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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, >>Next

 Age_Word_Problems/727298: When I add 3 times my age 3 years from now to 4 times my age 4 years from now, I get 8 times my current age. How old will I be 2 years from now1 solutions Answer 445058 by stanbon(57209)   on 2013-03-17 22:47:43 (Show Source): You can put this solution on YOUR website!When I add 3 times my age 3 years from now to 4 times my age 4 years from now, I get 8 times my current age. How old will I be 2 years from now ----- Let your age be "x". Equation: 3(x+3) + 4(x+4) = 8x 3x+9 + 4x+16 = 8x x = 25 ---- x+2 = 27 yrs (your age in 2 years) ============================= Cheers, Stan H. =============================
 Miscellaneous_Word_Problems/727309: Hello I have tried to solve this using the 2x2x2 method. I don't believe I'm on the right track. Please give me a similar problem so that I make work the one stated below. Thank you in advance! Here is the word problem: "A pizza parlor offers green peppers, mushrooms, sausage and tomatoes as toppings for the plain cheese base. How many different types of pizza's can be made?1 solutions Answer 445057 by stanbon(57209)   on 2013-03-17 22:44:04 (Show Source): You can put this solution on YOUR website!A pizza parlor offers green peppers, mushrooms, sausage and tomatoes as toppings for the plain cheese base. How many different types of pizza's can be made? ----- Each of the toppings is either included or not included in the final product. --- # of pizzas = 2^4 = 16 ========================== Cheers, Stan H.
 Triangles/727313: a triangle has two angles with a measure of 60 degrees and one side with a length of 12. What is the perimeter of the triangle? 1 solutions Answer 445055 by stanbon(57209)   on 2013-03-17 22:38:57 (Show Source): You can put this solution on YOUR website!a triangle has two angles with a measure of 60 degrees and one side with a length of 12. What is the perimeter of the triangle? ---- The 3rd angle must be 60 degrees also. The triangle is equilateral. Perimeter = 3*12 = 36 ========================== Cheers, Stan H. =============
 Linear_Equations_And_Systems_Word_Problems/727310: A bobcat population is classified by age into kittens (less than 1 year old) and adults (at least 1 year old). All adult females, including those born the prior year, have a litter each June, with an average litter size of 3 kittens. The springtime population of bobcats in a certain area is estimated to be 5,400, and the male-female ratio is one. Estimate the number of adults and kittens in the population. adults ________ kittens ________ 1 solutions Answer 445054 by stanbon(57209)   on 2013-03-17 22:36:26 (Show Source): You can put this solution on YOUR website!The springtime population of bobcats in a certain area is estimated to be 5,400, and the male-female ratio is one. Estimate the number of adults and kittens in the population. ---- Let # of males be x Then # of females is x And # of kittens is 3x ---- x + x + 3x = 5400 5x = 5400 x = 1080 --- # of adults = 2x = 2160 # of kittens = 3x = 3240 ------------------- Cheers, Stan H. =================== ---
 Equations/727312: what does x equal when 4*16^(2x)=8^(x-5)?1 solutions Answer 445053 by stanbon(57209)   on 2013-03-17 22:30:07 (Show Source): You can put this solution on YOUR website!answered
 test/727305: The temperature has been as high as 89 and low as 43. Find values for a and b so that the solution to |x-a|_< b expresses the temperatures in terms of x. (The phone won't allow me to input less than or equal to, but that's what comes after the absolute value. 1 solutions Answer 445051 by stanbon(57209)   on 2013-03-17 22:22:26 (Show Source): You can put this solution on YOUR website!The temperature has been as high as 89 and low as 43. Find values for a and b so that the solution to |x-a|_< b expresses the temperatures in terms of x. ------------------------- Find the midpoint of the interval. (89+43)/2 = 66 ---- Find the distance to an endpoint. 89-66 = 23 ----- |x-66| <= 23 ================= Ans: a = 66 ; b = 23 ================== Cheers, Stan H. ===============
