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# Recent problems solved by 'stanbon'

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

 Radicals/522953: I am having a very hard time with understanding how to come up with an answer to this word problem. During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?1 solutions Answer 347115 by stanbon(57328)   on 2011-10-28 22:23:00 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip? -------------------- 1st part DATA: distance = 91 miles ; rate = r mph ; time = d/r = 91/r hrs --------------------------- 2nd part DATA: distance = 21 miles ; rate = r-5 mph ; time = d/r = 21/(r-5) hrs ---------------- Equation: time + time = 5 hrs 91/r + 21/(r-5) = 5 ---- 91(r-5) + 21r = 5r(r-5) 112r - 455 = 5r^2-25r --- Rearrange: 5r^2 - 137r + 455 = 0 Positive solution: r = 23.5331 mph (1st part speed) r-5 = 18.5331 mph (2nd part speed) ==================================== Cheers, stan H. ==============
 Polygons/522948: The sum of the interior angles of a polygon is 8y. If Y is 15 greater than the number of sides of the polygon, how many sides does the polygon have?1 solutions Answer 347114 by stanbon(57328)   on 2011-10-28 22:15:28 (Show Source): You can put this solution on YOUR website!The sum of the interior angles of a polygon is 8y. If Y is 15 greater than the number of sides of the polygon, how many sides does the polygon have? --- Let number of sides be "n": sum of interior angles = (n-2)180 = 8Y y = n+15 --- Substitute for "y" and solve for "n" ----------------------- (n-2)180 = 8(n+15) ---- (n-2)180 = 8n+120 180n-360 = 8n+120 172n = 480 ----- That does not turn out to be a whole number. Please check the wording of your problem. I have some suspicion about that "8Y". ---- Cheers, Stan H. ==============
 Probability-and-statistics/522945: 3. A sample of consumers was surveyed regarding their visits to a computer chain store and if the store was conveniently located. The following table summarizes the results of that survey: Visits Convenient Not Convenient Totals Often 60 20 80 Occasional 25 35 60 Never 5 50 55 Column Totals 90 105 195 a. What is this table called b. Are frequency of visits and convenience independent or related? Explain your answer. What is the probability of a survey respondent being convenient to a store? c. What is the probability of a survey respondent being not convenient to a store and never visiting a store in the chain? 1 solutions Answer 347111 by stanbon(57328)   on 2011-10-28 22:02:39 (Show Source): You can put this solution on YOUR website!A sample of consumers was surveyed regarding their visits to a computer chain store and if the store was conveniently located. The following table summarizes the results of that survey: Visits Convenient Not Convenient Totals Often 60 20 80 Occasional 25 35 60 Never 5 50 55 Column Totals 90 105 195 a. What is this table called: A contingency table. ------------------------------- b. Are frequency of visits and convenience independent or related? Explain your answer. P(often) = 80/195 ; P(convenient) = 90/195 P(often)*P(confenient) = 0.1893 P(often | convenient) = 60/90 = 2/3 Since P(oft | conven) is not equal to P(oft)*P(conven) they are dependent factors. -------------------------------------------------------------- What is the probability of a survey respondent being convenient to a store? P(convenient+ = 90/195 ----------------------------- c. What is the probability of a survey respondent being not convenient to a store and never visiting a store in the chain? P(not convenient AND never visiting) = P(con | never)*P(never) = 5/55 * 55/195 = 5/195 =========================== Cheers, Stan H. ================================
