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Recent problems solved by 'stanbon'

stanbon answered: 57288 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, >>Next

test/556844: my problem: Where would you expect the vertex on the graph Y= (x-4)^2 +5 to be? Explain why? Thank You 1 solutions Answer 362267 by stanbon(57361)   on 2012-01-13 08:35:08 (Show Source): You can put this solution on YOUR website! my problem: Where would you expect the vertex on the graph Y= (x-4)^2 +5 to be? Explain why? The graph is a parabola opening upward. It has a minimum point at its vertex. -- The smallest value y can have occurs when x = 4. That y-value is 5 --- So the vertex is at (4,5) =============================== Cheers, Stan H. ============

Travel_Word_Problems/556832: A bicycle leaves town at 16 mph at 8 AM. A car leaves at 11 AM traveling the same direction at 45 mph. How many minutes after 11 AM is it when the car overtakes the bicycle? 1 solutions Answer 362266 by stanbon(57361)   on 2012-01-13 08:32:34 (Show Source): You can put this solution on YOUR website! A bicycle leaves town at 16 mph at 8 AM. A car leaves at 11 AM traveling the same direction at 45 mph. How many minutes after 11 AM is it when the car overtakes the bicycle? ----- Bike DATA: rate = 16 mph ; time = x hrs ; distance = 16x miles --- Car DATA: rate = 45 mph ; time = x-3 hrs ; distance = 45x-135 miles ----- Equation: distance = distance 16x = 45x -135 29x = 135 x = 4.66 hrs x-3 = 1.66 hrs = 99.31 minutes ==================================== Cheers, Stan H. ==================

Quadratic_Equations/556842: Find the x- and y-intercepts. F(x)25x+10x+1 I got.. y-intercept is (0,1) x-intercept is ((-1/5,0) Am I correct? 1 solutions Answer 362264 by stanbon(57361)   on 2012-01-13 08:27:02 (Show Source): You can put this solution on YOUR website! F(x)25x+10x+1 I got.. y-intercept is (0,1) ------- x-intercept is ? Let y = 0 Then 35x+1 = 0 x = -1/35 x-int is (-1/35 , 0) ============= Cheers, Stan H.

Quadratic_Equations/556843: Solve for x. x^2+32=8x I got (8+8i/2 , 8-8i/2) Am I on the right track? Thank you 1 solutions Answer 362263 by stanbon(57361)   on 2012-01-13 08:23:58 (Show Source): You can put this solution on YOUR website! Solve for x. x^2+32=8x --- x^2-8x+32 = 0 --- x = [8 +- sqrt(64-128)]/2 --- x = [8 +- sqrt(-64)]/2 --- x = [8 +- 8i]/2 --- x = (4+4i) or x = (4-4i) ========================== Cheers, Stan H. ===============

Permutations/556831: A class consists of 40 girls and 60 boys.in how many ways can a president,treasurer and secretary be chosen if the treasurer must be a girl,the secretary must be a boy and a student may not hold more than one office? 1 solutions Answer 362262 by stanbon(57361)   on 2012-01-13 08:20:52 (Show Source): You can put this solution on YOUR website! A class consists of 40 girls and 60 boys.in how many ways can a president,treasurer and secretary be chosen if the treasurer must be a girl,the secretary must be a boy and a student may not hold more than one office? -------- 40 ways to choose the treasurer 60 ways to choose the secretary 98 ways to choose the president --- Total choices: 235,200 Cheers, Stan H. =============

Pythagorean-theorem/556837: beginning with a 3 dimentional rectangular box, how is the degree of the angle of turn determined where a line enters the box and then proceeds to the furthest corner within the box 1 solutions Answer 362261 by stanbon(57361)   on 2012-01-13 08:17:34 (Show Source): You can put this solution on YOUR website! What are the dimensions of the box and what angle are you trying to size? Cheers, Stan H.