 percentage/727302: 20 is what percent of 14801 solutions Answer 445047 by stanbon(57209)   on 2013-03-17 22:13:14 (Show Source): You can put this solution on YOUR website!20 is what percent of 1480 ---- x/100 = 20/1480 ------ x = 100(20/1480) --- x = 2000/1480 x = 1.35 ---- 20 is 1.35% of 1480 =============== Cheers, Stan H. ===============
 Probability-and-statistics/727012: How many 5-letter words containing at least one “a” can be made out of 26 letters?1 solutions Answer 444977 by stanbon(57209)   on 2013-03-17 16:04:27 (Show Source): You can put this solution on YOUR website!How many 5-letter words containing at least one “a” can be made out of 26 letters? ----- # of ways to get no "a": 25^5 # of ways to get a random 5-letter word: 26^5 ------- # with at least one "a": 26^5 - 25^5 = 2,115,751 ---------------- Cheers, Stan H. ------
 Probability-and-statistics/727138: A bag contains 5 red marbles, 10 blue marbles, and 20 green marbles. If two marbles are taken out at random, one by one, without replacement, what is the probability that they are both blue? I know the total is 35 marbles but I am unsure how to calculate. I attempted to do 10/35, 9/34 and so forth and added all the results together but I fear it is not correct. 1 solutions Answer 444975 by stanbon(57209)   on 2013-03-17 15:57:17 (Show Source): You can put this solution on YOUR website! A bag contains 5 red marbles, 10 blue marbles, and 20 green marbles. If two marbles are taken out at random, one by one, without replacement, what is the probability that they are both blue? I know the total is 35 marbles but I am unsure how to calculate. I attempted to do 10/35, 9/34 and so forth and added all the results together but I fear it is not correct. ---- # of ways to pick 2 blue: 10C2 = 45 # of ways to pick a random pair: 35C2 = 595 ---- P(2 blue without replacement) = 45/595 = 9/119 ------------------ Cheers, Stan H. ==================
 absolute-value/727114: 8|y+3|+1>251 solutions Answer 444973 by stanbon(57209)   on 2013-03-17 15:53:40 (Show Source): You can put this solution on YOUR website!8|y+3|+1>25 ----- 8|y+3| > 24 ----- |y+3| > 3 ---- y+3 < -3 or y+3 > 3 ------ y < -6 or y > 0 ====================== Cheers, Stan H. ============
 Linear-systems/727134: 2x – y = 6 -x + y = 2 1 solutions Answer 444971 by stanbon(57209)   on 2013-03-17 15:47:49 (Show Source): You can put this solution on YOUR website!2x – y = 6 -x + y = 2 ----- Add and solve for "x": x = 8 ---- Solve for "y": 2x - y = 6 16 - y = 6 y = 10 ------------ Cheers, Stan H.
 Mixture_Word_Problems/727133: How many grams of lidocaine total are in 200 mL of 2% lidocaine solution added to 300 mL of 3% lidocaine solution1 solutions Answer 444970 by stanbon(57209)   on 2013-03-17 15:45:59 (Show Source): You can put this solution on YOUR website!How many grams of lidocaine total are in 200 mL of 2% lidocaine solution added to 300 mL of 3% lidocaine solution ---- lido = 0.02*200 + 0.03*300 = 4 + 9 = 13 mL of lido ------------ Cheers, Stan H. ============
 Mixture_Word_Problems/727128: How many liters of a 10% solution of acid should be mixed with 60% solution of acid to obtain 20 liters of 50% solution? I need to solve this using systems of Equations, but I have no idea how to set it up. I have so far stated that x = 10% solution and that y = 60% solution1 solutions Answer 444967 by stanbon(57209)   on 2013-03-17 15:41:17 (Show Source): You can put this solution on YOUR website!How many liters of a 10% solution of acid should be mixed with 60% solution of acid to obtain 20 liters of 50% solution? ---- Quantity Eq: t + s = 20 liters Acid Eq:: 10t+60s = 50*20 ------- Modify: 6t + 6s = 6*20 t + 6s = 5*20 ----- 5t = 1*20 t = 4 liters (amt. of 10% solution needed) ============== Cheers, Stan H.