 Travel_Word_Problems/522934: Somebody was travelling 25.5 km at an average speed of 18km/hr Whats the time taken?1 solutions Answer 347089 by stanbon(57328)   on 2011-10-28 20:15:52 (Show Source): You can put this solution on YOUR website!Somebody was travelling 25.5 km at an average speed of 18km/hr Whats the time taken? ---- time = distance/rate ---- time = 25.5 km/18 km/hr time = 1.4167 hrs = 1 hr 25 minutes ==================================== Cheers, Stan H. ==========
 Probability-and-statistics/522912: the manager of a store counted the number of sales during a 60-hour week-this is the frequency distrubution: ______________________________ number of number of sales/hr occurrences ______________________________ 6 25 number of occurrences add up to 60 7 20 so that's 60hrs/wk 8 10 9 0 I need to find the relative frequency 10 5 of 7 sales during an hour ______________________________ possible answers: 1/4, 1/3, 7/40, 7/60 Please help me with this question1 solutions Answer 347088 by stanbon(57328)   on 2011-10-28 20:13:10 (Show Source): You can put this solution on YOUR website!the manager of a store counted the number of sales during a 60-hour week-this is the frequency distrubution: ______________________________________ number of number of relative sales/hr occurrences frequency _______________________________________ 6 25 25/60 number of occurrences add up to 60 7 20 20/60 so that's 60hrs/wk 8 10 10/60 9 0 0/60 I need to find the relative frequency 10 5 5/60 of 7 sales during an hour ______________________________ possible answers: 1/4, 1/3, 7/40, 7/60 ============================================== Answer: 20/60 = 1/3 ========================== Cheers, Stan H. ==========================
 Expressions-with-variables/522914: rewrite the equation so that y is a function of x. 1/2(y+5)+4x=3x1 solutions Answer 347086 by stanbon(57328)   on 2011-10-28 20:08:14 (Show Source): You can put this solution on YOUR website! rewrite the equation so that y is a function of x. (1/2)(y+5)+4x=3x ----- (1/2)(y+5) = -x --- (y+5) = -2x --- y = -2x-5 =============== Cheers, Stan H. ===========
 Probability-and-statistics/522937: 6. Fifty faculty travel expense vouchers were submitted to the statistics department during the summer. Of these 20 contained errors. If five vouchers are selected at random what is the probability that: a. None contain errors. b. One contains an error c. Three or more contain errors d. What kind of probability distribution did you use to solve this problem? e. Make a graph of the PDF 1 solutions Answer 347085 by stanbon(57328)   on 2011-10-28 20:00:46 (Show Source): You can put this solution on YOUR website!Fifty faculty travel expense vouchers were submitted to the statistics department during the summer. Of these 20 contained errors. If five vouchers are selected at random what is the probability that: --- Binomial Problem with n = 5 and p(error) = (20/50) = 2/5 p(no error) = 3/5 ----------------------- a. None contain errors.::::(3/5)^5 -------------------------------------- b. One contains an error:::5C1*(2/5)(3/5)^4 ----------------------------------------------- c. Three or more contain errors::: 1 - binomcdf(5,2/5,2) ------------------------------------------------ d. What kind of probability distribution did you use to solve this problem? Binomial -------- e. Make a graph of the PDF If you have a TI calculator use the binompdf function key to find P(x = 0), P(x=1)....,P(x=5) where P(x=k) = nCk*p^k*q*(n-k) ====================================== Cheers, Stan H.
 Graphs/522924: I need help with my appendix sheet. I do not understand what to do in this website to help me. My instructor told me to come here and your tool to graph it. I do not know what to do. Please help.1 solutions Answer 347074 by stanbon(57328)   on 2011-10-28 19:03:29 (Show Source): You can put this solution on YOUR website!Post your problem and ask how to graph it. Cheers, Stan H.
