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# Recent problems solved by 'stanbon'

stanbon answered: 57894 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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 Equations/128072: Simplify: 3/4/4/5 Possible Answers: A. 16/15 B. 15/16 C. 5/3 D. 3/5 I am coming up with 3/80, since that is not one of the possible answers then I think I need some assistance. Thanks1 solutions Answer 93769 by stanbon(57967)   on 2008-02-20 19:33:17 (Show Source): You can put this solution on YOUR website!Simplify: 3/4/4/5 Possible Answers: A. 16/15 B. 15/16 C. 5/3 D. 3/5 ------------------- Invert the denominator and multiply to get: (3/4)*(5/4) = 15/16 ========================== Cheers, Stan H.
 Equations/128058: The sun is approximately 1.496 * 10^8 kilometres from earth. If light travels at three hundred million metres per second, how long does it take for light to travel from the sun to the earth ?1 solutions Answer 93761 by stanbon(57967)   on 2008-02-20 18:55:11 (Show Source): You can put this solution on YOUR website!The sun is approximately 1.496 * 10^8 kilometres from earth. If light travels at three hundred million metres per second, how long does it take for light to travel from the sun to the earth ? -------------------------------------- First: Change the kilometers to meters. (1.496x10^8 km)(1000 meters/km) = 1.496x10^11 meters ----------------- Divide distance by the speed of light: (1.496x10^11 meters m) / (3.00x10^8 m/s) = 4.9867x10^2 seconds = 8.111 minutes ================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/128030: selling tickets for a play, 4 dollars for student 6 dollars for general. you sell 525 tickets and collect \$2876. how many types of tickets did you sell. 1 solutions Answer 93744 by stanbon(57967)   on 2008-02-20 16:35:27 (Show Source): You can put this solution on YOUR website!selling tickets for a play, 4 dollars for student 6 dollars for general. you sell 525 tickets and collect \$2876. how many types of tickets did you sell. ----------------------------- Let # of student tickets sold be "x" ; Value of these is 4x dollars. -------------------- # of general tickets sold is "525-x" ; Value is 6(525-x)= 3150-6x dollars --------------------- EQUATION: value + value = 2876 dollars 4x + 3150-6x = 2876 -2x = -274 x = 137 (# of student tickets sold) 525-x = 388 (# of general tickets sold) ===================== Cheers, Stan H.
 Money_Word_Problems/128022: What simple interest rate will Susan need to secure to make \$2,500 in interest on a \$10,000 principal over 5 years? 1 solutions Answer 93743 by stanbon(57967)   on 2008-02-20 16:30:17 (Show Source): You can put this solution on YOUR website!What simple interest rate will Susan need to secure to make \$2,500 in interest on a \$10,000 principal over 5 years? ------------------------------------- I = Prt 2500 = 10000*r*5 r = 2500/50000 = 0.05 = 5% ============================= Cheers, Stan H.
 Coordinate-system/128027: This question is from textbook algebra: structure and method: book1 I am supposed to write an equation in standard form of the line passing through these points. (-2,0) and (2,-3). PLEASE HELP!!!!!! The answer is 3x+4y=-6, but I don't know how to get there. HELP MUCH APPRECIATED!!!!1 solutions Answer 93742 by stanbon(57967)   on 2008-02-20 16:26:41 (Show Source): You can put this solution on YOUR website!write an equation in standard form of the line passing through these points. (-2,0) and (2,-3) ------------------ slope = (-3-0)/(2--2) = -3/4 -------------------------------- Form of the equation: y = mx + b You now know x,y, and m; solve for b as follows: -3 = (-3/4)*2+b -3 = (-3/2) + b b = (-3/2) -------------------- EQUATION: y = (-3/4)x - (3/2) ---------------------- Write it in standard form: Multiply thru by 4 to get: 4y = -3x - 6 Rearrange: 3x+4y = -6 ----------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/128020: This question is from textbook Algebra structure and method book 1 Finding number of books. Verna decided to sell her collection of paperback books. To Fred, she sold 2 books, and one fifth of what was left. Later to Joan she sold 6 books, and one fifth of what then remained. If she sold more books to Fred than Joan, what was the least possible number of books in her original collection?1 solutions Answer 93741 by stanbon(57967)   on 2008-02-20 16:20:33 (Show Source): You can put this solution on YOUR website!Verna decided to sell her collection of paperback books. To Fred, she sold 2 books, and one fifth of what was left. Later to Joan she sold 6 books, and one fifth of what then remained. If she sold more books to Fred than Joan, what was the least possible number of books in her original collection? --------------- Let "x" be the original number of books. --------------------------------------- Sold to Fred: 2+(1/5)(x-2) = (1/5)x+(8/5) = (x+8)/5 ------------------ Sold to Joan: 6+(1/5)[(x+8)/5 - 6] = 6+[(x+8)/25]-(6/5) = (x+128)/25 --------------------- Your Problem: She sold more books to Fred that to Joan: (x+8)/5 > (x+128)/25 5x+40 > x+128 4x > 88 x > 22 books in the original collection. ================== Cheers, Stan H.
