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Recent problems solved by 'stanbon'

stanbon answered: 57145 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, >>Next

test/700942: -3x+3y=3 -5x+y=13 Solve by subsitution 1 solutions Answer 432072 by stanbon(57213)   on 2013-01-11 09:58:55 (Show Source): You can put this solution on YOUR website! -3x+3y=3 -5x+y=13 -------------- y = 5x+13 --- Substitute for "y" and solve for "x": -3x+3y = 3 Divide thru by 3 to get: -x + y = 1 Substitute: -x + (5x+13) = 1 4x= -12 x = -3 ------ Solve for "y": y = 5x+13 y = 5*-3+13 y = -2 ---------- Cheers, Stan H

Problems-with-consecutive-odd-even-integers/700934: What are four consecutive integers whose sum is 98 1 solutions Answer 432061 by stanbon(57213)   on 2013-01-11 09:32:33 (Show Source): You can put this solution on YOUR website! What are four consecutive integers whose sum is 98 === 1st: x-2 2nd: x-1 3rd: x 4th: x+1 ------ Equation: sum = 98 4x -2 = 98 4x = 100 x = 25 ----- 1st: 23 2nd: 24 3rd: 25 4th: 26 ----- Cheers, Stan H.

Linear-equations/700935: Is (1,10) a solution of y= x -9 1 solutions Answer 432059 by stanbon(57213)   on 2013-01-11 09:28:07 (Show Source): You can put this solution on YOUR website! Is (1,10) a solution of y= x -9 ----- Substitute for x and for y and see if you get a true statement. ----- 10 = 1-9 10 = -8 ----- That is not true so (1,10) is not a solution. Cheers, Stan H. ==============

Miscellaneous_Word_Problems/700794: a local dairy has three machines to fill half gallon milk cartons.The machine can fill the daily quota in 4 hours, 5 hours, and 8.5 hours, respectively. Find how long it takes to fill the daily quota if all three machines are running 1 solutions Answer 432000 by stanbon(57213)   on 2013-01-10 21:27:05 (Show Source): You can put this solution on YOUR website! a local dairy has three machines to fill half gallon milk cartons.The machine can fill the daily quota in 4 hours, 5 hours, and 8.5 hours, respectively. Find how long it takes to fill the daily quota if all three machines are running ----- Let "x" be the time for all 3 to do the job. ----------------------------------------------------------------- Rate Equation: 1/4 + 1/5 + 1/8.5 = 1/x --------- 1/4 + 1/5 + 2/17 = 1/x --------- [17*5x + 17*4x + 2*4*5x] = 17*4*5 -------- 85x + 68x + 40x = 17*20 ---- 193x = 340 --- x = 1.76 hrs = 1 hour 45 min 36 seconds ============================================ Cheers, Stan H.

Probability-and-statistics/700788: What is the probability that 3 machines out of 10 will break down on any day if one machine has .10 probability? Would my answer be .30??? 1 solutions Answer 431996 by stanbon(57213)   on 2013-01-10 20:42:00 (Show Source): You can put this solution on YOUR website! What is the probability that 3 machines out of 10 will break down on any day if one machine has 0.10 probability? ----------------------------- These events are independent. P(3 machines break) = 0.10^3 = 0.001 =============== Cheers, Stan H.

Quadratic_Equations/700758: instructions: graph each quadratic function. name the axis of symmetry and the coordinates of the vertex. 1. y=-x^2+7x-2 1 solutions Answer 431995 by stanbon(57213)   on 2013-01-10 20:36:35 (Show Source): You can put this solution on YOUR website! graph each quadratic function. name the axis of symmetry and the coordinates of the vertex. y = -x^2+7x-2 ----- The 1st coordinate of the vertex and the equation of the axis of symmetry are x = -b/(2a) = -7/(2*-1) = -7/-2 = 7/2 ------ The 2nd coordinate of the vertex is f(7/2) ----- f(7/2) = -(7/2)^2 + 7(7/2) -2 = -(49/4) + (49/2) - 2 --- = (-49 + 98 - 8)/4 ---- = 41/4 ---- Vertex: (7/2 , 41/4) ------- ========================= Cheers, Stan H.

Permutations/700778: from the deck of 52 playing cards how many ways can be drawn such that: a. they both red? b. one is a diamond card and the other is a spade card? 1 solutions Answer 431989 by stanbon(57213)   on 2013-01-10 20:21:54 (Show Source): You can put this solution on YOUR website! from the deck of 52 playing cards how many ways can be drawn such that: a. they both red? Ans: 26C2 = (26*25)/(1*2) = 325 ways ------------------------------------------- b. one is a diamond card and the other is a spade card? Ans: 13*13 = 169 ways ========================== Cheers, Stan H.

