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Recent problems solved by 'stanbon'

stanbon answered: 57351 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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�t�e�s�t/598425: NO CALCULATIONS REQUIRED!!! Just tell whether or not you reject the null hypothesis and then write a vali conclusion. 2. You want to see if a quarter you have is a fair quarter so you flip it 100 times and get 58 heads. does this prove at the .01 significance level that the quarter is fair? P-Value = .1096 1 solutions Answer 378571 by stanbon(57424)   on 2012-04-12 23:13:04 (Show Source): You can put this solution on YOUR website! You want to see if a quarter you have is a fair quarter so you flip it 100 times and get 58 heads. does this prove at the .01 significance level that the quarter is fair? P-Value = .1096 ---- Since the p-value is greater than 1%, fail to reject Ho. ---- The coin is fair since Ho was "p = 1/2". ================== Cheers, Stan H. ==================

logarithm/598413: solve for x: (e^2x)-36=16e^x 1 solutions Answer 378570 by stanbon(57424)   on 2012-04-12 23:06:48 (Show Source): You can put this solution on YOUR website! solve for x: (e^2x)-36=16e^x ---------------------- That is a quadratic in e^x: (e^x)^2 - 16e^x - 36 = 0 ----- Let e^x = w ---- w^2 - 16w - 36 = 0 ---- w^2-18w+2w-36 = 0 ----- w(w-18) + 2(w-18) = 0 ------------ (w-18)(w+2) = 0 w = 18 or w = -2 ---------- e^x = 18 or e^x = -2 Note: e^x cannot be negative. --------------------------------- Solve e^x = 18 x = ln(18) ================ Cheers, Stan H.

Functions/598417: Function A pairs each integer with its absolute value. What is the range? 1 solutions Answer 378568 by stanbon(57424)   on 2012-04-12 22:57:41 (Show Source): You can put this solution on YOUR website! Function A pairs each integer with its absolute value. What is the range? ------ Range: All non-negative integers. ---------------------------------- Cheers, Stan H.

Functions/598416: Why is rounding to the nearest tenth a function? 1 solutions Answer 378567 by stanbon(57424)   on 2012-04-12 22:55:37 (Show Source): You can put this solution on YOUR website! Why is rounding to the nearest tenth a function? ---- It is not a function. Both 2.32 and 2.34 round down to 2.3 -------------------------------------------- Cheers, Stan H.

�t�e�s�t/598411: 1. Data was collected from 74 mature great white sharks and they had a mean of 13.8 feet and a standard deviation of 2.7 feet. Furthermore, 23 0f those sharks were over 16 feet long. a. can you say at the .01 significance length that average length of a mature great white shark is less than 15 feet? 1 solutions Answer 378565 by stanbon(57424)   on 2012-04-12 22:53:04 (Show Source): You can put this solution on YOUR website! Data was collected from 74 mature great white sharks and they had a mean of 13.8 feet and a standard deviation of 2.7 feet. Furthermore, 23 0f those sharks were over 16 feet long. a. can you say at the .01 significance length that average length of a mature great white shark is less than 15 feet? ------------------------------- Ho: u >= 15 Ha: u < 15 claim ------ x-bar = 13.8 z(13.8) = (13.8-15)/[2.7/sqrt(74)] = -3.8233 ---- p-value = P(z < -3.8233) = normalcdf(-100,-3.8233) = 0.00006586 --- Since the p-value is less than 1%, reject Ho. The test results support the claim. ======================================== Cheers, Stan H.

Quadratic_Equations/598408: i just did this problem x^2-5x+6=0 and i got 2,3 as my answer. i cant figure out got in the world i got (2+ -1x) (3+ -1x) as my trinomials.. 1 solutions Answer 378562 by stanbon(57424)   on 2012-04-12 22:42:25 (Show Source): You can put this solution on YOUR website! x^2-5x+6=0 ------ Factor: (x-3)(x-2) = 0 x = 3 or x = 2 ================== Cheers, Stan H.