 Triangles/522903: the measure of a base angle of an isosceles triangle is 4 times the measure of the vertex angle. what is the number of degrees in the vertex angle?1 solutions Answer 347068 by stanbon(57328)   on 2011-10-28 17:43:16 (Show Source): You can put this solution on YOUR website!the measure of a base angle of an isosceles triangle is 4 times the measure of the vertex angle. what is the number of degrees in the vertex angle? -------- Let vertex angle be "x". Each base angle is "4x". ---- Equation: x + 4x + 4x = 180 degrees ----- 9x = 180 x = 20 degrees (vertex angle) ================================== Cheers, Stan H. ==============
 Travel_Word_Problems/522890: I don't know how to figure this out. "My little brother left 2 minutes ago on his bike to ride with his friends to the cemetery. If he pedals at 5 mph to the cemetery, which is 1 mile from here, and I go the back way (2.5 miles) so he doesn't see the car, how fast do I have to drive Mom's car to get there at least a full minute ahead of him so I can hide and scare him? I know the brother needs 12 minutes to go a mile, and he left 2 minutes ago, so he has 10 minutes to go. I know the car driver needs to be there in 9 minutes. That makes 3.6 minutes a mile. What do I do from here? Thank you!1 solutions Answer 347067 by stanbon(57328)   on 2011-10-28 17:40:01 (Show Source): You can put this solution on YOUR website!My little brother left 2 minutes ago on his bike to ride with his friends to the cemetery. If he pedals at 5 mph to the cemetery, which is 1 mile from here, and I go the back way (2.5 miles) so he doesn't see the car, how fast do I have to drive Mom's car to get there at least a full minute ahead of him so I can hide and scare him? ------------------ Brother DATA: rate = 5 mph ; distance = 1 miles ; time = d/r = 1/5 = 12 minutes -------------------------- You DATA: distance = 2.5 miles ; time = 11 minutes ; rate = d/t = 2.5/11 miles/min --- 11 min = 11/60 hr = 0.1833 hr ---- 2.5/11 (miles/min) = 2.5/0.1833 = 13.64 miles/hr ================================= Cheers, Stan H. ================
 Linear-equations/522893: find the slope, if it exists, of the line containing the points (-8,1/2)and (-9,1/2)1 solutions Answer 347064 by stanbon(57328)   on 2011-10-28 17:30:31 (Show Source): You can put this solution on YOUR website!find the slope, if it exists, of the line containing the points (-8,1/2)and (-9,1/2) ---- The y-values are the same, so the slope is zero. --- m = (1/2 - 1/2)/(-9--8) = 0/-1 = 0 =============================== Cheers, Stan H. ==============
 Quadratic_Equations/522895: Which of the following is one of the two binomial factors of 6s2 + 40s – 64?1 solutions Answer 347062 by stanbon(57328)   on 2011-10-28 17:26:40 (Show Source): You can put this solution on YOUR website!Which of the following is one of the two binomial factors of 6s^2 + 40s – 64? ---- Common Factor: 2 2[3s^2+20s-32] ---- = 2(3s-4)(s+8) ================= Cheers, Stan H. =================
 Trigonometry-basics/522884: SOlve 3sin(2a)-2cos(a)=0 for all solutions a= 1 solutions Answer 347059 by stanbon(57328)   on 2011-10-28 17:19:40 (Show Source): You can put this solution on YOUR website!Solve 3sin(2a)-2cos(a)=0 for all solutions --- 3*2sin(a)*cos(a) - 2cos(a) = 0 Factor: 2cos(a)[3sin(a) - 1] = 0 --- cos(a) = 0 or 3sin(a)-1 = 0 a = 90 or 270 degree or a = invsin(1/3) = 19.47 or 160.53 degrees ============================================================= Cheers, Stan H. ============
 Trigonometry-basics/522875: If tanx=-1/3 ; cosx>0 then sin2x= cos2x= tan2x=1 solutions Answer 347052 by stanbon(57328)   on 2011-10-28 16:41:09 (Show Source): You can put this solution on YOUR website!If tanx=-1/3 ; cosx>0 -- Since tan is negative and cos is positive, x is in the 4th quadrant. -------------- tan = y/x = -1/3, so y = -1 and x = 3 Therefore r = sqrt[1^2 + 3^2] = sqrt(10) -------- sin(x) = y/r = -1/sqrt(10) ; cos(x) = x/r = 3/sqrt(10) ---- then sin2x= 2sin(x)*cos(x) = 2*(-1/sqrt(10))*(3/sqrt(10)) = -6/10 = -3/5 ----- cos2x= cos^2 - sin^2 = (9/10) - (1/10) = 8/10 = 4/5 --------- tan2x= sin(2x)/cos(2x) = [-3/5]/[4/5] = -3/4 =============================================== Cheers, Stan H. ===========