 Probability-and-statistics/128007: I didn't know how to answer this question. Can someone help me? Thanks A governor would like to find out how people in his state feel about state subsidized public art. How might a cluster sample be selected?1 solutions Answer 93725 by stanbon(57967)   on 2008-02-20 14:35:35 (Show Source): You can put this solution on YOUR website!Select random clusters based on age: 15-25,26-37,38-50,51 and older ---------------- Take a random sample from each cluster for testing. ----------------- OR Select random clusters based on household income: Pick three or four income ranges. Take a random sample from each for testing. ============= Cheers, Stan H.
 Exponents/128012: AFTER BEING AWAY FROM SCHOOL FOR OVER 30 YEARS - I AM TRYING TO HELP A YOUNG WOMAN WITH HER HOMEWORK. (HER MOTHER PASSED AWAY RECENTLY). I AM LOOKING AT: X = 4 TO THE THIRD TO THE 4TH. I'VE NEVER SEEN AN EXPONENT HAVE AN EXPONENT.PLEASE SHOW ME HOW TO WORK SUCH A PROBLEM STEP BY STEP. dO I ASSUME THERE ARE PARENTHESIS SOMEWHERE?1 solutions Answer 93723 by stanbon(57967)   on 2008-02-20 14:31:04 (Show Source): You can put this solution on YOUR website!I AM LOOKING AT: X = 4 TO THE THIRD TO THE 4TH. I'VE NEVER SEEN AN EXPONENT HAVE AN EXPONENT.PLEASE SHOW ME HOW TO WORK SUCH A PROBLEM STEP BY STEP. ---------------- You may recall x^2 = x*x The exponent is a counter telling you how many x's you have to multiply. --------------------------- You have: (x^3)^4) which means: (x^3)*(x^3)*(x^3)^(x^3) ----------------- But each of those x^3's means x*x*x ----------------------- So you have (x*x*x) four times You have a total of 12 x's --------------- Final Answer (x^3)^4 = x^12 =============================== Cheers, Stan H.
 Probability-and-statistics/128008: Here is another problem that I don't understand. Can someone help me with this? The following statistics provide information about the scores on a national mathematics exam. Mean 312 | First Quartile 201 Median 296 | Third Quartile 423 Mode 326 | 49th Percentile 307 a) What score did half of the test takers surpass? b) What was the most common score? c) What percentage of the test takers scored 201 or better? d) If Joe had a score of 307, explain the meaning of his score. 1 solutions Answer 93721 by stanbon(57967)   on 2008-02-20 14:25:28 (Show Source): You can put this solution on YOUR website!The following statistics provide information about the scores on a national mathematics exam. Mean 312 | First Quartile 201|Median 296 | Third Quartile 423|Mode 326 | 49th Percentile 307 ------------------ a) What score did half of the test takers surpass? Median = 296 b) What was the most common score? Mode = 326 -------------- c) What percentage of the test takers scored 201 or better? 75% -------------- d) If Joe had a score of 307, explain the meaning of his score. More than 50% of the scores were lower than his. --------------- Cheers, Stan H.
