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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>Next

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. =============

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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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(57967)   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.

Linear-equations/327546: Is the following equation a function. y=5 I think it is.Am I correct? 1 solutions Answer 234588 by stanbon(57967)   on 2010-07-31 19:16:28 (Show Source): You can put this solution on YOUR website! Yes, it is a function because each value of x has only one corresponding y-value. =================================== Cheers, Stan H.

Inequalities/327512: I am having a really hard time trying to learn Algebra. Need assistace Please. For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve. 1 solutions Answer 234587 by stanbon(57967)   on 2010-07-31 19:14:49 (Show Source): You can put this solution on YOUR website! For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve. ---------------------- Money remaining after rock is purchased: 2500 - 60*30 = $700 ----- Number of trees you can purchase = 700/84 = 8 1/3 Round down to 8 trees. ------ Inequality # of trees <= [2500-60*30]/84 ================================== Cheers, Stan H.

Polynomials-and-rational-expressions/327508: Multiply and simplify (y^2-8)(9y^2-9y+8) The solution I got was 9y^4-9y^3-64y^2+72Y-64 Is this correct 1 solutions Answer 234575 by stanbon(57967)   on 2010-07-31 17:55:37 (Show Source): You can put this solution on YOUR website! (y^2-8)(9y^2-9y+8) ------ 9y^4-9y^3+9y^2-73y2+72y-64 --- 9y^4-9y^3-64y^2+72y-64 ============================= Cheers, Stan H.

Age_Word_Problems/327498: If 7 ballerinas dance for 8 hours and lose a total of 20 pounds, how many more ballerinas dancing would it take to lose a total of 20 pounds in only 4 hours if the new dancers lost weight only half as fast as the original 7 ? 1 solutions Answer 234574 by stanbon(57967)   on 2010-07-31 17:45:23 (Show Source): You can put this solution on YOUR website! If 7 ballerinas dance for 8 hours and lose a total of 20 pounds, Rate at which they lost weight was 20/8 = 5/2 = 2.5 lbs per hour or 7 2.5/7 = 0.3571 lbs per hr. per ballerina --------------------------------------------------------- Note: rate = total loss/[total hours*# of ballarina) ========================================================= How many more ballerinas dancing would it take to lose a total of 20 pounds in only 4 hours if the new dancers lost weight only half as fast as the original 7 ? --- Let Let "x" be the total # of ballarinas required. Equations: (0.3571/2) = 20/[4x] 0.1786 = 5/x x = 5/0.1786 x = 28 ballarinas would be required ================================ Cheers, Stan H.

Numeric_Fractions/327431: if 21-2x=-9x then x= 1 solutions Answer 234554 by stanbon(57967)   on 2010-07-31 16:50:34 (Show Source): You can put this solution on YOUR website! A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area is 576 square meters more than the area of the pool, find the dimensions of the pool. How do they get the answer? I've tried by making Total Area = x^2+6x+576, but have been unable to obtain the answer. ------------------ Pool width: "x" meters Pool length: "x+6" meters Area of the pool: x^2+6x sq. meters ----------------------------- Total width : x+8 Total length: x+6+8 = x+14 Total Area: (x+8)(x+14) = x^2+22x+112 sq meters ------------------------------ Equation: Total area - Pool area = 576 sq. meters ------------------ x^2+22x+112 - x^2+6x = 576 16x +112= 576 16x = 464 x = 29 meters (pool width) x+6 = 35 meters (pool length) ------------------------------- Cheers, Stan H.