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Recent problems solved by 'stanbon'

stanbon answered: 57259 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, >>Next

Pythagorean-theorem/743311: Give an exact answer and, where appropriate, an approximation to three decimal places. A right triangle's hypotenuse is 8m and one leg is 4m. Find the length of the other leg. 1 solutions Answer 452827 by stanbon(57332)   on 2013-04-29 21:39:32 (Show Source): You can put this solution on YOUR website! Give an exact answer and, where appropriate, an approximation to three decimal places. A right triangle's hypotenuse is 8m and one leg is 4m. Find the length of the other leg. ---- hypo^2 = leg^2 + leg^2 ------------ (8m)^2 = [4sqrt(3)m]^2 + leg^2 -------- 64m^2 = 16*3*m^2 + leg^2 ------- 16m^2 = leg^2 leg = 4m ================== Cheers, Stan H.

Rational-functions/743235: Ms. Mendez is sorting her photographs. She notes that 12 of the photos are black and white and that 40% of the photos are color. How many photos does she have? 1 solutions Answer 452811 by stanbon(57332)   on 2013-04-29 18:57:20 (Show Source): You can put this solution on YOUR website! Ms. Mendez is sorting her photographs. She notes that 12 of the photos are black and white and that 40% of the photos are color. How many photos does she have? --------- 60% of the photos must be black and white. --- Let x be the total # of photos. 0.60x = 12 x = 12/0.60 x = 20 ----- Cheers, Stan H. =================

Polynomials-and-rational-expressions/743228: How do I factor b to the third power plus 49b completely. I have broke down into prime factors giving me b*b*b+7*7*b. This gives me b squared plus 49. Please advise if I am doing this polynomial correctly. 1 solutions Answer 452809 by stanbon(57332)   on 2013-04-29 18:51:54 (Show Source): You can put this solution on YOUR website! correct Cheers, Stan H.

Mixture_Word_Problems/743226: An herbalist has 40 oz of herbs costing $3 per ounce. How many ounces of herbs costing $2 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2.50 per ounce? 1 solutions Answer 452807 by stanbon(57332)   on 2013-04-29 18:44:03 (Show Source): You can put this solution on YOUR website! An herbalist has 40 oz of herbs costing $3 per ounce. How many ounces of herbs costing $2 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2.50 per ounce? ----------------------------------- Equation: value + value = value 3*40 + 2x = 2.5*40 120 + 2x = 100 2x = 20 x = 10 oz (# of ounces of $2 herbs needed) ============================================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/743227: Elimination/solving linear equations One airplane costs four times as much as a certain car. Two such planes cost 6000 more than six of the cars. Find the cost of each 1 solutions Answer 452806 by stanbon(57332)   on 2013-04-29 18:36:44 (Show Source): You can put this solution on YOUR website! One airplane costs four times as much as a certain car. Two such planes cost 6000 more than six of the cars. Find the cost of each ------------ Equations: a = 4b 2a = 6b + 6000 --------------------- a = 4b a = 3b + 3000 --- 4b = 3b + 3000 b = $3000 (cost of one of the cars) a = 4b = $12,000 (cost of one of the airplanes) ============================ Cheers, Stan H. ============================

Money_Word_Problems/743222: a girl traveled 1350 mi by jet then an additional 135 mi by helicopter. the rate of the jetis five times the rate of the helicopter. The entire trip took 4.5 hours.what is the rate of the jet. How to solve. 1 solutions Answer 452805 by stanbon(57332)   on 2013-04-29 18:32:03 (Show Source): You can put this solution on YOUR website! a girl traveled 1350 mi by jet then an additional 135 mi by helicopter. the rate of the jet is five times the rate of the helicopter. The entire trip took 4.5 hours.what is the rate of the jet. --------------------------------------------- Let the rate of the helicopter be x mph Then the rate of the jet is 5x mph ------------------------------------- time for the jet = 1350/5x = 270/x hrs time for the helicopter = 135/x hrs -------- Equation: time + time = 4.5 hrs (270/x) + (135/x) = 4.5 ----- (270+135)/x = 4.5 x = 405/4.5 x = 90 mph (speed of the helicopter) 5x = 450 mph (speed of the jet) =================================== Cheers, Stan H.

