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Recent problems solved by 'stanbon'

stanbon answered: 57308 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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Money_Word_Problems/389909: Anne has $3.90 in dimes and quarters she has 4 more dimes than quarters how many coins of each kind does she have. 1 solutions Answer 276426 by stanbon(57381)   on 2011-01-02 13:42:19 (Show Source): You can put this solution on YOUR website! Anne has $3.90 in dimes and quarters she has 4 more dimes than quarters how many coins of each kind does she have. ------- Equations: Quantity: d = q + 4 Value:: 10d + 25q = 390 cents ----- Substitute for "d" and solve for "q": 10(q+4) + 25q = 390 10q+40 + 25q = 390 35q = 350 q = 10 (# of quarters) =========================== Since d = q+r, d = 14 (# of dimes) =========================== Cheers, Stan H.

Miscellaneous_Word_Problems/389887: In 1988, Florence Griffith Joyner set a record of the 10.49 sec in the women’s 100-m dash. The equation can be used to estimate the world record in the women’s 100-m dash years after 1988. For what years was the record between 10.15 and 10.35 sec? Show your work not just the final answer. 1 solutions Answer 276425 by stanbon(57381)   on 2011-01-02 13:33:17 (Show Source): You can put this solution on YOUR website! Equation not shown. Cheers, Stan H.

test/389901: sin(x+y)=x^2 find the derivative 1 solutions Answer 276424 by stanbon(57381)   on 2011-01-02 13:30:39 (Show Source): You can put this solution on YOUR website! sin(x+y)=x^2 find the derivative ---- Derivative: cos(x+y)*(1+y') = 2x --- Solve for y': cos(x+y) + y'[cos(x+y)] = 2x --- y' = [2x-2(x+y)]/cos(x+y) ============================== Cheers, Stan H.

Complex_Numbers/389895: if the roots of a quadratic equation are -3 and 3, write the equation in ax^2+bx+c=0 form 1 solutions Answer 276421 by stanbon(57381)   on 2011-01-02 13:27:34 (Show Source): You can put this solution on YOUR website! if the roots of a quadratic equation are -3 and 3, write the equation in ax^2+bx+c=0 form --- (x+3)(x-3) = 0 --- x^2-9 = 0 ================= Cheers, Stan H. ========

Trigonometry-basics/389898: True or false: sin(-85)=-sin85 Thank you so much for all of your help!!!! God Bless!!!! 1 solutions Answer 276418 by stanbon(57381)   on 2011-01-02 13:22:03 (Show Source): You can put this solution on YOUR website! True or false: sin(-85)=-sin85 ---------- True ---- In general sin(-x) = -sin(x) ====== Cheers, Stan H.

test/389891: Find the equation of the tangent line to the curve x^2 +2xy-y^2 +x=2 at (1,2) 1 solutions Answer 276413 by stanbon(57381)   on 2011-01-02 13:12:53 (Show Source): You can put this solution on YOUR website! Find the equation of the tangent line to the curve x^2 +2xy-y^2 +x=2 at (1,2) ---------------------- Derivative: 2x + 2[xy'+y]-2yy'+1= 0 --- Solve for y': 2x + 2xy' +2y - 2yy' + 1 =0 --- y'(2x-2y) = -[2x+2y+1] --- y' = -[2x+2y+1]/[2x-2y] --- Slope at (1,2) = -[2+4+1]/[2-4] --- Slope at (1,2) = 7/2 =========================== Cheers, Stan H. ===================

Complex_Numbers/389890: (-2+i square root of 2)(3-4i square root of 2) simplifly in a+bi form 1 solutions Answer 276411 by stanbon(57381)   on 2011-01-02 13:06:19 (Show Source): You can put this solution on YOUR website! (-2+i square root of 2)(3-4i square root of 2) simplifly in a+bi form ----------- = -6 + 8isqrt(2) + 3isqrt(2) +4(2) -------- = 2 + 11sqrt(2)i =================== Cheers, Stan H. ===================

