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# Recent problems solved by 'stanbon'

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 , 57270..57299, >>Next

 Angles/653197: (2x) degree (4x+108) degree1 solutions Answer 408283 by stanbon(57362)   on 2012-09-18 10:28:11 (Show Source): You can put this solution on YOUR website!Are you adding, multiplying, or just what are you asked to do? Cheers, Stan H.
 expressions/653196: i need to solve this problem:(a+2)(a+2) my answer:a squared+(a2+2a)+2squared=a2squared+2+2+2squared1 solutions Answer 408282 by stanbon(57362)   on 2012-09-18 10:26:42 (Show Source): You can put this solution on YOUR website!:(a+2)(a+2) ---- Use a procedure called FOIL: F: first * first = a*a = a^2 O: multiply the outers: a*2 = 2a I: Multiply the inners: 2*a = 2a L: last * last = 2*2 ---- Combine those to get a^2 + 2a + 4 ============================ Cheers, Stan H.
 absolute-value/653148: 1 divided by the absolute value of x+3 is greater than 71 solutions Answer 408265 by stanbon(57362)   on 2012-09-18 08:34:43 (Show Source): You can put this solution on YOUR website!|x+3| is greater than 7 ----- x+3 > 7 or x+3 < -7 ----------------------------- x > 4 or x < -10 ===================== Cheers, Stan H.
 Travel_Word_Problems/653151: Two airplanes fly toward each other from points 900 miles apart, at the rates, per hour, of 300 miles and 250 miles. When will they meet if they start at the same instant? 1 solutions Answer 408263 by stanbon(57362)   on 2012-09-18 08:26:39 (Show Source): You can put this solution on YOUR website!Two airplanes fly toward each other from points 900 miles apart, at the rates, per hour, of 300 mph and 250 mph. When will they meet if they start at the same instant? --------- Time is the same for both. Rate*Time = Distance ----- Equation: distance + distance = 900 miles 300t + 250t = 900 550t = 900 t = 900/550 hrs t = 1.64 hrs = 1hr 38 min 11 seconds ========================= Cheers, Stan H.
 Angles/653154: an angle is four fifth of its complement what is its magnitude1 solutions Answer 408259 by stanbon(57362)   on 2012-09-18 08:18:56 (Show Source): You can put this solution on YOUR website!an angle is four fifth of its complement what is its magnitude ----- 1st: x 2nd: 90-x ---- Equation: 90-x = (4/5)x 450 - 5x = 4x 9x = 450 x = 50 degrees 90-x = 40 degrees ======= Cheers, Stan H.
 Travel_Word_Problems/653152: A cheetah runs 70mi/hr if he runs for 15 mins how far will it reach?1 solutions Answer 408256 by stanbon(57362)   on 2012-09-18 08:15:00 (Show Source): You can put this solution on YOUR website!A cheetah runs 70mi/hr if he runs for 15 mins how far will it reach? ---- distance = rate*time = 70 *(15/60) = 70*(1/4) = 17.5 miles ====================== Cheers, Stan H.
 Linear-equations/653150: Find the equation of the line, F(2)=3 F(6)=3 1 solutions Answer 408252 by stanbon(57362)   on 2012-09-18 08:08:35 (Show Source): You can put this solution on YOUR website!Find the equation of the line, F(2)=3 ; F(6)=3 ---- You have 2 points (2,3) and (6,3) ------ slope = (3-3)/(6-2) = 0 ---- Notice that both points have y = 3 --- The line is the horizontal line: y = 3 ================== Cheers, Stan H.
