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Recent problems solved by 'stanbon'

stanbon answered: 57269 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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269, >>Next

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(57342)   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(57342)   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(57342)   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(57342)   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(57342)   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(57342)   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. =============

Probability-and-statistics/328062: For this assignment you are to imagine that you are part of a select marketing group. This select group has been asked to consider the Colorado City Convention and Visitors Bureau survey of 25 hotels in the local area. The survey is concerned with the current availability of rooms. The availability of the rooms was as follows: 90, 72, 75, 60, 75, 72, 84, 72, 88, 74, 105, 115, 68, 74, 80, 64, 414, 82, 48, 58, 60, 80, 48, 58, and 108. Each person in the marketing group must select a sample of 10 hotels from the list. In a report prepared and submitted by yourself only, describe the methods your imaginary group chose to select the 10 hotels. Discuss the pros and cons of each sampling method. Calculate the average number of available rooms in one sample. Calculate the standard deviation of the number of available rooms in that sample. Construct a frequency distribution of the sample mean, and plot a histogram of this distribution. Use the central limit theorem to calculate and identify the sampling distribution of the sample mean. 1 solutions Answer 234963 by stanbon(57342)   on 2010-08-02 13:24:28 (Show Source): You can put this solution on YOUR website! duplicate

Probability-and-statistics/328069: Please help me solve this problem. The table below describes the smoking habits of a group of asthma sufferers. Nonsmokers Light Smoker Heavy Smoker Total Men 311 82 74 467 Women 329 68 60 457 Total 640 150 134 924 If a woman is randomly selected, find the probability that she is a nonsmoker. A) 0.395 B) 0.720 C) 0.514 D) 0.356 1 solutions Answer 234962 by stanbon(57342)   on 2010-08-02 13:22:07 (Show Source): You can put this solution on YOUR website! Please help me solve this problem. The table below describes the smoking habits of a group of asthma sufferers. Nonsmokers Light Smoker Heavy Smoker Total Men 311 82 74 467 Women 329 68 60 457 Total 640 150 134 924 If a woman is randomly selected, find the probability that she is a nonsmoker. ------------ P(nonsmocker|woman) = P(nonsmoke AND woman)/P(woman) = 329/457 = 0.720 ==================== Cheers, Stan H. ==================== A) 0.395 B) 0.720 C) 0.514 D) 0.356

Probability-and-statistics/328009: A standard six-sided die is thrown four times. What is the probability that all four rolls show a six? 1 solutions Answer 234885 by stanbon(57342)   on 2010-08-02 09:48:57 (Show Source): You can put this solution on YOUR website! A standard six-sided die is thrown four times. What is the probability that all four rolls show a six? ---------------- (1/6)^4 = 0.000772.. ================= Cheers, Stan H. =================

Linear-equations/327897: I am having a hard time trying to finding a slope and y intercept for 5y + 4x + 4 = 14 + 4x.... please help 1 solutions Answer 234807 by stanbon(57342)   on 2010-08-01 22:36:08 (Show Source): You can put this solution on YOUR website! slope and y intercept for 5y + 4x + 4 = 14 + 4x --- 5y = 10 Y = 2 ------- slope = 0 intercept = 2 ============== Cheers, Stan H. ==============

Quadratic_Equations/327900: i am doing completing the square and i want to make sure i have it right solve: x squared + 2x = 8 by completing the square 1 solutions Answer 234806 by stanbon(57342)   on 2010-08-01 22:33:02 (Show Source): You can put this solution on YOUR website! solve: x squared + 2x = 8 by completing the square ------------- x^2 + 2x + 1 = 8 + 1 -------------------------- (x+1)^2 = 9 --- x+1 = +3 or x+1 = -3 x = 2 or x = -4 ===================== Cheers, Stan H.

Linear-systems/327903: Solve by elimination method x + 6y = 55 -x + 3y = 17 1 solutions Answer 234805 by stanbon(57342)   on 2010-08-01 22:26:16 (Show Source): You can put this solution on YOUR website! Solve by elimination method x + 6y = 55 -x + 3y = 17 -------------------- Add to get: 9y = 72 y = 8 ------ Since x +6*8 = 55 x = 7 ======= Cheers, Stan H.