Travel_Word_Problems/743218: Teri drove an average of 52 miles per hour on a 5-hour trip. During the first 3 hours, she drove 60 miles per hour. What was her average speed for the last 2 hours of the trip? 1 solutions Answer 452804 by stanbon(57332)   on 2013-04-29 18:19:26 (Show Source): You can put this solution on YOUR website! Teri drove an average of 52 miles per hour on a 5-hour trip. During the first 3 hours, she drove 60 miles per hour. What was her average speed for the last 2 hours of the trip? -------------------- Total distance: 5*52 = 260 miles --- 1st 3 hrs: 3*60 = 180 miles ---- Last 2 hrs: (260-180)/2 = 40 mph ================================= cheers, Stan H. ========================

Polynomials-and-rational-expressions/743219: Write 3 different polynomials whose sum is 5m^4+6m 1 solutions Answer 452802 by stanbon(57332)   on 2013-04-29 18:05:39 (Show Source): You can put this solution on YOUR website! Write 3 different polynomials whose sum is 5m^4+6m ------- (3m^4+2m)+(2m^4+4m) ====================== Cheers, Stan H. ======================

Numeric_Fractions/743217: 8-4/5f>-4-2f 1 solutions Answer 452801 by stanbon(57332)   on 2013-04-29 18:02:39 (Show Source): You can put this solution on YOUR website! 8-4/5f > -4-2f --- Comment: You don't have to fool with fractions. ------ Multiply thru by 5 to get rid of the fraction: 40 - 4f > -20 -10f ----- 6f > -60 ----- f > -10 ===================== Cheers, Stan H.

Probability-and-statistics/743034: What is the probability of getting at least 70 shoppers in our sample of 100 preferring Brand A if the true proportion of the population who prefers Brand A is 60%? Im not necessarily interested in the answer although it would be nice so I can check that the explanation is legit. Im just wondering how to do this type of question. 1 solutions Answer 452743 by stanbon(57332)   on 2013-04-29 10:06:50 (Show Source): You can put this solution on YOUR website! What is the probability of getting at least 70 shoppers in our sample of 100 preferring Brand A if the true proportion of the population who prefers Brand A is 60%? -------- p = 0.6 std = sqrt[pq/n] = sqrt[0.6*0.4/100] = sqrt(0.24)/10 = 0.049 ---- z(0.7) = (0.7-0.6)/0.049 = 2.041 ---- P(x >= 0.7) = P(z > 2.041) = normalcdf(2.041,100) = 0.0206 ================== Cheers, Stan H.

Rational-functions/743029: find all the numbers for which the rational expression is undefined -25 ___ 13z 1 solutions Answer 452741 by stanbon(57332)   on 2013-04-29 09:56:36 (Show Source): You can put this solution on YOUR website! find all the numbers for which the rational expression is undefined -25/ 13z is undefined if 13z = 0 13z = 0 when z = 0 ===================== Cheers, Stan H. ================

Parallelograms/743030: Are you a homosexual? 1 solutions Answer 452740 by stanbon(57332)   on 2013-04-29 09:54:31 (Show Source): You can put this solution on YOUR website!

Exponents/743031: Simplify these and do not leave any negatives. These two are similar. I think I have the answers but I would like to double check. a. 5^1/2 b. 5^-(1/2) 1 solutions Answer 452739 by stanbon(57332)   on 2013-04-29 09:53:43 (Show Source): You can put this solution on YOUR website! Simplify these and do not leave any negatives. These two are similar. I think I have the answers but I would like to double check. a. 5^1/2 = sqrt(5) ------ b. 5^-(1/2) = 1/sqrt(5) = 5/sqrt(5) ======================================= Cheers, Stan H. =================