 Mixture_Word_Problems/727123: A chemist needs to produce a 60% acid mixture. She has 25% strength solution and 80% strength solution on hand. Rounding to the nearest thousandth (3 decimal places; nearest mL), how many liters of 80% solution does she add to create 1 liter of the 60% strength mixture? 1 solutions Answer 444963 by stanbon(57209)   on 2013-03-17 15:30:19 (Show Source): You can put this solution on YOUR website!A chemist needs to produce a 60% acid mixture. She has 25% strength solution and 80% strength solution on hand. Rounding to the nearest thousandth (3 decimal places; nearest mL), how many liters of 80% solution does she add to create 1 liter of the 60% strength mixture? -------- Equation: acid + acid = acid 0.25x + 0.80(1-x) = 0.60*1 ------- 25x + 80 - 80x = 60 -55x = -20 x = 4/11 liter (amt. of 25% solution needed) ---- 1-4/11 = 7/11 liter (amt of 80% solution needed) ============== Cheers, Stan H. ==============
 Miscellaneous_Word_Problems/727112: The Nielsen Company reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If a group of 20 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the number of hours they watch television will be greater than 26.3 hours.1 solutions Answer 444962 by stanbon(57209)   on 2013-03-17 15:04:28 (Show Source): You can put this solution on YOUR website!The Nielsen Company reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If a group of 20 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the number of hours they watch television will be greater than 26.3 hours. ------------------ z(26.3) = (26.3-25)/[3/sqrt(20)] = 1.9379 P(z > 26.3) = P(z> 1.9379) = 0.0263 --- If you use the t-distribution you will get: P(t > 26.3) = tcdf(1.9379,100,19) = 0.0338 ===================== Cheers, Stan H. ================ Cheers, Stan H.
 Miscellaneous_Word_Problems/727110: The net worth of senior citizens is normally distributed with mean equal to \$225,000 and standard deviation equal to \$35,000. What is the probability that a single randomly selected senior citizen will have a net worth less than \$300,0001 solutions Answer 444961 by stanbon(57209)   on 2013-03-17 14:56:21 (Show Source): You can put this solution on YOUR website!The net worth of senior citizens is normally distributed with mean equal to \$225,000 and standard deviation equal to \$35,000. What is the probability that a single randomly selected senior citizen will have a net worth less than \$300,000 ------- z(300,000) = (300,000-225000)/35000 = 75/35 = 2.1429 --- P(x > 300,000) = P(z > 2.1429) = 0.0161 ============ Cheers, Stan H.
 Probability-and-statistics/727060: A bag of M&M's contains 7 red, 8 blue, 10 b rown, 6 yellow and 4 green M&M's. Find the probability of drawing each without replacing the first. Show work and write the each probability as a fraction in simplest form. (see below) a) P(red/green)___ (I did 7/4) b) P(blue/yellow)____ (I did 4/3) c) P(red/red)_____ (I did 1) d) P(brown/orange) ____ (I did 10/0) Thank you.1 solutions Answer 444953 by stanbon(57209)   on 2013-03-17 12:59:28 (Show Source): You can put this solution on YOUR website! A bag of M&M's contains 7 red, 8 blue, 10 b rown, 6 yellow and 4 green M&M's. Find the probability of drawing each without replacing the first. Show work and write the each probability as a fraction in simplest form. (see below) a) P(red/green)___ (4/34) b) P(blue/yellow)____ (6/34) c) P(red/red)_____ (6/34) d) P(brown/orange) ____ (0/34) ======= Cheers, Stan H. ==========
 Functions/727056: HARD QUESTION HELP NEEDED 3. Givin g(x)=absx. Sketch f(x)=g(x-2)-4. The state the domain and range 1 solutions Answer 444952 by stanbon(57209)   on 2013-03-17 12:54:29 (Show Source): You can put this solution on YOUR website!Givin g(x)=|x|. Sketch f(x)=g(x-2)-4. f(x) = |x-2|-4 ---------------------- Domain: All Real Numbers Range: All Real Numbers >= -4 ================================== Cheers, Stan H. Then state the domain and range
 Functions/727059: CONFUSED HELP WOULD BE VERY MUCH APPRECIATED .Sketch graph of f-1, givin the graph (-4,3)(0,3) (2,-1) (4,1) b)If the graph isn`t a inverse function, then restrict the domain of the original relation SO the inverse a function. 1 solutions Answer 444950 by stanbon(57209)   on 2013-03-17 12:49:10 (Show Source): You can put this solution on YOUR website!.Sketch graph of f-1, givin the graph (-4,3)(0,3) (2,-1) (4,1) ----- Procedure: Switch the x and y values to get: (3,-4)(3,0)(-1,2)(1,4) ------------------------------------- b)If the graph isn`t a inverse function, then restrict the domain of the original relation SO the inverse a function. ---- It is not a function because x = 3 has 2 y-values. ------ Restrict the domain of the original function by eliminating 0 or -4 from it's domain so the inverse will be a function. =========== Cheers, Stan H.
