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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, >>Next

 Travel_Word_Problems/636657: how far will you travel in 5 minutes running at a rate of 7m/s? 1 solutions Answer 401165 by stanbon(57222)   on 2012-08-11 21:06:27 (Show Source): You can put this solution on YOUR website!how far will you travel in 5 minutes running at a rate of 7m/s? ------ 5 min = 5*60 sec = 300 seconds ------------------------------------------ distance = rate * time = (7 m/s)(300 s) = 2100 meters ---------------------- Cheers, Stan H.
 Matrices-and-determiminant/636648: Solve using matrices. If the system has no solution, say that it is inconsistent. 2x+y+z=5 4x-y-3z=1 8x+y-z=51 solutions Answer 401164 by stanbon(57222)   on 2012-08-11 20:54:52 (Show Source): You can put this solution on YOUR website!Solve using matrices. If the system has no solution, say that it is inconsistent. 2x+y+z=5 4x-y-3z=1 8x+y-z=5 ------ The determinant of the coefficient matrix is zero. The system is inconsistent. ======================== Cheers, Stan H. ===================
 Exponents/636651: x^6 + 1000 Please show how to factor this. 1 solutions Answer 401159 by stanbon(57222)   on 2012-08-11 20:35:48 (Show Source): You can put this solution on YOUR website!x^6 + 1000 --- = (x^2)^3 + 10^3 ----- = (x^2+10)((x^2)^2-10x^2+10^2) ----- = (x^2+10)(x^4-10x^2+100) ============================= Cheers, Stan H.
 Geometry_Word_Problems/636631: I have right triangle. Other angles are 38 and 52. The longest side is 4.25 inches. What length should the other two sides be?1 solutions Answer 401155 by stanbon(57222)   on 2012-08-11 19:03:32 (Show Source): You can put this solution on YOUR website!I have right triangle. Other angles are 38 and 52. The longest side is 4.25 inches. What length should the other two sides be? ----- 3rd angle = (180)-(38+52) = 90 degrees ------ So the hypotenuse = 4.25 ------- Draw the picture. Side opposite the 38 degree angle = 4.25*sin(38) = 2.62 ---- Side opposite the 52 degree angle = 4.25sin(52) = 3.35 ============================ Cheers, Stan H. =========
 Surface-area/636635: The angles in a convex quadrilateral add to be _________ degrees.1 solutions Answer 401152 by stanbon(57222)   on 2012-08-11 18:57:56 (Show Source): You can put this solution on YOUR website!The angles in a convex quadrilateral add to be _________ degrees. sum of the interior angles = (4-2)180 = 2*180 = 360 degrees. Stan H.
 Surface-area/636633: What is the measure of one angle of a regular convex 100-gon?1 solutions Answer 401150 by stanbon(57222)   on 2012-08-11 18:56:31 (Show Source): You can put this solution on YOUR website!What is the measure of one angle of a regular convex 100-gon? ---- The sum of the exterior angles is 360 Each exterio is 360/100 = 3.6 degrees --- Therefore, each interior angle is 180-3.6 = 176.4 degrees ======================== Cheers, Stan H. ===============
 Equations/636627: Find the prime factorization of three common multiples of 7560 and 18000. 1 solutions Answer 401148 by stanbon(57222)   on 2012-08-11 18:25:00 (Show Source): You can put this solution on YOUR website!Find the prime factorization of three common multiples of 7560 and 18000. ---- 7560/2 = 3780 3780/2 = 1890 1890/2 = 945 945/3 = 315 945/3 = 105 105/3 = 35 35/5 = 7 ---- Prime factor form: 5*7*3^3*2^3 ==================================== Use the same process to find the answer for 18000. Cheers, Stan H. ================
 expressions/636615: k + 4 + k^2 -5k + 8 ------- ------ --------------- = k + 1 1 - k k^2 -11 solutions Answer 401147 by stanbon(57222)   on 2012-08-11 18:20:13 (Show Source): You can put this solution on YOUR website!k 4 k^2 -5k + 8 ------- + ------ + ------------ k + 1 1 - k k^2 -1 ------------------------- Rewrite: k 4 k^2 -5k + 8 ------- - ------ + ------------ k + 1 k - 1 k^2 -1 lcm = (k^2-1) ----- Rewrite each fraction with the lcm as its denominator: ------ [k(k-1) -4(k+1) +k^2-5k+8]/[k^2-1] ------ [k^2-k-4k-4+k^2-5k+8]/[k^2-1] ------ [2k^2-10k+8]/[k^2-1] ---- = [2(k^2-5k+4)]/[k^2-1] ----- = [2(k-4)(k-1)]/[(k+1)(k-1)] ----- = [2(k-4)]/[k+1] ===================== Cheers, Stan H. ====================
 �t�e�s�t/636616: 2x^2-4x+1 ----------- change to a mixed expression x+2 1 solutions Answer 401143 by stanbon(57222)   on 2012-08-11 17:54:02 (Show Source): You can put this solution on YOUR website!2x^2-4x+1 ----------- change to a mixed expression x+2 ------------ Use synthetic division. ----- -2)....2....-4....1 ........2....-8..|..17 ------- Quotient: 2x-8 Remainder: 17/(x+2) ========================== Cheers, Stan H.
