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Recent problems solved by 'stanbon'

stanbon answered: 57135 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

Linear-equations/642399: What is the answer and steps to solving this problem 1/15(2x+5)=x+2/9 1 solutions Answer 404097 by stanbon(57203)   on 2012-08-28 16:39:07 (Show Source): You can put this solution on YOUR website! 1/15(2x+5)= (x+2)/9 --------- Multiply both sides by 9*15 = 135 ----- 9(2x+5) = 15(x+2) ---------------- 18x + 45 = 15x + 30 3x = -15 x = -5 ----------------------- Cheers, Stan H. =======================

Linear-equations/642388: I have 3 questions dealing with linear equations, slopes, etc... that I can not figure out. Can someone show me the steps on how to solve these problems, please??? 1. Find the slope of y=-8x+4 ( I came up with -8, but not sure if that's correct) 2. Find the intercepts for the graph of the given equation x=-6y 3. Find an equation of the line containing the given pair of points (-2,-7) and (-9, -8) 1 solutions Answer 404092 by stanbon(57203)   on 2012-08-28 16:30:54 (Show Source): You can put this solution on YOUR website! 1. Find the slope of y=-8x+4 ( I came up with -8, but not sure if that's correct) ---- You are correct. ----------------------------------- 2. Find the intercepts for the graph of the given equation x=-6y x-intercept occurs when y = 0. x = -6*0 x = 0 So, x-intercept is (0,0) --- Y-intercept occurs when x = 0. y-intercept is (0,0) ===================================== 3. Find an equation of the line containing the given pair of points (-2,-7) and (-9, -8) --- slope = (-7--8)/(-2--9) = 1/7 --- Form: y = mx + b Solve for "b": -7 = (1/7)(-2) + b -7 = -2/7 + b b = -49/7+2/7 b = -47/7 ---- Equation: y = (1/7)x - (47/7) ======================== Cheers, Stan H.

Miscellaneous_Word_Problems/642381: i need to write a memo explaining how to keep the customers satisfaction and maintain a consistent number of pieces of our product per bag with no less then 18 pieces of candy and and no more then 22 pieces of candy. i have to explain it as if my math teacher does not know math. how do i do this? 1 solutions Answer 404083 by stanbon(57203)   on 2012-08-28 16:17:12 (Show Source): You can put this solution on YOUR website! Put 20 pieces in each bag. Cheers, Stan H.

test/642362: If m<6=50, what is m<11 1 solutions Answer 404082 by stanbon(57203)   on 2012-08-28 16:10:11 (Show Source): You can put this solution on YOUR website! If m<6=50, what is m<11 ----- You cannot have "less than" and "equal to". =================== Cheers, Stan H. ===================

Triangles/642338: Using the Pythagorean Theorem, find the missing side for these right triangles. If the answer is not a perfect square, leave it in radical form. Here's the problem: C = 5 B = 4 A = (blank space and has a radical sign over it) Thank's so much for your help!!! 1 solutions Answer 404062 by stanbon(57203)   on 2012-08-28 14:35:08 (Show Source): You can put this solution on YOUR website! Using the Pythagorean Theorem, find the missing side for these right triangles. If the answer is not a perfect square, leave it in radical form. Here's the problem: C = 5 B = 4 A = (blank space and has a radical sign over it) ------- A = sqrt[5^2-4^2] A = sqrt[9] ---- Cheers, Stan H.

