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Recent problems solved by 'stanbon'

stanbon answered: 57158 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

Linear-systems/391771: Linear and non-linear Inequalities For what values of x does the expression represent a real number? Please solve this inequality drawing a number line and showing the interval notations. 1 solutions Answer 277942 by stanbon(57226)   on 2011-01-07 13:40:41 (Show Source): You can put this solution on YOUR website! sqrt(( x )/(2-x)(5+x)) ---- The radicand must be positive. Solve: (( x )/(2-x)(5+x))> 0 --- Draw a number line and plot -5,0,2 --- Test a value from each of the resulting intervals in the inequality: If x = -10 you get -/[+*-]>0; true so solutions in (-inf,-5) ----- If x = -2 you get -/[+*+]>0; false ----- If x = 1 you get +/[+*+]>0; true so solutions in (0,2) ----- If x = 5 you get +/[-*+]>0; false ---------------------------------------- Conclusion: (-inf,-5)U(0,2) =================================== Cheers, Stan H.

expressions/391739: logbx + logb(x+2)-logb8 assume that x, y amd x are positive numbers. Use the properties of logarithms to write each expression as the logarithm of one quantity 1 solutions Answer 277921 by stanbon(57226)   on 2011-01-07 10:44:30 (Show Source): You can put this solution on YOUR website! logbx + logb(x+2)-logb8 --- = logb[x(x+2)/8] ---- = logb[(x^2+2x)/8] ====================== Cheers, Stan H.

logarithm/391736: log base 5 of sqrt 125 - log base 2 of sqrt 2 1 solutions Answer 277920 by stanbon(57226)   on 2011-01-07 10:42:42 (Show Source): You can put this solution on YOUR website! log base 5 of sqrt 125 - log base 2 of sqrt 2 --- log5(125^(1/2)) - log2(2^(1/2)) ---------------------- = (1/2)log5(125) - (1/2)log2(2) --- = (1/2)3 - (1/2)1 --- = (1/2)(3-1) = 1 ================ Cheers, Stan H.

Complex_Numbers/391737: Find ∫(x^5+1)dx Thank you so much for all of your help!!!!! God Bless!!!!!!! 1 solutions Answer 277919 by stanbon(57226)   on 2011-01-07 10:39:40 (Show Source): You can put this solution on YOUR website! Find ∫(x^5+1)dx -------- = (1/6)x^6 + x + C ======================= Cheers, Stan H.

Functions/391726: I have two questions on two math problems. 1. f(x)=x+5 2. f(4)=8x+2 If you could help me solve these that would really help me out. Thank you. 1 solutions Answer 277917 by stanbon(57226)   on 2011-01-07 10:37:26 (Show Source): You can put this solution on YOUR website! I have two questions on two math problems. --- You cannot "solve" them; You can graph them. --- 1. f(x)=x+5 Let x = 0, Then y = 5 giving you point (0,5) Let x = 2, then y = 7 giving you point (2,7) Plot those points and draw a line thru them to get: --------------------------------------------- 2. f(4)=8x+2 Let x = 0, then y = 2 giving you point (0,2) Let x = 2, then y = 18 giving you point (2,18) Plot the points and draw a line thru them to get: -------------- Cheers, Stan H. ==========

Proportions/391734: if the fare of 12 quintal luggage for a distance of 18km is 20 rupees,how much fare be aluggage of 8 quintal for a distance of 20km? 1 solutions Answer 277914 by stanbon(57226)   on 2011-01-07 10:31:58 (Show Source): You can put this solution on YOUR website! if the fare of 12 quintal luggage for a distance of 18km is 20 rupees,how much fare be aluggage of 8 quintal for a distance of 20km? ----------- Fare, number of luggage and distance are all directly related. f = k(nd) --- Solve for "k" using "the fare of 12 quintal luggage for a distance of 18km is 20 rupees" 20 = k(12*18) k = 0.09259 --- Equation: f = 0.09259nd ----------- Solve:"how much fare be aluggage of 8 quintal for a distance of 20km? f = 0.09259*8*20 f = 14.82 rupee ==================== Cheers, Stan H.

