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Recent problems solved by 'stanbon'

stanbon answered: 57151 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, >>Next

Problems-with-consecutive-odd-even-integers/626435: an antique jar is forty five years older than the mug. in thirteen years the jar will be four times as old as the mug will be then. find the present age of the jar 1 solutions Answer 394162 by stanbon(57219)   on 2012-07-07 08:54:21 (Show Source): You can put this solution on YOUR website! answered

Equations/626436: What is the equation to solve this formula? 0.47 = 3,547,000 * x / 10,300,000 Thanks in advance!! 1 solutions Answer 394161 by stanbon(57219)   on 2012-07-07 08:53:23 (Show Source): You can put this solution on YOUR website! What is the equation to solve this formula? 0.47 = 3,547,000 * x / 10,300,000 ---- Multiply both sides by 10,300,000 to get: 3,547,000x = 4841000 Divide both sides by 3,547,000 to get: x = 1.364815337... Cheers, Stan H.

Money_Word_Problems/626441: Judy bought P pencils at 14 cents each and n notebooks at 1.25$ each. Write an equation for the total dollar amount, A, that Judy spent. 1 solutions Answer 394160 by stanbon(57219)   on 2012-07-07 08:49:47 (Show Source): You can put this solution on YOUR website! Judy bought P pencils at 14 cents each and n notebooks at 1.25$ each. Write an equation for the total dollar amount, A, that Judy spent. ------- Equation: value = value + value A = 0.14P + 1.25n ========================== Cheers, Stan H.

percentage/626440: A single die with 6 faces numbered 1 through 6 is thrown thrice. What is the probability that the sum of the number appearing after each throw is more than 15? A)5/216 B)5/108 C)5/36 D)1/5 E)1/6 1 solutions Answer 394159 by stanbon(57219)   on 2012-07-07 08:46:52 (Show Source): You can put this solution on YOUR website! A single die with 6 faces numbered 1 through 6 is thrown thrice. What is the probability that the sum of the number appearing after each throw is more than 15? ---- Ways to win: 666-----1 way 665-----3 ways 664-----3 ways 655-----3 ways ----- Ans: 10/216 = 5/108 ======================= Cheers, Stan H. ======================= A)5/216 B)5/108 C)5/36 D)1/5 E)1/6

Travel_Word_Problems/626438: A bus traveled at an average rate of 50mph and then reduced the average rate to 40mph for the rest of the trip. If the 220 mile trip took 5 hour, determine how long the bus traveled at each rate. 1 solutions Answer 394158 by stanbon(57219)   on 2012-07-07 08:41:14 (Show Source): You can put this solution on YOUR website! A bus traveled at an average rate of 50mph and then reduced the average rate to 40mph for the rest of the trip. If the 220 mile trip took 5 hour, determine how long the bus traveled at each rate. ---- Faster-leg DATA: rate = 50 mph ; time = x hrs ; distance = 50x miles ---- Slower-leg DATA: rate = 40 mph ; time = 5-x hrs ; distance = 40(5-x) miles ------ Equation: distance + distance = 220 miles 50x + 200 - 40x = 220 10x = 20 x = 2 hrs --- fast-leg time = 2 hrs slow-leg time = 5-2 = 3 hrs. ================================ cheers, Stan H. =================

percentage/626437: There are 89 students in senior year out of whom all but 3 study latin, spaniah or french. If 25 take latin, 32 spanish and 37 french and no student takes all three languages, how many students take more than one language? A)0 B)3 C)5 D)8 E)10 1 solutions Answer 394157 by stanbon(57219)   on 2012-07-07 08:37:20 (Show Source): You can put this solution on YOUR website! There are 89 students in senior year out of whom all but 3 study latin, spaniah or french. If 25 take latin, 32 spanish and 37 french and no student takes all three languages, how many students take more than one language? ---- Draw the Venn Diagram of 3 intersecting circles. Label the circles latin, span, and french. ---- The universe has 89 elements. 3 elements are not in any of the circles, leaving 86 in the circles. ---- latin has 25 elements span has 32 elements french has 37 The intersection of the 3 circles has 0 elements ---- (25+32+37)-86 = 94-86 = 8 students take more than one language. ============ Cheers, Stan H. =============== A)0 B)3 C)5 D)8 E)10