Permutations/642257: If you have 9 ties, 8 pairs of pants and 6 pairs of shoes how many outfits can you make without wearing the same combination? 1 solutions Answer 404002 by stanbon(57203)   on 2012-08-28 09:49:14 (Show Source): You can put this solution on YOUR website! If you have 9 ties, 8 pairs of pants and 6 pairs of shoes how many outfits can you make without wearing the same combination? ------ Ans: 9*8*6 = 432 unique outfits --------- Cheers, Stan H. ============

Triangles/642251: Hello, can anyone help me with solving this? Two sides of a triangle have the same length. The third side measures 3m less than twice the common length. The perimeter of the triangle is 13m. What is the length of the two sides that have the same length? What is the length of the third side? 1 solutions Answer 404001 by stanbon(57203)   on 2012-08-28 09:45:49 (Show Source): You can put this solution on YOUR website! Two sides of a triangle have the same length. The third side measures 3m less than twice the common length. The perimeter of the triangle is 13m. ------ Let the length of the 2 equal sides be "x" meters: Length of 3rd side is 2x-3 meters Equation: x + x + 2x-3 = 13 4x = 16 x = 4 meters 2x-3 = 5 meters -------------------------------- What is the length of the two sides that have the same length?::::4 meters What is the length of the third side?:::: 5 meters ============================= Cheers, Stan H. =============================

Travel_Word_Problems/642232: Hannah traveled the 320 mile trip in 2 hours more than Anna. This was because Anna traveled twice as fast as Hannah. How fast did each travel and for how long? 1 solutions Answer 403994 by stanbon(57203)   on 2012-08-28 08:20:33 (Show Source): You can put this solution on YOUR website! Hannah traveled the 320 mile trip in 2 hours more than Anna. This was because Anna traveled twice as fast as Hannah. How fast did each travel and for how long? -------- Hannah DATA: distance = 320 miles ; time = x + 2 hrs ; rate = 320/(x+2) mph ---------------- Anna DATA: distance = 320 miles ; time = x hrs ; rate = 320/x mph ------------------ Equation: 320/x = 2[320/(x+2)] 1/x = 2/(x+2) 2x = x+2 x = 2 hrs ----- Hannah's rate: 320/(x+2) = 320/4 = 80 mph ----- Anna's rate: 320/x = 320/2 = 160 mph =========================================== Cheers, Stan H.

Probability-and-statistics/642229: 3 white chips, 7 blue chips, 16 green chips, 2 chips drawn from the box in succession what is the probability that one is blue and other is white? 1 solutions Answer 403993 by stanbon(57203)   on 2012-08-28 08:11:56 (Show Source): You can put this solution on YOUR website! 3 white chips, 7 blue chips, 16 green chips, 2 chips drawn from the box in succession what is the probability that one is blue and other is white? ---------------------- # of ways to succeed: 7*3 = 21 ---- # of possible outcomes:26C2 = (26*25)/(1*2) = 325 ----------- Ans: 21/325 = 0.0646 ======================== Cheers, Stan H. ========================

Travel_Word_Problems/642230: A jogger leaves home and runs at a constant speed of 4 miles per hour. Nine minutes later a bicyclist follows along the same route at a constant speed of 15 miles per hour. Find the bicyclists travel time needed to catch the jogger. 1 solutions Answer 403992 by stanbon(57203)   on 2012-08-28 08:07:32 (Show Source): You can put this solution on YOUR website! A jogger leaves home and runs at a constant speed of 4 miles per hour. Nine minutes later a bicyclist follows along the same route at a constant speed of 15 miles per hour. Find the bicyclists travel time needed to catch the jogger. ------------------- Jogger DATA: rate = 4 mph ; time = x hrs ; distance = 4x miles ------------------- Bicyclist DATA: rate = 15 mph ; time = x-(9/60) hrs ; distance = 15[x-(9/60)] miles ------- Equation: distance = distance 4x = 15x - (9/4) 11x = 9/4 x = 9/44 hrs. x = (9/44)60 = 12.27 minutes ----- Bicyclist's time: 12.27 min - 9 min = 3.27 minutes ============== Cheers, Stan H.

Equations/642224: Write an algebric expression for the quotient of a number and thirty-one 1 solutions Answer 403990 by stanbon(57203)   on 2012-08-28 07:56:55 (Show Source): You can put this solution on YOUR website! Write an algebric expression for the quotient of a number and thirty-one ---- Let the number be "x". Ans: The quotient is x/31 ================================ Cheers, Stan H.

