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Recent problems solved by 'stanbon'

stanbon answered: 57304 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/586158: Flip a coin until you get a head or 3 consecutive tails; record each flip. I'm not sure how to answer this question 1 solutions Answer 373664 by stanbon(57377)   on 2012-03-13 10:35:54 (Show Source): You can put this solution on YOUR website! Flip a coin until you get a head or 3 consecutive tails; record each flip. I'm not sure how to answer this question ---- The problem is telling you to do something. There is no answer other than the result of your doing it. So flip a coin untill you get a head or 3 consecutive tails. Record each flip result as you do it. Cheers, Stan H. ============

Probability-and-statistics/586220: Suppose we are testing the hypotheses H0 : u=100 versus Ha : u<100. Which sample mean will have the smaller p-value, X bar=90 or X bar=85? Select all that apply. Assume std. Deviation is the same. A. X bar=85 will have a smaller p-value because it's furthest from (null) u0=100 B. X bar=90 will have a smaller p-value because it's closer to (null) u0=100 C. X bar=85 will have a smaller p-value because it provides more support for Ha. D. X bar= 90 will have a smaller p-value because it provides more support for Ha. *it can be any combination of the following answers, more than 1 may be right 1 solutions Answer 373663 by stanbon(57377)   on 2012-03-13 10:01:00 (Show Source): You can put this solution on YOUR website! Suppose we are testing the hypotheses H0 : u=100 versus Ha : u<100. Which sample mean will have the smaller p-value, X bar=90 or X bar=85? Select all that apply. Assume std. Deviation is the same. A. X bar=85 will have a smaller p-value because it's furthest from (null) u0=100 B. X bar=90 will have a smaller p-value because it's closer to (null) u0=100 C. X bar=85 will have a smaller p-value because it provides more support for Ha. D. X bar= 90 will have a smaller p-value because it provides more support for Ha. *it can be any combination of the following answers, more than 1 may be right ------- Answer: C Because the left tail of x-bar = 85 is smaller then the left-tail of 90. Cheers, Stan H.

Functions/586120: I need to solve this function to the nth term. x = 1; y = 8 x = 2; y = 14 x = 3; y = ? x = ?; y = 24 x = ?; y = 28 x = 6; y = ? I am noticing several patterns. Y increases by six and then maybe 4? 1 solutions Answer 373625 by stanbon(57377)   on 2012-03-12 21:32:27 (Show Source): You can put this solution on YOUR website! I need to solve this function to the nth term. Assuming y = 6x+2 you would get: x = 1; y = 8 x = 2; y = 14 x = 3; y = 20 x = ?; y = 24 Solve for "x": 24 = 6x + 2 6x = 22 x = 11/3 ----------------- x = ?; y = 28 28 = 6x+2 6x = 26 x = 13/3 --------------------- x = 6; y = 6*6+2 = 38 ============================ cheers, Stan H. =========

Travel_Word_Problems/586109: Two vans leave at the same time, one headed north, one headed south. The one headed north is 10 km/h faster than the one headed south. In 3 hours, they are 420 km apart. I think I already have one equation , which would be x=y+10, however, I don't understand how to set the other one. 1 solutions Answer 373623 by stanbon(57377)   on 2012-03-12 21:23:38 (Show Source): You can put this solution on YOUR website! Two vans leave at the same time, one headed north, one headed south. The one headed north is 10 km/h faster than the one headed south. In 3 hours, they are 420 km apart. --- North van DATA: time = 3 hrs ; rate = x+10 km/hr ; distance = r*t = 3x+30 km --- South van DATA: time = 3 hrs ; rate = x km/hr distance = r*t = 3x km ---- Equation: distance + distance = 420 km 3x+30 + 3x = 420 6x = 390 x = 65 km/hr (rate of South-bound van) ---- x+10 = 75 km/hr (rate of North-bound van) =================== Cheers, Stan H.