 Surface-area/636620: For a convex 51-gon, what is the sum of the measures of the interior angles?1 solutions Answer 401140 by stanbon(57222)   on 2012-08-11 17:48:35 (Show Source): You can put this solution on YOUR website!For a convex 51-gon, what is the sum of the measures of the interior angles? ----- sum of interior angles = (51-2)180 = 49*180 = 8820 degrees =================== Cheers, Stan H.
 Complex_Numbers/636617: 1 + 1 -- a ------------------- 1 - 1 -- 2a 1 solutions Answer 401138 by stanbon(57222)   on 2012-08-11 17:44:59 (Show Source): You can put this solution on YOUR website!1 + 1 -- a ------------------- 1 - 1 -- 2a ====================== = [(1+a)/a]/[(1-2a)/2a] ------- Invert the denominator and multiply: ----- = [(1+a)/a] times [(2a)/(1-2a)] ------ Cancel the common "a" factor to get: ----- = [(1+a)/1] times [(2)/(1-2a)] ---- = (2+2a)/(1-2a) ==================== Cheers, Stan H. =============
 Finance/636619: julie and kristen are the partners in a local sporting good shop . they needed \$51,000 to start the buisness. they invested in the ratio 5:12 respectively. what percent of the business was owned by Kristen ? if the business grows to \$3,000,000 what percent of it will julie own ?1 solutions Answer 401136 by stanbon(57222)   on 2012-08-11 17:39:39 (Show Source): You can put this solution on YOUR website! julie and kristen are the partners in a local sporting good shop . they needed \$51,000 to start the buisness. they invested in the ratio 5:12 respectively. what percent of the business was owned by Kristen ? if the business grows to \$3,000,000 what percent of it will julie own ? ---- 5:12 is the same as 5x:12x where Kristen's share is 12x --- Julie's percentage = 5x/17x = 5/17 = 29.4% --- Kristen's percentage = 12x/17x = 12/17 = 70.6% ========================== Cheers, Stan H. ==========================
 Rational-functions/636618: The intensity of sound (in Watts per square meter, or "W"/"m" ^2) varies inversely with the distance from the source. Suppose that a particular sound has in intensity of 90 "W"/"m" ^2 at a distance of 5 meters. How much farther away would you find the intensity at 40 "W"/"m" ^2? thanks so much for your help on this I really appreciate your time :)1 solutions Answer 401134 by stanbon(57222)   on 2012-08-11 17:31:52 (Show Source): You can put this solution on YOUR website!The intensity of sound (in Watts per square meter, or "W"/"m" ^2) varies inversely with the distance from the source. Suppose that a particular sound has in intensity of 90 "W"/"m" ^2 at a distance of 5 meters. How much farther away would you find the intensity at 40 "W"/"m" ^2? ------- W =k/d --- Solve for "k": 90 = k/5 k = 450 ------- Equation: 40 = 450/d d = 450/40 d = 11 1/4 meters ==================== Cheers, Stan H. ===============
 Permutations/636582: How many 3-digits numbers can be formed from the digits 0,1,2,3,4,5 and 6 if each digit can be used only once.1 solutions Answer 401128 by stanbon(57222)   on 2012-08-11 16:51:56 (Show Source): You can put this solution on YOUR website!How many 3-digits numbers can be formed from the digits 0,1,2,3,4,5 and 6 if each digit can be used only once. ======== Left-most digit: 5 ways Middle digit: 5 ways Right-most digit: 4 ways ----- Total = 5*5*4 = 100 3-digit numbers. Cheers, stan H.