Linear-equations/700775: Find all points on the y-axis that are 6 units from the point (4, -3) 1 solutions Answer 431986 by stanbon(57213)   on 2013-01-10 20:18:29 (Show Source): You can put this solution on YOUR website! Find all points on the y-axis that are 6 units from the point (4, -3) -------- Equation of circle with center at (4,-3) and radius = 6. ---- (x-4)^2 + (y+3)^2 = 36 ---- To find points on the y-axis, let x = 0. ------ (-4)^2 + (y+3)^2 = 36 ------ (y+3)^2 = 20 ---- y+3 = sqrt(20) or y+3 = -sqrt(20) --- y = -3+2sqrt(5) or y = -3-2sqrt(5) ---------- Points: (0, -3+2sqrt(5)) and (0,-3-2sqrt(5)) ============================== Cheers, Stan H.

Quadratic_Equations/700770: instructions: evaluate the discriminant of each equation. determine how many real solutions each equation has. 1. 16x^2-8x+1=0 1 solutions Answer 431981 by stanbon(57213)   on 2013-01-10 20:12:29 (Show Source): You can put this solution on YOUR website! evaluate the discriminant of each equation. determine how many real solutions each equation has. 16x^2-8x+1 = 0 ------ b^2-4ac = (-8)^2 - 4*16*1 = 64 - 64 = 0 ----------- Ans: 2 equal Real solutions. ===================================== Cheers, Stan H.

Travel_Word_Problems/700772: Hammad Drove 8 Hours From His Home To A City 520 Miles Away. At What Average Speed Did He Travel? 1 solutions Answer 431978 by stanbon(57213)   on 2013-01-10 20:07:04 (Show Source): You can put this solution on YOUR website! Hammad Drove 8 Hours From His Home To A City 520 Miles Away. At What Average Speed Did He Travel? ------------------------------ rate = distance/time ------ rate = 520/8 (miles/hours) = 65 mph ========================== Cheers, Stan H.

Travel_Word_Problems/700771: Jerry traveled 110 miles in his car at a constant rate of 22 miles per hour. How many hours did he travel? 1 solutions Answer 431976 by stanbon(57213)   on 2013-01-10 20:02:53 (Show Source): You can put this solution on YOUR website! Jerry traveled 110 miles in his car at a constant rate of 22 miles per hour. How many hours did he travel? ------- time = distance/rate ---- time = 110/22 (miles/(miles/hr)) ----- time = 5 hrs =================== Cheers, Stan H.

Square-cubic-other-roots/700769: Can you please explain how to multiply square roots? For example, √5(√5-5√3). 1 solutions Answer 431974 by stanbon(57213)   on 2013-01-10 19:59:23 (Show Source): You can put this solution on YOUR website! √5(√5-5√3). ---- = 5 - 5*sqrt(15) --------------------- Cheers, Stan H.

Numeric_Fractions/700768: What is 1/3-1/4 1 solutions Answer 431972 by stanbon(57213)   on 2013-01-10 19:57:34 (Show Source): You can put this solution on YOUR website! What is 1/3-1/4 ----- = (4-3)/12 = 1/12 ====================== Cheers, Stan H. ======================

Complex_Numbers/700687: I just want to check my answer. Im supposed to express in terms of 'i'. So would my answer be 1 solutions Answer 431948 by stanbon(57213)   on 2013-01-10 18:23:39 (Show Source): You can put this solution on YOUR website! 7 sqrt (-88) ----- = 7* sqrt(-4*22) ----- = 7*sqrt(-4)*sqrt(22) ----- = 7*2i*sqrt(22) ------ = 14sqrt(22)i ================= Cheers, Stan H. =================

Age_Word_Problems/700682: The Lee's have three children. The oldest is twice as old as the youngest. The middle child is five years older than the youngest. If the sum of the age is 57, how old is each child? 1 solutions Answer 431945 by stanbon(57213)   on 2013-01-10 18:20:04 (Show Source): You can put this solution on YOUR website! The Lee's have three children. The oldest is twice as old as the youngest. The middle child is five years older than the youngest. If the sum of the age is 57, how old is each child? --------------------------------- Let oldest be "a" middle be "b" youngest be "c" ----------------- Equations: a = 2c b = c+5 a + b + c = 57 ---------------------------- Substitute for "a" and "b": 2c + c+5 + c = 57 4c = 52 c = 13 years (youngest) --- a = 2c = 26 years (oldest) ---- b = c+5 = 18 years (middle) =============================== Cheers, Stan H.