Problems-with-consecutive-odd-even-integers/626434: an antique jar is 45 years older than the mug. in 13 years, the jar will be 4 times as old as the mug will be then. find the present age of the jar 1 solutions Answer 394156 by stanbon(57219)   on 2012-07-07 08:28:52 (Show Source): You can put this solution on YOUR website! an antique jar is 45 years older than the mug. in 13 years, the jar will be 4 times as old as the mug will be then. find the present age of the jar -------------- Equations: j = m + 45 j+13 = 4(m+13) ----- Substitute for "j" and solve for "m": m+45 + 13 = 4m+52 3m = 58-52 m = 6/3 m = 2 years (age of the mug) ---- Solve for "j": j = m + 45 m = 2 + 45 m = 47 years (age of the jar) ============== Cheers, Stan H. ===============

test/626366: A hospital day staff consist of 2( registered nurses 75 unlicensed assistants five staff and 45 physicians one summer dad the staff was at only 68% strength. How many ppl were working that day 1 solutions Answer 394128 by stanbon(57219)   on 2012-07-06 21:59:12 (Show Source): You can put this solution on YOUR website! A hospital day staff consists of 2 registered nurses, 75 unlicensed assistants, 5 staff and 45 physicians. One summer day the staff was at only 68% strength. How many ppl were working that day? ================ # of people working was 0.68(2+75+5+45) = 0.68*127 = 86.36 = 86 rounded down. ========== Cheers, Stan H. ==============

logarithm/626356: Use the Laws of Logarithms to combine the expression. 5log(x)-((1)/(5))log(x^(2)+1)+5log(x-1) 1 solutions Answer 394126 by stanbon(57219)   on 2012-07-06 21:54:23 (Show Source): You can put this solution on YOUR website! 5log(x)-((1)/(5))log(x^(2)+1)+5log(x-1) -------------------- log(x^5) - log(x^2+1)^(1/5) + log(x-1)^5 ------ = log[(x(x-1)^5)/(x^2+1)^(1/5)] ========================================= Cheers, Stan H. =========================

Graphs/626365: solve each by the substitution method. Y=2x+6 3x-2y=-11 x+3y=-3 2x+y=4 1 solutions Answer 394125 by stanbon(57219)   on 2012-07-06 21:48:45 (Show Source): You can put this solution on YOUR website! solve each by the substitution method. Y=2x+6 3x-2y=-11 --- Substitute for "y" and solve for "x": 3x - 2(2x+6) = -11 3x - 4x - 12 = -11 -x = 1 x = -1 --- Solve for "y": y = 2x+6 y = 2*-1+6 y = 4 ----------------- x+3y=-3 2x+y=4 ---- Solve 1st for "y": y = 4-2x --- Substitute for "y" and solve for "x": x + 3(4-2x) = -3 x + 12 - 6x = -3 -5x = -15 x = 3 --- Solve for "y": y = 4-2x y = 4-2*3 y = -2 ================== Cheers, Stan H. =====================

Unit_Conversion_Word_Problems/626361: Last night at the hospital 76 babies were born of the births 45% were girls. How many boys were born last night 1 solutions Answer 394123 by stanbon(57219)   on 2012-07-06 21:43:25 (Show Source): You can put this solution on YOUR website! Last night at the hospital 76 babies were born of the births 45% were girls. How many boys were born last night --- If 45% are girls, 55% must be boys. --- # of boys = 0.55*76 = 41.8 = 42 when rounded up. =============== Cheers, Stan H. ==================

Triangles/626364: The sides of one triangle are 12,11 and 11. The sides of the smaller triangle are 3,3 and 3. Find the scale factor of the smaller triangle (the object) with the larger triangle (the image) 1 solutions Answer 394122 by stanbon(57219)   on 2012-07-06 21:41:14 (Show Source): You can put this solution on YOUR website! There is no single scale factor. The triangles are not similar. ============ Cheers, Stan H. ==============