Quadratic_Equations/391733: Ok so i've done this problem at least 20 times and i don't know what i am doing wrong! The work seems to be right, but every time that i have done it, it does not check out properly. Please help! Question: If the square of a positive number is decreased by twice the number the result is 15. Find the number. Thank you! 1 solutions Answer 277912 by stanbon(57226)   on 2011-01-07 10:25:58 (Show Source): You can put this solution on YOUR website! If the square of a positive number is decreased by twice the number the result is 15. Find the number. -------------- Equation: x^2-2x = 15 --- x^2-2x-15 = 0 Factor: (x-5)(x+3) = 0 --- Positive solution: x = 5 ==================== Check: 5^2-2*5 = 15 25-10 = 15 15 = 15 ==================== Cheers, Stan H. ---

Average/391587: A white-tailed deer is running from a black bear at 20 mph. It is 1/3 mile in front of the bear. The bear is running at 30 mph. How long will it take the bear to catch the deer? Assume both continue running at the same pace. 1 solutions Answer 277805 by stanbon(57226)   on 2011-01-06 20:22:36 (Show Source): You can put this solution on YOUR website! A white-tailed deer is running from a black bear at 20 mph. It is 1/3 mile in front of the bear. The bear is running at 30 mph. How long will it take the bear to catch the deer? Assume both continue running at the same pace. -------------- Deer Data: rate = 20 mph ; time = x hrs. ; distance = 20x miles ----- Bear Data: rate = 30 mph ; time = x hrs. ; distance = 30x miles ---- Equation: bear distance - deer distance = 1/3 mile ---- 30x - 20x = 1/3 10x = 1/3 x = 1/30 hr. x = (1/30)(60 minutes) = 2 minutes ========================= Cheers, Stan H.

Polynomials-and-rational-expressions/391578: 18z^2+36z+16, I am stumped in factoring this 1 solutions Answer 277802 by stanbon(57226)   on 2011-01-06 20:01:20 (Show Source): You can put this solution on YOUR website! 18z^2+36z+16 ----------------- = 2(9z^2+18z+8) --- = 2(3z+4)(3z+2) ==================== Cheers, Stan H.

Inequalities/391581: How would you solve an inequalitie problem, with perentheses? For Example: K+(-5)<-12 1 solutions Answer 277801 by stanbon(57226)   on 2011-01-06 19:52:03 (Show Source): You can put this solution on YOUR website! K+(-5)<-12 --- Add 5 to each side of the inequality to get: K < -7 ================= Cheers, Stan H.

Probability-and-statistics/391579: I'm sorry if this is the wrong place to put this so if it's wrong just please redirect. Please help with this The shoe sizes of women in a survey are distributed normally about the mean. Suppose the survey included data on 200 women. About how many women would you expect to wear sizes 5-7? 1 solutions Answer 277800 by stanbon(57226)   on 2011-01-06 19:50:32 (Show Source): You can put this solution on YOUR website! The shoe sizes of women in a survey are distributed normally about the mean. Suppose the survey included data on 200 women. About how many women would you expect to wear sizes 5-7? ---------------------------- Looking at your bar chart, it looks like the mean size is 7 and the range of sizes is 4 to 10 ---- The range for a normal distribution is commonly considered to be 6 sigma. So 6 sigma = 10-4 = 6 Therefore the standard deviation is 1. --- Find the z-values of 5 and 7. z(5) = (5-7)/1 = -2 z(7) = (7-7)/1 = 0 --- P(5< x <7) = P(-2< z <0) = 0.4773 ---- Question: About how many women would you expect to wear sizes 5-7? Ans: 0.4773*200 = 95.449 Rounding up you get "about 96". ---------------------------- Cheers, Stan H.

