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Recent problems solved by 'stanbon'

stanbon answered: 57288 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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Sequences-and-series/691886: The answer to the question is 15 terms. But, I can't find the answer without knowing what to find, first. I tried the formulas and to no avail. Here is the question, "How many terms are in the sum of an arithmetic sequence if the first term is 21, the common difference is 9 and the sum is 1,260?" I know that (a one) is 21, d=9 and n=1260 I first tried to see if 1,260 could be a term and calculated it with the An = A1 + (n-d)d and that didn't work. Then, I tried to plug in the numbers with the Sn=n(A1+An)/2, that further confused me. I have no idea what to do when provided the total first and how to work from that in order to find the terms. There are no examples in both my math books and I'm stuck. Help. 1 solutions Answer 426887 by stanbon(57361)   on 2012-12-09 16:18:47 (Show Source): You can put this solution on YOUR website! "How many terms are in the sum of an arithmetic sequence if the first term is 21, the common difference is 9 and the sum is 1,260?" I know that (a one) is 21, d=9 and n=1260 ------ Sum Formula: S(n) = (n/2)(a(1)+(a(n))) 1260 = (n/2)(21 + [21+ (n-1)9] ---- 1260 = (n/2)[42+9n-9] --- 2520 = (n)[33+9n] ---- 2520 = 33n + 9n^2 ----- 3n^2 + 11n - 840 = 0 (n-15)(3n+ 56) = 0 --- Positive solution: n = 15 ============== cheers, Stan H.

Polynomials-and-rational-expressions/691870: Hi I am in Pre Calc with Trig, and I know there isn't a section for this, but I was hoping you could show me how to answer my question. I don't need the answer. I just need to know how to work it out. The question is "Perform the indicated operations, leave your answer in simplest form and identify the restrictions" and the problem is (80a^3 b^(2 )-60a^2 bc)/(120a^2 b^3-90ab^2 c). So I think I may have simplified it, but I don't know if it is right and how to find the restrictions. I have it simplified as 2a/3b because I got it down to (20a^2b(4ab-3c))/(30ab^2(4ab-3c)). 1 solutions Answer 426878 by stanbon(57361)   on 2012-12-09 15:56:54 (Show Source): You can put this solution on YOUR website! (80a^3*b^2-60a^2bc)/(120a^2b^3-90ab^2c) ----------- Factor numerator and denominator: ------ = [20a^2b(4a-3c)] / [30ab^2(4ab-3c) ---- Cancel all factors common to numerator and denominator to get: ----- = [2a(4a-3c)]/[3b(4ab-3c)] ====== Cheers, Stan H. =================================

Mixture_Word_Problems/691863: a dairy owner mixes 5 gal of cream that is 30% butterfat and 8 gal of milk that is 4% butterfat. find the percent concentration of butterfat in the resulting mixture. 1 solutions Answer 426876 by stanbon(57361)   on 2012-12-09 15:25:06 (Show Source): You can put this solution on YOUR website! a dairy owner mixes 5 gal of cream that is 30% butterfat and 8 gal of milk that is 4% butterfat. find the percent concentration of butterfat in the resulting mixture. ------ Equation: fat + fat = fat ------ 0.30*5 + 0.04*8 = x*13 ---- 1.5 + 0.32 = 13x ----- 13x = 1.82 --- x = 14% ====================== Cheers, Stan H. ================

test/691865: -18<2(12-3b) 1 solutions Answer 426874 by stanbon(57361)   on 2012-12-09 15:17:37 (Show Source): You can put this solution on YOUR website! -18<2(12-3b) ------- -18 < 24 - 6b ---- Add 6b to both sides. Add 18 to both sides. --- 6b < 42 --- b = 7 ================ Cheers, Stan H.