Polynomials-and-rational-expressions/598398: Find the real values of z for which the given expression is undefined 2z/2z^2+z 1 solutions Answer 378561 by stanbon(57424)   on 2012-04-12 22:38:32 (Show Source): You can put this solution on YOUR website! Find the real values of z for which the given expression is undefined 2z/2z^2+z ----- Factor: (2z)/(z(2z+1)) --- Undefined with the denominator = 0. --- Note: 0/0 is said to be undetermined because it can be any value. (2z)/0 is said to be undefined because it can be no value. ---- Your problem is "undefined" when z = -1/2. It is undetermined when z = 0 ============================================== Cheers, Stan H.

logarithm/598392: ln(2x-7)+1=5 1 solutions Answer 378560 by stanbon(57424)   on 2012-04-12 22:29:09 (Show Source): You can put this solution on YOUR website! ln(2x-7)+1=5 ----- ln(2x-7) = 4 --- 2x-7 = e^4 2x = e^4+7 -- x = (e^4+7)/2 --- x = 30.8 ============ Cheers, Stan H.

Probability-and-statistics/598197: Consider a binomial experiment with 20 trials and probability 0.45 on a single trial. Use an approximatation to the normal distribution to find the probability of exactly 10 successes. Round your answer to the thousandths place. 1 solutions Answer 378494 by stanbon(57424)   on 2012-04-12 16:34:49 (Show Source): You can put this solution on YOUR website! Consider a binomial experiment with 20 trials and probability 0.45 on a single trial. Use an approximatation to the normal distribution to find the probability of exactly 10 successes. Round your answer to the thousandths place. --- u = np = 20*0.45 = 9 s = sqrt(npq) = sqrt(9*0.55) = 2.22 ----- z(9.5) = (9.5-9)/[2.22/sqrt(20) = 1.007 z(10.5) = (10.5-9)/[2.22/sqrt(20)] = 3.0217 ----------- P(x = 10) ~ P(1.007< z < 3.0217) = 0.1557 =========================================== Cheers, Stan H.

Probability-and-statistics/598203: What is the probability of observing a a value more then .75 from a standard normal distribution? I got 1-.7734 What is the probability of observing a number less then 5 or more than 10 from a normal distribution with mean 9 and standard deviation 2? 1 solutions Answer 378492 by stanbon(57424)   on 2012-04-12 16:23:49 (Show Source): You can put this solution on YOUR website! What is the probability of observing a a value more then .75 from a standard normal distribution? I got 1-.7734 = 0.2266 ----------------------------------- What is the probability of observing a number less then 5 or more than 10 from a normal distribution with mean 9 and standard deviation 2? --- z(5) = (5-9)/2 = -2 z(10) = (10-9)/2 = 1/2 ------- P(x < -2) or P(x > 1/2) = 0.0228 + 0.3985 --- = 0.3303 ================== Cheers, Stan H. ==================

Travel_Word_Problems/598124: a tortoise and a hare decide to reenact the fabled race between their species, but this time with a slight twist. They start at the same place, but to be fair, the hare gives the tortoise a 40- second head start. If the tortoise runs at a constant speed of 3 meters per second, and the hare runs at a constant speed of 11 meters per second, how many meters will the hare run until he catches the tortoise? 1 solutions Answer 378462 by stanbon(57424)   on 2012-04-12 12:21:53 (Show Source): You can put this solution on YOUR website! a tortoise and a hare decide to reenact the fabled race between their species, but this time with a slight twist. ------------------------------------ They start at the same place, but to be fair, the hare gives the tortoise a 40- second head start. If the tortoise runs at a constant speed of 3 meters per second, and the hare runs at a constant speed of 11 meters per second, how many meters will the hare run until he catches the tortoise? -------------------------------- Hare DATA: time = x sec ; rate = 11 m/s ; distance = 11x meters ---- Tortoise DATA: time = x sec ; rate = 3 m/s ; distance = 3x meters ---- Equations: t-distance + t-distance = h-distance 3x + 3*40 = 11x 3x + 120 = 11x 8x = 120 x = 15 seconds --- Hare distance: 11x = 165 meters ==================================== Cheers, Stan H.

