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Recent problems solved by 'stanbon'

stanbon answered: 57327 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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Surface-area/291344: if the area of a circular pond is 153.86 sq. yd. what is the circumference of the pond? 1 solutions Answer 210705 by stanbon(57400)   on 2010-04-12 18:25:54 (Show Source): You can put this solution on YOUR website! if the area of a circular pond is 153.86 sq. yd. what is the circumference of the pond? ------------------------- Area = (pi)r^2 = 153.86 sq. yd. r^2 = 153.86/pi r = sqrt(48.98) ----- Circumference = 2(pi)r C = 2(pi)sqrt(48.98) C = 43.97... Cheers, Stan H.

Linear-equations/291340: y+10x=-170 graph please 1 solutions Answer 210701 by stanbon(57400)   on 2010-04-12 18:18:48 (Show Source): You can put this solution on YOUR website! y+10x=-170 graph please ---- x-intercept = ? Let y = zero, and solve for "x": 10x = -170 x = -17 --------------------- y-intercept = ? Let x = zero, and solve for "y": y = -170 --------------------- Plot the two points (0,-170) and (-17,0) ============================= ============================= Cheers, Stan H.

Exponents/291336: how do i write 4.321 x neitive ten to the tenth power in standard notaion ? 1 solutions Answer 210695 by stanbon(57400)   on 2010-04-12 18:09:59 (Show Source): You can put this solution on YOUR website! how do i write 4.321 x neitive ten to the tenth power in standard notaion ? ----- 4.321 x (-10)^10 --- = 4.321 x 10^10 Move the decimal point 10 steps to the right: --- = 43,210,000,000 ========================== Cheers, Stan H. ==========================

Graphs/291335: what is the slope in 2y+4 = x+ 3 1 solutions Answer 210686 by stanbon(57400)   on 2010-04-12 18:00:20 (Show Source): You can put this solution on YOUR website! what is the slope in 2y+4 = x+ 3 ---------- 2y = x - 1 --- y = (1/2)x - (1/2) ----------------------- slope = 1/2 ========================== Cheers, Stan H.

Numbers_Word_Problems/291334: The square of a number equals thirty-one times that number. Find the number. 1 solutions Answer 210682 by stanbon(57400)   on 2010-04-12 17:56:28 (Show Source): You can put this solution on YOUR website! The square of a number equals thirty-one times that number. Find the number. ----------------- Equation: x^2 = 31x x^2-31x = 0 x(x-31) = 0 x = 0 or x = 31 -----------------------------

Probability-and-statistics/291207: What is the probability that 6 people in 10 will agree on 7 out of 10 random answers, where the answer can be either a "yes" or a "no"? 1 solutions Answer 210681 by stanbon(57400)   on 2010-04-12 17:53:52 (Show Source): You can put this solution on YOUR website! What is the probability that 6 people in 10 will agree on 7 out of 10 random answers, where the answer can be either a "yes" or a "no"? ---------------------------------------------------------- Binomial Problem with n = 10 ; p = 1/2 P(x = 6) = 10C6(1/2)^6*(1/2)^4 = 210(1/2)^10 = 0.2051 ===================== Cheers, Stan H.

Linear-equations/291309: Write the linear equation x = 1/3 y – 2/3 in standard form. 1 solutions Answer 210677 by stanbon(57400)   on 2010-04-12 17:33:44 (Show Source): You can put this solution on YOUR website! Write the linear equation x = 1/3 y – 2/3 in standard form. ----- Multiply thru by 3 to get: 3x = y - 2 3x - y = -2 (standard form) ============================ Cheers, Stan H. ============================

Probability-and-statistics/291273: Of the 400 students at a school, 35% have part-time jobs. Find the probability that two students selected at random have part-time jobs. Hello, I'm not sure what to do in this one. I was thinking maybe using a combination or permutation would work but I am just dumb founded. Thank you for your help. 1 solutions Answer 210674 by stanbon(57400)   on 2010-04-12 17:29:50 (Show Source): You can put this solution on YOUR website! Of the 400 students at a school, 35% have part-time jobs. Find the probability that two students selected at random have part-time jobs. ----------------------------- P(2 of 2 have part-time jobs) = (0.35)^2 = 0.1225 ---------------------- Cheers, Stan H. ----------------------