test/743023: 8x²+7x=-2 Solve quadtic formula 1 solutions Answer 452738 by stanbon(57332)   on 2013-04-29 09:18:41 (Show Source): You can put this solution on YOUR website! 8x²+7x=-2 ----------- 8x^2 + 7x +2 = 0 ---- x = [-7 +- sqrt(49-4*8*2)]/16 ---- x = [-7 +- sqrt(-15)]/16 ============== cheers, Stan H. -----

test/743024: (2x-1)(x+1)=4 Solve quadtic formula 1 solutions Answer 452737 by stanbon(57332)   on 2013-04-29 09:15:08 (Show Source): You can put this solution on YOUR website! (2x-1)(x+1)=4 2x^2 + 2x -x -1 = 4 ----- 2x^2 +x -5 = 0 ----- x = [-1 +- sqrt(1-4*2*-5)]/4 ------ x = [-1 +- sqrt(41)]/4 =========================== Cheers, Stan H. ==============

Polynomials-and-rational-expressions/743020: I need help solving this question The perimeter of the quandrilateral is 43 centimeters. find the length of each side x+7, x2-3x, 3x-2, x+3 1 solutions Answer 452736 by stanbon(57332)   on 2013-04-29 09:12:43 (Show Source): You can put this solution on YOUR website! I need help solving this question The perimeter of the quandrilateral is 43 centimeters. find the length of each side x+7, x2-3x, 3x-2, x+3 --------------------- x+7 + x^2-3x + 3x-2 + x+3 = 43 ------- x^2 +2x +8 = 43 x^2 + 2x - 35 = 0 ---- Factor: (x+7)(x-5) = 0 ---- Usable answer: x = 5 ---- Sides: x+7 = 12 x^2-3x = 10 3x-2 = 13 x+3 = 8 ================== Cheers, Stan H. ==================

Equations/743021: 1.|7x-1|=15 2.5(x-1)+4=2(x+3)-1 Help me for my homework I don't know how to solve this ecuatios. 1 solutions Answer 452732 by stanbon(57332)   on 2013-04-29 09:05:06 (Show Source): You can put this solution on YOUR website! 1. |7x-1|=15 7x-1 = 15 or 7x-1 = -15 7x = 16 or 7x = -14 x = 16/7 or x = -2 =============================== 2. 5(x-1)+4=2(x+3)-1 5x-5+4 = 2x+6-1 5x-1 = 2x+5 3x = 6 x = 2 ============= Cheers, Stan H. =============

Sequences-and-series/743009: List the first four terms of the sequence defined by an =(n + 1)!/2n for for n is greater than or equal to 1. 1 solutions Answer 452730 by stanbon(57332)   on 2013-04-29 08:24:47 (Show Source): You can put this solution on YOUR website! List the first four terms of the sequence defined by an =(n + 1)!/2n for for n is greater than or equal to 1. ----- a(1) = (1+1)!/(2*1) = 2/2 = 1 a(2) = (2+1)!/(2*2) = 6/4 = 3/2 a(3) = (3+1)!/(2*3) = 24/6 = 4 a(4) = (4+1)!/(2*4) = 120/8 = 15 ============================ Cheers, Stan H. ====================

Linear-equations/743006: Hi! I have a question that asks me to find the equation of a line with gradients and intercepts on the y axis. I am given points such as -2/7, 6/7. With those two points I understand the answer is 7y+6-2x. But I can't get my head round the answer to this one following (and my exams are sooo soon!): Can you help me to understand -4/5, 2 and why this gives the answer 5y+4x=10? Thanks ever so much! ~Chris 1 solutions Answer 452729 by stanbon(57332)   on 2013-04-29 08:20:35 (Show Source): You can put this solution on YOUR website! I have a question that asks me to find the equation of a line with gradients and intercepts on the y axis. I am given points such as -2/7, 6/7. slope = -2/7 ; y-intercept = 6/7 y = (-2/7)x + (6/7) 7y = -2x + 6 7y = With that information I understand the answer is 7y = 6-2x. ------------------------ But I can't get my head round the answer to this one following (and my exams are sooo soon!): Can you help me to understand -4/5, 2 and why this gives the answer 5y+4x=10? ------------------ slope = -4/5 y-intercept = 2 -------------------------- y = (-4/5)x + 2 5y = -4x + 10 5y + 4x = 10 =================== Cheers, Stan H.