Polynomials-and-rational-expressions/586111: How to check whether (x-1) is a factor of the polynomial of x^4 +x^3 +x^2 -5x +2 1 solutions Answer 373621 by stanbon(57377)   on 2012-03-12 21:18:20 (Show Source): You can put this solution on YOUR website! How to check whether (x-1) is a factor of the polynomial of x^4 +x^3 +x^2 -5x +2 --- Use synthetic division to find f(1): 1)....1....1....1....-5....2 .......1....2....3.....-2..|..0 f(1) = 0 so x-1 is a factor. ================================ Cheers, Stan H. =============

Equations/586116: Twice the difference of four and n is the same as one subtracted from negative one times n. 1 solutions Answer 373618 by stanbon(57377)   on 2012-03-12 21:13:55 (Show Source): You can put this solution on YOUR website! Twice the difference of four and n is the same as one subtracted from negative one times n. ------------------------ Equation: 2(4-n) = -n-1 --- 8-2n = -n-1 ----- n = 9 =============== Cheers, Stan H. ==================

Average/586113: Mark rides his bike 100 meters in 5 min,225 meters in 8 mins. and 175 meters in 7 mins.what is his average speed? 1 solutions Answer 373614 by stanbon(57377)   on 2012-03-12 21:10:41 (Show Source): You can put this solution on YOUR website! Mark rides his bike 100 meters in 5 min,225 meters in 8 mins. and 175 meters in 7 mins.what is his average speed? -------- average speed = total distance/total time ------ speed = (100+225+175)/(5+8+7) = 500/20 = 25 meters per minutes ============== Cheers, Stan H. ==============

Geometry_Word_Problems/586112: Please show me how to plot this: 1 solutions Answer 373613 by stanbon(57377)   on 2012-03-12 21:07:50 (Show Source): You can put this solution on YOUR website! L(r)= 2 pi r + 12 ---- Let r = 0, then L = 12 --- Let r = 2, then L = 4pi+12 ------------- Plot: (0,12) and (2, 4pi+12) and draw a line thru the points to get: ------ Cheers, Stan H. ===========

Probability-and-statistics/585973: If a thumbtack is dropped, the probability of it landing point up is .4. If 12 tacks are dropped, find the probability of at least 9 points up in fraction form 1 solutions Answer 373599 by stanbon(57377)   on 2012-03-12 20:14:15 (Show Source): You can put this solution on YOUR website! If a thumbtack is dropped, the probability of it landing point up is .4. If 12 tacks are dropped, find the probability of at least 9 points up in fraction form ----- Binomial Problem with n = 12; p(up) = 0.4 ; p(other) = 0.6 --------- P(9<= x <=12) = 1 - binomcdf(12,0.4,8) = 0.0153 = 153/10000 =================================================== Cheers, Stan H. ============

Probability-and-statistics/586058: If each in a set of scores is increased by 5 points, then how will this affect the median, mode and mean of the scores? 1 solutions Answer 373596 by stanbon(57377)   on 2012-03-12 20:07:00 (Show Source): You can put this solution on YOUR website! If each in a set of scores is increased by 5 points, then how will this affect the median: same position but increased by 5 ------------------ mode: increased by 5 ------------------ mean of the scores: increased by 5

Probability-and-statistics/586054: from the perspective of insurance company health policies are set up in such a way a healthy person has a negative expected value and a sickly person a positive one. Right or Wrong 1 solutions Answer 373595 by stanbon(57377)   on 2012-03-12 20:02:24 (Show Source): You can put this solution on YOUR website! from the perspective of insurance company health policies are set up in such a way a healthy person has a negative expected value and a sickly person a positive one. Right or Wrong ----- Wrong For the company the healthy person will pay for insurance and not have claims resulting in a positive gain for the company. ---- For the company the sickly person will pay for insurance and will make claims resulting in a loss for the company. ------------ Cheers, Stan H.

Probability-and-statistics/586040: 1. It is asserted that 65 percent of the cars approaching an individual toll both in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of seven cars: (a) All seven will have the transponder. (Round your answer to 4 decimal places.) Probability (b) At least four will have the transponder. (Round your answer to 4 decimal places.) Probability (c) None will have a transponder. (Round your answer to 6 decimal places.) Probability 1 solutions Answer 373593 by stanbon(57377)   on 2012-03-12 19:58:38 (Show Source): You can put this solution on YOUR website! 1. It is asserted that 65 percent of the cars approaching an individual toll both in New Jersey are equipped with an E-ZPass transponder. Binomial Problem with n = 7; p(have) = 0.65 ; p(not have) = 0.35 ------------------------------ Find the probability that in a sample of seven cars: (a) All seven will have the transponder. (Round your answer to 4 decimal places.) Ans: 0.65^7 = 0.0490 -------------------------- Probability (b) At least four will have the transponder. (Round your answer to 4 decimal places.) Ans: P(4<= x <=7) = 1 - P(0<= x <=3) = 0.8002 Probability (c) None will have a transponder. (Round your answer to 6 decimal places.) Ans: P(x = 0) = 0.35*7 = 0.000064339 -------------------- Cheers, Stan H. =================