 Graphs/636593: / = a fraction 1/5x + 1/3y = 22/15 1/5x + 3y = 74/5 solve the system by the substitution method. 1 solutions Answer 401121 by stanbon(57222)   on 2012-08-11 16:12:11 (Show Source): You can put this solution on YOUR website!1/5x + 1/3y = 22/15 1/5x + 3y = 74/5 solve the system by the substitution method. ----- Modify the equations: 3x + 5y = 22 3x + 45y = 222 ---- 3x = 22-5y ---- Substitute for 3x and solve for "y": 22-5y + 45y = 222 40y = 200 y = 5 --- Solve for "x": 3x = 22-5y 3x = -3 x = -1 =========================== Cheers, Stan H.
 Functions/636405: Good day Please help me with this function f(x) = (x^4 – 16)/(x^2 -4) excludes the domain X=-2 and x = +2 but the following table shows when the variable X aproaches to X=+2. x=+2 x 1.950 1.990 1.999 1.9999 ----------2.0001 2.001 2.005 2.010 f(x) 7.802 7.960 7.996 7.9996----------- 8.0003 8.004 8.020 8.040 which is the correct answer im kind of confuse: lim f (x) = 8 when x tends to +2 OR lim f (x) = 2 when x tends to +8 Please help me :)1 solutions Answer 401005 by stanbon(57222)   on 2012-08-10 16:41:13 (Show Source): You can put this solution on YOUR website!f(x) = (x^4 – 16)/(x^2 -4) excludes from the domain X=-2 and x = +2, but the following table shows when the variable X aproaches to X = -2. x=+2 x 1.950 1.990 1.999 1.9999 ----------2.0001 2.001 2.005 2.010 f(x) 7.802 7.960 7.996 7.9996----------- 8.0003 8.004 8.020 8.040 which is the correct answer im kind of confuse: lim f (x) = 8 when x tends to -2 OR lim f (x) = 9 when x tends to +2 ----------- f(x) = (x^4 – 16)/(x^2 -4) --- Factor: f(x) = [(x-2)(x+2)(x^2+4)]/[(x-2)(x+2)] This function has a hole at x = -2 and at x = 2 ---- Cheers, Stan H.
 test/636410: 1 solutions Answer 401001 by stanbon(57222)   on 2012-08-10 16:18:22 (Show Source): You can put this solution on YOUR website!Express in simplest form: (2x-4)/(x^2+4x-12) Factor: (2(x-2))/[(x+6)(x-2)] ----- Cancel: = 2/(x+6) ============== Cheers, Stan H.
 Linear-systems/636407: Solve l 2-3x l <=4...Solve absolute value sign 2-3x absolute value sign is less than or equal to 4. 1 solutions Answer 401000 by stanbon(57222)   on 2012-08-10 16:11:20 (Show Source): You can put this solution on YOUR website!Solve l 2-3x l <=4 ------ -4 <= 2-3x <= 4 ------ Subtract 2 along the line to get: -6 <= -3x <= 2 ---- Divide thru by -3. Remember: the inequality reverses: -2/3 <= x <= 2 =================== Cheers, Stan H.