Travel_Word_Problems/391566: The total proceeds from a used book store sale were $250. A total of 91 books were sold. The books were priced at $2.50 and 3.00 each. How man more books were sold for $2.50 then were sold for $3.00? 1 solutions Answer 277799 by stanbon(57226)   on 2011-01-06 19:47:41 (Show Source): You can put this solution on YOUR website! The total proceeds from a used book store sale were $250. A total of 91 books were sold. x + y = 91 ------------ The books were priced at $2.50 and 3.00 each. 2.5x + 3y = 250 ----------- How many more books were sold for $2.50 then were sold for $3.00? ------------------------ x = 91-y Substitute for "x" and solve for "y": 2.5(91-y)+3y = 250 227.5 +0.5y = 250 0.5y = 22.5 y = 45 (# of books sold at $3.00 --- x = 46 (# of books sold at $2.50 ================================ Cheers, Stan H.

Numeric_Fractions/391572: -5/8x(-2/3) 1 solutions Answer 277798 by stanbon(57226)   on 2011-01-06 19:40:57 (Show Source): You can put this solution on YOUR website! -5/8x(-2/3) ----- = 10/24 --- = 5/12 ============= Cheers, Stan H. =============

Angles/391573: (5x - 18) + (4x + 7 ) = 1 solutions Answer 277796 by stanbon(57226)   on 2011-01-06 19:39:02 (Show Source): You can put this solution on YOUR website! (5x - 18) + (4x + 7 ) = --- = 5x+4x +7-18 --- = 9x-11 ============= Cheers, Stan H.

Volume/391570: A radio tower casts a shadow 8 feet long at the same time that a vertical yardstick casts a shadow half an inch long. How tall is the radio tower? 1 solutions Answer 277794 by stanbon(57226)   on 2011-01-06 19:37:26 (Show Source): You can put this solution on YOUR website! A radio tower casts a shadow 8 feet long at the same time that a vertical yardstick casts a shadow half an inch long. How tall is the radio tower? ---------------------- Solve the proportion: tower/96" = 36"/(1/2)" ----- tower = 96*36/(1/2) tower = 96*72 tower = 6912 inches tower = 576 ft. ==================== Cheers, Stan H. ===========

Equations/391569: for what value of k does the graph of y=kx^3 pass through the point (1,4)? 1 solutions Answer 277790 by stanbon(57226)   on 2011-01-06 19:33:44 (Show Source): You can put this solution on YOUR website! for what value of k does the graph of y=kx^3 pass through the point (1,4)? ---- Substitute for x and y and solve for "k". --- 4 = k*1^3 k = 4 ------------- Cheers, Stan H. ========

Radicals/391567: Hi thank you for reading this, I am having a little bit of trouble with solving this problem about simplifying radical expressions.Can you please help me solve this problem: Thank you so much, I keep thinking I am not distributing the coefficient and square root correctly. Once again thank you! 1 solutions Answer 277788 by stanbon(57226)   on 2011-01-06 19:31:39 (Show Source): You can put this solution on YOUR website! sqrt( 6 )(7sqrt( 3 )+ 6) --- = 7sqrt(18) + 6sqrt(6) ---- = 7*3*sqrt(2) + 6sqrt(6) ---- = 21sqrt(2) + 6sqrt(6) ========================= Cheers, Stan H. =========

Miscellaneous_Word_Problems/391504: Hi, Here is the question. The base of a triangle is 4 cm greater than the height. The area is 30cm^2, find the height and length. I have done this so far,A=1/2 bh=30 bh=60 (h+4)H=60 H^2+4h=60 h^2 +4h - 60 =0 (h+ ) *(h- ) This is where I get very confused. I know triangles must add up to 90 , any help would be greatly appreciated! 1 solutions Answer 277763 by stanbon(57226)   on 2011-01-06 18:13:38 (Show Source): You can put this solution on YOUR website! Hi, Here is the question. The base of a triangle is 4 cm greater than the height. The area is 30cm^2, find the height and length. I have done this so far, A= (1/2)bh = 30 --- (1/2)(x+4)x = 30 x^2+4x = 60 x^2+4x-60 = 0 x^2+10x-6x-60 = 0 x(x+10)-6(x+10) = 0 (x+10)(x-6) = 0 Positive solution: x = 6cm(height) x+4= 10cm(base) ==================== Cheers, Stan H. ==========