Probability-and-statistics/586049: if the mean of 12 numbers id 15, then what is the sum of the numbers? 1 solutions Answer 373590 by stanbon(57377)   on 2012-03-12 19:52:05 (Show Source): You can put this solution on YOUR website! if the mean of 12 numbers id 15, then what is the sum of the numbers? ------ average = (sum of numbers)/(# of numbers) ----- 15 = sum/12 ---- sum = 12*15 sum 180 ============= Cheers, Stan H. -------------

Linear-equations/586046: A spool contains 25 1/3 yards of ribbon. It takes 2 ½ yards of ribbon to make a bow. How many bows can be made? I have already solved this problem...I know you can make 10 with 2/15 left. I need help solving this by solving an equation graphically, guess and check, using a table, repeated addition or subtraction. I also need to some how use technology to solve. Any ideas would be great-Thanks! 1 solutions Answer 373588 by stanbon(57377)   on 2012-03-12 19:48:56 (Show Source): You can put this solution on YOUR website! A spool contains 25 1/3 yards of ribbon. It takes 2 ½ yards of ribbon to make a bow. How many bows can be made? ---- # of bows = 25 1/3 / 2 1/2 ---- = [(3*25+1)/3]/[(2*2+1)/2] --- = [76/3]/[5/2] ---- Invert and multiply = [76/3] ---- = [152/15] ---- = 10 2/15 =================== Graph: ---------------------- Reaated subtraction 76/3 - 5/2 = (152-15)/6 = 137/6 137/6 - 5/2 = (274-30)/12 = 244/12 244/12- 5/2 = 61/3-5/2 = (122-15)/6 = 107/6 etc. Keep repeating the subtraction till you get down to 2/15 ================ Technology: Using a TI-84 Enter: (25+(1/3))/(2 + (1/2)) Hit ENTER to get 10.1333 Subtract 10 to get 0.1333 Hit MATH, then Frac to get 2/15 ======================================== Cheers, Stan H. Cheers, Stan H. ===================

Triangles/586047: A = 36m squared, b = , h = 12 m 1 solutions Answer 373586 by stanbon(57377)   on 2012-03-12 19:43:05 (Show Source): You can put this solution on YOUR website! A = 36m squared, b = , h = 12 m ----------- Area = (1/2)b*h 36 = (1/2)b*12 36 = 6b b = 6 meters -------------------- Cheers, Stan H. ========

Functions/586044: Find the variation constant and an equation of variation where y varies directly as x and y = 16 when x = 8? 1 solutions Answer 373584 by stanbon(57377)   on 2012-03-12 19:40:15 (Show Source): You can put this solution on YOUR website! Find the variation constant and an equation of variation where y varies directly as x y = kx ---- Solve for "k" using "y = 16 when x = 8". --------------------- 16 = k*8 k = 2 ------------ Equation: y = 2x ================= Cheers, Stan H.

Rational-functions/585614: f(x)= x^3-5x^2+5x+3 Find the zeros of and their multiplicity 1 solutions Answer 373427 by stanbon(57377)   on 2012-03-11 20:48:50 (Show Source): You can put this solution on YOUR website! f(x)= x^3-5x^2+5x+3 Find the zeros of and their multiplicity --- I graphed it and found zeroes at x = -0.4142, and x = 3 (multiplicity 2). ==== ---------------- Cheers, Stan H. ============

Functions/585611: Find the range given the domain: y= 6 over x + 1 Domain: {-2, 3, 6} 1 solutions Answer 373423 by stanbon(57377)   on 2012-03-11 20:40:30 (Show Source): You can put this solution on YOUR website! Find the range given the domain: y= 6 over x + 1 Domain: {-2, 3, 6} ------ y = 6/(x+1) f(-2) = 6/(-1) = -6 f(3) = 6/(4) = 3/2 f(6) = 6/7 ---- Range = {-6,3/2,6/7} ========================= Cheers, Stan H. =================

Mixture_Word_Problems/585605: A solution of 75% pesticide is to be mixed with a solution of 35% pesticide to form 440 liters of a 43% solution. How many liters of the 75% solution must be used? 1 solutions Answer 373420 by stanbon(57377)   on 2012-03-11 20:37:36 (Show Source): You can put this solution on YOUR website! A solution of 75% pesticide is to be mixed with a solution of 35% pesticide to form 440 liters of a 43% solution. How many liters of the 75% solution must be used? ---------------------- Equation: active + active = active 0.75x + 0.35(440-x) = 0.43*440 ----- 75x + 35*440 - 35x = 43*440 40x = 8*440 x = (1/5)*440 x = 88 liters (amt of 75% solution needed) ---- 440-x = 352 liters (amt. of 35% solution needed) ================================================ Cheers, Stan H.