Surface-area/556840: A park has a circular goldfish pond. What is A, the apporximate are of the surface of the pond, if its radius, r, is 5 feet? 1 solutions Answer 362260 by stanbon(57361)   on 2012-01-13 08:15:15 (Show Source): You can put this solution on YOUR website! A park has a circular goldfish pond. What is A, the apporximate are of the surface of the pond, if its radius, r, is 5 feet? --- Area = (pi)r^2 --- Area = 25pi sq ft ====================== Cheers, Stan H.

Angles/556839: Bruce is 36 years old. His son is 8 years old. In how many years will Bruce be three times as old as his son? 1 solutions Answer 362259 by stanbon(57361)   on 2012-01-13 08:13:12 (Show Source): You can put this solution on YOUR website! Bruce is 36 years old. His son is 8 years old. In how many years will Bruce be three times as old as his son? ---- Let the "number of years" be "x": --- Equation: 36+x = 3(8+x) 36+x = 24+3x 2x = 12 x = 6 years --- Bruce will be 36+6 = 42 His son will be 8+6 = 14 -- And 42 = 3*14 =================== Cheers, Stan H. ===================

Probability-and-statistics/556683: A disc jockey has 11 songs to play. Eight are slow songs, and three are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 11 songs if The songs can be played in any order. The first song must be a slow song and the last song must be a slow song. The first two songs must be fast songs. 1 solutions Answer 362209 by stanbon(57361)   on 2012-01-12 21:25:43 (Show Source): You can put this solution on YOUR website!

Probability-and-statistics/556660: Show all work. A disc jockey has 11 songs to play. Eight are slow songs, and three are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 11 songs if The songs can be played in any order. The first song must be a slow song and the last song must be a slow song. The first two songs must be fast songs. 1 solutions Answer 362208 by stanbon(57361)   on 2012-01-12 21:24:49 (Show Source): You can put this solution on YOUR website! These conditions are contradictory.

Probability-and-statistics/556664: between what two numbers inclusively will all probabilities lie? 1 solutions Answer 362207 by stanbon(57361)   on 2012-01-12 21:23:34 (Show Source): You can put this solution on YOUR website! Ans: Between zero and one. Cheers, Stan H. =============

Probability-and-statistics/556676: If we want to be 99% confident that our estimate of the population percentage (p) of green M&M candies is within 4% of the actual population percentage, how many M&M's must be in our sample? 1 solutions Answer 362206 by stanbon(57361)   on 2012-01-12 21:21:41 (Show Source): You can put this solution on YOUR website! If we want to be 99% confident that our estimate of the population percentage (p) of green M&M candies is within 4% of the actual population percentage, how many M&M's must be in our sample? ------ n = [z/E]pq ----- n = [2.5758/0.04]^2*(1/2)(1/2) ------ n = 1037 when rounded up ============================== Cheers, Stan H. =============

Polynomials-and-rational-expressions/556220: 10cm^3 of a normal specimen of human blood contains 1.2 g of hemoglobin. How many grams does 31 cm^3 of the same blood cantain? 31 cm^3 of the blood cantain _____ grams of hemoglobin 1 solutions Answer 362083 by stanbon(57361)   on 2012-01-12 09:05:40 (Show Source): You can put this solution on YOUR website! 10cm^3 of a normal specimen of human blood contains 1.2 g of hemoglobin. How many grams does 31 cm^3 of the same blood cantain? ----- Use a proportion: ----- x/31 = 1.2/10 --- x = 3.1*1.2 = 3.72 g's ----- Cheers, Stan H. ============ 31 cm^3 of the blood cantain 3.72 grams of hemoglobin