 Inequalities/128011: How do you know if a value is a solution for an inequality and how is this different from determing a valua is a solution to equation?1 solutions Answer 93720 by stanbon(57967)   on 2008-02-20 14:16:54 (Show Source): You can put this solution on YOUR website!The procedure is the same. If you find a variable value or two values for an inequality statement, substitute those values for the variable(s) and see if you get a true statement. --------------------------------------- Example: 3x + 4y >6 y > (-3/4)x + (3/2) ---------------------- Question: Is (0,0) part of the solution? Substitute to get 0 > (-3/4)*0+(3/2) 0 > 3/2 That is false so (0,0) is not part of the solution. ----------------- Is (0,5) part of the solution? Substitute to get 5 > (-3/2)*0+(3/2) 5 > (3/2) That is true so (0,5) is part of the solution. ======================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/127911: If one-fourth a number is subtracted from one-half of the number, the difference is 3. Setup an algebraic equation, find the number and check your answer1 solutions Answer 93690 by stanbon(57967)   on 2008-02-19 22:28:06 (Show Source): You can put this solution on YOUR website!If one-fourth a number is subtracted from one-half of the number, the difference is 3. Setup an algebraic equation, find the number and check your answer -------------- EQUATION: Let the number be "x": (1/2)x - (1/4)x = 3 (1/4)x = 3 x = 12 ------------------ Cheers, Stan H.
 Linear-systems/127913: graph y=1.5x1 solutions Answer 93686 by stanbon(57967)   on 2008-02-19 22:21:33 (Show Source): You can put this solution on YOUR website!graph y=1.5x ----------------------------- y = (3/2)x Plot two points: If x = 0, y = 0 If x = 2, y = 3 ----------------- Plot the points: (0,0) and (2,3) and draw a line thru them. ------------------------------ ========================================== Cheers, Stan H.
 Linear-systems/127908: graph y=2/5x-3 2/5 means 2 over 51 solutions Answer 93682 by stanbon(57967)   on 2008-02-19 22:16:04 (Show Source): You can put this solution on YOUR website!graph y=2/5x-3 --------------- Plot two points: If x = 0, y = -3 If x = 5, = -1 ------------------- Plot (0,-3), and (5,-1) and draw a line thru them. ========================================= Cheers, Stan H.
 Volume/127903: Please solve my assignment. Thanks. A cylindrical flower base is 6 in. high and a diameter of 2 in. How many cubic inches of water is needed to fill up the vase an inch less from its mouth?1 solutions Answer 93677 by stanbon(57967)   on 2008-02-19 22:09:34 (Show Source): You can put this solution on YOUR website!A cylindrical flower base is 6 in. high and a diameter of 2 in. How many cubic inches of water is needed to fill up the vase an inch less from its mouth? --------------------------------- The area of the base is (pi)*1^2 = pi sq. in. ----------------- The height of the water is 5 in. ------------------ Volume of water = 5*pi cu.in. ================================= Cheers, Stan H.
 Age_Word_Problems/127900: Sherman's age and his grandpa's age together equal 72. His grandpa's age is 7 times greater than his age. How old are they. (in fourth grade) 1 solutions Answer 93676 by stanbon(57967)   on 2008-02-19 22:02:32 (Show Source): You can put this solution on YOUR website!Sherman's age and his grandpa's age together equal 72. His grandpa's age is 7 times greater than his age. How old are they. ------------- Let Sherman be x yrs. old Then grandpa is 7*x = 7x yrs. old ------------------------------------- EQUATION: Sherman's age + Grandpa's age = 72 x + 7x = 72 8x = 72 Divide both sides by 8 to get : x = 9 yrs. (Sherman's age) 7x = 63 yrs. (Grandpa's age) ------------------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/127898: This question is from textbook prentice hall mathematics Write a polynomial that has a common factor in each term. Factor your polynomial.1 solutions Answer 93675 by stanbon(57967)   on 2008-02-19 21:56:52 (Show Source): You can put this solution on YOUR website!3x^2 + 6x + 15 = 3(x^2+2x+5) ================== Cheers, Stan H.
 Probability-and-statistics/127605: 3.)A contest where the winning ticket belongs to the one contestant whose ticket has 1 letter (A-Z) followed by 3 digits (0-9) in the proper order. -How many different tickets could be made for this contestant? Letters and numbers can be repeated. -How many tickets could be made for this contest if letters and numbers cannot be repeated? 1 solutions Answer 93674 by stanbon(57967)   on 2008-02-19 21:54:49 (Show Source): You can put this solution on YOUR website!A contest where the winning ticket belongs to the one contestant whose ticket has 1 letter (A-Z) followed by 3 digits (0-9) in the proper order. -How many different tickets could be made for this contestant? Letters and numbers can be repeated. -------------- Pick a letter: 26 ways Pick three digits: 10*10*10 = 1000 ------------------------------- Total number of tickets: 26,000 ================================= Cheers, Stan H.