Age_Word_Problems/691839: ahmed is 7 years older than his sister if the sun of their ages is 21 years find their ages 1 solutions Answer 426872 by stanbon(57361)   on 2012-12-09 15:14:35 (Show Source): You can put this solution on YOUR website! ahmed is 7 years older than his sister if the sun of their ages is 21 years find their ages ------ Equations: a = s + 7 a + s = 21 ---- Substitute for "a" and solve for "s": s+7 + s = 21 2s = 14 s = 7 (sister's age now) ---------------------- Solve for "a" a = s + 7 a = 7+7 a = 14 yrs (ahmed's) age now ================================ cheers, Stan H. ================

Inequalities/691835: Use the multiplication property of inequalities to solve the inequality. 7/8x > -9/16 1 solutions Answer 426859 by stanbon(57361)   on 2012-12-09 14:40:33 (Show Source): You can put this solution on YOUR website! Use the multiplication property of inequalities to solve the inequality. 7/8x > -9/16 --- Multiply both sides by 8/7 to get: ------- x > (-9/16)(8/7) ---- x > -9/14 =============== cheers, Stan H.

logarithm/691840: Use the change of base rule to find the logarithm to four decimal places for the following. log8 24.16 1 solutions Answer 426858 by stanbon(57361)   on 2012-12-09 14:36:51 (Show Source): You can put this solution on YOUR website! Use the change of base rule to find the logarithm to four decimal places for the following. log8 24.16 ----- = log(24.16)/log(8) ----- = 1.5315 ============= Cheers, Stan H. ================

Exponents/691823: A certain radioactive isotope has a half-life of approximately 850 years. How many years to the nearest year would be required for a given amount of this isotope to decay 20% of that amount? 1 solutions Answer 426857 by stanbon(57361)   on 2012-12-09 14:32:43 (Show Source): You can put this solution on YOUR website! A certain radioactive isotope has a half-life of approximately 850 years. How many years to the nearest year would be required for a given amount of this isotope to decay 20% of that amount? --------------------- A(t) = Ao(1/2)^(t/850) ----- 0.20 = (1/2)^(t/850) --- (t/850) = log(0.2)/(0.5) --- t/850 = 2.3219 ----- t = 1974 years ============== Cheers, Stan H> ==============

Numeric_Fractions/691825: how to solve (1/4)(x)=(10)(1 3/8) thank you 1 solutions Answer 426856 by stanbon(57361)   on 2012-12-09 14:21:26 (Show Source): You can put this solution on YOUR website! how to solve (1/4)(x)=(10)(1 3/8) ------ x = 4(10)(11/8) ------ x = 55 ================= Cheers, Stan H.

logarithm/691758: log(x-1)+log(x+1)=Log(x+2)^2 1 solutions Answer 426854 by stanbon(57361)   on 2012-12-09 14:18:42 (Show Source): You can put this solution on YOUR website! log(x-1)+log(x+1)=Log(x+2)^2 ------- log[(x-1)(x+1)] = log(x+2)^2 --- x^2-1 = (x+2)^2 --- x^2-1 = x^2 + 4x + 4 --- 4x = -5 x = -5/4 ---- Result: No solution as that solution is extraneous. Cheers, Stan H.

logarithm/691811: Solve the equation and express the solution in exact form. ln(32x - 1) = ln 15 1 solutions Answer 426851 by stanbon(57361)   on 2012-12-09 14:12:29 (Show Source): You can put this solution on YOUR website! Solve the equation and express the solution in exact form. ln(32x - 1) = ln 15 ---- Take the inverse log of both sides to get: 32x-1 = 15 32x = 16 x = 1/2 ================= Cheers, Stan H.

logarithm/691812: Solve the Equation. 2x+9 = 9x 1 solutions Answer 426850 by stanbon(57361)   on 2012-12-09 14:09:29 (Show Source): You can put this solution on YOUR website! 2x+9 = 9x ---- 7x = 9 x = 9/7 ================ Cheers, Stan H. ===================

logarithm/691815: Simplify each expression: (a) log5b^(5b) (b) log9b((9b)^7) (c) log 11b ((11b)^-12) 1 solutions Answer 426849 by stanbon(57361)   on 2012-12-09 14:06:52 (Show Source): You can put this solution on YOUR website! (a) log5b^(5b)= 5b ------ (b) log9b((9b)^7)= 7 ------------------------ (c) log 11b ((11b)^-12 = -12 =============== Cheers, Stan H.