Matrices-and-determiminant/556199: integral 9x+4 ----- dx x2-7x+15 1 solutions Answer 362081 by stanbon(57361)   on 2012-01-12 09:02:00 (Show Source): You can put this solution on YOUR website! integral [(9x+4)/(x^2-7x+15)] dx --- Use partial fraction decompostion to get:: ------------ = [(A/(x-5))+(B/(x-3)] = (9x/4)/(x^2-7x+15) ----- A(x-3)+B(x-5) = 9x+4 ---- A+B = 9 -3A-5B = 4 ----- 3A+3B = 27 -3A-5B = 4 -------- -2B = 31 B = -31/2 --- A = 49/2 --------------- integra[((49/2)/(x-5) - (31/2)/(x-3)] ---- = (49/2)ln(x-5) - (31/2)ln(x-3) ---- Check the following site to see how this all works. =============== http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/ partialfracsoldirectory/PartialFracSol.html#SOLUTION 1 ===================== Cheers, Stan H. ==============

Matrices-and-determiminant/556198: 2 14 y= - x + -- 3 3 14 x=0,y= -- 3 1 solutions Answer 362074 by stanbon(57361)   on 2012-01-12 07:45:32 (Show Source): You can put this solution on YOUR website! 2 14 y= - x + -- 3 3 If x=0 ,y= 14/3 ------------------- That is true. And if x = 3, y = 20/3 -------------------------- Plot those 2 points and draw a line thru them. ---- Cheers, Stan H. ====

Age_Word_Problems/556012: bill is 4 times as old as john.five year ago the sum of their ages was 50 how old are they now 1 solutions Answer 362016 by stanbon(57361)   on 2012-01-11 20:25:09 (Show Source): You can put this solution on YOUR website! bill is 4 times as old as john.five year ago the sum of their ages was 50 how old are they now --- Equations: b = 4*j (b-5)+(j-5) = 50 ----- Substitute for "b" and solve for "j": 4j-5+j-5 = 50 5j = 60 j = 12 yrs. (john's age now) ---- Solve for "b": b = 4*j b = 4*12 = 48 yrs (Bill's age now) =======================================

Travel_Word_Problems/556002: I am unsure as to how to begin to solve this word problem. The OfficeJet printer can copy Maria's dissertation in 8 minutes. The LaserJet printer can copy the same document in 12 minutes. If the two machines worked together, how long would they take to copy the dissertation? Thank you for any help you can provide on this one. 1 solutions Answer 362012 by stanbon(57361)   on 2012-01-11 20:21:01 (Show Source): You can put this solution on YOUR website! The OfficeJet printer can copy Maria's dissertation in 8 minutes. The LaserJet printer can copy the same document in 12 minutes. If the two machines worked together, how long would they take to copy the dissertation? ----- Office Jet time = 8 min/job ; rate = 1/8 job/min ----- Laser Jet time = 12 min/job ; rate = 1/12 job/min ----- Together time = x min/job ; rate = 1/x job/min --------------------------------- Equation: rate + rate = together rate 1/8 + 1/12 = 1/x ---- Multiply thru by 24x to get: 3x + 2x = 24 5x = 24 x = 4.8 minutes/job (time to do the job together) ===================================================== Cheers, Stan H. =================

Linear-systems/556004: what is the first step to this equation 8x-9y=19 4x+y=-7 1 solutions Answer 362009 by stanbon(57361)   on 2012-01-11 20:15:44 (Show Source): You can put this solution on YOUR website! what is the first step to this equation 8x-9y=19 4x+y=-7 ----- Multiply thru the bottom equation by 2 to get: 8x-9y=19 8x+2y=-14 ============== Cheers, Stan H. ================

Inequalities/556003: (|3h+1|)/(2)<8 1 solutions Answer 362007 by stanbon(57361)   on 2012-01-11 20:12:48 (Show Source): You can put this solution on YOUR website! (|3h+1|)/(2)<8 ------- (|3h+1|) < 16 ---- -16 < 3h+1 < 16 ----- -17 < 3h < 15 ----- -17/3 < h < 5 ================= Cheers, Stan H. =================