 Miscellaneous_Word_Problems/653144: Jumbo Market makes \$0.10 on a head of lettuce and \$0.08 on a bunch of carrots. Last week, a total of 12,900 heads of lettuce and bunches of carrots were sold, with a profit of \$1,174. How many heads of lettuce and how many bunches of carrots were sold?1 solutions Answer 408251 by stanbon(57362)   on 2012-09-18 08:04:37 (Show Source): You can put this solution on YOUR website! Jumbo Market makes \$0.10 on a head of lettuce and \$0.08 on a bunch of carrots. Last week, a total of 12,900 heads of lettuce and bunches of carrots were sold, with a profit of \$1,174. How many heads of lettuce and how many bunches of carrots were sold? ---------- Quantity Equation: L + C = 12,900 items Value Equation:::10L +8C = 117400 cents ----- Multiply thru 1st equation by 10: 10L + 10C = 129000 10L + 8C = 117400 --------- Subtract and solve for "C": 2C = 11600 C = 5800 (# of bunches of carrots sold) --- Solve for "L": L + C = 12900 L + 5800 = 12900 L = 7100 (# of heads of lettuce sold) ======================== Cheers, Stan H. ==================
 Numeric_Fractions/653143: kindly solve my some ...... 3 x 8 = 8 x .................... ?1 solutions Answer 408249 by stanbon(57362)   on 2012-09-18 07:57:09 (Show Source): You can put this solution on YOUR website! kindly solve my some ...... 3 x 8 = 8 x .................... ? ----- Answer: 3 x 8 = 8 x 3 ================ Cheers, Stan H.
 Probability-and-statistics/652883: If two different students are randomly selected from a class of 12 boys and 8 girls, what is the probability that both students are girls. (express your answer as a common fraction.) show all work1 solutions Answer 408155 by stanbon(57362)   on 2012-09-17 19:54:33 (Show Source): You can put this solution on YOUR website!If two different students are randomly selected from a class of 12 boys and 8 girls, what is the probability that both students are girls. ---- # of ways to succeed: 8C2 = (8*7)/(1*2) = 28 ------------ # of possible outcomes: 20C2 = (20*19)/(1*2) = 190 ---- P(2 girls) = 28/190 = 0.1474 =============================== Cheers, Stan H.
 Trigonometry-basics/652831: : What is the simplified form of sin(x + P)? A cos x B sin x C -sin x D -cos x1 solutions Answer 408147 by stanbon(57362)   on 2012-09-17 19:21:02 (Show Source): You can put this solution on YOUR website!What is the simplified form of sin(x + pi)? A cos x B sin x C -sin x D -cos x ------- Ans: -sin(x) ================ Cheers, Stan H.
 percentage/652841: 92 % of UHS students were in attendance today.If 21 students were absent.How many students attend UHS?1 solutions Answer 408145 by stanbon(57362)   on 2012-09-17 19:11:21 (Show Source): You can put this solution on YOUR website! 92 % of UHS students were in attendance today.If 21 students were absent.How many students attend UHS? ------------- Let "x" be the total # of students. ------ 8% were absent. Equation: 0.08x = 21 --- x = 21/0.08 --- x = 262 when rounded down ============== Cheers, Stan H.
 Expressions-with-variables/652834: The polynomial of degree 5, P(x) has a leading coefficient 1, has roots of multiplicity 2 at x=5 and x=0, and a root of multiplicity 1 at x=-5. find a possible formula for P(x)1 solutions Answer 408143 by stanbon(57362)   on 2012-09-17 18:59:09 (Show Source): You can put this solution on YOUR website!The polynomial of degree 5, P(x) has a leading coefficient 1, has roots of multiplicity 2 at x=5 and x=0, and a root of multiplicity 1 at x=-5. find a possible formula for P(x) ----- Note: If k is a root, x-k is a factor. ------------------------------------------ P(x) = (x-5)^2(x^2)(x+5) ----------------------------- Cheers, Stan H.
 Mixture_Word_Problems/652806: Select ALL calculations that are measured in square units. The amount of soil needed to fill a flower pot The amount of viewing space of a TV screen The amount of curtains needed to cover a window The amount of chalk needed to outline a rectangular field The amount of fabric needed to cover a dining room table The amount of trim needed to surround a picture frame 1 solutions Answer 408141 by stanbon(57362)   on 2012-09-17 18:46:41 (Show Source): You can put this solution on YOUR website!Select ALL calculations that are measured in square units. The amount of soil needed to fill a flower pot---no The amount of viewing space of a TV screen---yes The amount of curtains needed to cover a window---yes The amount of chalk needed to outline a rectangular field---no The amount of fabric needed to cover a dining room table---yes The amount of trim needed to surround a picture frame---no ============== Cheers, Stan H.