Miscellaneous_Word_Problems/389883: Cole’s two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed $1024.40 in interest. What was the amount of each loan? Show your work not just the final answer. 1 solutions Answer 276410 by stanbon(57381)   on 2011-01-02 12:56:18 (Show Source): You can put this solution on YOUR website! Cole’s two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed $1024.40 in interest. What was the amount of each loan? ----- Equation: interest + interest = interest 0.028x + 0.045(31000-x) = 1024.40 --- Multiply thru by 1000 to get: --- 28x + 45*31000 - 45x = 1000*1024 --- -17x = -371000 --- x = $21,823.53 (amt. invested at 2.8% ---- 31000-x = $9176.47 (amt. invested at 4.5% ======================= Cheers, Stan H. ==============

Complex_Numbers/389857: A fast food restaurant specializes in ham sandwiches. A customer may chose to add any or none of the following set of goodies: {Mayonnaise, Lettuce, Ketchup, Onion, Olive}. How many different ham sandwich combinations are possible? 1 solutions Answer 276396 by stanbon(57381)   on 2011-01-02 11:13:57 (Show Source): You can put this solution on YOUR website! A fast food restaurant specializes in ham sandwiches. A customer may chose to add any or none of the following set of goodies: {Mayonnaise, Lettuce, Ketchup, Onion, Olive}. How many different ham sandwich combinations are possible? ------ Each of those additives may be added or not added. --- # of combinations = 2^5 = 32 ------------------------- Cheers, Stan H.

Exponential-and-logarithmic-functions/389863: 4^(2x+7)=32^(x+3) 1 solutions Answer 276395 by stanbon(57381)   on 2011-01-02 11:10:26 (Show Source): You can put this solution on YOUR website! 4^(2x+7)=32^(x+3) ---- [2^2]^(2x+7) = [2^5]^(x+3) ---- 2^(4x+14) = 2^(5x+15) ---- 4x+14 = 5x+15 x = -1 ======= Cheers, Stan H.

Triangles/389794: an urn contains 3 red marbles and 1 green marbles. if 2 marbles are selected at random without replacement. what is the probability that they are both green? 1 solutions Answer 276340 by stanbon(57381)   on 2011-01-01 22:27:01 (Show Source): You can put this solution on YOUR website! an urn contains 3 red marbles and 1 green marbles. if 2 marbles are selected at random without replacement. what is the probability that they are both green? ------ Ans: 0 There are not 2 green marbles in the urn. ===== Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/389799: the greatest of four consecutive even integers is 14 less than twice the smallest integer. what are the integers? 1 solutions Answer 276338 by stanbon(57381)   on 2011-01-01 22:24:51 (Show Source): You can put this solution on YOUR website! the greatest of four consecutive even integers is 14 less than twice the smallest integer. what are the integers? ---- 1st: 2x-2 2nd: 2x 3rd: 2x+2 4th: 2x+4 ----- Equation: 2x+4 = 2(2x-2)-14 2x+4 = 4x-18 2x = 22 x = 11 ---- 1st: 20 2nd: 22 3rd: 24 4th: 26 ============= Cheers, Stan H.

Quadratic_Equations/389810: A toy rocket is launched from the top of a mountain and falls on the ground below. The height of the rocket above the ground is modeled by the relation H= -5t 2 + 20t + 105 where H is the height in meters and t is the elapsed time in seconds. How high is the mountain? 1 solutions Answer 276337 by stanbon(57381)   on 2011-01-01 22:21:35 (Show Source): You can put this solution on YOUR website! A toy rocket is launched from the top of a mountain and falls on the ground below. The height of the rocket above the ground is modeled by the relation H(t) = -5t^2 + 20t + 105 where H is the height in meters and t is the elapsed time in seconds. How high is the mountain? ---- The height of the mountain is the height of the rocket at time t=0. H(0) = -5*0^2+20*0+105 = 105 meters. =============================== Cheers, Stan H. ==========

Rational-functions/389811: Given that x is an integer between -2 and 2, state the relation represented by the equation y=2-|x| by listing a set of ordered pairs. Then state whether the relation is a function Thank you so much!!!!!! God Bless and Happy New Year!!!!!!!! 1 solutions Answer 276335 by stanbon(57381)   on 2011-01-01 22:18:50 (Show Source): You can put this solution on YOUR website! Given that x is an integer between -2 and 2, state the relation represented by the equation y=2-|x| by listing a set of ordered pairs. Then state whether the relation is a function ----------- If x = -4, y = 2-4 = -2 If x = -3, y = 2-3 = -1 If x = -2, y = 2-2 = 0 If x = -1, y = 2-1 = 1 If x = 0, y = 2-0 = 2 --- Plot those points and connect them to get get: --- Yes it is a function. Cheers, Stan H.