Sequences-and-series/642225: The formula for the general term of the infinite sequence 12,17,22,27,32....is 5n-7 5n 5n+2 5n+7 ?? Thank you for the help 1 solutions Answer 403987 by stanbon(57203)   on 2012-08-28 07:45:29 (Show Source): You can put this solution on YOUR website! Ans: 5n+7

absolute-value/642088: |x|=15 1 solutions Answer 403959 by stanbon(57203)   on 2012-08-27 21:36:40 (Show Source): You can put this solution on YOUR website! |x|=15 ---- x = 15 or x = -15 ---------------------- Cheers, Stan H.

Linear-equations/642003: 5y/4-11/12=y/3 1 solutions Answer 403926 by stanbon(57203)   on 2012-08-27 19:46:52 (Show Source): You can put this solution on YOUR website! 5y/4-11/12=y/3 ---- Multiply thru by 12 to get: 15y - 11 = 4y --- 11y = 11 y = 1 =============== Cheers, Stan H.

Linear-equations/642005: What is the slope and y-intercept of 2x+4y=16 1 solutions Answer 403924 by stanbon(57203)   on 2012-08-27 19:44:37 (Show Source): You can put this solution on YOUR website! What is the slope and y-intercept of 2x+4y=16 --- Solve for "y": 4y = -2x+16 y = (-1/2)x + 4 --- slope = -1/2 intercept = 4 ========================== Cheers, Stan H.

Linear_Algebra/641970: Which values of x and y minimize N for the objective function N= 2x+y? constraints {x+y >=8, x+2y >=14, x>=0,y>=0} a) (0,0) b) (0,7) c) (2,6) d) (8,0) I came up with the answer c, but the book says a is the answer. How can a be the answer? 1 solutions Answer 403922 by stanbon(57203)   on 2012-08-27 19:42:18 (Show Source): You can put this solution on YOUR website! Which values of x and y minimize N for the objective function N= 2x+y? constraints {x+y >=8, x+2y >=14, x>=0,y>=0} a) (0,0) b) (0,7) c) (2,6) d) (8,0) I came up with the answer c, but the book says a is the answer. How can a be the answer? ---------------------- Ans: "a" is not the answer, if the constraints you posted are correct. (0,0) is not in the solution set for x + y >= 8 ==================================================== Cheers, Stan H.

Expressions-with-variables/641980: what is half the sum of 12 and the quotient of a number y 1 solutions Answer 403911 by stanbon(57203)   on 2012-08-27 19:21:19 (Show Source): You can put this solution on YOUR website! what is half the sum of 12 and the quotient of a number y ---- (1/2)(12 + (1/y)) ------ = 6 + (1/2y) ------------ Cheers, Stan H. ==============

Linear_Algebra/641974: n OVER 8 is less than or equal to negative n OVER 3 To you have to change them to a common denominator? If so, what do the variables become? 1 solutions Answer 403910 by stanbon(57203)   on 2012-08-27 19:18:39 (Show Source): You can put this solution on YOUR website! n OVER 8 is less than or equal to negative n OVER 3 --- n/8 <= -n/3 ---- Multiply both sides by 24 to get: 3n <= -8n --- Add 8n to both sides to get: 11n <= 0 --- n <= 0 ============= Cheers, Stan H. =============

Linear-systems/641863: I need help with a linear equation that has a division sign in it. It looks like this: (4x+2)/2 = 3x-5. I have forgotten the process to solve it so please help me. 1 solutions Answer 403860 by stanbon(57203)   on 2012-08-27 16:51:49 (Show Source): You can put this solution on YOUR website! (4x+2)/2 = 3x-5 ---- Multiply both sides by "2" to get: 4x+2 = 6x-10 2x = 12 x = 6 =========== Cheers, Stan H.

