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Recent problems solved by 'stanbon'

stanbon answered: 57240 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269, >>Next

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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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(57308)   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.

Exponents/389259: the model y = 17(1.9)x is classified as a. exponential growth b. exponential decay. The model y = 22(0.8)x is classified as a. exponential growth b. exponential decay. 1 solutions Answer 275795 by stanbon(57308)   on 2010-12-29 13:18:04 (Show Source): You can put this solution on YOUR website! duplicate

Exponents/389260: the model y = 17(1.9)x is classified as a. exponential growth b. exponential decay. The model y = 22(0.8)x is classified as a. exponential growth b. exponential decay. 1 solutions Answer 275794 by stanbon(57308)   on 2010-12-29 13:17:20 (Show Source): You can put this solution on YOUR website! the model y = 17(1.9)^x is classified as a. exponential growth b. exponential decay. Since 1.9 is greater than 1, it is exponential growth. --- The model y = 22(0.8)^x is classified as a. exponential growth b. exponential decay. Since 0.8 is greater than zero and less than one it is exponential decay. --- Cheers, Stan H. ===========

Permutations/389187: Please help me solve this problem. How many distinct arrangements can be made with the letters in the palindrome “Madam I’m Adam”? (Disregard the apostrophe and capitalization.) 1 solutions Answer 275758 by stanbon(57308)   on 2010-12-29 10:08:03 (Show Source): You can put this solution on YOUR website! How many distinct arrangements can be made with the letters in the palindrome “Madam I’m Adam”? (Disregard the apostrophe and capitalization.) ------------ 11!/[4!*4!*2!) = 34650 ========== Cheers, Stan H.

Polynomials-and-rational-expressions/389177: How do I determine the values of a if f(x)=3a square x cube - ax +4 and f(2)=6? 1 solutions Answer 275706 by stanbon(57308)   on 2010-12-28 21:54:59 (Show Source): You can put this solution on YOUR website! How do I determine the values of a if f(x)=3a square x cube - ax +4 and f(2)=6? -------- f(x) = 3a^2x^3 - ax + 4 Solve for "a" if y = 6 when x = 2 --- 6 = 3a^2*2^3 - a*2 + 4 -------------- 24a^2 - 2a + 4 = 0 --- a = [2 +- sqrt(4-4*24*4)]/(24) --- a = [2 +- sqrt(-380)](24) ---- a = [2 +-i19.49]/(24) etc. ====================== Cheers, Stan H.

Polynomials-and-rational-expressions/389171: The measure of the second angle of a triangle is 30 degree less than the measure of the first angle. The measure of the third angle is one -third of the measure of the first angle .Find the measure of the three angles of the triangle.( Solution of the equations is not required) Thanks. 1 solutions Answer 275699 by stanbon(57308)   on 2010-12-28 21:25:02 (Show Source): You can put this solution on YOUR website! The measure of the second angle of a triangle is 30 degree less than the measure of the first angle. The measure of the third angle is one -third of the measure of the first angle .Find the measure of the three angles of the triangle.( Solution of the equations is not required) --- 1st angle: x 2nd angle: x-30 3rd angle: (1/3)x -------------------------------- Equation: x + x-30 + (1/3)x = 180 =========================== Cheers, Stan H. ==========

Rectangles/389172: the perimeter of a rectangle is 72 mm. the height is three more than two times the base. what is the area 1 solutions Answer 275697 by stanbon(57308)   on 2010-12-28 21:20:49 (Show Source): You can put this solution on YOUR website! the perimeter of a rectangle is 72 mm. the height is three more than two times the base. --- Let the base be "x". Then the height is "2x+3" ---- Perimeter = 2(base + height) ----- 72 = 2(x + 2x+3) 3x+3 = 36 3x = 33 x = 11 mm (base) 2x+3 = 2*11+3 = 25 mm (height) =========================== what is the area ? Area = base *height Area = 11*25 = 275 mm^2 =========================== Cheers, Stan H.

Complex_Numbers/389056: Find the solution set of 18 - |2y-6| > 45 Find the values of k so that the line Y = KX + 10 will form a triangle of area 60 with the coordinate axis. Give your answers in simplified fraction form. The female born in the later part of 20th century will be x years old in the year x squared. In what year was she born? (x is in integers) 1 solutions Answer 275696 by stanbon(57308)   on 2010-12-28 21:09:13 (Show Source): You can put this solution on YOUR website! Find the solution set of 18 - |2y-6| > 45 ---- -|2y-6| > 27 |2y-6| < -27 No solutions as an absolute value cannot be negative. =========================================================== Find the values of k so that the line Y = KX + 10 will form a triangle of area 60 with the coordinate axis. Give your answers in simplified fraction form. --- The y-intercept is (0,10) Plot the point (0,10). Note that the height of the triangle is 10. So, if the area is 60, Area = (1/2)*height*base 60 = (1/2)10*base base = 12 So the x-intercept is 12 Plot (12,0) --- Solve 0 = k*12 +10 --- k = -5/6 ========================================== The female born in the later part of 20th century will be x years old in the year x squared. In what year was she born? (x is in integers) ---- I'll leave that to you. cheers, Stan H.