Rational-functions/389809: how do you find the zeros in this equation? x^5-5x^4-3x^3+15x^2-4x+20=0 1 solutions Answer 276332 by stanbon(57381)   on 2011-01-01 22:14:22 (Show Source): You can put this solution on YOUR website! find the zeros in this equation? x^5-5x^4-3x^3+15x^2-4x+20=0 --- I graphed it and found Real zeros at x = 2 and x = -2 and x = 5 ---- Use synthetic division to look for other zeros: 2)....1....-5....-3....15....-4....20 ........1.....-3....-9....-3....-10...|..0 ==== -2)......1......-5....1.....-5....|..0 ==== 5)........1.......0.....1.....|0 ---- Quotient: x^2+1 --- Complex zeros: x^2+1 = 0 (x+i)(x-i) = 0 x = -i or x = i ========================= Cheers, Stan H.

test/389807: What is the sulm of the polynomials 3a2b + 2a2b2 and -ab2 + a2b2 1 solutions Answer 276329 by stanbon(57381)   on 2011-01-01 22:00:21 (Show Source): You can put this solution on YOUR website! What is the sum of the polynomials 3a^2b + 2a^2b^2 and -ab^2 + a^2b^2 ----- Add "like" terms to get: ---- (3a^2b) + (2a^2b^2+a^2b^2)-ab^2 --- = 3a^2b + 3a^2b^2 - ab^2 ========================= Cheers, Stan H. ============

Probability-and-statistics/389806: 4. What is the probability that a that a worker at Random drives more that 15 miles to work if the distribution of all worker’s mileage is a Normal Distribution that ranges from 4 miles to 26 miles? 1 solutions Answer 276328 by stanbon(57381)   on 2011-01-01 21:56:39 (Show Source): You can put this solution on YOUR website! What is the probability that a worker at Random drives more that 15 miles to work if the distribution of all worker’s mileage is a Normal Distribution that ranges from 4 miles to 26 miles? ---- range = 6 sigma ---- 6 sigma = 26-4 = 22 --- sigma = 11/3 --- mean = 4+(22/2) = 15 ------------------------- P(x > 15) = 0.5000 ======================== Cheers, Stan H.

test/389808: Which of the following is a factor of the polynomial x2 - x - 20? 1 solutions Answer 276326 by stanbon(57381)   on 2011-01-01 21:52:20 (Show Source): You can put this solution on YOUR website! Which of the following is a factor of the polynomial x^2 - x - 20? ----- Factor form: (x-5)(x+4) =============================== Cheers, Stan H.

Triangles/389800: The sine ratio of any acute angle is equal to the cosine ratio of its complement ? true or false 1 solutions Answer 276322 by stanbon(57381)   on 2011-01-01 21:04:48 (Show Source): You can put this solution on YOUR website! true --- Cheers, Stan H.

Volume/389770: the sum of the digits of a two digit number is 11 and the difference of the digit is 5. what is the number 1 solutions Answer 276308 by stanbon(57381)   on 2011-01-01 18:46:11 (Show Source): You can put this solution on YOUR website! the sum of the digits of a two digit number is 11 and the difference of the digit is 5. what is the number ---- Let the number be 10t+u --- Equations: t + u = 11 t - u = 5 ----- 2t = 16 t = 8 --- Since t + u = 11, u = 3 ---------------- Ans: Number is 83 ====================== Cheers, Stan H.

Volume/389774: what is the height of a rectangular solid with a lenght of 7 feet width of 5 feet and a volume of 105 cubic feet 1 solutions Answer 276306 by stanbon(57381)   on 2011-01-01 18:36:54 (Show Source): You can put this solution on YOUR website! what is the height of a rectangular solid with a length of 7 feet, width of 5 feet and a volume of 105 cubic feet --------- Volume = height*width*length 105 sq.ft. = h*5'*7' ---- h = 105/35 --- height = 3 ft. ==================== Cheers, Stan H.