 Linear-systems/652796: Hi I need help graphing y=-2/3x+30 Thanks in advance for all of your help have a great day!!1 solutions Answer 408139 by stanbon(57362)   on 2012-09-17 18:35:54 (Show Source): You can put this solution on YOUR website!need help graphing y=(-2/3)x+30 --- Plot two points: If x = 0 y = 30 If x = 3 y = 28 ----- Plot (0,30) and (3,28) and draw a line thru them. ----------- ----- Cheers, Stan H. ==========
 Square-cubic-other-roots/652792: how do you do a problem like sqaure root then under that you 3n+12= sqaure root n+81 solutions Answer 408133 by stanbon(57362)   on 2012-09-17 18:26:40 (Show Source): You can put this solution on YOUR website!sqaure root then under that you 3n+12= sqaure root n+8 ----- sqrt(3n+12) = sqrt(n+8) ---- Square both sides to get: 3n + 12 = n+8 2n = -4 n = -2 ------- Cheers, Stan H. =============
 Graphs/652695: please help me solve these equations using elimination y=(1/3)x+2 and y=(5/2)x-1 1 solutions Answer 408131 by stanbon(57362)   on 2012-09-17 18:23:39 (Show Source): You can put this solution on YOUR website!solve these equations using elimination y=(1/3)x+2 y=(5/2)x-1 ----- Subtract and solve for "x": [(5/2)-(1/3)]x -3 = 0 ---- [(15-2)/6]x = 3 ----- (13/6)x = 3 x = 18/13 ------- Solve for "y": y = (1/3)(18/13)+2 ----- y = (6/13)+(26/13) y = 32/13 ------------------------ Cheers, Stan H.
 Miscellaneous_Word_Problems/652686: A Little League baseball player throws a ball upward. The height h of the ball (in feet) t seconds after the ball is released is given by the quadratic equation h = -16t2 +30t +4 a) How long does it take the ball to reach a height of 18ft? b) How long does it take the ball to hit the ground? 1 solutions Answer 408061 by stanbon(57362)   on 2012-09-17 16:16:43 (Show Source): You can put this solution on YOUR website!A Little League baseball player throws a ball upward. The height h of the ball (in feet) t seconds after the ball is released is given by the quadratic equation h = -16t2 +30t +4 a) How long does it take the ball to reach a height of 18ft? ----- Solve: -16t^2 + 30t + 4 = 18 ---- -16t^2 + 30t - 14 = 0 ---- -8t^2 + 15t - 7 = 0 ----- t = [-15 +- sqrt(225 - 4*-8*-7)]/(-16) ---- t = [-15 +- sqrt(29)]/-16 --- t = 0.6 seconds and t = 1.274 seconds ================================= =============== b) How long does it take the ball to hit the ground? Solve: -16t^2 + 30t - 4 = 0 -8t^2 + 15t - 2 = 0 t = 1.73 seconds =================== Cheers, Stan H. ===================
 Polynomials-and-rational-expressions/652688: Fing two numbers whose sum is 60 adn whose difference is 36?1 solutions Answer 408056 by stanbon(57362)   on 2012-09-17 16:02:26 (Show Source): You can put this solution on YOUR website!Find two numbers whose sum is 60 and whose difference is 36? ----- x + y = 60 x-y = 36 --- Add and solve for "x": 2x = 96 x = 48 ---- Solve for "y": x + y = 60 48 + y = 60 y = 60-48 y = 12 -------------- Cheers, Stan H.
 Linear-equations/652687: Suppose L1 is the line with equation x - 2y = 6. What is the slope of L1?1 solutions Answer 408054 by stanbon(57362)   on 2012-09-17 15:59:25 (Show Source): You can put this solution on YOUR website!Suppose L1 is the line with equation x - 2y = 6. What is the slope of L1? ------- Solve for "y": 2y = x-6 y = (1/2)x - 3 ---- slope = 1/2 ============== Cheers, Stan H.