Linear_Equations_And_Systems_Word_Problems/626362: Write an expression that represents the area of a rectangle given that the length =(x+4) and the width =(5x+2) 1 solutions Answer 394121 by stanbon(57219)   on 2012-07-06 21:38:42 (Show Source): You can put this solution on YOUR website! Write an expression that represents the area of a rectangle given that the length =(x+4) and the width =(5x+2) ----- Area = length*width = (x+4)(5x+2) = x(5x+2) + 4(5x+2) = 5x^2 + 2x + 20x + 8 = 5x^2 + 22x + 8 ======================= Cheers, Stan H. =======================

Unit_Conversion_Word_Problems/626363: A farmer raises chickens for eggs and meat any chicken that does not lag at least one egg a week is moved to the slaughterhouse the farmer has 765 chicks s that can lay one egg each day. Each day 80% of the chickens lay egss. How man eggs does the farmer collect each day 1 solutions Answer 394120 by stanbon(57219)   on 2012-07-06 21:35:05 (Show Source): You can put this solution on YOUR website! A farmer raises chickens for eggs and meat any chicken that does not lag at least one egg a week is moved to the slaughterhouse the farmer has 765 chicks s that can lay one egg each day. Each day 80% of the chickens lay egss. How man eggs does the farmer collect each day ---- # of eggs = 0.80*765 = 612 ============= Cheers, Stan H. ================

Probability-and-statistics/626355: Hi. I often want to calculate stuff like the example listed below, but am not sure how to do it. I don’t want to bother others with that, would love to learn how to do it properly myself. Can you please help me out? 6 competitions are being played. In each of them there are 32 teams (a total of 192 teams). What are the chances (probability) of someone predicting all champions correctly (if we assume there are no favourites nor underdogs, all teams are of exactly the same strength on paper). Cup A – 32 teams Cup B – 32 teams Cup C – 32 teams Cup D – 32 teams Cup E – 32 teams Cup F – 32 teams I’m interested in the probability of guessing all six champions, also (if it’s not too much work to calculate), what is the probability of guessing 5/6, 4/6 and 3/6. I am not using this for any real-life betting, it’s just for an online management game with no money involved. :) Thanks!! 1 solutions Answer 394119 by stanbon(57219)   on 2012-07-06 21:31:26 (Show Source): You can put this solution on YOUR website! In each of them there are 32 teams (a total of 192 teams). What are the chances (probability) of someone predicting all champions correctly (if we assume there are no favourites nor underdogs, all teams are of exactly the same strength on paper). Cup A – 32 teams Cup B – 32 teams Cup C – 32 teams Cup D – 32 teams Cup E – 32 teams Cup F – 32 teams I’m interested in the probability of guessing all six champions, also (if it’s not too much work to calculate), what is the probability of guessing 5/6, 4/6 and 3/6. ----- Probability a team takes the Cup: 1/32 --- Probability you choose 6 Cup takers: (1/32)^6 = 9.31x10^-10. That means 0.000000000931 --------------- Probability you choose 5 winners: 6C5(1/32)^5*(31/32) = 1.73x10^-7 That means 0.000000173 ----- Pick 4: 6C4(1/32)^4(31/32)^2 = 0.0000134 ----- Pick 3: 6C3(1/32)^3(31/32)^3 = 0.000555 ============================================== Cheers, Stan H.

Travel_Word_Problems/626358: Greg is traveling north on a road while peter is traveling south on the same road. they pass by each other at noon, Greg driving at 35 mph and peter driving at 55 mph. at what time will they be 225 mi apart? 1 solutions Answer 394118 by stanbon(57219)   on 2012-07-06 21:19:40 (Show Source): You can put this solution on YOUR website! Greg is traveling north on a road while peter is traveling south on the same road. they pass by each other at noon, Greg driving at 35 mph and peter driving at 55 mph. at what time will they be 225 mi apart? ---- Draw the picture. You have a crossing point, a line segment going north that is 35x miles long where "x" is time for Gregg and for Peter, and a line segment going south that is 55x miles long. ---- Equation: distance + distance = 225 miles 35x + 55x = 225 90x = 225 x = 2.5 hrs ---- Time when they are 225 miles apart: noon + 2.5 miles = 2:30 PM ================= Cheers, Stan H. ================

Trigonometry-basics/625832: Solve on 0≤ θ < 2 π, using a calculator, the equation θ cos θ/2- sin 2 θ = 0. 1 solutions Answer 393815 by stanbon(57219)   on 2012-07-04 09:33:01 (Show Source): You can put this solution on YOUR website! Solve on 0≤ θ < 2 π, using a calculator, the equation θ cos θ/2- sin 2 θ = 0. ------- ------- Ans: theta = o.628 or 1.047 or 3.14 or 5.24 or 5.65 -------- Cheers Stan H.