Permutations/743005: Six people are playing five rounds of golf in groups of three. How can I ensure the other players at least twice? Thanks in advance 1 solutions Answer 452728 by stanbon(57332)   on 2013-04-29 08:05:37 (Show Source): You can put this solution on YOUR website! Please read your post and see if it makes any sense to you. Cheers, Stan H.

Trigonometry-basics/742970: find an interval for theta for which the graph is traced only once r=2sin(3theta/2) a-0<=theta<=pie/3 b-0<=theta<=pie c-0<=theta<=4pie d-0<=theta<=4pie/3 e- -2pie<=theta<=2pie 1 solutions Answer 452727 by stanbon(57332)   on 2013-04-29 08:03:51 (Show Source): You can put this solution on YOUR website! find an interval for theta for which the graph is traced only once r=2sin(3theta/2) = 2sin((3/2)theta) Form: r = asin(bx) + c ----- That would be one period. Period = (2pi/b) = (2pi/(3/2)) = (4/3)pi ---------------------------------- Answer: "d" ---------------- Cheers, Stan H. ================== a-0<=theta<=pie/3 b-0<=theta<=pie c-0<=theta<=4pie d-0<=theta<=4pie/3 e- -2pie<=theta<=2pie

Travel_Word_Problems/742976: can you please help me with performing the operations and giving all answers in a+bi form. (2+sqrt(-128)(3-sqrt-(-98)) 1 solutions Answer 452725 by stanbon(57332)   on 2013-04-29 07:55:44 (Show Source): You can put this solution on YOUR website! give all answers in a+bi form. (2+sqrt(-128)(3-sqrt(-98)) ----- Using FOIL: = 6 - 2sqrt(-98) + 3sqrt(-128)- sqrt(128*98) ====== = 6 -14sqrt(-2) + 24sqrt(-2) - 112 ---- = -106 +10sqrt(2)i ====================== cheers, Stan H. =======================

Money_Word_Problems/743001: If I invested $2000.00 at the interest rate of 15%, compounded daily, for 52 weeks. How long would it take to reach $8000.00? 1 solutions Answer 452723 by stanbon(57332)   on 2013-04-29 07:47:38 (Show Source): You can put this solution on YOUR website! If I invested $2000.00 at the interest rate of 15%, compounded daily, for 52 weeks. How long would it take to reach $8000.00? ------- A(t) = P(1+(r/n))^(nt) ---- 8000 = 2000(1+0.15/365)^(365t) ---- 4 = (1.0004110)^(365t) ---- (365t) = log(4)/log(1.0004110) --- t = 9.24 years ================ Cheers, Stan H. ================

Probability-and-statistics/743003: Given a discrete probability distribution, how do I find P(x = 7 or x = 9)? I don't know how to handle the "OR". Thanks! 1 solutions Answer 452719 by stanbon(57332)   on 2013-04-29 07:35:26 (Show Source): You can put this solution on YOUR website! Given a discrete probability distribution, how do I find P(x = 7 or x = 9)? I don't know how to handle the "OR". Thanks! ---- "OR" requires that you add the P(x=7) to P(x=9). Cheers, Stan H.

Money_Word_Problems/743002: How long does a $4000 investment take to earn $720 interest if the interest rate is 6% per year? 1 solutions Answer 452717 by stanbon(57332)   on 2013-04-29 07:25:19 (Show Source): You can put this solution on YOUR website! How long does a $4000 investment take to earn $720 interest if the interest rate is 6% per year? ------ A(t) = P(1+rt) 4720 = 4000(1+0.06t) ----- 1.18 = 1 + 0.06t --- 0.06t = 0.18 t = 3 years ================= Cheers, Stan H.