 Linear-systems/127882: Graph the system of 5x – 2y < 10, x + 2y > -2, x – y > -4 Where do I begin and how do I graph? I have been having a difficult time with graphing. 1 solutions Answer 93660 by stanbon(57967)   on 2008-02-19 20:46:11 (Show Source): You can put this solution on YOUR website!Graph the system of 5x – 2y < 10 x + 2y > -2 x – y > -4 ---------------- Solve each for "Y": y > (5/2)x - 5 y > (-1/2)x - 1 y < x + 4 ------------------- Graph the boundary for each of these inequalities by graphing each EQUALITY: y = (5/2)x - 5 y = (-1/2)x - 1 y = x +4 -------------------- ------------------- Shade the half-plane above (5/2)x-5 Shade the half-plane above (-1/2)x-1 Shade the half-plane below x+4 ----------------------------- The intersection of these half-planes is the solution set for the system of three inequalities. ------------------------------- Cheers, Stan H.
 Probability-and-statistics/127610: Ten people in our class want to sign up for the 5-person UA chess team. How many different teams could be chosen?1 solutions Answer 93658 by stanbon(57967)   on 2008-02-19 20:32:58 (Show Source): You can put this solution on YOUR website!Ten people in our class want to sign up for the 5-person UA chess team. How many different teams could be chosen? ---------- 10C5 = 10!/[(10-5)!*5!] = 252 ================================= Cheers, Stan H.
 Square-cubic-other-roots/127873: Determine whether each statement is sometimes, always, or never true. a. √(a2+b2) is a real number.1 solutions Answer 93654 by stanbon(57967)   on 2008-02-19 20:25:38 (Show Source): You can put this solution on YOUR website!Determine whether each statement is sometimes, always, or never true. a. √(a2+b2) is a real number. ---------- a^2 is always >= zero b^2 is always >= zero -------- Therefore a^2+b^2 >=0 Therefore sqrt(a^2+b^2) is always a Real Number. ================ Cheers, Stan H.
 Expressions-with-variables/127837: This problem is similar to the one I posted earlier. The fraction bar confuses me. I have no trouble solving problems like this: 6^5(6)^-3 The worksheet from McDougal Littell A;gebra 1 Lesson 8.2 Practice C is the one I'm workig on. Number 22. 8^-2/2^-4x^-41 solutions Answer 93653 by stanbon(57967)   on 2008-02-19 20:21:42 (Show Source): You can put this solution on YOUR website!6^5(6)^-3 ------------- Since the bases are the same, add the exponents to get: 6^2 = 36 --------------- 8^-2/2^-4x^-4 Change all these bases to two: = 2^-6/(2x)^-4 = (2x)^4/2^6 = x^4/2^2 = (1/4)x^4 ================ Cheers, Stan H.
 Linear-equations/127875: . Solve the system by graphing. x + 3y = -3, 2x – y = 8 Do I solve this first and then graph it? How do I graph it? 1 solutions Answer 93651 by stanbon(57967)   on 2008-02-19 20:14:49 (Show Source): You can put this solution on YOUR website!Solve the system by graphing. x + 3y = -3 2x – y = 8 -------------- Solve each equation for "y". y = (-1/3)x -1 y = 2x - 8 ---------------- Plot points for each equation: y = (-1/3)x - 1 If x = 0, y = -1 If x = 3, y = -2 Plot the points: (0,-1) and (3,-2) and draw a line thru them. ------------------------------ y = 2x - 8 If x = 0, y = -8 If x = 1, y = -6 --------------------- plot the points: (0,-8) and (1,-6) and draw a line thru them. ============================= Solution: (3,-2) ============================== Cheers, Stan H.