Travel_Word_Problems/555998: I am in an online college class for algebra 2 and get stuck on word problems quite easily. This is the problem: Elena bicycles 6 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Elena can bicycle 75 km. How fast is both bicyclist traveling? 1 solutions Answer 362006 by stanbon(57361)   on 2012-01-11 20:09:46 (Show Source): You can put this solution on YOUR website! Elena bicycles 6 km/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Elena can bicycle 75 km. How fast is both bicyclist traveling? -------------- Javier DATA: rate = x km/h ; distance = 57 km ; time = d/r = 57/x hrs. ----- Elena DATA: rate = (x+6) km/h ; distance = 75 km ; time = d/r = 75/(x+6) hrs ====================== Equation: time = time 57/x = 75/(x+6) 75x = 57(x+6) 75x-57x = 6*57 18x = 6*57 x = (1/3)57 x = 19 km/h (Javier's rate) x+6 = 25 km/h (Elena's rate) ================================ Cheers, Stan H. =================

Percentage-and-ratio-word-problems/555994: 12 items cost $120.00 wHAT IS THE LOSS PERCENT IF THEY ARE SOLD FOR $9.00 EACH 1 solutions Answer 362002 by stanbon(57361)   on 2012-01-11 20:03:32 (Show Source): You can put this solution on YOUR website! 12 items cost $120.00 wHAT IS THE LOSS PERCENT IF THEY ARE SOLD FOR $9.00 EACH ------ Original cost per item 120/12 = $10 ----- Selling price per item $9 ----- Quantity loss per item: $1 --- Percentage loss peritme: 1/10 = 10% ======================================= Cheers, Stan H.

Probability-and-statistics/555592: I am really confused. I am in MM207 and do not understand how to solve this problem. Could someone please take me step by step through it so that I understand what I am doing? Assume you want to estimate with the proportion of students who commute less than 5 miles to work within 2%, what sample size would you need? This question relates to a survey that was done at the done at the beginning of the term. 1 solutions Answer 361955 by stanbon(57361)   on 2012-01-11 16:47:14 (Show Source): You can put this solution on YOUR website! answered

Probability-and-statistics/555613: i am in MM207 and have a question that I cannot answer. This question comes from a survey that was done. Assume you want to estimate with the proportion of students who commute less than 5 miles to work within 2%, what sample size would you need? 1 solutions Answer 361954 by stanbon(57361)   on 2012-01-11 16:46:07 (Show Source): You can put this solution on YOUR website! answered

Probability-and-statistics/555694: A single die is rolled. What is the probability of rolling the following: (a) P(4) (b) P(a number greater than 4) (c) P(a number greater than 6) (d) P(a number less than 7)? 1 solutions Answer 361951 by stanbon(57361)   on 2012-01-11 16:44:40 (Show Source): You can put this solution on YOUR website! A single die is rolled. What is the probability of rolling the following: (a) P(4) = 1/6 (b) P(a number greater than 4):: = 2/6 = 1/3 (c) P(a number greater than 6):: 0/6 = 0 (d) P(a number less than 7)?:: 6/6 = 1 =========================================== Cheers, Stan H.

Probability-and-statistics/555809: At the play there is a raffle. Each student is given a number card. The seniors are given 592 cards numbered consecutively with the first number being 358. When the winners are announced, all numbers that are multiples of 50 win a free T-shirt. How many seniors won a free t-shirt? Show your work to explain your answer. 1 solutions Answer 361949 by stanbon(57361)   on 2012-01-11 16:41:28 (Show Source): You can put this solution on YOUR website! At the play there is a raffle. Each student is given a number card. The seniors are given 592 cards numbered consecutively with the first number being 358. When the winners are announced, all numbers that are multiples of 50 win a free T-shirt. How many seniors won a free t-shirt? Show your work to explain your answer. ----- Ans: Multiples of 50: 400,450,500,550 --- 4 Seniors won a t-shirt ============================= Cheers, Stan H.