Probability-and-statistics/691593: A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level. H0: µ1 ≤ µ2 H1: µ1 > µ2 State the decision rule. (Round your answer to 2 decimal places.) a) The decision rule is to reject H0 if z greater than ........ b)What is the p-value? 1 solutions Answer 426781 by stanbon(57361)   on 2012-12-08 23:19:30 (Show Source): You can put this solution on YOUR website! A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level. H0: µ1 ≤ µ2 H1: µ1 > µ2 State the decision rule. (Round your answer to 2 decimal places.) a) The decision rule is to reject H0 if z greater than invNorm(0.92) = 1.4051........ b)What is the p-value? P(z > 0.6071) = 0.2719 ========================== Cheers, Stan H.

Probability-and-statistics/691603: the lengths of steel rods cut by a machine are normally distributed with mean 13.8com. It is found that 1.5% of all rods are less than 13.2cm long. Find the standard deviation of rod lengths produced by this machine. 1 solutions Answer 426779 by stanbon(57361)   on 2012-12-08 23:10:50 (Show Source): You can put this solution on YOUR website! the lengths of steel rods cut by a machine are normally distributed with mean 13.8com. It is found that 1.5% of all rods are less than 13.2cm long. Find the standard deviation of rod lengths produced by this machine. ------ Draw a normal curve. Put x = 13.8 in the middle Plot x = 13.2 on the horizontal axis Shade the tail to the left of 13.2 ; That tail has area 0.015 ---- Find the z-value with a left tail of 0.015: invNorm(0.015) = -2.1700 ---- Find the standard deviation using x = z*s + u ---- 13.2 = -2.17s + 13.8 ---- -2.17s = -0.6 --- s = 0.2765 =============== Cheers, Stan H. ===============

Probability-and-statistics/691608: A) If two fair dice are rolled, what is the probability that a total showing is more than 3? B) if two fair dice are rolled, what is the probability that a total showing is either even or less than nine? 1 solutions Answer 426776 by stanbon(57361)   on 2012-12-08 22:56:33 (Show Source): You can put this solution on YOUR website! A) If two fair dice are rolled, what is the probability that a total showing is more than 3? # of ways to succeed: 36-(1+2) = 33 # of possible outcomes: 36 P(condition) = 33/36 = 11/12 ------------------------------------- B) if two fair dice are rolled, what is the probability that a total showing is either even or less than nine? ------- # of ways to succeed: 18 + 15 - 9 = 24 --- # of possible outcomes: 36 P(condition) = 24/36 = 2/3 =============================== cheers, Stan H. =======================

Rectangles/691604: the perimeter of a rectangle park is 300 feet. The length of the park is 20 feet longer than the width. Find the length of the park 1 solutions Answer 426773 by stanbon(57361)   on 2012-12-08 22:26:54 (Show Source): You can put this solution on YOUR website! the perimeter of a rectangle park is 300 feet. The length of the park is 20 feet longer than the width. Find the length of the park ------------------------ P = 2(L + W) --- 300 = 2(W+20 + W) 150 = 2W + 20 2W = 130 W = 65 feet (width) L = W+20 = 85 feet (length) =============================== Cheers, Stan H. =================

Linear-equations/691605: Graph the following system of equations using slope and Y-intercept. Determine the number of solutions for the system: 3x-5y=-5 and 6x-10y=-10 1 solutions Answer 426772 by stanbon(57361)   on 2012-12-08 22:15:06 (Show Source): You can put this solution on YOUR website! 3x-5y=-5 6x-10y=-10 ---- Multiply the top equation by 2: 6x -10y = -10 6x-10y = -10 ------ The 2 equations are really the same equation. ---- Solution: All points of the form (x, (3/5)x +1) ---------- Cheers, Stan H. ----------

Probability-and-statistics/691568: There are 8 blue and 5 black socks in a drawer. In the dark you randomly chose two socks; what is the probability that they formed a pair. 1 solutions Answer 426769 by stanbon(57361)   on 2012-12-08 21:47:03 (Show Source): You can put this solution on YOUR website! There are 8 blue and 5 black socks in a drawer. In the dark you randomly chose two socks; what is the probability that they formed a pair. ------ # of ways to succeed: 8C2 + 5C2 = 28 + 10 = 38 ways ------ # of possoble pairs: 13C2 = 78 ------ Ans: 38/78 = 19/39 ====================== Cheers, Stan H.