Miscellaneous_Word_Problems/700679: Karen brought 10 stamps. Some cost $.32 and some cost $.20. SHe spent $2.84. How many of each did she buy? 1 solutions Answer 431941 by stanbon(57213)   on 2013-01-10 18:12:11 (Show Source): You can put this solution on YOUR website! Karen bought 10 stamps. Some cost $.32 and some cost $.20. SHe spent $2.84. How many of each did she buy? ---------- Quantity Eq:::: a + b = 10 Value Eq::::: 32a + 20b = 284 cents ------- 32a + 32b = 32*10 32a + 20b = 284 ------- Subtract and solve for "b": 12b = 36 b = 3 (# of 20 cent stanps) ------ Solve for "a": a + b = 10 a + 3 = 10 a = 7 (# of 32 cent stamps) ------------------------------- Cheers, Stan H. ===============

Equations/700673: I need an equation to find how many quarts in 16 pints? 1 solutions Answer 431937 by stanbon(57213)   on 2013-01-10 18:06:42 (Show Source): You can put this solution on YOUR website! 1 quart = 2 pints ----- 1 pint = (1/2)quart ------------------------- I need an equation to find how many quarts in 16 pints? 16*1 pint = 16(1/2)quarts 16 pint = 8 quarts ====================== Cheers, Stan H. =========================

Finance/700670: Last month, Raj earned $1,200. This month, he earned $1,104. By what percentage did his earning decrease? 1 solutions Answer 431934 by stanbon(57213)   on 2013-01-10 18:02:13 (Show Source): You can put this solution on YOUR website! Last month, Raj earned $1,200. This month, he earned $1,104. By what percentage did his earning decrease? ----- Quantitative decrease: 1200-1104 = 96 --- Percent decrease: 96/1200 = 0.08 = 8% ====================== Cheers, Stan H. ======================

Travel_Word_Problems/700664: Dora rode her bike 5 miles to her grandmothers house. The ride took 30 minutes. On average, how many minutes did it take Dora to ride each mile? 1 solutions Answer 431933 by stanbon(57213)   on 2013-01-10 17:56:16 (Show Source): You can put this solution on YOUR website! Dora rode her bike 5 miles to her grandmothers house. The ride took 30 minutes. On average, how many minutes did it take Dora to ride each mile? --------- time = distance/rate --- time = 5 miles/30 min = (1/6)(mile/minute) ================================== Cheers, Stan H. -------------------

Mixture_Word_Problems/700667: A person is mixing soda and juice that is 45% juice. If this person uses 3 qts of soda, how many qts of fruit juice must be added to produe a drink that is 30% juice? 1 solutions Answer 431931 by stanbon(57213)   on 2013-01-10 17:52:12 (Show Source): You can put this solution on YOUR website! A person is mixing soda and juice that is 45% juice. If this person uses 3 qts of soda, how many qts of fruit juice must be added to produe a drink that is 30% juice? ----- Equation: juice + juice = juice 0.45x + 0*3 = 0.30(x+3) ------- 45x = 30x + 30*3 15x = 90 x = 6 qts (amt of soda needed) ================================= Cheers, Stan H.

Linear-equations/700665: whats the slope of -5,10 and 0,13? sorry i can't put the parenthesis on this 1 solutions Answer 431929 by stanbon(57213)   on 2013-01-10 17:48:34 (Show Source): You can put this solution on YOUR website! whats the slope of (-5,10) and (0,13)? ----------- slope = (13-10)/(0--5) = 3/5 ======== Cheers, Stan H. ===========

Travel_Word_Problems/700663: Describe the distance in meters you could walk in a given number of seconds? 1 solutions Answer 431926 by stanbon(57213)   on 2013-01-10 17:45:45 (Show Source): You can put this solution on YOUR website! at what rate?

Rectangles/700662: how do you find the length of a diagonal if all you have is an equation: 7x-2 for one diagonal and 4x+3 for the other diagonal? 1 solutions Answer 431925 by stanbon(57213)   on 2013-01-10 17:42:49 (Show Source): You can put this solution on YOUR website! diagonals of what? Cheers, Stan H.

Miscellaneous_Word_Problems/700592: A board 65 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board. 1 solutions Answer 431883 by stanbon(57213)   on 2013-01-10 15:53:37 (Show Source): You can put this solution on YOUR website! A board 65 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board. ------ Equations: x + y = 65 feet x = (2/3)y ===== Substitute and solve for "y": (2/3)y + y = 65 (5/3)y = 65 (1/3)y = 13 y = 39 feet ===== Solve for "x": x = (2/3)y x = (2/3)39 x = 26 feet ================== Cheers, Stan H. ================ x =

Triangles/700591: One angle measure is an isosceles triangle is 100 degrees.what is the measure of each of the other two angles 1 solutions Answer 431881 by stanbon(57213)   on 2013-01-10 15:50:35 (Show Source): You can put this solution on YOUR website! One angle measure is an isosceles triangle is 100 degrees.what is the measure of each of the other two angles ----- The sum of the angles is 180. The 100 degree angle cannot be a base angle as then the sum of the base angles would be 200 degrees. --- The 100 must be the vertex angle. --- Let the base angles be "x" and "x": Equation: x + x + 100 = 180 2x = 80 x = 40 degrees. Each of the base angles is 40 degrees. Cheers, Stan H.