 Probability-and-statistics/522867: a certain class consisted of 25 males and 15 females. if 10 students were randomly selected, what is the probability that 4 males were selected?1 solutions Answer 347051 by stanbon(57328)   on 2011-10-28 16:33:46 (Show Source): You can put this solution on YOUR website!a certain class consisted of 25 males and 15 females. if 10 students were randomly selected, what is the probability that 4 males were selected? ------------- Binomial Problem with n = 10 and p(male) = 25/40 = 5/8 --------- P(x = 4) = 10C4*(5/8)^4*(3/8)^6 = 0.0891 ---- Cheers, Stan H. ===========
 Angles/522864: find the supplement of a 106 degree angle.1 solutions Answer 347050 by stanbon(57328)   on 2011-10-28 16:27:30 (Show Source): You can put this solution on YOUR website!find the supplement of a 106 degree angle. ------ Supplement = 180-106 = 74 degrees. ----------------------------------- Cheers, Stan H. ==========
 Rectangles/522863: I AM BUYING A 70" DIAGANOL TV, WHAT IS THE LENGTH AND THE HIEGTH? 1 solutions Answer 347049 by stanbon(57328)   on 2011-10-28 16:21:39 (Show Source): You can put this solution on YOUR website!I AM BUYING A 70" DIAGANOL TV, WHAT IS THE LENGTH AND THE HIEGTH? The Aspect Ratio of wide-screen TV's is 16:9 --- Solve: The width and length of your TV are 16x and 9x --- Use Pytagoras to solve for "x": (16x)^2 + (9x)^2 = 70^2 --- 337x^2 = 4900 x^2 = 14.54 x = 3.8131 --- Width = 16x = 61" Height = 9x = 31.3" ========================= Cheers, Stan H. =========================
 Polynomials-and-rational-expressions/522832: let f(x) be a cubic polynomial with zeros -5,4 and 5. If the graph of f passes through the point (0,25) write the complete factored form of f(x) type your answer in factored form1 solutions Answer 347047 by stanbon(57328)   on 2011-10-28 16:12:07 (Show Source): You can put this solution on YOUR website!let f(x) be a cubic polynomial with zeros -5,4 and 5. If the graph of f passes through the point (0,25) write the complete factored form of f(x) type your answer in factored form ---- f(x) = a(x+5)(x-5)(x-4) --- Solve for "a" using (0,25) --- 25 = a(5)*(-5)(-4) 25 = a*100 a= 1/4 --- Equation: f(x) = (1/4)(x+5)(x-5)(x-4) ============================= cheers, Stan H. ===============
 Exponents/522859: How do you simplify (2^3 - 2(3-1)(2^3-3))/ 2^2(2^2-1)1 solutions Answer 347046 by stanbon(57328)   on 2011-10-28 16:08:51 (Show Source): You can put this solution on YOUR website!simplify (2^3 - 2(3-1)(2^3-3))/ 2^2(2^2-1) ---- (8 -2(2)(5))/(4(3)) --- (8-20)/12 --- = -12/12 ---- = -1 ============ Cheers, Stan H.
 Polynomials-and-rational-expressions/522862: I need to derive a linear polynomial function(in point slope form) with this information: y-intercept of 10, decreasing on [-2,-4] with a slope of -.5 i have tried to do it myself, but i could not figure out the x-intercept. This is what I have so far: y-10 = -.5(x-x) 1 solutions Answer 347045 by stanbon(57328)   on 2011-10-28 16:06:03 (Show Source): You can put this solution on YOUR website!derive a linear polynomial function(in point slope form) with this information: y-intercept of 10, decreasing on [-2,-4] with a slope of -.5 i have tried to do it myself, but i could not figure out the x-intercept. ---- Form: y = mx + b m is the slope = -0.5 b is the y-intercept = 10 ---- Equation: y = -0.5x + 10 ================================= x-intercept ?? Let y = 0 and solve for "x"; 0 = -0.5x + 10 0.5x = 10 x = 20 ============== Cheers, Stan H. ======================