Rational-functions/585599: f(x)= x^2-4x+4/x-1 a) Identify the x & y-intercepts b) Find all vertical, horizontal and slant asymptotes c) Check for symmetry d) Plot sufficient solution points e) Sketch the graph of f(x) 1 solutions Answer 373415 by stanbon(57377)   on 2012-03-11 20:33:09 (Show Source): You can put this solution on YOUR website! f(x)= (x^2-4x+4)/(x-1) a) Identify the x & y-intercepts x-intercept ? Let y = 0; then x^2-4x+4 = (x-2)^2 = 0 x = 2 is the x-intercept. ---- y-intercept ? Let x = 0, then y = 4/(-1) = -4 ------------------------------- b) Find all vertical, horizontal and slant asymptotes Vertical with x = 1 Horizontal with y = x^2/0x^2 is undefined. So no horizontal asymptote. Slant: (x^2-4x+4)/(x-1) = (x-3)(x-1)+1 Slant asymptote: y = x-3 ----------------------------------- c) Check for symmetry f(-x) = (x^2+4x+4)/(-x-1) -f(-x) = (x^2+4x+4)/(x+1) Since f(x) is not equal to f(-x), no y-axis symmetry. Since f(x) is not equal to -f(-x), no origin symmetry. ------------------------------------- d) Plot sufficient solution points e) Sketch the graph of f(x) ------------------ Cheers, Stan H.

Quadratic_Equations/585401: which is the standard to H=-16t^2+vt+s 1 solutions Answer 373331 by stanbon(57377)   on 2012-03-11 14:07:08 (Show Source): You can put this solution on YOUR website! which is the standard to H=-16t^2+vt+s --- The standard what??

Geometry_Word_Problems/585397: What is the effect on the area of a triangle if the base is doubled and the height is cut in half? What happens to the area, if the base is doubled and the height remains the same? 1 solutions Answer 373329 by stanbon(57377)   on 2012-03-11 14:04:16 (Show Source): You can put this solution on YOUR website! Area = (1/2)base*h -------------------- What is the effect on the area of a triangle if the base is doubled and the height is cut in half? Area = (1/2)(2b)(h/2) = (1/2)bh No change in Area ---------------------------- What happens to the area, if the base is doubled and the height remains the same? Area = (1/2)(2b)h = 2[(1/2)bh] The area is doubled. ========================= Cheers, Stan H.

Miscellaneous_Word_Problems/585398: The time t required to drive a fixed distance varies inversely as the speed r. It takes 5 hrs at a speed of 80 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 70 km/h? 1 solutions Answer 373328 by stanbon(57377)   on 2012-03-11 13:51:27 (Show Source): You can put this solution on YOUR website! The time t required to drive a fixed distance varies inversely as the speed r. ----- t = k/r ------ Solve for "k" using "It takes 5 hrs at a speed of 80 km/h to drive a fixed distance". 5 = k/80 k = 400 ----- Equation: t = 400/r ------------------- How long will it take to drive the same distance at a speed of 70 km/h? ---------------------------------------------- t(70) = 400/70 = 5.71 hours ========================================= Cheers, Stan H. ------------------

Triangles/585301: the hypotenuse in a right-angled isosceles triangle measures 4.5cm. determine the length of the other two sides A= 3.18cm 1 solutions Answer 373265 by stanbon(57377)   on 2012-03-11 06:32:03 (Show Source): You can put this solution on YOUR website! the hypotenuse in a right-angled isosceles triangle measures 4.5cm. determine the length of the other two sides A= 3.18cm ----- Let the length of the 2 equal sides each be "x". Equation; x^2 + x^2 = 4.5^2 2x^2 = 20.25 x^2 = 10.125 x = 3.18cm =============== Cheers, Stan H.