Money_Word_Problems/391502: you deposit $2000 in an account that pays 4.5 % interest compounded annually. Write a model giving the account balance A after T years. In about how many years will the balance double? 1 solutions Answer 277762 by stanbon(57226)   on 2011-01-06 18:08:53 (Show Source): You can put this solution on YOUR website! You deposit $2000 in an account that pays 4.5 % interest compounded annually. Write a model giving the account balance A after T years. A(t) = 2000(1+(0.045))^(t) ---------------------------------- In about how many years will the balance double? 4000 = 2000(1.045)^t 2 = 1.045^t --- t*log(1.045) = log(2) --- t = log(2)/log(1.045) --- t = 15.75 years ==================== Cheers, Stan H. ===============

Coordinate-system/391499: Tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. 1. The cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for 4 tickets. 2. The late fee is $2 regardless of the number of days the movie is late. 3. On the trip, Jerry had his cruise control set at 60 mi/h for 4 hours. 4. The contract states that every day past the agreed upon completion date the project is not finished, the price is reduced by $25. 1 solutions Answer 277761 by stanbon(57226)   on 2011-01-06 18:04:17 (Show Source): You can put this solution on YOUR website! Tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. 1. The cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for 4 tickets. --- slope = (78-19.50)/(4-1) is positive. =========================================== 2. The late fee is $2 regardless of the number of days the movie is late. slope = zero ------ 3. On the trip, Jerry had his cruise control set at 60 mi/h for 4 hours. slope = 0 ---------------- 4. The contract states that every day past the agreed upon completion date the project is not finished, the price is reduced by $25. Slope = -25 ================ Cheers, Stan H. ================

Probability-and-statistics/391498: Find the first three iterates of the function f(x)=x^2-2, if the initial value is -2 Thank you so much for all of your help!!!!!!! God Bless!!!!!!! 1 solutions Answer 277760 by stanbon(57226)   on 2011-01-06 17:59:43 (Show Source): You can put this solution on YOUR website! Find the first three iterates of the function f(x)=x^2-2, if the initial value is -2. ---------- f(-2) = (-2)^2-2 = 4-2 = 2 --- f(2) = 2^2-2 = 2 --- f(2) = 2^2-2 = 2 ================== Cheers, Stan H.

Polygons/391488: the measure of an exterior angle of an equiangular polygon is twice that of an interior angle. What is the name of the polygon? 1 solutions Answer 277759 by stanbon(57226)   on 2011-01-06 17:42:41 (Show Source): You can put this solution on YOUR website! The measure of an exterior angle of an equiangular polygon is twice that of an interior angle. What is the name of the polygon? ---------------- Let the interior angle be "x". Then the exterior angle is "2x". --- Equation: x + 2x = 180 3x = 180 x = 60 (interior angle) 2x = 120 (exterior angle) --- The sum of the exterior angles is 360 degrees. # of exterior angles = 360/120 = 3 Therefore, # of sides is 3. ---- The polygon is an equilateral triangle. ========================================= Cheers, Stan H.

Angles/391478: Two angles are supplementary. One is 56 degrees more than 3 times the other. Find the measures of the angles 1 solutions Answer 277758 by stanbon(57226)   on 2011-01-06 17:35:09 (Show Source): You can put this solution on YOUR website! Two angles are supplementary. One is 56 degrees more than 3 times the other. Find the measures of the angles ------ Angle: x Supplementary Angle: 180-x ------------------------------- Equation: x = 3(180-x)+56 ------- x = 3*180-3x+56 --- 4x = 596 --- x = 149 180-x = 31 ============== Cheers, Stan H.

Polynomials-and-rational-expressions/391483: multiply these binomial (2x-5)(x+3) 1 solutions Answer 277757 by stanbon(57226)   on 2011-01-06 17:29:44 (Show Source): You can put this solution on YOUR website! (2x-5)(x+3) ----- 2x(x+3) -5(x+3) --- = 2x^2+6x-5x-15 --- = 2x^2 + x - 15 ================== Cheers, Stan H. ==================

Inequalities/391485: a saving account decreased by $ 75 is now less than $500 1 solutions Answer 277755 by stanbon(57226)   on 2011-01-06 17:27:31 (Show Source): You can put this solution on YOUR website! What is the question?

