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# Recent problems solved by 'stanbon'

stanbon answered: 57151 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, >>Next

 Permutations/428745: Mr. Johnson is a faculty advisor to the National Honor Society. There are 30 members. How many ways can he choose 4 members to attend a conference? (1)3_P_4 (2)30! (3)30_C_4 (4)30x41 solutions Answer 297943 by stanbon(57219)   on 2011-03-29 16:27:30 (Show Source): You can put this solution on YOUR website!Ans: 30C4 = (30*29*28*27)/(1*2*3*4) = 27,405 === Cheers, Stan H.
 Mixture_Word_Problems/428740: How many gallons of cream that is 23% butterfat and milk that is 3% butterfat must a dairy farmer mix to make a 30 gallon mixture of milk that is 4% butterfat?1 solutions Answer 297942 by stanbon(57219)   on 2011-03-29 16:25:08 (Show Source): You can put this solution on YOUR website!How many gallons of cream that is 23% butterfat and milk that is 3% butterfat must a dairy farmer mix to make a 30 gallon mixture of milk that is 4% butterfat? -------------------- Equation: fat + fat = fat 0.23x + 0.03(30-x) = 0.04*30 ---- Multiply thru by 100 to get: 23x + 3*30-3x = 4*30 20x = 30 x = 3/2 gallons (amt. of 23% cream needed) ================= Cheers, Stan H. =================
 Linear-systems/428739: 2/3x+3/5y=-17 1/2x-1/3y=-1 solve using elimination1 solutions Answer 297940 by stanbon(57219)   on 2011-03-29 16:21:30 (Show Source): You can put this solution on YOUR website!2/3x+3/5y=-17 1/2x-1/3y=-1 ============== Multiply thru 1st by 15. Multiply thru 2nd by 6. -------------- 10x + 9y = -15*17 3x - 2y = -6 --- Multiply thru 1st by 3 Multiply thru 2nd by 10 ----- 30x + 27y = -45*17 30x - 20y = -60 ----------------------- Subtract and solve for "y": 47y = -705 y = -15 --- Solve for "x": 3x-2y = -6 3x+30 = -6 3x = -36 x = -12 =========== Cheers, Stan H. ===========
 Linear_Equations_And_Systems_Word_Problems/428731: Hey My math question is How many seconds will it take for an object dropped off the top of 555 ft Washingtin Monument to hit the ground. h=16tsquared + 64t?1 solutions Answer 297937 by stanbon(57219)   on 2011-03-29 16:12:20 (Show Source): You can put this solution on YOUR website!How many seconds will it take for an object dropped off the top of 555 ft Washingtin Monument to hit the ground. h=16tsquared - 64t? ------- Solve -16t^2+64t+555 = 0 --- t = [-64 +- sqrt(64^2-4*-16*555)]/(2*-16) --- t = 8.297872 seconds ========================== Cheers, Stan H.
 test/428738: What are the Trig identities and reciprical identities that need to be known to simplify and prove Trig identities? I know the basics like csc=1/sin, sec is 1/cos and tan is 1/cot.1 solutions Answer 297935 by stanbon(57219)   on 2011-03-29 16:07:48 (Show Source): You can put this solution on YOUR website!Use Google to search for "basic trigonometry identities". ====== Cheers, Stan H.
 Rational-functions/428715: whats the function for each, find f(-5), f(-3), f(1/2), and f(4). f(h)= -6h-2/31 solutions Answer 297930 by stanbon(57219)   on 2011-03-29 15:51:38 (Show Source): You can put this solution on YOUR website!find f(-5), f(-3), f(1/2), and f(4) if f(h)= -6h-2/3 ---- f(-5)= -6*-5 -2/3 = 30-(2/3) = 29 1/3 ----------------- f(-3) = -6*-3 -(2/3) 18-(2/3) = 17 1/3 ----------------------- f(1/2) = -6*(1/2)-(2/3) = -3-(2/3) = (-9/3)-(2/3) = -11/3 --------------- f(4)= -6(4)-(2/3) = -24-(2/3) --- = (-72/3)-(2/3) --- = -74/3 ======== Cheers, Stan H.