Probability-and-statistics/700589: If P=5/6 and n=125 find P( x≤ 100) using normal distribution on TI-83 exact steps 1 solutions Answer 431880 by stanbon(57213)   on 2013-01-10 15:47:31 (Show Source): You can put this solution on YOUR website! If P=5/6 and n=125 find P( x≤ 100) using normal distribution on TI-83 exact steps ---- u = np = 125(5/6) = 104.16 s = sqrt(npq) = sqrt(104.16*(1/6)) = 4.1667 ------ P(x <= 100) = P(0<= x <=100.5) ---- z(0) = (0-104.16)/4.1667 = -24.9984 z(105) = (100.5-104.16)/4.1667 = -0.8784 ---- P(0<= x <=100.5) = P(-25<= z <= -0.8784) = normalcdf(-25,-0.8784) = 0.1899 =================================== Cheers, Stan H. =========================

Exponential-and-logarithmic-functions/700587: What does x equal if 9^2x+1=27^x And... What does x equal if log x+log 5=2 1 solutions Answer 431878 by stanbon(57213)   on 2013-01-10 15:36:33 (Show Source): You can put this solution on YOUR website! What does x equal if 9^2x+1=27^x 9^(2x+1) = 27^x ----- Change the base: 3^(4x+2) = 3^(3x) ----- Equate the exponents: 4x+2 = 3x x = -2 ================ And... What does x equal if log x+log 5=2 ----- log(5x) = 2 5x = 10^2 5x = 100 x = 20 ================ Cheers, Stan H. ------------------

Linear_Equations_And_Systems_Word_Problems/700585: in a class,45 students take the SAT exam. the number of boys is 8 more than the number of girls. write a system that models the above situation and find the solution. do you need to multiply any of the equations by a constant?if so, which equation and what is the constant? 1 solutions Answer 431877 by stanbon(57213)   on 2013-01-10 15:32:47 (Show Source): You can put this solution on YOUR website! in a class,45 students take the SAT exam. the number of boys is 8 more than the number of girls. write a system that models the above situation and find the solution. ---------- Using 2 equations: b + g = 45 b = g + 8 ------- Rearrange: b + g = 45 b - g = 8 ------ Add and solve for "b": 2b = 53 b = 26.5 Rounding up b = 27 (# of boys) ------- Solve for "g": b + g = 45 27 + g = 45 g = 18 (# of girls) ======= Cheers, Stan H. =======

Permutations/700434: How many different ways can a manager and supervisor from a company branch in Manila be selected if there are 8 employees available? 1 solutions Answer 431875 by stanbon(57213)   on 2013-01-10 15:23:22 (Show Source): You can put this solution on YOUR website! How many different ways can a manager and supervisor from a company branch in Manila be selected if there are 8 employees available? --- Because the 2 positions are not the same, order is implied. ----- Ans: 8P2 = 8*7 = 56 ways =========================== Cheers, Stan H. =============

Exponential-and-logarithmic-functions/700443: Kindly please assist. Solve 2^x=5^x^2 for x a)0.431 b)2.322 c)0 and 0.431 d)0 and 2.322 1 solutions Answer 431827 by stanbon(57213)   on 2013-01-10 06:39:54 (Show Source): You can put this solution on YOUR website! Solve 2^x=5^x^2 for x ------ 2^x = 5^(x^2) --- Take the log of both sides: x*log(2) = x^2(log(5)) ----- 0.6990x^2 - 0.3010x = 0 --- x[0.6990x - 0.3010] = 0 --- x = 0 or x = (0.3010/0.6990) --- x = 0 or x = 0.431 ================ Cheers, Stan H. --------------- a)0.431 b)2.322 c)0 and 0.431 d)0 and 2.322

Money_Word_Problems/700193: If at the end of 13 years, I have $836 in my account after investing it at 3.11% per year, how much money did I invest? 1 solutions Answer 431713 by stanbon(57213)   on 2013-01-09 17:23:49 (Show Source): You can put this solution on YOUR website! If at the end of 13 years, I have $836 in my account after investing it at 3.11% per year, how much money did I invest? -------- Simple interest problem: A(t) = P(1 + rt) 836 = P(1 + 0.0311*3) --- 836 = P(1.0933) Principal = 836/1.0933 = $764.66 ================================== Cheers, Stan H. ================