Radicals/389115: sum of radical 50 and x radical 2 is 9 radical 2 find x 1 solutions Answer 275623 by stanbon(57308)   on 2010-12-28 15:03:04 (Show Source): You can put this solution on YOUR website! sum of radical 50 and x radical 2 is 9 radical 2 find x --- (sqrt(50)+x*sqrt(2)) = 9*sqrt(2) --- 5sqrt(2) + xsqrt(2) = 9sqrt2 ---- Divide thru by sqrt(2) ---- 5 + x = 9 x = 4 ============== Cheers, Stan H.

Miscellaneous_Word_Problems/389102: Can someone help me with this problem please. I do not understand how to work this out. Please show me step by step. Top bond fund. An investment of $10,000 in the Emerging Country Debt Fund in 2001 was worth $24,780 in 2006 (www.money.com). Use the formula from the previous exercise to find the 5-year average annual return. The formula is r=(s/p)^1/n -1 the -1 is after the rt 1/n to the right but on the same level as the (s/p) I hope that makes sense. r=investment on annual return S=value after n years P=initial investment n=number of years Thank you very much! 1 solutions Answer 275621 by stanbon(57308)   on 2010-12-28 15:00:16 (Show Source): You can put this solution on YOUR website! Top bond fund. An investment of $10,000 in the Emerging Country Debt Fund in 2001 was worth $24,780 in 2006 (www.money.com). Use the formula from the previous exercise to find the 5-year average annual return. The formula is r=(s/p)^1/n -1 --------------- S = P(1+(r/n))^(nt) --- 1+(r/n) = [s/p]^(1/nt) ---- r = n[(s/p)^(1/nt)-1] --- r = 1[(24,780/10,000)^(1/(1*5)-1] --- r = 2.478^(1/5) --- r = 1.199.. Rounding you would get rate = 20% ================================= Cheers, Stan H.

Geometry_Word_Problems/388992: let f(x)=x+2 and g(x)= 1-x^2. Which of the following properly expresses g(f(x+1))? a. -x^2+6x+10 b. -x^2-6x-8 c. -x^2+x+3 d. x^2-6x+8 e. x^2-x+10 1 solutions Answer 275451 by stanbon(57308)   on 2010-12-27 22:21:59 (Show Source): You can put this solution on YOUR website! let f(x)=x+2 and g(x)= 1-x^2. Which of the following properly expresses g(f(x+1))? ----------- g[f(x+1)] = g[x+1+2} = g[x+3] = 1-(x+3)^2 = 1-[x^2+6x+9] = -x^2-6x-8 =============== Cheers, Stan H. =============== a. -x^2+6x+10 b. -x^2-6x-8 c. -x^2+x+3 d. x^2-6x+8 e. x^2-x+10

Age_Word_Problems/388994: Jeff is Three times as old as his son. In nine years, Jeff will be twice as old as his son. How old is each now? 1 solutions Answer 275450 by stanbon(57308)   on 2010-12-27 22:17:50 (Show Source): You can put this solution on YOUR website! Jeff is Three times as old as his son. In nine years, Jeff will be twice as old as his son. How old is each now? --- Equations: j = 3s (j+9) = 2(s+9) ---- Substitute for "j": (3s+9) = 2s+18 s = 9 (Son's age now} --- j = 3s = 27 (Jeff's age now) ============================== Cheers, stan H. =============

Geometry_Word_Problems/388993: if x^10 * x^2a= x^100, what is the value of a? 1 solutions Answer 275447 by stanbon(57308)   on 2010-12-27 22:13:44 (Show Source): You can put this solution on YOUR website! if x^10 * x^2a= x^100, what is the value of a? ------------- x^(10+2a) = x^100 --- 10+2a = 100 2a = 90 a = 45 =========== Cheers, stan H. ===========

Rate-of-work-word-problems/388990: This is my math homework : You want to go with your sister to the museum to see the dinosaur exhibit. The museum has 3 different plans to pay for going to see the dinosaur. Plan A: Pay $3.00 per person to visit the museum Plan B: Monthly membership is $8.00 for each person but you can go as many times as you like during the month. Plan C: A family membership for a month is $17.00. Everyone in your family can go as often as they like for a month. Its asking me to pick a plan that'll save more money Plan A: i divided $3.00 by 2 = $1.50 Plan B: Multiplied $8.00 by 2 - $16.00 divided by 31 and i got stuck. can you help me 1 solutions Answer 275445 by stanbon(57308)   on 2010-12-27 22:11:54 (Show Source): You can put this solution on YOUR website! You want to go with your sister to the museum to see the dinosaur exhibit. The museum has 3 different plans to pay for going to see the dinosaur. Plan A: Pay $3.00 per person to visit the museum Cost = $6 ------------------- Plan B: Monthly membership is $8.00 for each person but you can go as many times as you like during the month. Cost = $16 ------------------- Plan C: A family membership for a month is $17.00. Everyone in your family can go as often as they like for a month. Cost = $17 ---------------------- Its asking me to pick a plan that'll save more money That depends on how many times you and your family members intend to visit the museum. ======================= Cheers, stan H.