Equations/389776: The sum of two number is 33. Thier different is 7. what are the two number help please 1 solutions Answer 276305 by stanbon(57381)   on 2011-01-01 18:32:12 (Show Source): You can put this solution on YOUR website! The sum of two number is 33. Their difference is 7. what are the two numbers? ==================== Equations: x+y = 33 x-y = 7 --- Add and solve for "x": 2x = 40 x = 20 ---- Substitute and solve for "y": 20 + y = 33 y = 13 ----------------- Cheers, Stan H.

Money_Word_Problems/389761: four years ago, jonny invested $4000 at 5.4% intrest compunded annually. five years ago, he invested $3700 at 5.6% intrest compounded quartly. when are the two investments worth the same (or has the smaller one alwreday surprassed the greater one)? 1 solutions Answer 276303 by stanbon(57381)   on 2011-01-01 18:27:46 (Show Source): You can put this solution on YOUR website! four years ago, johnny invested $4000 at 5.4% interest compounded annually. ---- five years ago, he invested $3700 at 5.6% interest compounded quarterly. ==== when are the two investments worth the same (or has the smaller one already surpassed the greater one)? ------ Value of the $3700 investment after one year. 3700(1+0.056) = $3907 ------ Solve for "t": 3907(1+0.056)^t = 4000(1+0.054)^t [1.056/1.054]^t = 4000/3907 1.001898^t = 1.02375 ---- t = log(1.02375)/log(1.001898) --- t = 12.38 years ====================== Same value 8 1/3 years from now. ====================== Cheers, Stan H.

Matrices-and-determiminant/389758: What is Matrices, determinant, and the cramer rule? 1 solutions Answer 276299 by stanbon(57381)   on 2011-01-01 17:55:50 (Show Source): You can put this solution on YOUR website! Please use Google or other search engine to find extensive discussion of these topics. ---- Cheers, Stan H. ====

Equations/389768: find the range,median and mode for 80,80,100,90,85 1 solutions Answer 276298 by stanbon(57381)   on 2011-01-01 17:52:06 (Show Source): You can put this solution on YOUR website! find the range,median and mode for 80,80,100,90,85 ---- range = 100-80 = 20 ---- median = 85 ---- mode = 80 ==================== Cheers, Stan H.

Functions/389763: I am trying to solve by factoring, and I do not know if I am doing this correctly. Here is my work and answer: If f(x) = 20x and g(x) = x - 4, what is g(g(f(3))? f(3) = 20(3) g(60) = 60 - 4 g(56) = 56 - 4 = 52 [this is my answer, but I need someone to check the answer and walk me through the solution.] Thanks in advance for any assistance. 1 solutions Answer 276297 by stanbon(57381)   on 2011-01-01 17:50:08 (Show Source): You can put this solution on YOUR website! If f(x) = 20x and g(x) = x - 4, what is g(g(f(3))? ------- g(g(f(3)) --- = g(g(60)) --- = g(56) ----- = 52 ============ Cheers, Stan H.

Evaluation_Word_Problems/389731: a scientist develops a formula which can turn a light bulb into a camel.working alone it takes the scientist 4 hours to create one dose of formula.the scientist assistant can make one dose in 12 hours. how long working together will it take the scientist and his assistant to create one dose of formula? please answer the question by using a table and the 5 step method. thank you. 1 solutions Answer 276280 by stanbon(57381)   on 2011-01-01 15:28:31 (Show Source): You can put this solution on YOUR website! a scientist develops a formula which can turn a light bulb into a camel. --------- working alone it takes the scientist 4 hours to create one dose of formula. --------- the scientist assistant can make one dose in 12 hours. --------- how long working together will it take the scientist and his assistant to create one dose of formula? --- Your able has three rows: scientist ; assistant ; together --- Your table has two coluns: time and rate ----- Scientist time = 4 hrs ; rate = 1/4 job/hr --- Assistant time = 12 hrs ; rate = 1/12 job/hr --- Together time = x hrs ; rate = 1/x job/hr ------------------------------------------- Equation: rate + rate = rate 1/4 + 1/12 = 1/x Multiply thru by 12x --- 3x + x = 12 4x = 12 x = 3 hrs (time to do the job together) ========= Cheers, Stan H.