Volume/625839: If a pool has a radius of 4 meters and is 1.4 meters high how big will the pools top need to be- how do i figure the problem out? 1 solutions Answer 393813 by stanbon(57219)   on 2012-07-04 09:10:08 (Show Source): You can put this solution on YOUR website! If a pool has a radius of 4 meters and is 1.4 meters high how big will the pools top need to be- how do i figure the problem out? ----------- Area of the top = pi*r^2= 3.14*16 = 50.14 sq. meters ------------- Cheers Stan H.

Rational-functions/625840: kjopllllll 1 solutions Answer 393812 by stanbon(57219)   on 2012-07-04 09:04:38 (Show Source): You can put this solution on YOUR website!

Sequences-and-series/625808: There are 6 chairs in a row. There are 11 students. How many ways can these students sit in the 6 chairs? 1 solutions Answer 393811 by stanbon(57219)   on 2012-07-04 09:03:02 (Show Source): You can put this solution on YOUR website! There are 6 chairs in a row. There are 11 students. How many ways can these students sit in the 6 chairs? ------- And: 11P6 = 11!/(11-6)! = 332640 -------- Cheers Stan H.

Quadratic_Equations/625837: The graph of y=ax^2+bx+c cannot have points in the third or fourth quadrants if a) b^2-4ac>0 and b>a b) b^2-4ac>0 and b<0 c) b^2-4ac=0 and a<0 d) b^2-4ac<0 and a<0 e) b^2-4ac<0 and a>0 1 solutions Answer 393810 by stanbon(57219)   on 2012-07-04 08:52:53 (Show Source): You can put this solution on YOUR website! The graph of y=ax^2+bx+c cannot have points in the third or fourth quadrants if a) b^2-4ac>0 and b>a b) b^2-4ac>0 and b<0 c) b^2-4ac=0 and a<0 d) b^2-4ac<0 and a<0 e) b^2-4ac<0 and a>0 ------------ Ans: e because no x-intercepts and the parabola opens up ----------------- Cheers Stan H.

real-numbers/625831: the circumference of a compact disk is computed by using the diameter measured to the nearest te nth of a centimeter and 3.14 as an approximation of pie. which subset of numbers corresponds best to this situation? rational numbers integers- this was my answer real numbers whole numbers can you explain this, I thought irrational numbers were those that represented pie. 1 solutions Answer 393809 by stanbon(57219)   on 2012-07-04 08:44:06 (Show Source): You can put this solution on YOUR website! The circumference of a compact disk is computed by using the diameter measured to the nearest te nth of a centimeter and 3.14 as an approximation of pie. which subset of numbers corresponds best to this situation? rational numbers integers- this was my answer real numbers whole numbers can you explain this, I thought irrational ------------ Ans: 3.14 is rational Limiting the diameter to tenths gives a rational Therefore circumference = Pie*d will be rational. Cheers Stan H.

Rational-functions/625834: how do I use this formula? the number of haircuts c completed by a hair stylist after t hours of work on a recent day is given by c(t) = 2t + 1 how many hours does it take to complete 8 haircuts? 3 3.5 4.5 17 18 1 solutions Answer 393808 by stanbon(57219)   on 2012-07-04 08:28:25 (Show Source): You can put this solution on YOUR website! how do I use this formula? the number of haircuts c completed by a hair stylist after t hours of work on a recent day is given by c(t) = 2t + 1 how many hours does it take to complete 8 haircuts? C(8) = 2*8+1 = 17 –----------- Cheers Stan H. 3 3.5 4.5 17 18

Permutations/625835: In how many ways can a group of 4 people be selected for a party planning committee from a class of 25? 1 solutions Answer 393806 by stanbon(57219)   on 2012-07-04 08:23:51 (Show Source): You can put this solution on YOUR website! In how many ways can a group of 4 people be selected for a party planning committee from a class of 25? -------- And: 25C4 = 25!/(21!*4!) = 12650 Cheers Stan H.