Functions/598122: How do I graph this g(x)=2x+5 1 solutions Answer 378461 by stanbon(57424)   on 2012-04-12 12:04:45 (Show Source): You can put this solution on YOUR website! graph this g(x)=2x+5 --------------- 2 points determine a line: If x = 0, y = 5 If x = 2, y = 9 --- Plot the two points: (0,5) and (2,9) and draw a line thru them. ---- That is the graph you want. Cheers, Stan H.

Polynomials-and-rational-expressions/598118: write (-10) to the fifth power in standard notation? 1 solutions Answer 378460 by stanbon(57424)   on 2012-04-12 12:01:30 (Show Source): You can put this solution on YOUR website! write (-10) to the fifth power in standard notation? ---- (-10)^5 = -10,0000 ===================== Cheers, Stan H.

Geometry_Word_Problems/598121: The base of a fish tank has an area of 62.3 feet2. What is the volume of water in the tank? 1 solutions Answer 378459 by stanbon(57424)   on 2012-04-12 11:59:14 (Show Source): You can put this solution on YOUR website! insufficient information

Numbers_Word_Problems/598120: The sum of 4 consecutive numbers is 98. What is the smallest number? 1 solutions Answer 378457 by stanbon(57424)   on 2012-04-12 11:58:09 (Show Source): You can put this solution on YOUR website! The sum of 4 consecutive numbers is 98. What is the smallest number? --- 1st: x-2 2nd: x-1 3rd: x 4th: x+1 -------- Equation: sum = 98 4x-2 = 98 4x = 100 x = 25 ---- 1st: x-2 = 23 2nd: x-1 = 24 3rd: x = 25 4th: x+1 = 26 ===================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/598117: A community sponsored a charity square dance where admission was $3 for adults and $1.50 for children. If 168 people attended the dance and the money raised was $432, how many adults and how many children attended the dance? a. What are the two system of equations that you could write to sole this problem? b. What would you use to solve the system? Why? c. How many adults and how many children attended the dance? 1 solutions Answer 378454 by stanbon(57424)   on 2012-04-12 11:52:24 (Show Source): You can put this solution on YOUR website! A community sponsored a charity square dance where admission was $3 for adults and $1.50 for children. If 168 people attended the dance and the money raised was $432, how many adults and how many children attended the dance? a. What are the two system of equations that you could write to sole this problem? b. What would you use to solve the system? Why? c. How many adults and how many children attended the dance? -------------------------- Equations: Quantity: c + a = 168 Value: 1.5c +3a = 432 --------------------------------- Multiply thru the Quantity Equation by 3 to get: 3c + 3a = 3*168 1.5c+3a = 432 ---- Subtract lower from upper to get: 1.5c = 72 c = 48 (# of childred) Solve for "a": c + a = 168 48 + a = 168 a = 120 (# of adults) ============================ Cheers, Stan H. ===================

Linear_Equations_And_Systems_Word_Problems/598116: A chemist is mixing a solution that is 32% sodium and another solution that is 12% sodium. How many liters of each type should the chemist use to produce 50 liters of the solution that is 20% sodium? 1 solutions Answer 378453 by stanbon(57424)   on 2012-04-12 11:47:16 (Show Source): You can put this solution on YOUR website! A chemist is mixing a solution that is 32% sodium and another solution that is 12% sodium. How many liters of each type should the chemist use to produce 50 liters of the solution that is 20% sodium? ----------------------- Equation: sodium + sodium = sodium 0.32x + 0.12(50-x) = 0.20*50 ----- Multiply thru by 100 to get: 32x + 12*50 - 12x = 20*50 20x = 8*50 x = 20 liters (amt. of 32% solution needed) --- 50-x = 30 liters (amt. of 12% solution needed) ========================== Cheers, Stan H. ================

percentage/598115: hi if there is 30 qustions on a test sheet and my score was 93% how many did i get wrong Thanks 1 solutions Answer 378452 by stanbon(57424)   on 2012-04-12 11:43:31 (Show Source): You can put this solution on YOUR website! hi if there is 30 qustions on a test sheet and my score was 93% how many did i get wrong Thanks ------ 93% right means 7% wrong: Ans: 0.07*30 = 2.1 wrong ============================================== Cheers, Stan H.