Expressions-with-variables/327904: solve by elimation 4x-8y=5 4x-8y=6 I know I must multiply to make one of the equations the opposite of the other, but I am not sure which or by what number. I am thinking (-1) and the first equation. but that is just going to bring the equation to -4x+8y=-5 4x-8y=6 which still doesnt work..So I am all sorts of confused, if you can please help me out and explain..Much appreciated!!!THANKS A BUNCH!!! 1 solutions Answer 234803 by stanbon(57342)   on 2010-08-01 22:22:14 (Show Source): You can put this solution on YOUR website! solve by elimation 4x-8y=5 4x-8y=6 --------------- If we assume the x's and the y's have the same value respectively, we can subtract the 1st equation from the 2nd to get: 0 = 1 ------ That is a contradiction. That result tells us the x's and the y's do not have the same meaning in the two equations. ------- Conclusion: No solution for the system of equations. ======================================================== Cheers, Stan H.

Polynomials-and-rational-expressions/327906: 3x^3 + 24x^2 + 48x can you help me factor showing steps 1 solutions Answer 234801 by stanbon(57342)   on 2010-08-01 22:17:00 (Show Source): You can put this solution on YOUR website! 3x^3 + 24x^2 + 48x --- = 3x(x^2 + 8x + 16) ------ = 3x(x+4)(x+4) ======================== Cheers, Stan H.

Rational-functions/327664: solve the system by the elimination method x+3y=-4 2x+2y=-1 1 solutions Answer 234695 by stanbon(57342)   on 2010-08-01 11:15:15 (Show Source): You can put this solution on YOUR website! solve the system by the elimination method x+3y=-4 2x+2y=-1 --------------- Multiply thru the 1st by 2: 2x+6y = -8 2x+2y = -1 ---- Subtract the 2nd from the 1st and solve for "y": 4y = 9 y= 9/4 -------- Substitute into x + 3y = -4 to solve for "x": x + 3(9/4) = -16/4 x = -(43/4) =============== Cheers, Stan H. ==============

Coordinate-system/327673: graph the equation using the slope and the y intercept of y=1/5x+7. i know the first corrdinates will be (0,7) need help with finiding the other? Thanks 1 solutions Answer 234694 by stanbon(57342)   on 2010-08-01 10:56:01 (Show Source): You can put this solution on YOUR website! graph the equation using the slope and the y intercept of y=(1/5)x+7. i know the first cordinates will be (0,7) need help with finding the other? ----- Plot that y-intercept: (0,7) ---- Slope = 1/5 which means "y increases 1/5 when x increases 1". --- Let x increase by 5, then y will increase by 1+7 = 8. That gives you the point (5,8) --- Plot it and draw a line thru the two points you have plotted. --------------------- Cheers, Stan H.

Square-cubic-other-roots/327672: Hi...I have two problems I can seem to get correct... multipy sqrt7(sqrt3-sqrt7) ------------------------ multiply and simplify sqrt28a^9b * sqrt8a^10b^8 1 solutions Answer 234693 by stanbon(57342)   on 2010-08-01 10:51:11 (Show Source): You can put this solution on YOUR website! multipy sqrt7(sqrt3-sqrt7) --- = sqrt(21) - 7 ======================== ------------------------ multiply and simplify sqrt(28a^9b) * sqrt(8a^10b^8) --- = sqrt(4a^8*7ab) * sqrt(4a^10b^8*2) --- = 2a^4*sqrt(7ab) * 2a^5b^4*sqrt(2) --- = 4a^9b^4*sqrt(14ab) ========================= Cheers, Stan H.

Inequalities/327667: please help me with the follow question Factor by grouping, if possible. can you please show all work necessary. x^3 + 3x^2 + 8x + 24 1 solutions Answer 234692 by stanbon(57342)   on 2010-08-01 10:45:51 (Show Source): You can put this solution on YOUR website! Factor by grouping, if possible. can you please show all work necessary. x^3 + 3x^2 + 8x + 24 --- Rearrange: x^3+8x + 3x^2+24 --- Factor the 1st two and last two terms separately to get: = x(x^2+8) + 3(x^2+8) --- Factor again to get: = (x^2+8)(x+3) ================= Cheers, Stan H.