Exponents/291150: (5x^4+6y^6)^2 1 solutions Answer 210613 by stanbon(57400)   on 2010-04-12 12:30:29 (Show Source): You can put this solution on YOUR website! (5x^4+6y^6)^2 ------- (25x^8 + 2*5x^4*6y^6 + 36y^12) ------- = 25x^8 + 60x^4y^6 + 36y^12 =============================== Cheers, Stan H.

Functions/290961: Find the derivative of the function f(x)= 3x(4x+3)^5 y'=20(4x+3)^4 1 solutions Answer 210511 by stanbon(57400)   on 2010-04-11 21:19:28 (Show Source): You can put this solution on YOUR website! Find the derivative of the function f(x)= 3x(4x+3)^5 Form: f'(x) = gh' + hg' --- f'(x) = (3x)[(5(4x+3)^4*4)] + [(4x+3)^5*3] --- f'(x) = 60x(5x+3)^4 + 3(4x+3)^5 ------------------------------ Cheers, Stan H. ==============================

Linear_Equations_And_Systems_Word_Problems/290964: Is (-1,2), (1,2), (-2,4, (2,4) a linear equation. I put no since the domain does not equal one range number 1 solutions Answer 210509 by stanbon(57400)   on 2010-04-11 21:13:06 (Show Source): You can put this solution on YOUR website! Is (-1,2), (1,2), (-2,4), (2,4) a linear equation. ------- slope from 1st to 2nd point is (2-2)/(1--1) = 0/2 = 0 slope from 2nd to 3rd point is (4-2)/(-2-1) = 2/-3 = -2/3 --------------------- since the slopes are not the same the four points are not on a line. ======================== Cheers, Stan H.

Rate-of-work-word-problems/290965: Brett usually takes 50 minutes to groom the horses. After working 10 minutes, he was joined by Angela and they finished the grooming in 15 minutes. How long would it have taken Angela working alone? 1 solutions Answer 210506 by stanbon(57400)   on 2010-04-11 21:08:37 (Show Source): You can put this solution on YOUR website! Brett usually takes 50 minutes to groom the horses. Brett rate = 1/50 job/min -------------------------------- After working 10 minutes, he was joined by Angela and they finished the grooming in 15 minutes. --- Brett worked a total of 25 minutes at (1/50) job/min He completed 25(1/50) = 1/2 of the job. --- So Angela does the other half of the job in 15 minutes. ---- How long would it have taken Angela working alone? Angela could do the whole job in 30 minutes. ==================================================== Cheers, Stan H.

Equations/290963: Please solve {{4/5x = -14}} showing all work and steps Thank You 1 solutions Answer 210504 by stanbon(57400)   on 2010-04-11 21:01:26 (Show Source): You can put this solution on YOUR website! 4/5x = -14 --- Multiply both sides by (5/4) to get: (5/4)(4/5)x = (5/4)(-14) x = -70/4 x = -35/2 x = -17.5 ================= Cheers, Stan H.

Probability-and-statistics/290944: a machine that fills quart milk is set up to average 32.2 oz per carton, with a standard deviation of 1.2 oz. assuming the distribution is normal find the following: if five cartons are selected at random, what proportion will have less than 32oz of milk? 1 solutions Answer 210503 by stanbon(57400)   on 2010-04-11 20:58:50 (Show Source): You can put this solution on YOUR website! a machine that fills quart milk is set up to average 32.2 oz per carton, with a standard deviation of 1.2 oz. assuming the distribution is normal find the following: if five cartons are selected at random, what proportion will have less than 32oz of milk? ----- t(32) = (32-32.2)/(1.2/sqrt(5)) = -0.3726 ---------------------- P(x < 32) = P(t < -0.3726 when df = 4) = 0.3642 or 36.42% ======================================================== Cheers, Stan H.