Polynomials-and-rational-expressions/598111: How do I solve the equation b/b-1 + 2/b-4 ? can I just use the quadratic equation? when I use the quadratic equation it comes out is that the correct answer? 1 solutions Answer 378451 by stanbon(57424)   on 2012-04-12 11:41:08 (Show Source): You can put this solution on YOUR website! How do I solve the equation b/b-1 + 2/b-4 ? can I just use the quadratic equation? when I use the quadratic equation it comes out is that the correct answer? ------ Least common Divisor: (b-1)(b-4) ---- Rewrite each fraction with the lcm as its denominator: ---- (b(b-4))/lcm + (2(b-1))/lcm ---- Combine the numerators over the denominator to get: ---- = (b^2-4b+2b-2)/lcm --- Simplify: = (b^2-2b-2)/[(b-1)(b-4)] =========================== Cheers. Stan H.

Age_Word_Problems/597927: Darlas dad is 4 times older than Darla. Darlas mom is 3 times older that Darla. The sum of all thier ages is 88. How do I find the age of each person?? 1 solutions Answer 378401 by stanbon(57424)   on 2012-04-11 21:32:18 (Show Source): You can put this solution on YOUR website! Darlas dad is 4 times older than Darla. Darlas mom is 3 times older that Darla. The sum of all thier ages is 88. ----- Equations: f + d + m = 88 f = 4d m = 3d ---- Substitute for "f" and "m" and solve for "d": 4d + d + 3d = 88 8d = 88 d = 11 (Darla's age now) f = 4d = 44 (Father's age now) m = 3d = 33 (Mom's age now) =================== Cheers, Stan H. ==============

Probability-and-statistics/597923: Use the given degree of confidence and sample data to construct a confidence interval for the population mean u. Assume that the population has a normal distribution n=12, x=21.3, s=6.3, 99% 1 solutions Answer 378395 by stanbon(57424)   on 2012-04-11 21:25:18 (Show Source): You can put this solution on YOUR website! Use the given degree of confidence and sample data to construct a confidence interval for the population mean u. Assume that the population has a normal distribution n=12, x=21.3, s=6.3, 99% --- Sample mean = x-bar = 21.3 ME = z*s/sqrt(n) = 2.5758*6.3/sqrt(12) = 4.6845 --- 99% CI: 21.3-4.68 < u < 21.3+4.68 ---- (16.62,25.98) ------------------ Cheers, Stan H.

Polynomials-and-rational-expressions/597921: factor the area to determine the length and width of this rectangle A=8x squared+14x-15 1 solutions Answer 378392 by stanbon(57424)   on 2012-04-11 21:18:45 (Show Source): You can put this solution on YOUR website! factor the area to determine the length and width of this rectangle A=8x squared+14x-15 ---- A = 8x^2 + 14x - 15 A = 8x^2 + 20x-6x -15 A = 4x(2x+5)-3(2x+5) A = (4x-3)(2x+5) ===== length = one of the factors widt = the other. ====================== Cheers, Stan H.

logarithm/597918: how to solve log(10y)? 1 solutions Answer 378391 by stanbon(57424)   on 2012-04-11 21:14:05 (Show Source): You can put this solution on YOUR website! insufficient information

Equations/597912: $17,5550 is 27% of what number? 1 solutions Answer 378389 by stanbon(57424)   on 2012-04-11 21:11:32 (Show Source): You can put this solution on YOUR website! $17,550 is 27% of what number? ------ Equation: 0.27x = 17,550 x = 17,550/0.27 = $65000 ============================= Cheers, Stan H. =================