logarithm/691570: The mass m(t) remaining after t days from a 25-g sample of thorium-234 is given by m(t)=25e^(-0.0277)t a) How much of the sample will remain after 70 days? Round the answer to the nearest integer. (Answer should be in terms of grams) b) After how long will only 10g of the sample remain? Round the answer to the nearest integer. (Answer should be in terms of days) c) Find the half-life of thorium-234. Round the answer to the nearest integer. (Answer should be in terms of days) 1 solutions Answer 426768 by stanbon(57361)   on 2012-12-08 21:29:26 (Show Source): You can put this solution on YOUR website! The mass m(t) remaining after t days from a 25-g sample of thorium-234 is given by m(t)=25e^(-0.0277)t a) How much of the sample will remain after 70 days? Round the answer to the nearest integer. (Answer should be in terms of grams) m(70) = 25*e^(-0.0277*70) = 3.5962 grams -------------------------------------------------------- b) After how long will only 10g of the sample remain? Round the answer to the nearest integer. (Answer should be in terms of days) 25*e^(-0.0277t) = 10 e^(-0.0277t) = 2/5 -0.0277t = ln(0.4) t = 33.079 days ---------------------------------- c) Find the half-life of thorium-234. Round the answer to the nearest integer. (Answer should be in terms of days) e^(-0.0277t) = 1/2 -0.0277t = ln(.5) t = 25 days when rounded down ==================================== Cheers, Stan H.

logarithm/691579: e^(5x-1)+3=4 What are the proper steps in solving this problem? 1 solutions Answer 426766 by stanbon(57361)   on 2012-12-08 21:22:04 (Show Source): You can put this solution on YOUR website! e^(5x-1)+3=4 Subtract 3 from both sides: ---- e^(5x-1) = 1 Take the natural log of both sides ---- 5x-1 = ln(1) Evaluate ln(1) --- 5x-1 = 0 Add 1 to both sides -------------------- 5x = 1 Divide both sides by 5: -------------------- x = 1/5 ============== Cheers, Stan H.

logarithm/691584: What are the proper steps into making this problem into a single logarithm? (Assume log is base 10) 4log(x)+(1/3)log(x-2)-2log(x+1) 1 solutions Answer 426765 by stanbon(57361)   on 2012-12-08 21:19:03 (Show Source): You can put this solution on YOUR website! 4log(x)+(1/3)log(x-2)-2log(x+1) ---- log(x^4) + log(x-2)^(1/3) - log(x+1)^2 ----- = log[(x^4*(x-2)^(1/3)/(x+1)^2] ==================================== Cheers, Stan H. ====================

Expressions-with-variables/691585: rewrite the equation 20l+10c=2000 to express C as a linear function of L 1 solutions Answer 426763 by stanbon(57361)   on 2012-12-08 21:16:31 (Show Source): You can put this solution on YOUR website! rewrite the equation 20L+10c=2000 to express C as a linear function of L ---- Solve for "c": 10c = -20L + 2000 Divide thru by 10: c = -2L + 200 ------ c(L) = -2L + 200 =================== Cheers, Stan H. ===================

logarithm/691562: The population of a certain city was 116,000 in 1995, and the observed relative growth rate is 4% per year. a) Find a function that models the population after t years. n(t)=_______ b) Find the projected population in the year 2004. Round the answer to the nearest thousand. c) In what year will the population reach 200,000? 1 solutions Answer 426758 by stanbon(57361)   on 2012-12-08 20:52:50 (Show Source): You can put this solution on YOUR website! The population of a certain city was 116,000 in 1995, and the observed relative growth rate is 4% per year. a) Find a function that models the population after t years. n(t)=116,000(1.04)^t --------------------------- b) Find the projected population in the year 2004. Round the answer to the nearest thousand. n(9) = 116,000(1.04)^9 = 165,104 ---------------------------------------- c) In what year will the population reach 200,000? Solve: 200,000 = 116,000*1.04^t ----- 1.04^t = 1.7241 --- Take the log of both sides: t*log1.04 = log1.7241 t = log(1.7241)/log(1.04) t = 13.88 = 14 years when rounded up ----------- Ans: 1995 + 14 = 2009 (Year the population will be 200,000)