Polynomials-and-rational-expressions/389745: What would the polynomial with real coefficients whose zeroes are -4, 1-i, and 1 + i be? 1 solutions Answer 276277 by stanbon(57381)   on 2011-01-01 15:20:08 (Show Source): You can put this solution on YOUR website! What would the polynomial with real coefficients whose zeroes are -4, 1-i, and 1 + i be? ---- f(x) = (x+4)(x-(1-i))(x-(1+i)) ---- f(x) = (x+4)((x-1)+i)((x-1)-i) ---- f(x) = (x+4)((x-1)^2+1) --- f(x) = (x+4)(x^2-2x+2) --- f(x) = x^3+2x^2-4x+8 =========================== Cheers, stan H.

Trigonometry-basics/389206: I really need to answer these trigonometry problems. 1. The measure of two of the angles of a triangle are 50 degrees and 55 degrees. If its longest side measures 17 cm, find the perimeter of the triangle. 2. The vertex angle of an isosceles triangle is 72 degrees and each of the equal sides is 10 cm. Find the perimeter and are of the triangle. 3. The diameter of a circle C is 34 cm. Two radii AC and BC from the angle of 96 degrees. Find the length of the cord AB. 1 solutions Answer 275829 by stanbon(57381)   on 2010-12-29 17:08:11 (Show Source): You can put this solution on YOUR website! I really need to answer these trigonometry problems. 1. The measure of two of the angles of a triangle are 50 degrees and 55 degrees. If its longest side measures 17 cm, find the perimeter of the triangle. ---- The measure of the third angle is 180-(50+55) = 75 degrees ---- Find the length of the side opposite the 50 degree angle. Use the Law of Sines: a/sin(50) = 17/sin(75) --- a = sin(50)[17/sin(75)] ---- a = 13.48 ================== Find the length of the side opposite the 55 degree angle. Use the Law of Sines: b/sin(55) = [17/sin(75)] b = sin(55)[17/sin(75)] b = 14.42 ======================= Perimeter: 17 + 13.48 + 14.42 =================================== 2. The vertex angle of an isosceles triangle is 72 degrees and each of the equal sides is 10 cm. Find the perimeter and area of the triangle. --- Use the Law of Sines as in problem #1. =================================== 3. The diameter of a circle C is 34 cm. Two radii AC and BC form the angle of 96 degrees. Find the length of the cord AB. --- Perimeter = (pi)d = 34pi --- arc = (96/360)(34pi) = 28.48...cm Cheers, Stan H.

Triangles/389289: Find the value of x. A triangle. One exterior angle is 70 and the nonadjacent interior angles are X and 2X + 10. 1 solutions Answer 275828 by stanbon(57381)   on 2010-12-29 16:37:33 (Show Source): You can put this solution on YOUR website! A triangle. One exterior angle is 70 and the nonadjacent interior angles are X and 2X + 10. --- The sum of the exterior angles is 360 degrees. The exterior corresponding to "x" is 180-x The exterior correspondiing to "2x+10" = 180-(2x+10) = -2x+170 --- Solve: (180-x)+(-2x+170) + 70 = 360 -3x + 420 = 360 -3x = -60 x = 20 degrees ================= Cheers, Stan H. ============ ===========================

Equations/389243: hello, I really need help in solving these two equations. The question is as following: write the following as a single power, then evaluate. (-32)^3/5 x (-32)^4/5 / (-32)^2/5 and 4096^3/4 / 4096^2/3 x 4096^5/6 thanking you in advance! 1 solutions Answer 275797 by stanbon(57381)   on 2010-12-29 13:24:09 (Show Source): You can put this solution on YOUR website! write the following as a single power, then evaluate. (-32)^3/5 x (-32)^4/5 / (-32)^2/5 --- = (-32)^[3/5 + 4/5 - 2/5] --- = (-32)^[5/5] -- = -32 ================================== and 4096^3/4 / 4096^2/3 x 4096^5/6 --- = 4096^[3/4 + 2/3 + 5/6] --- = 4096^[(9+8+10)/12] --- = 4096^(27/12) --- = 2^27 --- Cheers, Stan H.