Polynomials-and-rational-expressions/327671: can you please help me Factor completely showing all steps please -5x^3 - 15x^2 + 20x 1 solutions Answer 234691 by stanbon(57342)   on 2010-08-01 10:42:11 (Show Source): You can put this solution on YOUR website! Factor completely showing all steps please -5x^3 - 15x^2 + 20x --- Greatest Common Factor: -5x --- = -5x(x^2 + 3x -4) --- = -5x(x+4)(x-1) ================= Cheers, Stan H.

Distributive-associative-commutative-properties/327655: Please show me the domain of: y=-3x+1: Is it all negative numbers, all real numbers, x=3 or x>0 Thanks 1 solutions Answer 234690 by stanbon(57342)   on 2010-08-01 10:39:56 (Show Source): You can put this solution on YOUR website! Please show me the domain of: y=-3x+1: Is it all negative numbers, all real numbers, x=3 or x>0 ------------------------- Domain for a function is always "all Real Numbers" unless there is somehing about the Rule for the function which restricts the domain. -- The restrictions are: 1. zero in the denominator 2. even roots of negative numbers 3. log or ln of negative numbers ------------ Your problem has none of these restrictions, so the domain is All Real Numbers. ------------- Cheers, Stan H.

Polynomials-and-rational-expressions/327548: If y varies inversely as x and y = 2 when x = 6, find y when x = 36 A) 1/6 B) 6 C) 3 D) 1/3 1 solutions Answer 234602 by stanbon(57342)   on 2010-07-31 20:12:49 (Show Source): You can put this solution on YOUR website! If y varies inversely as x --- y = k/x ---- Solve for "k" using y = 2 when x = 6 ---- 2 = k/6 k - 12 ----- Equation for this situation: y = 12/x ------------------------------ Find y when x = 36 y = 12/36 y = 1/3 ========================== Cheers, Stan H. ========================== A) 1/6 B) 6 C) 3 D) 1/3

Polynomials-and-rational-expressions/327563: List all numbers for which the rational expression is undefined: x^2-4 ____________ x^2-8x+15 Thanks in advance :) 1 solutions Answer 234601 by stanbon(57342)   on 2010-07-31 20:05:20 (Show Source): You can put this solution on YOUR website! List all numbers for which the rational expression is undefined: x^2-4 ____________ x^2-8x+15 ===================== The expression is undefined when the denominator is zero. --------------- Solve: x^2-8x+15 = 0 Factor: (x-5)(x-3) = 0 --- Undefined when x = 3 and when x = 5 ====================================== Cheers, Stan H.

Miscellaneous_Word_Problems/327562: tickets=-0.2x^2+12x+11 Appendix F, math 117 projected ticket sales, will tickets peak or be at a low during the middle of the sale? How do you know? 1 solutions Answer 234600 by stanbon(57342)   on 2010-07-31 20:02:50 (Show Source): You can put this solution on YOUR website! tickets=-0.2x^2+12x+11 Appendix F, math 117 projected ticket sales, will tickets peak or be at a low during the middle of the sale? Ans: Peak because the parabola opens downward when the coefficient of the x^2 term is negative. --------- Cheers, stan H. How do you know?

decimal-numbers/327533: add -7/11+4/13= 1 solutions Answer 234599 by stanbon(57342)   on 2010-07-31 19:57:10 (Show Source): You can put this solution on YOUR website! add -7/11+4/13 ---- lcd = (11*13) --- Rewrite each fraction with the lcd as its denominator: --- =[-7*13/lcd + [4*11/lcd] ------ = [-91+44]/lcd --- = -47/143 ============== Cheers, Stan H.