Exponential-and-logarithmic-functions/691558: Solve the Equation. (x^3)(9^x) - 9^x =0 1 solutions Answer 426756 by stanbon(57361)   on 2012-12-08 20:43:42 (Show Source): You can put this solution on YOUR website! Solve the Equation. (x^3)(9^x) - 9^x =0 ---- Factor: (9^x)[x^3-1] = 0 --- 9^x = 0 or x^3 -1 = 0 ---- Note: 9^x cannot be zero ---- x^3-1 can be factored to get: (x-1)(x^2+x+1) = 0 x = 1 or you may find 2 complex solutions to x^2+x+1 using the Quadratic Formula. Cheers, Stan H. ===========

Exponential-and-logarithmic-functions/691559: e^2x - 5e^x +4 = 0 1 solutions Answer 426755 by stanbon(57361)   on 2012-12-08 20:38:11 (Show Source): You can put this solution on YOUR website! answered

logarithm/691551: Solve the equation. e^2x - 5e^x +4 = 0 1 solutions Answer 426754 by stanbon(57361)   on 2012-12-08 20:36:56 (Show Source): You can put this solution on YOUR website! e^2x - 5e^x +4 = 0 ---------------- Factor: (e^x-4)(e^x-1) = 0 --- e^x = 4 or e^x = 1 ------------------------ x = ln(4) or x = ln(1) = 0 ============================== cheers, Stan H. ===================

logarithm/691552: (ln(x))^2=ln(x)^2 solve for x 1 solutions Answer 426753 by stanbon(57361)   on 2012-12-08 20:34:11 (Show Source): You can put this solution on YOUR website! (ln(x))^2=ln(x)^2 solve for x ----- (ln(x))^2 - 2ln(x) = 0 --- Factor: ln(x)[ln(x)-2] = 0 ln(x) = 0 or ln(x) = 2 --- x = 1 or x = 100 ===================== Cheers, Stan H. =====================

Miscellaneous_Word_Problems/691553: Bobo can wash the car in 36 minutes by himself. When his brother Otto helps, they finish in 20 minutes. How long would it take Otto to wash the car by himself? 1 solutions Answer 426752 by stanbon(57361)   on 2012-12-08 20:30:21 (Show Source): You can put this solution on YOUR website! Bobo can wash the car in 36 minutes by himself. When his brother Otto helps, they finish in 20 minutes. How long would it take Otto to wash the car by himself? ---- Bobo rate = 1/36 job/min ---- Together rate = 1/20 job/min --- Otto rate = 1/x job/min --------------------------- Equation: rate + rate = together rate 1/36 + 1/x = 1/20 ------ 20x + 20*36 = 36x ------------ 16x = 20*36 ----- 4x = 5*36 x = 5*9 --- x = 45 minutes (time for Otto to do the job alone) ====================== Cheers, Stan H.

Polynomials-and-rational-expressions/691554: solve the following quadractic equation by factoring: x2 squared - x=6 1 solutions Answer 426751 by stanbon(57361)   on 2012-12-08 20:26:26 (Show Source): You can put this solution on YOUR website! solve the following quadractic equation by factoring: x^2 - x -6 = 0 ----- (x-3)(x+2) = 0 x = 3 or x = -2 ================== Cheers, Stan H. ==================

logarithm/690978: Expand (Express as (+),(-),(/),(*), without using exponents logb 4root x^7b^3/y^2z^12 1 solutions Answer 426717 by stanbon(57361)   on 2012-12-08 16:32:50 (Show Source): You can put this solution on YOUR website! Expand (Express as (+),(-),(/),(*), without using exponents logb 4root x^7b^3/y^2z^12 ----- logb[x^(7/4)*b(3/4)/y^(1/2)z^(3)] ---- = (7/4)logb(x)+(3/4)logb(b) - (1/2)logb(y)-3logb(z) ----- = (-5/4)logb(x) + (3/4) - (1/2)logb(y) ======================== Cheers, Stan H.