Inequalities/742995: Solve the inequality. -x divided by 7 + 4 >= 3x 1 solutions Answer 452716 by stanbon(57332)   on 2013-04-29 07:22:15 (Show Source): You can put this solution on YOUR website! Solve the inequality. -x divided by 7 + 4 >= 3x ------ -x/7 + 4 >= 3x ---- Add (x/7) to both sides to get: ------ (3 1/7)x <= 4 --- (22/7)x <= 4 x <= 4(7/22) x <= 14/11 ================ Cheers, Stan H.

Numbers_Word_Problems/743000: The sum of two positive integers is 1,287. If the larger number is 9 1/2 more than 2 1/2 times the smaller number, what are the two numbers? Thankyou! 1 solutions Answer 452715 by stanbon(57332)   on 2013-04-29 07:16:57 (Show Source): You can put this solution on YOUR website! The sum of two positive integers is 1,287. If the larger number is 9 1/2 more than 2 1/2 times the smaller number, what are the two numbers? ------ Equations: a + b = 1287 a = (5/2)b + (19/2) ----- Substitute for "a" and solve for "b": (5/2)b + (19/2) + b = 1287 -------------------------------- 5b + 19 + 2b = 2574 7b = 2555 b = 365 ---- Solve for "a": a + 365 = 1287 a = 922 -------------------- Cheers, Stan H. ====================

Word_Problems_With_Coins/742999: Any help would be appreciated, thankyou! Brian has a total of 241 dimes and nickels. If he has $15.65 total in dimes and nickles, then how many nickels does he have? 1 solutions Answer 452714 by stanbon(57332)   on 2013-04-29 07:11:59 (Show Source): You can put this solution on YOUR website! Brian has a total of 241 dimes and nickels. If he has $15.65 total in dimes and nickles, then how many nickels does he have? ----- Quantity Equation: n + d = 241 Value Equation::: 5n +10d = 1565 cents --------- Modify: n + d = 241 n +2d = 313 ------------------ Substract and solve for "d": d = 72 (# of dimes) ----- Solve for "n": n + d = 241 n = 241-72 = 169 (# of nickels) ================================== Cheers, Stan H. ===============

Probability-and-statistics/742850: how many teams of three students can you make from a class of 27? 1 solutions Answer 452713 by stanbon(57332)   on 2013-04-29 07:07:54 (Show Source): You can put this solution on YOUR website! how many teams of three students can you make from a class of 27? ------------------------- Ans: 27C3 = (27*26*25)/(1*2*3) = 2925 ------------- Cheers, Stan H. =============

Probability-and-statistics/742934: the stretch in a loaded spring varies directly as the load it supports. A load of 15 kg stretches a certain spring 3.6 cm What load would stretch the spring 6 cm? 1 solutions Answer 452711 by stanbon(57332)   on 2013-04-29 07:03:23 (Show Source): You can put this solution on YOUR website! the stretch in a loaded spring varies directly as the load it supports. A load of 15 kg stretches a certain spring 3.6 cm ----- s = k*L Solve for "k": 3.6 = k*15 k = 0.24 -------------------- What load would stretch the spring 6 cm? s = (0.24)*L 6 = 0.24*L L = 25 kg =============== Cheers, Stan H. ===============

Probability-and-statistics/742997: It has been found that 7 per cent of the tools manufactured by a factory are defective. What is the probability that in a shipment of 625 such tools (a) 8 per cent or more, and (b) 7 per cent or less will be defective 1 solutions Answer 452709 by stanbon(57332)   on 2013-04-29 06:53:26 (Show Source): You can put this solution on YOUR website! It has been found that 7 per cent of the tools manufactured by a factory are defective. What is the probability that in a shipment of 625 such tools (a) 8 per cent or more 8% of 625 = 50 Binomial Problem with n = 625 and p(defective) = 0.08 P(50<= x <=625) = 1 - binomcdf(625,0.07,49) = 0.1824 ------------------------------ (b) 7 per cent or less will be defective 7% of 625 = 44 P(0<= x <=44) = binomcdf(625,0.07,44) = 0.5556 ============================== Cheers, Stan H.