 = 2/3 =============== Cheers, Stan H. ===================

Equations/328518: write the equation of the line passing through point (-2,4) and parallel to the x-axis. 1 solutions Answer 235299 by stanbon(57967)   on 2010-08-03 15:19:32 (Show Source): You can put this solution on YOUR website! write the equation of the line passing through point (-2,4) and parallel to the x-axis. ----- 1st: plot the point 2nd: draw the line thru the point parallel to the x-axis --- 3rd: Notice that the line passes thru all the points where y = 4. ---- Equation: y = 4 =========== Cheers, Stan H.

Probability-and-statistics/328285: A painter has learned that the time it takes her to paint a random room in a house is normally distributed with a mean if 4 hours and a standard deviation of 45 minutes. If she is just starting work on a random room and has to leave in five hour, find a. The probablilty she can have lunch before she has to leave if she needs 30min. for lunch. b. the probability she does not finish before she leaves. c. The probability she works for more that 3 hours (don't forget she will stop working to leave on time.) 1 solutions Answer 235203 by stanbon(57967)   on 2010-08-03 09:12:26 (Show Source): You can put this solution on YOUR website! A painter has learned that the time it takes her to paint a random room in a house is normally distributed with a mean of 4 hours and a standard deviation of 45 minutes. If she is just starting work on a random room and has to leave in five hour, find a. The probablilty she can have lunch before she has to leave if she needs 30min. for lunch. She will be home for 4 1/2 hrs P(the job and lunch will be <= 4.5 hrs) = ? z(4.5) = (4.5-4)/0.75 = 2.3 So, P(she can do job and lunch) = P(z< 2/3) = 0.7475 --------------------------------------------------------- b. the probability she does not finish before she leaves. P(x > 5) = ? z(5) = (5-4)/0.75 = 4/3 So, P(x > 5) = P(z > 4/3) = 0.0912 ========================================================= c. The probability she works for more that 3 hours (don't forget she will stop working to leave on time.) P(3< x < 5) = ? z(3) = (3-4)/0.75 = -4/3 So, P(3 < x < 5) = P(-4/3 < z < 4/3) = 0.8176 ========================================================= Cheers, Stan H.

Probability-and-statistics/328294: Find... A. P(Z<1.52) B. P(1.25 C. P(-2.23 D. P(Z>1.63) E. P(-1.32 F. P(Z<-1.82) G. P(Z>-2.92) 1 solutions Answer 235184 by stanbon(57967)   on 2010-08-03 08:45:49 (Show Source): You can put this solution on YOUR website! Find... A. P(Z<1.52) B. P(1.25 C. P(-2.23 D. P(Z>1.63) E. P(-1.32 F. P(Z<-1.82) G. P(Z>-2.92) ---- Using a TI-84 I could give you the answers to these. But you still would not know how to perform this fundamental task. What is your difficulty with these questions? Are you using a z-chart, or a calculator, or some other technology? ============= Cheers, Stan H.

Linear-equations/328260: find the equation of the line that contains (0,4) and parallel to y = 1/2x +2 part two find the equation of the line that contains (0,4) and perpendicular to y = 1/2x +2 1 solutions Answer 235118 by stanbon(57967)   on 2010-08-02 21:34:05 (Show Source): You can put this solution on YOUR website! Find the equation of the line that contains (0,4) and parallel to y = 1/2x +2 --- slope = 1/2 intercept = 4 ------------------- Equation: y = (1/2)x + 4 ===================================== part two Find the equation of the line that contains (0,4) and perpendicular to y = 1/2x +2 --- slope = -2 intercept = 4 ------------------- Equation: Y = -2x+4 ========================= Cheers, Stan H.

Surface-area/328215: A pond is 50 meters long and 50 meters wide. There is a sidewalk 5 meters wide all around the pond. Tile is sold in crates of 45 square meters of tile. What will the tile cost be if the cost of each box of tile is $74.00? Answers given are $4,111, $1,480, $1,850, and $7,500. I have tried using the formula for a circle, but I am not getting any of the answers provided. Thank you for trying to help me figure this out! 1 solutions Answer 235117 by stanbon(57967)   on 2010-08-02 21:31:21 (Show Source): You can put this solution on YOUR website! A pond is 50 meters long and 50 meters wide. There is a sidewalk 5 meters wide all around the pond. Tile is sold in crates of 45 square meters of tile. ------------ Draw the picture of a rectangle inside a rectangle. The sidewalk is 50 + 2*5 = 60 meters long on the two outer sides. That area = 2(60*5) = 600 sq. meters ---------------- The area of the other two sides is 2(50*5) = 500 sq meters ------------------ Total area = 1100 sq meters --- What will the tile cost be if the cost of each box of tile is $74.00? # of crates needed = 1100/45 = 24.44 Rounded up that is 25 crates --- Cost of 25 crates = $1850.00 =============================== Cheers, Stan H. =============================== Answers given are $4,111, $1,480, $1,850, and $7,500.