Proportions/555780: on proportions and percents how would you work the question. what is 5/4% of ___ is 6 1 solutions Answer 361948 by stanbon(57361)   on 2012-01-11 16:38:35 (Show Source): You can put this solution on YOUR website! what is 5/4% of ___ is 6 ------ Equation: (5/4)%*x = 6 --- (5/400)x = 6 --- (1/80)x = 6 -- x = 480 ================== cheers, Stan H.

Expressions-with-variables/555801: How do you write the quantity of a number plus 4, divided by 9 1 solutions Answer 361945 by stanbon(57361)   on 2012-01-11 16:34:19 (Show Source): You can put this solution on YOUR website! How do you write the quantity of a number plus 4, divided by 9 Let the quantity be "x": Expression: (x+4)/9 ============ Cheers, Stan H.

Rational-functions/555584: what is the answer in the retional expression 6c raised to two minus 23c minus 4 all over c raised to two minus 6c plus 8? please show the solution. 1 solutions Answer 361851 by stanbon(57361)   on 2012-01-11 06:17:46 (Show Source): You can put this solution on YOUR website! what is the answer in the retional expression 6c raised to two minus 23c minus 4 all over c raised to two minus 6c plus 8? please show the solution. ----- (6c^2 - 23c - 4)/(c^2 -6c + 8) --- Factor:(6c^2-24c+c-4) / [(c-4)(c-2)] ---- = [(6c)(c-4)+(c-4)] / [(c-4)(c-2)] ---- = [(c-4)(6c+1)] / [(c-4)(c-2)] ---- Cancel the common (c-4) factors: ----- = (6c+1)/(c-2) ================== Cheers, Stan H. ===============

Probability-and-statistics/555436: a license plate is to consist of three digits followed by two uppercase letters. Determine the number of different license plates possible if the first digit cannot be zero, and repetition is not permitted 1 solutions Answer 361850 by stanbon(57361)   on 2012-01-11 06:10:50 (Show Source): You can put this solution on YOUR website! a license plate is to consist of three digits followed by two uppercase letters. Determine the number of different license plates possible if the first digit cannot be zero, and repetition is not permitted ------ 1st digit: 9 ways (0 is excluded) 2nd digit: 9 ways (0 is now included) 3rd digit: 8 ways (0 and the 2nd digit are excluded) --- 1st Letter: 26 ways 2nd Letter: 25 ways ---- Total # of license plates: 9^2*8*26*25 == 421,200 ================= Cheers, Stan H. =================

Probability-and-statistics/555587: I am really confused. I am in MM207 and do not understand how to solve this problem. Could someone please take me step by step through it so that I understand what I am doing? Assume you want to estimate with the proportion of students who commute less than 5 miles to work within 2%, what sample size would you need? 1 solutions Answer 361849 by stanbon(57361)   on 2012-01-11 06:06:29 (Show Source): You can put this solution on YOUR website! Assume you want to estimate with the proportion of students who commute less than 5 miles to work within 2%, what sample size would you need? --- As I told you two days ago, you have to know the confidence level for your problem because: n = [z/E]^2*pq --- If the confidence level is 95%, then z = 1.96 Since you have no p-value you use p = 1/2 = q --- Then you would get: n = [1.96/0.02]^2*(1/2)(1/2) = 2401 ======================================== Cheers, Stan H. ================

Graphs/555591: Good Morning, Can someone show me how to solve and graph the following system of inequalities: y<-1/2x +2 x-y <= 4 (the second line is x-4 is less than or equal to 4) Hope to hear from someone soon. Sincerely, T.H. 1 solutions Answer 361848 by stanbon(57361)   on 2012-01-11 05:54:24 (Show Source): You can put this solution on YOUR website! solve and graph the following system of inequalities: y<-1/2x +2 Graph the line y = (-1/2)x+2 as a dashed line. Shade the half-plane below that boundary line. --------------------------------- x-y <= 4 Solve for "y": y >= x-4 ---- Graph the line y = x-4 Shade the half-plane above that boundary line. ----- The solution set is the intersection of those 2 graphs. --- cheers, Stan H.