Mixture_Word_Problems/585304: how much water must be added to 500g of 30 acid solution in order to produce a 20% acid solution? 1 solutions Answer 373264 by stanbon(57377)   on 2012-03-11 06:28:11 (Show Source): You can put this solution on YOUR website! how much water must be added to 500g of 30 acid solution in order to produce a 20% acid solution? ---- Equation: water + water = water 0.70*500 + x = 0.80(500+x) ------ 70*500 + 100x = 80*500 + 80x 20x = 10*500 x = 250 g (amt. of water needed) ==================== Cheers, Stan H. ------------------------

Travel_Word_Problems/585032: Two rabbits start at a point P on a circular track and move in opposite directions. One travels at a speed of 11 ft/sec and the other at a speed of 8 ft/sec. If they start at the same time and stop when they meet again at point P, then the number of times they meet excluding the start and finish is 1 solutions Answer 373263 by stanbon(57377)   on 2012-03-11 06:24:59 (Show Source): You can put this solution on YOUR website! How long is the track?

Expressions-with-variables/585183: 0.3x-0.2y=4 0.5x+0.5y=-45/17 3x-2y=40 5x+5y=-450/17 15x-10y=200 15x-15y=1350/17 _________________ -25y= 4750/17 dont know how they got this? y=-190/17 3x-2(-190/17)=40 100/17 Solution 100/17,-190/17 1 solutions Answer 373192 by stanbon(57377)   on 2012-03-10 18:59:59 (Show Source): You can put this solution on YOUR website! 0.3x-0.2y = 4 0.5x+0.5y = -45/17 ------------------------ 3x-2y= 40 5x+5y= -450/17 -------------------- 15x-10y= 200 15x+15y= -1350/17 ________________ Add those two equation together to get: 5y= 2050/17 --------------------------------- y = 410/17 Solve for "x": ------------------------- 3x-2(410/17)=40 3x - 820/17 = 680/17 3x = 1500/17 x = 500/17 ===================== Solution 500/17 , 410/17 ================== Cheers, Stan H. ========================

Linear-equations/585182: I need to find the slope and the y intercept of 4x-3y=-9 in slope intercept form ,thank you :) 1 solutions Answer 373188 by stanbon(57377)   on 2012-03-10 18:39:05 (Show Source): You can put this solution on YOUR website! I need to find the slope and the y intercept of 4x-3y=-9 in slope intercept form ------------- 3y = 4x+9 --- y = (4/3)x + 3 ---- slope = 4/3 y-int = 3 ================ Cheers, Stan H. ============

Money_Word_Problems/585180: Pam borrows $3,000 from the bank. She pays 7% simple interests for 3 years. How much interest does she pay over the 3-year period? I don't understand what I should do first. 1 solutions Answer 373187 by stanbon(57377)   on 2012-03-10 18:37:10 (Show Source): You can put this solution on YOUR website! Pam borrows $3,000 from the bank. She pays 7% simple interests for 3 years. How much interest does she pay over the 3-year period? ---- Interest = P*r*t I = 3000*0.07*3 I = $630 =========== Cheers, Stan H. ===========

Geometry_Word_Problems/585175: the measure of an angle is 28 more than the measure of the smallest angle of the triangle. the measure of the third angle is twice the size of the measure of the the smallest angle. find all three measures 1 solutions Answer 373186 by stanbon(57377)   on 2012-03-10 18:34:37 (Show Source): You can put this solution on YOUR website! the measure of an angle is 28 more than the measure of the smallest angle of the triangle. the measure of the third angle is twice the size of the measure of the the smallest angle. find all three measures -------------------------------------------- Let the smallest angle be "x". 2nd angle is "x+28" 3rd angle is 2x ----- Equation: x + x+28 + 2x = 180 4x = 152 x = 38 degrees x+28 = 66 degrees 2x = 76 degrees ====================== Cheers, Stan H. ==============

Inequalities/585171: I am trying to factor the following: (x^2+20xy+100y^2)z^2-16(x^2+20xy+100y^2) Thank you for any help you can give me. I know each equation in the parenthesis is a special product but don't know really how to proceed? Thanking you inadvance for you're help! robin 1 solutions Answer 373179 by stanbon(57377)   on 2012-03-10 18:16:40 (Show Source): You can put this solution on YOUR website! (x^2+20xy+100y^2)z^2-16(x^2+20xy+100y^2) -------- (x+10y)^2*z^2-16(x+10y)^2 --- = (x+10y)^2[z^2-16) ---- = (x+10y)^2(z-4)(z+4) --------------- Cheers, Stan H.