 Linear-systems/522860: 6x-5y=-67 7x+83=y 7m+n=13 m-9n=11 4x+5y=15 -6x+y=37 6x+9y=-33 -3x+y=22 Im suppose to solve using the substition method, I am confused!1 solutions Answer 347044 by stanbon(57328)   on 2011-10-28 16:01:53 (Show Source): You can put this solution on YOUR website!6x-5y=-67 7x+83=y --- Substitute for "y" and solve for "x": 6x -5(7x+83) = -67 6x-35x-415 = -67 -29x = 348 x = -12 ---- Solve for "y: y = 7x+83 y = 7*-12 + 83 y = 0 =================================================== 7m+n=13 m-9n=11 --- Solve the bottom equation for "m": m = 9n+11 --- Substitute into the 1st equation and solve for "n": 7(9n+11) + n = 13 63n + 77 + n = 13 64n = - 64 n = -1 ---- Substitute for "n" an solve for "m": m = 8n+11 m = 8*-1 + 11 m = 3 ================== Work the others in a similar manner. Cheers, Stan H. ============= 4x+5y=15 -6x+y=37 6x+9y=-33 -3x+y=22 Im suppose to solve using the substition method
 Inequalities/522835: Solve the following inequality: -2x^(2/3)>(or equal to)61 solutions Answer 347041 by stanbon(57328)   on 2011-10-28 15:54:09 (Show Source): You can put this solution on YOUR website!Solve the following inequality: -2x^(2/3)>(or equal to)6 --- -2x^(2/3)>= 6 --- x^(2/3) >= -3 --- (x^(2/3))^3 = (-3)^3 x^2 = -27 --- x = 3sqrt(3)i ================= Cheers, Stan H. =================
 Points-lines-and-rays/522855: S, U, N are collinear. which point that satisfies the definition of betweenness if NU + US = NS? would it be S, N, or U? and why? thank you for helping!1 solutions Answer 347039 by stanbon(57328)   on 2011-10-28 15:48:29 (Show Source): You can put this solution on YOUR website!U is inbetween N and S Cheers, Stan H.
 Radicals/522854: How do you solve radical 3x+4 equals 8?1 solutions Answer 347037 by stanbon(57328)   on 2011-10-28 15:47:14 (Show Source): You can put this solution on YOUR website!How do you solve radical 3x+4 equals 8 ------- Square both sides to get: 3x+4 = 64 3x = 60 x = 20 ----------------- Cheers, Stan H.
 Points-lines-and-rays/522850: If U is between R and N on the same line, what terms describe the relationship the three points must have? noncollinear, betweenness of points, collinear, or coplanar? There could be more then 1 answer... but im pretty sure one of the answers is collinear, correct?1 solutions Answer 347036 by stanbon(57328)   on 2011-10-28 15:45:46 (Show Source): You can put this solution on YOUR website!Correct on collinear. Also coplanar because any 3 points lie in the same plane. ============ Cheers, Stan H.
 Exponents/522846: Solve: 86.11=R^(3/2)1 solutions Answer 347034 by stanbon(57328)   on 2011-10-28 15:43:45 (Show Source): You can put this solution on YOUR website!Solve: 86.11=R^(3/2) --- R = 86.11^(2/3) R = 19.5 =========== Cheers, Stan H. ===========
 Inequalities/522848: |X|+12<161 solutions Answer 347033 by stanbon(57328)   on 2011-10-28 15:42:03 (Show Source): You can put this solution on YOUR website!|X|+12<16 --- |x| < 4 -4 < x < 4 ================ Cheers, Stan H.
 Geometry_Word_Problems/522845: hi there the bed of the truck i am looking at is 8ft long and 4ft wide i have a surf board 9ft 10 would it fit from corner to corner all the best Nick 1 solutions Answer 347031 by stanbon(57328)   on 2011-10-28 15:39:04 (Show Source): You can put this solution on YOUR website!hi there the bed of the truck i am looking at is 8ft long and 4ft wide i have a surf board 9ft 10 would it fit from corner to corner all the best Nick ---- diagonal of the truck bed = sqrt[8^2+4^2] = sqrt(82) = 9.06 ft = 9 ft 1 inch ================== Cheers, Stan H.
 Quadratic_Equations/522843: How do you factor the equation 2a^2 + 8a = 0? Thank you.1 solutions Answer 347029 by stanbon(57328)   on 2011-10-28 15:35:33 (Show Source): You can put this solution on YOUR website!factor the equation 2a^2 + 8a = 0? Thank you. ---- Common Factor: 2a --- 2a(a+4) = 0 Either 2a is 0 or a+4 = 0 a = 0 or a = -4 ============================== cheers, Stan H. ===========