Polynomials-and-rational-expressions/327555: Identify the type of function represented by : y = x^2 - 9/x - 3 A) quadratic B) rational C) inverse variation D) direct variation 1 solutions Answer 234598 by stanbon(57342)   on 2010-07-31 19:49:34 (Show Source): You can put this solution on YOUR website! Identify the type of function represented by : y = (x^2 - 9)/(x - 3) y = (x+3) --- Ans: D ============== Cheers, Stan H. ============== A) quadratic B) rational C) inverse variation D) direct variation

Polynomials-and-rational-expressions/327549: The distance a car travel on a certain amount of fuel varies inversely with its speed. If a car traveling 50 mph con travel 300 miles on 10 gallons of fuel, how far could the car travel on10 gallons of fuel at 60 mph? 1 solutions Answer 234597 by stanbon(57342)   on 2010-07-31 19:42:04 (Show Source): You can put this solution on YOUR website! The distance a car travel on a certain amount of fuel varies inversely with its speed. If a car traveling 50 mph con travel 300 miles on 10 gallons of fuel, how far could the car travel on10 gallons of fuel at 60 mph? ------------- distance = k*fuel/rate --- Find "k" using d=300 when rate = 50 mph and fuel = 10 gals 300 = k*10/50 --- k = 1500 ---- Equation for this situation: d = 1500*f/r ------------------------- How far could the car travel on 10 gallons of fuel at 60 mph? ------------- distance = 1500*10/60 = (1/4)(1000) = 250 miles ========================================= Cheers, Stan H. ============= Cheers, Stan H.

Rational-functions/327553: Identify the type of function represented by y = (x + 1)^2 - 4 A) square root B) rational C) inverse variation D) quadratic 1 solutions Answer 234593 by stanbon(57342)   on 2010-07-31 19:32:41 (Show Source): You can put this solution on YOUR website! Quadratic Cheers, Stan H.

Polynomials-and-rational-expressions/327550: Fences R Us wants to replace their office’s traditional computers and two-dimensional monitors with a virtual reality system. The fixed monthly cost will be $400,000, and it will cost $700 to produce each system. 1. Write the cost function C, of producing x virtual reality systems. 1 solutions Answer 234592 by stanbon(57342)   on 2010-07-31 19:31:36 (Show Source): You can put this solution on YOUR website! Fences R Us wants to replace their office’s traditional computers and two-dimensional monitors with a virtual reality system. The fixed monthly cost will be $400,000, and it will cost $700 to produce each system. 1. Write the cost function C, of producing x virtual reality systems. ----- C(x) = 400,000 + 700x ========================= Cheers, Stan H.

Polynomials-and-rational-expressions/327536: How would I go about factoring this polynomial? 135x^4y^2 - 60y^2 Can you please break it down step by step and use layman's terms? I'm having a lot of trouble following textbook instructions. 1 solutions Answer 234591 by stanbon(57342)   on 2010-07-31 19:28:19 (Show Source): You can put this solution on YOUR website! How would I go about factoring this polynomial? 135x^4y^2 - 60y^2 ---- Find the GCF: gcf of 135 and 60 is 15 gcf of the x factors is 1 gcf of the y factors is y^2 ----------------------------------- So, GCF = 15y^2 ------- = 15y^2(9x^4-4) --- Note: 9x^4-4 is a difference of squares --------------- = 15y^2(3x^2-2)(3x^2+2) ---- Cheers, Stan H.

Polynomials-and-rational-expressions/327540: x^3+8/ x+2 divide please show steps 1 solutions Answer 234590 by stanbon(57342)   on 2010-07-31 19:23:04 (Show Source): You can put this solution on YOUR website! x^3+8/ x+2 ---------------- The numerator is "a sum of cubes". It factors as follows: x^3+2^3 = (x+2)(x^2 - 2x + 4) ----- Dividing by (x+2) you get: x^2-2x+4 ====================== Cheers, Stan H. ======================

Radicals/327544: What is product of sqrt(2)(sqrt(8)+sqrt(6))? 1 solutions Answer 234589 by stanbon(57342)   on 2010-07-31 19:19:08 (Show Source): You can put this solution on YOUR website! What is product of sqrt(2)(sqrt(8)+sqrt(6))? ----- sqrt(2)[sqrt(8)+sqrt(6)] --- = sqrt(16) + sqrt(12) --- = 4 + sqrt(4*3) --- = 4 + 2*sqrt(3) ================== Cheers, Stan H.