 Functions/636402: wich is the domain of this function g(x) = 1/(x – 7) Thanks in advance1 solutions Answer 400998 by stanbon(57222)   on 2012-08-10 15:56:55 (Show Source): You can put this solution on YOUR website!the domain of this function g(x) = 1/(x – 7) ---- Domain: All Real Numbers except x = 7 ===================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/636391: log(x-15)=21 solutions Answer 400996 by stanbon(57222)   on 2012-08-10 15:53:07 (Show Source): You can put this solution on YOUR website!log(x-15)=2 ------ base = 10 exponent = log = 2 result = x-15 ----- x-15 = 10^2 = 100 x = 115 ------------------ Cheers, Stan H.
 Reduction-of-unit-multipliers/636397: how do i solve a problem 2/3=m/32 what is the procedure1 solutions Answer 400994 by stanbon(57222)   on 2012-08-10 15:49:17 (Show Source): You can put this solution on YOUR website!how do i solve a problem 2/3=m/32 what is the procedure ------ (2/3) = m/32 ---- Multiply both sides by 32 to get: m = (2/3)32 ---- m = 64/3 --- m = 21 1/3 ======================== Cheers, Stan H. -----------------------
 Functions/636395: Good day I will like your help with the following function g (y) = y ^ 2, to calculate g (5 + x) - 3g (x) you got: I really apreciate your help1 solutions Answer 400993 by stanbon(57222)   on 2012-08-10 15:44:42 (Show Source): You can put this solution on YOUR website!g (y) = y ^ 2, to calculate g (5 + x) - 3g (x) ------- g(5+x)-3g(x) ------ = (5+x)^2 -3x^2 ------ = 25 + 10x + x^2 - 3x^2 ---- = -2x^2 + 10x + 25 ======= Cheers, Stan H. ============
 Rate-of-work-word-problems/636387: If it takes a 4 litre jerry can 20 mins to fill up a 1000 liter tank, 12 mins for a 6 liter jerry can to fill the same tank separately, and 10 mins for a 7 liter jerry can to fill the tank separately, how long will it take all together to fill the 1000 liter tank?1 solutions Answer 400990 by stanbon(57222)   on 2012-08-10 15:39:24 (Show Source): You can put this solution on YOUR website!If it takes a 4 litre jerry can 20 mins to fill up a 1000 liter tank, 12 mins for a 6 liter jerry can to fill the same tank separately, and 10 mins for a 7 liter jerry can to fill the tank separately, how long will it take all together to fill the 1000 liter tank? --- 4 litre rate: 1/20 job/min ---------- 6 litre rate: 1/12 job/min ---------- 7 litre rate: 1/10 job/min ---- Together rate: 1/x job/min ---- Eqution: rate + rate + rate = together rate ----- 1/20 + 1/12 + 1/10 = 1/x Multiply thru by 60x to get: 3x + 5x + 6x = 60 14x = 60 x = 30/7 = 4.2857 minutes (time to do the job together ------ Cheers, Stan H.
 test/636385: The sum of two numbers is 10. The first number is 2/3 of the second number. What are the numbers?1 solutions Answer 400986 by stanbon(57222)   on 2012-08-10 15:25:39 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 10. The first number is 2/3 of the second number. What are the numbers? ----- Equations: x + y = 10 x = (2/3)y ---- Substitute for "x" and solve for "y": (2/3)y + y = 10 (5/3)y = 10 (1/3)y = 2 y = 6 ------ Solve for "x": x + y = 10 x + 6 = 10 x = 4 --------- Cheers, Stan H. ==========
 Permutations/636382: A travel app will suggest 3 hotels and 5 restaurants at random for any city it has information. How many different suggestions can it make for a town that only has 8 hotels and 18 restaurants? My thinking is C(8,3) + C(18,5). Am I on the right track? Thank you in advance for any assistance.1 solutions Answer 400982 by stanbon(57222)   on 2012-08-10 15:17:57 (Show Source): You can put this solution on YOUR website!A travel app will suggest 3 hotels and 5 restaurants at random for any city it has information. How many different suggestions can it make for a town that only has 8 hotels and 18 restaurants? My thinking is C(8,3) + C(18,5). Am I on the right track? A travel app will suggest 3 hotels and 5 restaurants at random for any city it has information. How many different suggestions can it make for a town that only has 8 hotels and 18 restaurants? My thinking is C(8,3) + C(18,5). Am I on the right track? ---- You need to multiply, not add. Cheers, Stan H.