Systems-of-equations/625833: I am gearing up for my test and this is a practice question and I just can't remember the formula. one person traveled h hours at 60 mph. a second person traveled 2h-5 hours at 40 mph. both traveld the same distance. how many hors did the second person travel? 5 10 15 20 25 1 solutions Answer 393805 by stanbon(57219)   on 2012-07-04 08:18:19 (Show Source): You can put this solution on YOUR website! Systems-of-equations/625833 (2012-07-04 08:07:02): I am gearing up for my test and this is a practice question and I just can't remember the formula. one person traveled h hours at 60 mph. a second person traveled 2h-5 hours at 40 mph. both traveld the same distance. how many hors did the second person travel? _____ Equation: Distance = Distance 60h = (2h-5)40 60h = 80h - 200 20h = 200 h = 10 _______ 2h-5 = 15 hours ___________ Cheers Stan H. -----------------___ 5 10 15 20 25 0 solutions

Radicals/625295: Can anyone please help me with rationalizing, please? I just can't seem to understand the Exponent/Radical lessons. Only this lesson makes me slumped :( ANY HELP I WOULD BE GRATEFUL<3 ^3sqrt|2a^9b^5c^4 (The sqroot sign goes all the way to c^4.) (The 3 in the beginning, is written as an exponent before the sqroot) THANK YOU! 1 solutions Answer 393467 by stanbon(57219)   on 2012-07-02 09:24:28 (Show Source): You can put this solution on YOUR website! ^3sqrt|2a^9b^5c^4 -------------- cbrt(a^9b^3c^3)*cbrt(2b^2c) ------ a^3bc*cbrt(2b^2c) ------------ Cheers, Stan H.

Miscellaneous_Word_Problems/625292: R is what percent of 1000? Can someone go into detail on how to answer this? 1 solutions Answer 393407 by stanbon(57219)   on 2012-07-02 00:04:59 (Show Source): You can put this solution on YOUR website! -------------- R = R/1000 * 1000 = (0.1R/100)*1000 = (0 .1R%) of 1000 Cheers, Stan H.

Linear-systems/625290: Solve the following systems of equations and find all possible solutions as (x,y). 1 solutions Answer 393406 by stanbon(57219)   on 2012-07-01 23:46:19 (Show Source): You can put this solution on YOUR website! Solve the following systems of equations and find all possible solutions as (x,y). ------------- 2x-1 = x^2-3x-1 x^2 - 5x = 0 x(x - 5) = 0 x= 0 or x = 5 ------------- Cheers, Stan H.

logarithm/620640: How do I expand this logarithm? Log(base of 3)11p^3 1 solutions Answer 390300 by stanbon(57219)   on 2012-06-13 18:56:12 (Show Source): You can put this solution on YOUR website! expand this logarithm? Log(base of 3)11p^3 ------ log3(11p^3) --- = log3(11) + log3(p^3) --- = log3(11) + 3log3(p) ========================= Cheers, Stan H. ===================

Probability-and-statistics/620635: A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least 1 person's infection will not improve 1 solutions Answer 390299 by stanbon(57219)   on 2012-06-13 18:53:34 (Show Source): You can put this solution on YOUR website! A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least 1 person's infection will not improve ------- Binomial Problem with n = 12 and p(effective) = 0.75 ; P(not) = 0.25 ---- P(1<= x <=12 not improve) = 1 - P(x = 0 improve) = 1 - 0.25^12 = 0.999999940400.. ------------------------ Cheers, Stan H.

Probability-and-statistics/620632: If a population has a standard deviation of 18, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is within 2 of the true mean? 1 solutions Answer 390297 by stanbon(57219)   on 2012-06-13 18:43:15 (Show Source): You can put this solution on YOUR website! If a population has a standard deviation of 18, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is within 2 of the true mean? ------------------------------ n = [z*s/E]^2 --- n = [1.96*18/2]^2 = 312 when rounded up ================ Cheers, Stan H. ================