Matrices-and-determiminant/328240: The sum of 3 times a number and 10 is 25. Find the number 1 solutions Answer 235114 by stanbon(57967)   on 2010-08-02 21:05:21 (Show Source): You can put this solution on YOUR website! duplicate

Rectangles/328242: the height of a rectangle is 3mm less than twice the width. write an expression for each measure. 1 solutions Answer 235113 by stanbon(57967)   on 2010-08-02 21:04:25 (Show Source): You can put this solution on YOUR website! the height of a rectangle is 3mm less than twice the width. write an expression for each measure. ----- Let the width be "x" Then height = "2x-3". ============================== Cheers, Stan H.

Matrices-and-determiminant/328246: The sum of 3 times a number and 10 is 25. what is the number?? 1 solutions Answer 235112 by stanbon(57967)   on 2010-08-02 21:02:17 (Show Source): You can put this solution on YOUR website! The sum of 3 times a number and 10 is 25. what is the number?? --- Let the number be "x"; Equation: 3x+10 = 25 3x = 15 x = 5 ========== Cheers, Stan H.

Matrices-and-determiminant/328247: what is the slope-intercept form of the equation of a line which contains the points (–2, –1) and (3, 4). 1 solutions Answer 235110 by stanbon(57967)   on 2010-08-02 21:00:46 (Show Source): You can put this solution on YOUR website! what is the slope-intercept form of the equation of a line which contains the points (–2, –1) and (3, 4). ----- slope = (4--1)/(3--2) = 5/5 = 1 ============= Form: y = mx + b where m=1 and y=4 when x=3 ---- Solve for "b": 4 = 1*3 + b b = 1 --------------- Equation: y = x + 1 =============== Cheers, Stan H. ===============

Probability-and-statistics/328231: Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level. Treatment 1 8 11 10 Treatment 2 3 12 11 8 4 Treatment 3 11 20 18 12 a. Set up the null hypothesis and alternative hypothesis. b. State the decision rule. c. Use Excel or Megastat to complete an ANOVA table. Copy the table and paste it here, not as a separate attachment. 1 solutions Answer 235107 by stanbon(57967)   on 2010-08-02 20:57:42 (Show Source): You can put this solution on YOUR website! Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level. Treatment 1 8 11 10 Treatment 2 3 12 11 8 4 Treatment 3 11 20 18 12 a. Set up the null hypothesis and alternative hypothesis. Ho: the means are all equal Ha: At least one of the means is not equal ----------- b. State the decision rule. df numerator = k-1 = 3-1 = 2 df denominator = N-k = 12-3 = 9 --- F = 4.2565 c. Use Excel or Megastat to complete an ANOVA table. Copy the table and paste it here, not as a separate attachment. test stat: F = 4.6901 p-value = 0.0402 Factor df = 2 SS = 134.05 MS = 67.025 --- Error: df = 9 SS = 128.62 MS = 14.29 ============== Cheers, Stan H. ==============

Polynomials-and-rational-expressions/328232: I need help soving: 5+9/x=2 1 solutions Answer 235091 by stanbon(57967)   on 2010-08-02 20:11:34 (Show Source): You can put this solution on YOUR website! I need help solving: 5+9/x=2 ------- Multiply thru by x to get: 5x + 9 = 2x 3x = -9 x = -3 =============== Cheers, Stan H.

Exponents/328205: what is 4,564 in expanded form using exponents? 1 solutions Answer 235060 by stanbon(57967)   on 2010-08-02 18:14:42 (Show Source): You can put this solution on YOUR website! what is 4,564 in expanded form using exponents? --- 4*10^3 + 5*10^2 + 6*10 + 4 ================================== Cheers, Stan H.

Probability-and-statistics/328003: For any frequency distribution to be explained in well manner…… Answer A) Box and whisker plot is used B) Histogram is used C) Scatter graph is used D) All of the above 1 solutions Answer 234978 by stanbon(57967)   on 2010-08-02 14:00:41 (Show Source): You can put this solution on YOUR website! B Cheers, Stan H.

Probability-and-statistics/328005: 1.Theoretical and experimental probabilities ________ Answer A) are same B) are different C) sum is 1 D) none of above 2. A mapping that counts the number of observations that falls into various disjoint categories….. Answer A) Gives the relation between regression and correlation B) Is always linear C) Is known as histogram D) Is alw ays a scatter plot 1 solutions Answer 234977 by stanbon(57967)   on 2010-08-02 13:59:16 (Show Source): You can put this solution on YOUR website! 1.Theoretical and experimental probabilities ________ Answer A) are same B) are different C) sum is 1 D) none of above Ans: B ------------------------------ 2. A mapping that counts the number of observations that falls into various disjoint categories….. Answer A) Gives the relation between regression and correlation B) Is always linear C) Is known as histogram D) Is alw ays a scatter plot Ans: C ================================= Cheers, Stan H.

Probability-and-statistics/328013: if you were running a small sample (say n=24) two-tailed test, the critical t- value would be ____ if alpha was chosen as 5%? 1 solutions Answer 234975 by stanbon(57967)   on 2010-08-02 13:57:05 (Show Source): You can put this solution on YOUR website! if you were running a small sample (say n=24) two-tailed test, the critical t- value would be ____ if alpha was chosen as 5%? ---- invT(0.975 when df = 23) = 2.0687 ------------------------------------ Cheers, Stan H.