 Age_Word_Problems/727007: Deb is 4 years younger than Beth. Six years ago the sum of their ages was 46. How old are they now? I'm unfaliar with finding answer when asked "six years ago." How do I set this up? Thanks. 1 solutions Answer 444924 by stanbon(57209)   on 2013-03-17 09:47:31 (Show Source): You can put this solution on YOUR website!Deb is 4 years younger than Beth. Six years ago the sum of their ages was 46. How old are they now? I'm unfamiliar with finding answer when asked "six years ago." ------------ Now Eq: D = B - 4 6yrs ago Eq::: D-6 + B-6 = 46 -------------------- Simplify: D - B = -4 D + B = 58 ---- 2D = 54 Deb = 27 yrs (Deb's age now) B = 27-4 = 23 yrs (Beth's age now) =========== Cheers, Stan H.
 logarithm/727006: help solve, log16 32- log16 2=x1 solutions Answer 444921 by stanbon(57209)   on 2013-03-17 09:42:12 (Show Source): You can put this solution on YOUR website!log16 32- log16 2=x ---- log16(32)-log16(2) = x x = log16(32/2) x = log16(16) x = 1 ============= Cheers, Stan H.
 logarithm/727005: help solve, log2 x=1/3 log2 27 ?1 solutions Answer 444920 by stanbon(57209)   on 2013-03-17 09:40:29 (Show Source): You can put this solution on YOUR website!log2 x=1/3 log2 27 ----------- log2(x) = (1/3)log2(27) --- log2(x) = log2(3) ---- x = 3 ============ Cheers, Stan H.
 �t�e�s�t/727001: rakesh is standing at a point. He walks 20 m to the east, then further 10 m to the west and further 5 m to the north, than he walks 15 m to the east, what is the straight distance between his starting point and the point where he reached the last1 solutions Answer 444919 by stanbon(57209)   on 2013-03-17 09:38:01 (Show Source): You can put this solution on YOUR website! rakesh is standing at a point. He walks 20 m to the east, then further 10 m to the west and further 5 m to the north, than he walks 15 m to the east, what is the straight distance between his starting point and the point where he reached the last ---- Let him start at (0,0) 1st step to (20,0) 2nd step to (10,0) 3rd step to (10,5) Last step to (25,5) ---- distance = sqrt[25^2+5^2] = sqrt(650] = 5sqrt(26) meters ============ Cheers, Stan H. ==============
 logarithm/727000: log3 x-2 log3 2 = 3 Log3 3 help me solve this? p.s. the 3s' right next to the g's on log, are the base, sorry couldnt make them little threes.!1 solutions Answer 444918 by stanbon(57209)   on 2013-03-17 09:30:18 (Show Source): You can put this solution on YOUR website!log3 x-2 log3 2 = 3 Log3 3 ----- log3(x)-2log3(2) = 3log3(3) ----- log3[x/2] = log3(27) ---- x/2 = 27 x = 54 ============ Cheers, Stan H.