 Probability-and-statistics/636271: Help, The diameters of grapefruits in a certain orchard are normally distributed with a mean of 7.30 inches and a standard deviation of 0.80 inches. (A) What percentage of the grapefruits in this orchard have diameters less than 6.7 inches? (B) What percentage of the grapefruits in this orchard are larger than 7.20 inches?1 solutions Answer 400887 by stanbon(57222)   on 2012-08-10 08:30:16 (Show Source): You can put this solution on YOUR website!The diameters of grapefruits in a certain orchard are normally distributed with a mean of 7.30 inches and a standard deviation of 0.80 inches. (A) What percentage of the grapefruits in this orchard have diameters less than 6.7 inches? z(6.7) = (6.7-7.3)/0.8 = -0.75 P(x < 6.7) = P(z<-0.75) = normalcdf(-100,-0.75) = 0.2266 ------------------------- (B) What percentage of the grapefruits in this orchard are larger than 7.20 inches? Find the z-score of 7.20 Find the probability z is greater than that z-score. Ans: 0.5497 =============== Cheers, Stan H.
 Probability-and-statistics/636117: 9 character password has four numbers (from 1 to 7) followed by two letters (from A to Z) followed by three more numbers (from 1 to 7). A) How many different passwords can be formed? B) How many different passwords have no repeated letters or numbers? would this be 26*7? Any help would be greatly appreciated. thank you1 solutions Answer 400886 by stanbon(57222)   on 2012-08-10 08:24:54 (Show Source): You can put this solution on YOUR website!9 character password has four numbers (from 1 to 7) followed by two letters (from A to Z) followed by three more numbers (from 1 to 7). A) How many different passwords can be formed? Ans: 7^4*26^2*7^3 = 7^7*26^2 = 556715068 ---------------------------------- B) How many different passwords have no repeated letters or numbers? Ans: 7*6*5*26*25*4*3*2 = 7!*26*25 = 3276000 =============== Cheers, Stan H. ================
 Probability-and-statistics/636272: I must perform a two-tailed hypothesis test using a .05 significant level intrinsic by gender which there are 39 males and 27 female. I need to state the null and a alternative statement for the test. I need to identify the significant level, the test statistic, and the critical value. I need to explain weather rejecting or failing the null hypothesis statement.1 solutions Answer 400884 by stanbon(57222)   on 2012-08-10 08:18:12 (Show Source): You can put this solution on YOUR website!What is it about the genders that you are testing? Your problem statement does not make that clear. Cheers, Stan H.
 Exponents-negative-and-fractional/636284: "WHAT IS THE SOLUTION FOR r/11=-41 solutions Answer 400883 by stanbon(57222)   on 2012-08-10 08:13:54 (Show Source): You can put this solution on YOUR website!r/11=-4 --- Multiply both sides by 11 to get: r = -44 ============== cheers, Stan H.
 logarithm/636288: How do i express log base b to number cube root a tothe power -3 times b devided by q power -3 in terms of sums and differences1 solutions Answer 400882 by stanbon(57222)   on 2012-08-10 08:11:37 (Show Source): You can put this solution on YOUR website!How do i express log base b to number cube root a tothe power -3 times b devided by q power -3 in terms of sums and differences ------ logb[a^(-3)*b/q^-3] ----- = logb[b*q^3/a^3] --- = logb(b)+3logb(q)-3logb(a) ----- = 1 + 3[logb(q/a)] =========================== Cheers, Stan H.
 logarithm/636301: Hi, I have quite a bit of troublesome problem here... What is the log_4 of sq.rt2? 1 solutions Answer 400881 by stanbon(57222)   on 2012-08-10 08:05:05 (Show Source): You can put this solution on YOUR website!Hi, I have quite a bit of troublesome problem here... What is the log_4 of sq.rt2? ------ log4(sqrt(2) = log(sqrt(2))/log(4) --- Let the base be "2". Then log2(sqrt(2))/log2(4) --- = (1/2)/2 ---- = 1/4 =========== Cheers, Stan H. ===========