 Inequalities/652630: 10x^-2+33x^-1-7=0 How do you solve this equation?1 solutions Answer 408053 by stanbon(57362)   on 2012-09-17 15:57:39 (Show Source): You can put this solution on YOUR website!10x^-2+33x^-1-7=0 ----- It's a quadratic with variable x^-1 --- Let w = x^-1. --- 10w^2 + 33w -7 = 0 ----- 10w^2 + 35w-2w - 7 = 0 ---- 5w(2w+7)-(2w+7) = 0 (2w+7)(5w-1) = 0 w = -7/2 or w = 1/5 ---- Solve for x: x^-1 -7/2 or x^-1 = 1/5 --- x = -2/7 or x = 5 ======================= Cheers, Stan H. =================
 Polynomials-and-rational-expressions/652631: Says to find the degree and if its a monomial or a binomial. 9a^3 I keep getting this wrong1 solutions Answer 408036 by stanbon(57362)   on 2012-09-17 14:13:20 (Show Source): You can put this solution on YOUR website!Says to find the degree and if its a monomial or a binomial. 9a^3 ----- Degree = 3 ---- Monomial ============== Cheers, Stan H. ===============
 Probability-and-statistics/652623: The FBI claims that about 80% of all property crimes, the criminals are never found and the case is never solved. In a randomly selected city, what is the probability that at least 1 crime will be solved when 6 crimes are reported? I need help setting up the formulas1 solutions Answer 408034 by stanbon(57362)   on 2012-09-17 14:09:05 (Show Source): You can put this solution on YOUR website! The FBI claims that about 80% of all property crimes, the criminals are never found and the case is never solved. In a randomly selected city, what is the probability that at least 1 crime will be solved when 6 crimes are reported? I need help setting up the formulas ---------- Binomial Problem with n = 6 and p(never solved) = 0.8; p(solved) = 0.2 ---- P(none solved)+P(at least one solved) = 1 P(at least one solved) = 1 - P(none solved) --- = 1 - 6C0(0.2)^0*0.8^6 = 1 - 1*1*0.8^6 = 1 - 0.8^6 = 0.7389 ========================== Cheers, Stan H.
 �t�e�s�t/652395: a pitcher has given up 12 runs in 20 innings. if it is assumed that the number of runs varies directly as the number of innings, how many runs would he give up in 9 innings1 solutions Answer 407983 by stanbon(57362)   on 2012-09-16 21:53:21 (Show Source): You can put this solution on YOUR website!a pitcher has given up 12 runs in 20 innings. if it is assumed that the number of runs varies directly as the number of innings, how many runs would he give up in 9 innings ------- r = k*n --- Solve for "k" using "a pitch gives up 12 runs in 20 innings": 12 = k*20 k = 12/20 = 3/5 ---- Equation: r = (3/5)n --- How many runs would he give up in 9 innings? ---- r = (3/5)9 --- # of runs = 27/5 = 5 2/5 ========== Cheers, Stan H.
 Travel_Word_Problems/652358: A boy can row a boat at a constant rate of 5 mi/hr in still water. He rows upstream for 30 minutes and then rows downstream, returning to his starting point in another 10 minutes. (Round your answers to two decimal places.) Upstream net speed= 5-x mph downstream net speed = 5+x mph a)Find the rate of the current? b)Find the total distance traveled?1 solutions Answer 407967 by stanbon(57362)   on 2012-09-16 20:50:33 (Show Source): You can put this solution on YOUR website!A boy can row a boat at a constant rate of 5 mi/hr in still water. He rows upstream for 30 minutes and then rows downstream, returning to his starting point in another 10 minutes. (Round your answers to two decimal places.) Upstream net speed= 5-x mph downstream net speed = 5+x mph ------------------ Upstream DATA: time = 1/2 hr ; rate = 5-x ; distance = r*t = (1/2)(5-x) miles ----- Downstream DATA: time = 1/6 hr ; tate = 5+x ; distance = r*t = (1/6)(5+x) miles ----- Equation: distance = distance (1/2)(5-x) = (1/6)(5+x) 6(5-x) = 2(5+x) 30-6x = 10+2x 8x = 20 x = 5/2 = 2 1/2 mph (speed of the current) ======================= Cheers, Stan H. ==================== a)Find the rate of the current? b)Find the total distance traveled?
 logarithm/652347: rewrite log(x/x-1)-log(x/x+1)+log(x^2-1) as a single logarithm1 solutions Answer 407965 by stanbon(57362)   on 2012-09-16 20:45:17 (Show Source): You can put this solution on YOUR website!rewrite log(x/x-1)-log(x/x+1)+log(x^2-1) as a single logarithm ------------------------- = log[((x/(x-1))*(x^2-1)) / (x/(x+1))] ----- Cancel where you can to get: ------------- = log[((x)*(x+1)) / (x/(x+1))] ------ Invert the denominator and multiply to get: = log(1) --- = 0 =========== Cheers, Stan H.