 Square-cubic-other-roots/127874: For a polynomial of the form ax2 + bx + c = 0 to have real solutions, √(b2 – 4ac) must be a real number. Which of the following polynomials have real solutions? a. x2 – 12x + 3 = 01 solutions Answer 93650 by stanbon(57967)   on 2008-02-19 20:04:55 (Show Source): You can put this solution on YOUR website!x^2 – 12x + 3 = 0 ----------------- Checking the discriminant you get: b^2-4ac = 12^2-4*1*3 = 132 ------------ Since the discriminant is greater than zero the quadratic equation has two unequal Real solutions. ================= Cheers, Stan H.
 Square-cubic-other-roots/127870: Please help me solve this equation: √751 solutions Answer 93647 by stanbon(57967)   on 2008-02-19 19:58:43 (Show Source): You can put this solution on YOUR website!√75 = sqrt(25*3) =sqrt(25)*sqrt(3) = 5*sqrt(3) ================ Cheers, Stan H.
 Probability-and-statistics/127724: The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025? (See story.news.yahoo.com accessed June 25, 2004.)1 solutions Answer 93600 by stanbon(57967)   on 2008-02-19 11:57:32 (Show Source): You can put this solution on YOUR website!The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025? ------------ Ho: p = 0.95 Ha: p > 0.95 ---------------- one-tail z-test with critical value = 1.96; alpha = 2.5%; p-hat=485/500=0.97 --------------- Test Statistic: z(0.97) = (0.97-0.95)/sqrt((0.95*0.05)/500)= 2.052 p-value = 0.0201 --------------- Conclusion: Reject Ho because the test statistic > critical value; also the p-value is < alpha. There is significant statistical evidence that p is not 95%. ================== Cheers, Stan H.
 Probability-and-statistics/127725: Please help me. This question is taken from the Stats and Econ Question # 9.54 I checked the answers and this one is not answered. Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value. Thank you for your kind assistance. 1 solutions Answer 93598 by stanbon(57967)   on 2008-02-19 11:44:51 (Show Source): You can put this solution on YOUR website!Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? Ho: mu <= 10 Ha: mu > 10 --------------- one-tail t-test with alpha=1%; critical value for 34 df = 2.326 Test statistic: t(14.44) = (14.44-10)/[4.45/sqrt(35)] = 5.9028 Reject Ho; there is significal statistical evidence that the true mean is not <= 10 ------------------------------------------- (b) Use Excel to find the right-tail p-value. p-value = 0.00000057579 ============================= Cheers, Stan H.
 Radicals/127752: Could you help me with this? Its on simplifying radical expressions. sqrt of 81x^5y^9 and it has an index of 4 thank you 1 solutions Answer 93589 by stanbon(57967)   on 2008-02-19 09:44:52 (Show Source): You can put this solution on YOUR website!sqrt of 81x^5y^9 and it has an index of 4 --------------------------------------------- = 3xy^2* 4th rt. of (xy) OR = 3xy^2*(xy)^(1/4) ======================= Cheers, Stan H.
 Quadratic_Equations/127753: A certain radioactive element decays exponentially with a half-life of 5 hours. Find the time that has elapsed if a 50mg sample has decayed to 17 mg.1 solutions Answer 93588 by stanbon(57967)   on 2008-02-19 09:42:22 (Show Source): You can put this solution on YOUR website!A certain radioactive element decays exponentially with a half-life of 5 hours. Find the time that has elapsed if a 50mg sample has decayed to 17 mg. -------------------- A(t) = A(0)(1/2)^(t/5) 17 = 50 (1/2)^(t/5) 0.34 = (1/2)^(t/5) Take the log of both sides to get: (t/5)log(1/2) = log(0.34) t/5 = 1.5564 t = 7.782 hours ================ Cheers, Stan H.
 Quadratic_Equations/127759: Solve: a) t=5*logbase4 16 b) t=4*logbase1/3 3sqrt243 1 solutions Answer 93587 by stanbon(57967)   on 2008-02-19 09:37:42 (Show Source): You can put this solution on YOUR website!Solve: a) t=5*logbase4 16 t = 5*2 t = 10 -------------- b) t=4*logbase1/3 3sqrt243 t = 4* log base(1/3) 243^(1/3) t = 4* log base(1/3) (3)^(5/3) t = 4* log base(1/3) (1/3)^(-5/3) t = 4*(-5/3) t = -20/3 ============= Cheers, Stan H.