 Mixture_Word_Problems/726987: You are making iced tea for a friend who prefers it at 80% strength. The function gives the concentration of the tea after adding x fluid ounces of a 50% tea solution to 6 fluid ounces of 100% strength tea. How many fluid ounces of 50% strength tea should you add to 6 fl oz of 100% strength tea?1 solutions Answer 444917 by stanbon(57209)   on 2013-03-17 09:27:41 (Show Source): You can put this solution on YOUR website!You are making iced tea for a friend who prefers it at 80% strength. The function gives the concentration of the tea after adding x fluid ounces of a 50% tea solution to 6 fluid ounces of 100% strength tea. How many fluid ounces of 50% strength tea should you add to 6 fl oz of 100% strength tea? ----- Equation: tea + tea = tea 0.50x + 1*6 = 0.80(x+6) ----- Multiply thru by 100 to get: 50x + 100*6 = 80x + 80*6 30x = 20*6 x = 4 oz (amt. of 50% tea to add) ============ Cheers, Stan H. ==============
 Geometric_formulas/726822: What is the geometric series of 36+6+1.....S9?1 solutions Answer 444806 by stanbon(57209)   on 2013-03-16 16:24:15 (Show Source): You can put this solution on YOUR website!What is the geometric series of 36+6+1.....S9? ---- a(1) = 36 r = 6/36 = 1/6 ----- Not sure what you mean by S9, but I'll assume it you mean a(9). ------- a(9) = a(1)*r^8 == a(9) = 36*(1/6)^8 = 1/6^6 = 0.00002143... Cheers, Stan H.
 Permutations/726819: political polling organization wishes to select a smaller focus group from a group of of 7 Republicans, 3 Democrats, and 4 Independents. In how many ways can the group be chosen if: a) it will consist of 4 Republicans and 3 Democrats? b) it will consist of 2 Republicans, 2 Democrats, and 3 Independents? 1 solutions Answer 444803 by stanbon(57209)   on 2013-03-16 16:18:13 (Show Source): You can put this solution on YOUR website!political polling organization wishes to select a smaller focus group from a group of of 7 Republicans, 3 Democrats, and 4 Independents. In how many ways can the group be chosen if: a) it will consist of 4 Republicans and 3 Democrats? Ans:: 7C4 * 3C3 = (7*6*5)/(1*2*3) *1 = 35 ways ----------------------------- b) it will consist of 2 Republicans, 2 Democrats, and 3 Independents? Ans:: 7C2 * 3C2 * 4C3 = 21 * 3 * 4 = 252 ways ============= Cheers, Stan H. ==============
 Percentage-and-ratio-word-problems/726691: Dear Tutor I would like to know how much water needed to add in 8 percent alocohol to make it 37% proof ( for drinking alcohol) Thank you Valentina1 solutions Answer 444801 by stanbon(57209)   on 2013-03-16 16:12:31 (Show Source): You can put this solution on YOUR website!Dear Tutor I would like to know how much water needed to add in 8 percent alocohol to make it 37% proof ( for drinking alcohol) Thank you Valentina ----- You cannot increase the percent of alcohol by adding pure water. Cheers, Stan H.
 Trigonometry-basics/726610: Solve the equation when x is in the set of [0, 2(pi)). secx = 1 + tanx1 solutions Answer 444683 by stanbon(57209)   on 2013-03-15 20:50:37 (Show Source): You can put this solution on YOUR website!Solve the equation when x is in the set of [0, 2(pi)). secx = 1 + tanx ---- Multiply thru by cos(x) to get: 1 = cos + sin 1 = sqrt(1-sin^2) + sin 1-sin = sqrt(1-sin^2) (1-sin)^2 = 1-sin^2 1 - 2sin + sin^2 = 1-sin^2 2sin^2 -2sin = 0 sin(2sin-2) = 0 sin(x) = 0 or sin(x) = 1 x = 0 or x = pi/2 Usable solution: x = 0 Check sec(0) = 1 + tan(0) 1 = 1 + 0 1 = 1 ============= Cheers, Stan H.