Equations/290956: solve 6(4 - 5x)= 2 - 2(3 -x)show work step by step. 1 solutions Answer 210502 by stanbon(57400)   on 2010-04-11 20:48:23 (Show Source): You can put this solution on YOUR website! solve 6(4 - 5x)= 2 - 2(3 -x) --- 24 - 30x = 2 - 6 + 2x 24-30x = -4 + 2x 32x = 28 x = 7/8 ================= Cheers, Stan H. =================

Probability-and-statistics/289734: If you have 12 eggs, 3 of which are cracked, and you choose 5, what is the probability of 1) choosing all 3 cracked 2) choosing no cracked and 3) choosing 2 cracked. 1 solutions Answer 210500 by stanbon(57400)   on 2010-04-11 20:44:54 (Show Source): You can put this solution on YOUR website! Binomial Problem with: n = 5 and p(cracked) = 1/4 --- If you have 12 eggs, 3 of which are cracked, and you choose 5, what is the probability of 1) P(choosing all 3 cracked) = 5C3(1/4)^3(3/4)^2 = 0.08789 ------ 2) P(choosing no cracked) 5C0(1/4)^0*(3/4)^5 = 0.2373 ------------------------------- 3) P(choosing 2 cracked) = 5C2(1/4)^2(3/4)^3 = 0.2637 ======================================================= Cheers, Stan H.

Mixture_Word_Problems/290923: A candy mixture is created with 2 types of candy, one costing $4 per pound and the other $3.50 per pound. How much of each type is needed for a 5 pound box that costs $18? 1 solutions Answer 210493 by stanbon(57400)   on 2010-04-11 20:07:10 (Show Source): You can put this solution on YOUR website! A candy mixture is created with 2 types of candy, one costing $4 per pound and the other $3.50 per pound. How much of each type is needed for a 5 pound box that costs $18? ------------------ Equations: value + value = value 4x + 3.50(5-x) = 18 Multiply thru by 100 to get: 400x + 350*5 - 350x = 1800 50x = 50 x = 1 lb (amt. of $4.00 candy needed in the mixture) 5-x = 4 lb (amt. of $3.50 candy needed in the mixture) ====================== Cheers, Stan H.

Exponential-and-logarithmic-functions/290927: solve 8 log2.5x=12.5 1 solutions Answer 210491 by stanbon(57400)   on 2010-04-11 19:54:42 (Show Source): You can put this solution on YOUR website! solve 8 log2.5x=12.5 --- log(2.5x) = 12.5/8 = 1.5625 2.5x = 10^1.5625 x = 36.52 ================= Cheers, Stan H. =================

Linear_Equations_And_Systems_Word_Problems/290924: Hello all, I am struggling with the following problem. I know it is probably really easy and im just not understanding something, but I keep getting stuck on how to express the variable for calculating the amount of each coin and there $ value in each equation. Any help will be great. A jar contains 100 coins made up of 50 cent coins and 20 cent coins. How many coins are there if the total value of the coins is $38.00. Solve algebraically. a) Express this problem as a system of two equations. Define variables correctly. b) Solve system of equations simultaneously. Thanks, -Nick. 1 solutions Answer 210490 by stanbon(57400)   on 2010-04-11 19:50:15 (Show Source): You can put this solution on YOUR website! A jar contains 100 coins made up of 50 cent coins and 20 cent coins. How many coins are there if the total value of the coins is $38.00. Solve algebraically. a) Express this problem as a system of two equations. Define variables correctly. Quantity Eq:::: f + t = 100 Value Eq::::: 50f + 20t = 3800 cents --------- b) Solve system of equations simultaneously. Multiply thru the 1st Eq by 20: 20f + 20t = 20*100 50f + 20t = 3800 ----------------------- Subtract 1st from 2nd and solve for "f": 30f = 1800 f = 60 (# of first cent coins) --- Since f + t = 100, t = 40 (# of twenty cent coins) ==================================================== Cheers, Stan H. ====================================================

Quadratic_Equations/290925: what happens when you quadratic formula look like this. x^2=-x+4 1 solutions Answer 210489 by stanbon(57400)   on 2010-04-11 19:45:32 (Show Source): You can put this solution on YOUR website! what happens when your quadratic looks like this. x^2=-x+4 Rearrange: x^2 + x - 4 = 0 Use the quadratic formula: x = [-1 +- sqrt(1-4*-4)]/2 --- x = [-1+- sqrt(17)]/2 =========================== =========================== Cheers, Stan H.