Linear-equations/641856: c=5/9(f-32) and explain please.. and also can u Determine how many degrees Fahrenheit 2 degrees Celsius is. 1 solutions Answer 403859 by stanbon(57203)   on 2012-08-27 16:49:47 (Show Source): You can put this solution on YOUR website! c=5/9(f-32) and explain please.. and also can u Determine how many degrees Fahrenheit 2 degrees Celsius is. -------------------------- The formula is used to convert Fahrenheit temperature readings to Celcius temperature readings. -------------------------------------- C(2) = (5/9)(2-32) = (5/9)(-30) = -16 2/3 degrees ======================= Cheers, Stan H. =======================

Average/641857: If the average (arithmetic mean) of 8 numbers is 14, what is the average of five of the other three numbers? A. 14 B. 17 C. 20 D. 30 E. 34 1 solutions Answer 403856 by stanbon(57203)   on 2012-08-27 16:41:04 (Show Source): You can put this solution on YOUR website! answered

Average/641858: If the average (arithmetic mean) of eight numbers is 20 and the average of five of these numbers is 14, what is the average of the other three numbers? A. 14 B. 17 C. 20 D. 30 E. 34 1 solutions Answer 403855 by stanbon(57203)   on 2012-08-27 16:39:57 (Show Source): You can put this solution on YOUR website! If the average (arithmetic mean) of eight numbers is 20 and the average of five of these numbers is 14, what is the average of the other three numbers? ---------------- Total points for the eight numbers: 8*20 = 160 --- Total points for the five numbers: 5*14 = 70 points --- Average for the other three numbers: (160-70)/3 = 30 ---------------------------- Cheers, Stan H. =================== A. 14 B. 17 C. 20 D. 30 E. 34

Number-Line/641847: Hi, Could you please help me to understand the below question? Point A corresponds to -3 and point B corresponds to 5. What number corresponds to the point that is three times as far from A as it is from B? Thanks! 1 solutions Answer 403854 by stanbon(57203)   on 2012-08-27 16:35:32 (Show Source): You can put this solution on YOUR website! Point A corresponds to -3 and point B corresponds to 5. What number corresponds to the point that is three times as far from A as it is from B? ---- # of units from A to B: 5--3 = 8 ---- The point you want is (3/4) of the distance from A to B: --- Ans: -3 + (3/4)8 = -3+6 = 3 ================================== Cheers, Stan H.

test/641809: I just dont undertand trig... Can u help 1 solutions Answer 403853 by stanbon(57203)   on 2012-08-27 16:26:23 (Show Source): You can put this solution on YOUR website! Please post a couple of your trig problems. Cheers, Stan H.

Mixture_Word_Problems/641852: Suppose a fuel mixture is 6% ethanol and 94% gasoline. How much ethanol (in gallons) must you add to one gallon of the fuel so that the new mixture is 10% ethanol? 1 solutions Answer 403852 by stanbon(57203)   on 2012-08-27 16:19:24 (Show Source): You can put this solution on YOUR website! Suppose a fuel mixture is 6% ethanol and 94% gasoline. How much ethanol (in gallons) must you add to one gallon of the fuel so that the new mixture is 10% ethanol? ----- Equation: ethanol + ethanol = ethanol --- 0.06*1 + x = 0.10(1+x) ----- Multiply thru by 100 to get: 6 + 100x = 10 + 10x 90x = 4 x = 4/90 = 0.044 gallons (Amt of pure ethanol needed) ================================= Cheers, Stan H.