Expressions-with-variables/597907: Will you help me simply the expression: x^2+4x+4/x-2 * -(x-2)/3x+6 1 solutions Answer 378387 by stanbon(57424)   on 2012-04-11 21:08:52 (Show Source): You can put this solution on YOUR website! simply the expression: [x^2+4x+4/x-2] * [-(x-2)/3x+6] --------- Factor: [(x+2)^2/(x-2)] * [-(x-2)/(3(x+2)] ------ Cancel any factor common to a numerator and a denominator, such as (x+2), (x-2), to get: (x+2)/1 ---- = (-1/3)(x+2) ================ Cheers, Stan H. ==================

Polynomials-and-rational-expressions/597684: Please help me understand the following: Is the following true or false? Explain. 3x + 2y / 27x^3 + 8y^3 is equal to 1 / 9x^2 - 6xy + 4y^2 Thank you. 1 solutions Answer 378284 by stanbon(57424)   on 2012-04-11 15:00:58 (Show Source): You can put this solution on YOUR website! Is the following true or false? Explain. 3x + 2y / 27x^3 + 8y^3 is equal to 1 / 9x^2 - 6xy + 4y^2 -------- 3x + 2y / 27x^3 + 8y^3 -------- Factor: (3x+2y)/[(3x+2y)(9x^2 - 6xy + 4y^2)] ------- = 1/(9x^2-6xy+4y^2) ======================== Ans: Yes =========== Cheers, Stan H.

test/597681: 6x+6y/y-x / 18/5x-5y 1 solutions Answer 378283 by stanbon(57424)   on 2012-04-11 14:55:28 (Show Source): You can put this solution on YOUR website! [(6x+6y)/(y-x)] / [18/(5x-5y)] --------- = [(6(x+y))/(y-x)] / [18/(5(x-y))] ----- Invert the denominator fraction and multiply to get: ----- = [(x+y)/(-(x-y)] * [5(x-y)/3] ----- = [5(x+y)]/(-3) ---- = (-5/3)(x+y) ================= Cheers, Stan H. =================

Geometry_Word_Problems/597679: The sun deck at Francine's house is 30 feet above the beach.The slope of the stair's from the beach is 1.2. How long is the handrail for the stairs. 1 solutions Answer 378280 by stanbon(57424)   on 2012-04-11 14:48:02 (Show Source): You can put this solution on YOUR website! The sun deck at Francine's house is 30 feet above the beach.The slope of the stair's from the beach is 1.2. How long is the handrail for the stairs. --------------------- Draw the picture. You have a right triangle with height = 30 and slope = 1.2 slope = height/base = 1.2/1 base = height/1.2 base = 30/1.2 = 25 ---- hypotenuse = rail = sqrt[25^2+30^2] = 39.05 feet. =================================================== Cheers, Stan H.

logarithm/597677: log[3](x^(2)-2x)=1 1 solutions Answer 378279 by stanbon(57424)   on 2012-04-11 14:42:20 (Show Source): You can put this solution on YOUR website! log[3](x^(2)-2x)=1 ------ x^2-2x = 3 --- x^2-2x-3 = 0 Factor: (x-3)(x+1) = 0 x = 3 or x = -1 ---- Usable answer: x = 3 ======================== Cheers, Stan H.

sets-and-operations/597675: A set of data consists of the numbers 12, 20, 16, 31, 25, 22, 16, and 27. Which of thise measures would not change if 32 were added to the data set? 1 solutions Answer 378277 by stanbon(57424)   on 2012-04-11 14:40:21 (Show Source): You can put this solution on YOUR website! A set of data consists of the numbers 12, 20, 16, 31, 25, 22, 16, and 27. Which of thise measures would not change if 32 were added to the data set? --- The mode would still be 16. Cheers, Stan H.

Average/597672: The sum of two consecutive integers is -297. Find the larger integer. 1 solutions Answer 378276 by stanbon(57424)   on 2012-04-11 14:38:32 (Show Source): You can put this solution on YOUR website! The sum of two consecutive integers is -297. Find the larger integer. 1st: x 2nd: x+1 ---- Equation: x + x+1 = -297 2x = -298 x = -149 x+1 = -148 -------------------------------- Cheers, Stan H.