Probability-and-statistics/290906: Dear Tutor, I have always had trouble with probability, and I am faced with the following question: Delta Airlines quotes a flight time of 2hrs and 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 120 to 140 minutes. a. What is the probability that the flight will be more than 10 minutes late? b. What is the expected flight time? If you could answer one, or both parts of this question I would greatly appreciate it!!! Thank you 1 solutions Answer 210488 by stanbon(57400)   on 2010-04-11 19:41:33 (Show Source): You can put this solution on YOUR website! Delta Airlines quotes a flight time of 2hrs and 5 minutes (125 minutes) for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 120 to 140 minutes. a. What is the probability that the flight will be more than 10 minutes late? --- At least 10 minutes late is a flight of at least 135 minutes If flight times range from 120 to 140 minutes, 6*sigma = 20 and sigma = 10/3 ------------ Using the airlines schedule predictions, find the probability flight time >= 135 min, Find z(135) = (135-125)/(10/3) = 10/(10/3) = 3 Then P(x>= 135) = P(z> 3) = 0.00135 ----------------------------------------- b. What is the expected flight time? Based on our observed times, expected flight time is the average flight time = (140+120)/2 = 130 minutes. ========================================== Cheers, Stan H.

Expressions-with-variables/290910: Simplify m^3 - 8 / m - 2 = 0 1 solutions Answer 210487 by stanbon(57400)   on 2010-04-11 19:19:30 (Show Source): You can put this solution on YOUR website! Simplify (m^3 - 8) / m - 2 = 0 ----- The numerator factors as (m-2)(mx^2+m+4) ----- Dividing by m-2 gives a quotient of m^2+m+4 ======== Cheers, Stan H.

Finance/290884: If a concentration of a solution was 0.15 moles/liter 7 minutes after an experiment began, and 0.06 moles/liter 25 minutes after the experiment began, what would a linear model look like for a concentration (y) vs. time (x) when predicting the concentration 28 minutes in and when the concentration will go to zero? 1 solutions Answer 210485 by stanbon(57400)   on 2010-04-11 18:55:03 (Show Source): You can put this solution on YOUR website! If a concentration of a solution was 0.15 moles/liter 7 minutes after an experiment began, and 0.06 moles/liter 25 minutes after the experiment began, what would a linear model look like for a concentration (y) vs. time (x) when predicting the concentration 28 minutes in and when the concentration will go to zero? -------------------- you have two points (7,0.15) and (25,0.6) ---- slope = (0.60-0.15)/(25-7) = 0.45/18 = 0.025 ---- Equation Form: concentration = slope*time + b You know slope and concentration = 0.6 when time = 25 Solve for "b: 0.6 = 0.025*25 + b b = -0.025 --------------------- Equation: c = 0.025x - 0.025 ===================================== Cheers, Stan H.

Rectangles/290881: Find algebraic expression. The perimeter of a rectanle, given that the length is x yards and the width is 10 yards shorter 1 solutions Answer 210460 by stanbon(57400)   on 2010-04-11 17:49:42 (Show Source): You can put this solution on YOUR website! Find algebraic expression. The perimeter of a rectanle, given that the length is x yards and the width is 10 yards shorter --------------- Form: P = 2(L + W) P = 2(x + x-10) p = 2(2x-10) p = 4x-20 ============= Cheers, Stan H.