Probability-and-statistics/328099: Guessing A multiple choice quiz has three questions, each with five answer choices. Only one of the choices is correct. You have no idea what the answer is to any question, and have to guess each answer. d. Find the probability of answering the first question correctly. e. Find the probability of answer the first two questions correctly. f. Find the probability of answering all three questions correctly. g. Find the probability of answering none of the questions correctly. h. Find the probability if answering at least one of the questions correctly. 1 solutions Answer 234973 by stanbon(57967)   on 2010-08-02 13:54:36 (Show Source): You can put this solution on YOUR website! Guessing A multiple choice quiz has three questions, each with five answer choices. Only one of the choices is correct. You have no idea what the answer is to any question, and have to guess each answer. Binomial Problem with n = 3 and p = 1/5 -------- d. Find the probability of answering the first question correctly. 1/5 ------------------ e. Find the probability of answer the first two questions correctly. 1/5*1/5 = 1/25 ---------------------- f. Find the probability of answering all three questions correctly. (1/5)3 = 1/125 ---------------------------- g. Find the probability of answering none of the questions correctly. (4/5)^3 = 0.512 --------------------------- h. Find the probability if answering at least one of the questions correctly. 1 - 0.512 = 0.488 ======================== Cheers, Stan H. ========================

Probability-and-statistics/328101: A state’s department of transportation plans to develop a new section of interstate highway and receives 16 bids for the project. The state plans to hire four of the bidding companies. How many different combinations of four companies can be selected from the 16 bidding companies? 1 solutions Answer 234972 by stanbon(57967)   on 2010-08-02 13:49:50 (Show Source): You can put this solution on YOUR website! 16C4 = (16*15*14*13)/(1*2*3*4) = 1820 ========================================= Cheers, Stan H.

Probability-and-statistics/328041: Suppose a simple random sample of size n = 34 is obtained from a population with μ = 30 and σ = 4. a) Is the sampling distribution of x approximately normal. b) What is P(x > 30.2)? c) What is P(x ≤ 30.6)? d) What is P(28.7 ≤ x ≤ 31.1) 1 solutions Answer 234971 by stanbon(57967)   on 2010-08-02 13:47:58 (Show Source): You can put this solution on YOUR website! Suppose a simple random sample of size n = 34 is obtained from a population with μ = 30 and σ = 4. a) Is the sampling distribution of x approximately normal. Yes --------------------------- b) What is P(x > 30.2)? z(30.2) = (30.2-34)/4 = -3.8 P(x > 30.2) = P(z > -2.8) = 0.9974 --------------------------- c) What is P(x ≤ 30.6)? z(30.6) = (30.6-34)/4 = -3.4 P(x <= 30.6) = P(z <= -3.4) = 0.000337 ------------------------- d) What is P(28.7 ≤ x ≤ 31.1) z(31.1) = (31.1-34)/4 = -2.9 --- z(28.7) = (28.7-34)/4 =-5.3 P( 28.7 <= x <= 31.1) = P(-5.3 <= z <= -2.9)= 0.0019 ==================================================== Cheers, Stan H. ===============

Probability-and-statistics/328042: 2. In 2000, as reported by ACT Research Service, the mean ACT Math score was μ=20.7. If ACT Math scores are normally distributed with σ = 5, answer the following questions. a) What is the probability that a randomly selected student has an ACT Math score less than18? b) What is the probability that a random sample of 10 ACT test takers had a mean ACT Math score less than 18? 1 solutions Answer 234969 by stanbon(57967)   on 2010-08-02 13:37:04 (Show Source): You can put this solution on YOUR website! In 2000, as reported by ACT Research Service, the mean ACT Math score was μ=20.7. If ACT Math scores are normally distributed with σ = 5, answer the following questions. a) What is the probability that a randomly selected student has an ACT Math score less than 18? --- z(18) = (18-20.7)/5 = -0.54 P(x < 18) = P(z < -0.54) = 0.2946 ============================================ b) What is the probability that a random sample of 10 ACT test takers had a mean ACT Math score less than 18? --- z(18) = (18-20.7)/[5/sqrt(10)] = -1.7076 = 0.0439 ============= Cheers, Stan H.

Probability-and-statistics/328043: 3. 3% of Americans surveyed lie frequently. Suppose you conduct a survey of 500 college students and find that 20 of them lie frequently. Compute the probability that, in a random sample of 500 students, at least 20 lie frequently, assuming the true percentage is 3%. 1 solutions Answer 234965 by stanbon(57967)   on 2010-08-02 13:28:17 (Show Source): You can put this solution on YOUR website! 3% of Americans surveyed lie frequently. Suppose you conduct a survey of 500 college students and find that 20 of them lie frequently. Compute the probability that, in a random sample of 500 students, at least 20 lie frequently, assuming the true percentage is 3%. --- Binomial Problem with n=500 and p = 0.03 ---- P(x=500) = 1 - binomcdf(500,0.03,19) 0.1214 ============================================= Cheers, Stan H. =============