Miscellaneous_Word_Problems/641848: In the Carco Auto Factory, robots assemble cars. If 3 robots assemble 17 cars in 10 minutes, how many cars can 14 robots assemble in 45 minutes if all robots work at the same rate all the time? 1 solutions Answer 403849 by stanbon(57203)   on 2012-08-27 16:12:53 (Show Source): You can put this solution on YOUR website! In the Carco Auto Factory, robots assemble cars. If 3 robots assemble 17 cars in 10 minutes, how many cars can 14 robots assemble in 45 minutes if all robots work at the same rate all the time? ---------------------- # of cars is directly related to # of robots and directly to amt. of time. ---------------------- c = k*r*t -------- Solve for "k" using "3 robots assemble 17 cars in 10 minutes" 17 = k*3*10 k = 17/30 ---- Equation: c = (17/30)r*t ----- How many cars can 14 robots assemble in 45 minutes if all robots work at the same rate all the time? -------- c = (17/30)*14*45 # of cars = 357 ================== Cheers, Stan H.

Linear_Algebra/641843: Here is the problem I am having trouble with. x/(x^2-1) - (x+3)/(x^2-x) = -3/(x^2+x) 1 solutions Answer 403840 by stanbon(57203)   on 2012-08-27 15:50:19 (Show Source): You can put this solution on YOUR website! x/(x^2-1) - (x+3)/(x^2-x) = -3/(x^2+x) ----- Multiply thru by x(x-1)(x+1) to get: x^2 - (x+3)(x+1) = -3(x-1) ----- x^2 - [x^2+4x+3] = -3x+3 ----- x^2 - x^2 -4x - 3 = -3x+3 ---- x = -6 -------------- Cheers, Stan H.

Trigonometry-basics/641838: use the law of sines to solve triangle abc when a=1.43, b=4.21, & A=30.4. If no solution exists, write none. 1 solutions Answer 403838 by stanbon(57203)   on 2012-08-27 15:45:34 (Show Source): You can put this solution on YOUR website! use the law of sines to solve triangle abc when a=1.43, b=4.21, & A=30.4. If no solution exists, write none. ---- Sin(B)/4.21 = sin(30.4)/1.43 ------ sin(B) = [4.21/1.43]*sin(30.4) = 1.4598 --- But no angle has a sin that is greater than 1. --- Ans: No solution ===================== Cheers, Stan H.

Trigonometry-basics/641834: I need to find the exact value of this! sec^2 (pi/4) - 6 = How do I do this? 1 solutions Answer 403836 by stanbon(57203)   on 2012-08-27 15:33:16 (Show Source): You can put this solution on YOUR website! find the exact value of this! sec^2 (pi/4) - 6 = ------- Since sec(pi/4) = 2/sqrt(2), sec^2(pi/4) = 4/2 = 2 ---- Your Problem: = 2-6 = -4 ======================= Cheers, Stan H. ==================

Trigonometry-basics/641828: I need help adding sec and csc! The exact value of the expression is needed. sec (pi/4) + 8 csc (pi/6) = 1 solutions Answer 403834 by stanbon(57203)   on 2012-08-27 15:28:01 (Show Source): You can put this solution on YOUR website! sec (pi/4) + 8 csc (pi/6) = ? ----------------- Since cos(pi/4) = sqrt(2)/2, sec(pi/4) = 2/sqrt(2) ------ Since sec(pi/6) = 1/2, csc(pi/6) = 2 ---- Your problem: = 2/sqrt(2) + 8(2) ------ = (sqrt(2))/2 + 16 ------ = (32+sqrt(2)/2 ================================= Cheers, Stan H.

Trigonometry-basics/641829: if csc(theta)=13/5 and theta is in the second quadrant, what is sec(theta)? I have no clue how to do this, can you please help? Thank you very much! 1 solutions Answer 403831 by stanbon(57203)   on 2012-08-27 15:20:13 (Show Source): You can put this solution on YOUR website! if csc(theta)=13/5 and theta is in the second quadrant, what is sec(theta)? ------ csc(theta) = r/y, so r = 13 and y = 5 --- Solve for "x": x = sqrt[r^2-y^2] = sqrt(13^2-5^2] = sqrt[169-25] = sqrt(144) = 12 --- But x is negative in the sesond quadrant, so x = -12 ----- Ans: sec(theta) = r/x = 13/(-12) = -13/12 ====================================== Cheers, Stan H.