Angles/391480: The measure of an angle is fourteen times the measure of a complementary angle. What is the measure of each angle? 1 solutions Answer 277754 by stanbon(57226)   on 2011-01-06 17:26:05 (Show Source): You can put this solution on YOUR website! The measure of an angle is fourteen times the measure of a complementary angle. What is the measure of each angle? --- Angle : x Complementary Angle: 90-x ---- Equation: x = 14(90-x) x = 1260 - 14x 15x = 1260 x = 84 --- 90-x = 6 =============== Cheers, Stan H.

Quadratic_Equations/391479: two consecutive odd integers have a product of 99. find all sets of integers that satisfy this decription 1 solutions Answer 277752 by stanbon(57226)   on 2011-01-06 17:16:24 (Show Source): You can put this solution on YOUR website! two consecutive odd integers have a product of 99. find all sets of integers that satisfy this decription ----- 1st: 2x-1 2nd: 2x+1 ----- Equation: (2x-1)(2x+1) = 99 4x^2-1 = 99 4x^2 = 100 x^2 = 25 x = 5 or x = -5 ==================== If x = 5, 2x-1 = 9 2x+1 = 11 --- If x = -5 2x-1 = -11 2x+1 = -9 ============= Cheers, Stan H. ==============

Exponential-and-logarithmic-functions/391475: i need help on inverses and logaithms. y=log nine(x)... that nine is a small exponent on the botom right hand corner after log 1 solutions Answer 277750 by stanbon(57226)   on 2011-01-06 17:12:23 (Show Source): You can put this solution on YOUR website! i need help on inverses and logaithms. y=log nine(x) --- 1st: Interchange x and y to get: x = log9(y) --- 2nd: Solve for y: y = 9^x ================ Cheers, Stan H.

Equations/391248: Perform the indicated multiplication. Then simplify. sqrt of 7(6 sqrt 3 - 6 sqrt 7) 1 solutions Answer 277749 by stanbon(57226)   on 2011-01-06 17:08:26 (Show Source): You can put this solution on YOUR website! Perform the indicated multiplication. Then simplify. sqrt of 7(6 sqrt 3 - 6 sqrt 7) ---- sqrt(7)(6sqrt(3) - 7sqrt(7)) ---- = 6sqrt(21) - 7*7 --- = 6sqrt(21) - 49 ===================== Cheers, Stan H. ===========

Miscellaneous_Word_Problems/391349: The illumination (in foot-candles) of a light source varies directly as the intensity (in candle-power) of the source and inversely as the square of the distance from the source. If a certain light source with intensity of 300 candle-power provides an illumination of 2.5 foot-candles at a distance of 40 ft, what is the illumination at a distance of 20 ft? 1 solutions Answer 277662 by stanbon(57226)   on 2011-01-06 10:03:15 (Show Source): You can put this solution on YOUR website! The illumination (in foot-candles) of a light source varies directly as the intensity (in candle-power) of the source and inversely as the square of the distance from the source. ---- L = ki/d^2 ------ Solve for "k" using "If a certain light source with intensity of 300 candle-power provides an illumination of 2.5 foot-candles at a distance of 40 ft" 2.5 = k*300/40 k = 100/300 k = 3 ---- Equation for this problem: L = 3i/d^2 ============ What is the illumination at a distance of 20 ft? L = 3*300/20 L = 45 foot-candles ========================= Cheers, Stan H.

Functions/391350: We cannot find anything to help us understand a & h in Algebra II. One of the problems we have is: find g(a+h)-g(a)= 1 solutions Answer 277659 by stanbon(57226)   on 2011-01-06 09:58:23 (Show Source): You can put this solution on YOUR website! We cannot find anything to help us understand a & h in Algebra II. One of the problems we have is: find g(a+h)-g(a)= ---- You have to post the rule for g(x). Cheers, Stan H.