Quadratic_Equations/290877: find an equation for the parabola with vertex (-2,5) and y-intercept 1 1 solutions Answer 210458 by stanbon(57400)   on 2010-04-11 17:46:56 (Show Source): You can put this solution on YOUR website! find an equation for the parabola with vertex (-2,5) and y-intercept 1 --- Form: y = a(x-h)^2 + k ----------------------- h = -2, k = 5 Goes thru (0,1) ---- Using the vertex y = a(x+2)^2 + 5 ---- Using the intercept: 1 = a(0+2)^2 + 5 1 = 4a + 5 4a = -4 a = -1 --------------- Equation: y = -(x+2)^2 + 5 ======================== Cheers, Stan H.

Numbers_Word_Problems/290873: Yuri has a total of 8 dimes and quarters. If the value of the coins is $1.55, how many quarters does he have? 1 solutions Answer 210455 by stanbon(57400)   on 2010-04-11 17:38:13 (Show Source): You can put this solution on YOUR website! Yuri has a total of 8 dimes and quarters. If the value of the coins is $1.55, how many quarters does he have? ----------------- Equations: Quantity: d + q = 8 Value Eq:10d + 25q = 155 cents -------------------- Multiply thru 1st by 10 --- 10d + 10q = 80 10d + 25q = 155 ---- Subtract 1st from 2nd and solve for "q": 15q = 75 q = 5 (# of quarters) ========================= Cheers, Stan H.

Quadratic_Equations/290866: determine the nature of the roots of the quadratic equation if the discriminant is 31 1 solutions Answer 210453 by stanbon(57400)   on 2010-04-11 17:30:38 (Show Source): You can put this solution on YOUR website! determine the nature of the roots of the quadratic equation if the discriminant is 31 -------------- Since the discrimant is greater than zero, there are two unequal Real Number roots. --- Cheers, Stan H.

Angles/290864: Angle L & angle M are complementary; Angle N & angle P are complementary. -If the measure of angle M=y-2, the measure of angle M=2x+3, the meaure of angle N=2x-y and the measure of angle P=x-1 then.. A.) find the values of x and y. B.) find the measure of angle L and the measure of angle M. C.) find the measure of angle N and the measure of angle P. 1 solutions Answer 210452 by stanbon(57400)   on 2010-04-11 17:27:51 (Show Source): You can put this solution on YOUR website! What is the measure of "L"? --------------------------- Cheers, Stan H.

Equations/290861: Can you help solve this literal expression. I dont undersant it. A = 1 + prt; for r 1 solutions Answer 210451 by stanbon(57400)   on 2010-04-11 17:23:41 (Show Source): You can put this solution on YOUR website! A = 1 + prt; for r --------------------- prt = A - 1 r = (A-1)/(pt) ==================== Cheers, Stan H.

Equations/290860: the width of a rectangle is a fixed 17cm what lengths will make the perimeter grater then 92cm 1 solutions Answer 210448 by stanbon(57400)   on 2010-04-11 17:19:19 (Show Source): You can put this solution on YOUR website! the width of a rectangle is a fixed 17cm what lengths will make the perimeter greater then 92cm -------------------- P = 2(W + L) Your Problem: 2(17 + L) > 92 17+L > 46 Length > 29 cm ==================== Cheers, Stan H.

Percentage-and-ratio-word-problems/290858: The sum of a number and its reciprocal is 10/3 . what is the number? Also need to know how to check it.Thank you a bunch! 1 solutions Answer 210447 by stanbon(57400)   on 2010-04-11 17:12:52 (Show Source): You can put this solution on YOUR website! The sum of a number and its reciprocal is 10/3 . what is the number? Also need to know how to check it.Thank you a bunch! --------------------------- Equation: x + 1/x = 10/3 --- Multiply thru by 3x to get: 3x^2 + 3 = 10x --- Rearrange: 3x^2 - 10x + 3 = 0 Factor: 3x^2 - 9x - x + 3 = 0 3x(x-3)-(x-3) = 0 (x-3)(3x-1) = 0 Positive solution: x = 1/3 --------- Checking: x + (1/x) = 10/3 (1/3) + 3 = 10/3 (1/3)+(9/3) = 10/3 10/3 = 10/3 ============= Cheers, stan H.