 Angles/652349: I am not sure how to solve this, not looking for an answer, but rather instructions on how to solve this problem. M1 solutions Answer 407961 by stanbon(57362)   on 2012-09-16 20:35:30 (Show Source): You can put this solution on YOUR website!No Problem posted.
 Linear-systems/652343: The sum S of the measure of the measures of the angles of a polygon is S=(n-2)*180 degrees, where n is the number of sides of the polygon. Plot four points (n,s) that satisfy the equation . Do the points lie on a line? Explain your reasoning1 solutions Answer 407960 by stanbon(57362)   on 2012-09-16 20:32:27 (Show Source): You can put this solution on YOUR website!S=(n-2)*180 degrees, where n is the number of sides of the polygon. Plot four points (n,s) that satisfy the equation . Do the points lie on a line? ----- The points will be on the line S = 180n-360 ------------------- Cheers, Stan H. ==================
 Miscellaneous_Word_Problems/652335: Hi, I have a question on a word problem I came across in the Quadratic Equations section of my math homework. Thanks for your help! FOr a remodeling job, an architect suggested increasing the sides of a square patio by 3 feet per side. This made the area of the new patio 49 square feet. What was the area of the original patio?1 solutions Answer 407957 by stanbon(57362)   on 2012-09-16 20:29:06 (Show Source): You can put this solution on YOUR website!FOr a remodeling job, an architect suggested increasing the sides of a square patio by 3 feet per side. This made the area of the new patio 49 square feet. What was the area of the original patio? ----- Let original dimensions be x by x Then original area = x^2 ---- New Area = (x+3)^2 = x^2 + 6x+9 ---- Equations: New area - old area = 49 sq ft x^2+6x+9 - x^2 = 49 6x+9 = 49 6x = 40 x = 20/3 ft --- Original Area = x^2 = (20/3)^2 = 400/9 = 44.44 sq ft. ========================= Cheers, Stan H. ================
 Travel_Word_Problems/652326: At 6 A.M. a snowplow, traveling at a constant speed, begins to clear a highway leading out of town. At 8 A.M. an automobile begins traveling the highway at a speed of 35mi/hr and reaches the plow 20 minutes later. Find the speed of the snowplow.1 solutions Answer 407955 by stanbon(57362)   on 2012-09-16 20:21:33 (Show Source): You can put this solution on YOUR website!At 6 A.M. a snowplow, traveling at a constant speed, begins to clear a highway leading out of town. At 8 A.M. an automobile begins traveling the highway at a speed of 35mi/hr and reaches the plow 20 minutes later. Find the speed of the snowplow. -------- Snowplow DATA: time = 7/3 hrs ; rate = r mph ; distance = (7/3)r miles ---------------- Car DAA: time = 1/3 hr ; rate = 35 mph ; distance = (1/3)35 miles ================ Equation: distance = distance: (7/3)r = (1/3)35 --- 7r = 35 r = 5 mph (speed of the snowplow) ======================================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/652319: Hello, Im having difficulty figuring out this question. I found a solution to this problem on this site, but I do not think it was solved in the correct manner (I could be wrong though). Thanks for your help! The ratio of the weight of sodium to that of chlorine in common table salt is 5 to 3. Find the amount of each element in a salt compound weighing 200 pounds.1 solutions Answer 407954 by stanbon(57362)   on 2012-09-16 20:07:14 (Show Source): You can put this solution on YOUR website!The ratio of the weight of sodium to that of chlorine in common table salt is 5 to 3. Find the amount of each element in a salt compound weighing 200 pounds. ----- 5 to 3 is the same as 5x to 3x where wt. of sodium is 5x. ----- 5x + 3x = 200 lbs. --- 8x = 200 x = 25 ------------ Wt of sodium = 5x = 5*25 = 125 lbs Wt of chlorine = 3x = 3*25 = 75 lbs ======================================= Cheers, Stan H.