 Square-cubic-other-roots/428716: x(x-4) = 12 I do not know how to solve it, we're solving using factoring.1 solutions Answer 297922 by stanbon(57219)   on 2011-03-29 15:30:33 (Show Source): You can put this solution on YOUR website!x(x-4) = 12 --- x^2-4x-12 = 0 Factor: (x-6)(x+2) = 0 x = 6 or x = -2 ====================== Cheers, Stan H.
 logarithm/428620: how would i simplify 4 ln 1/3- 6 ln 1/9 into a single logrithm. what are the steps and where do i want to go ?1 solutions Answer 297889 by stanbon(57219)   on 2011-03-29 12:40:30 (Show Source): You can put this solution on YOUR website!4 ln 1/3- 6 ln 1/9 into a single logrithm ----- There are 3 laws you need to know: 1. ln(a) + ln(b) = ln(ab) 2. ln(a) - ln(b) = ln(a/b) 3. ln(a^n) = n*ln(a) ----------------------- Your Problem: = ln(1/3)^4-ln(1/9)^6 --- = ln[(1/3)^4/(1/9)^6] ---- = ln[(1/3)^4/(1/3^2)^6] --- = ln[(1/3)^4/(1/3)^12] --- = ln[1/(1/3)^8] --- = ln[3^(-8)] --- = -8ln(3) =============== Cheers, Stan H. ===============
 Polynomials-and-rational-expressions/428629: please help show me how to check this division problem its long division (x^3+2x^2+3x-6)/(x-1)= x^2+3x+6 I understand that now but I don't know how the check should look.1 solutions Answer 297887 by stanbon(57219)   on 2011-03-29 12:33:23 (Show Source): You can put this solution on YOUR website!check this division problem its long division (x^3+2x^2+3x-6)/(x-1)= x^2+3x+6 --- How would you check 6/2 = 3 ? You would multiply 2*3 to see if you get 6. ---- Similarly, to check you problem,multiply (x-1)(x^2+3x+6) to see if you get x^3+2x^2+3x-6. ---- Cheers, Stan H.
 test/428622: How to simplify: tan^2 theta/sin^2 theta...do I plug in the sin/cos for tan and csc for sin? Help! Thanks.1 solutions Answer 297886 by stanbon(57219)   on 2011-03-29 12:30:52 (Show Source): You can put this solution on YOUR website!simplify: tan^2 theta/sin^2 theta ---- = [sin^2/cos^2]/sin^2 --- Invert the denominator and cancel: --- = [sin^2/cos^2] ---- = 1/cos^2 = sec^2(theta) =================== Cheers, Stan H.
 test/428624: (1 + cos theta)(1 - cos theta) is that like a difference of squares? So how is it simplified? 1 solutions Answer 297883 by stanbon(57219)   on 2011-03-29 12:27:47 (Show Source): You can put this solution on YOUR website!(1 + cos theta)(1 - cos theta) is that like a difference of squares? So how is it simplified? ----- = 1-cos^2(theta) = sin^2(theta) =================== Cheers, Stan H.
 Geometry_Word_Problems/428625: How do you calculate angles using pythagoras theorem1 solutions Answer 297880 by stanbon(57219)   on 2011-03-29 12:23:26 (Show Source): You can put this solution on YOUR website!--- If hypotenuse^2 = leg1^2 + leg2^2 you know you have a right angle across from the hypotenuse. --- But Pythagoras is not a tool to calculate angle sizes. It is a tool to calculate side sizes. ---- cheers, Stan H.
 Sequences-and-series/428621: Write a variable expression to describe the rule for each sequence. Then find the hundredth term. 1. 3, 6, 9, 12, ... i am really really really really really really confused. please help??1 solutions Answer 297877 by stanbon(57219)   on 2011-03-29 12:08:44 (Show Source): You can put this solution on YOUR website!Write a variable expression to describe the rule for each sequence. Then find the hundredth term. 1. 3, 6, 9, 12, ... --- An arithmetic sequence with a = 1 and d = 3 --- a(n) = 1 + (n-1)3 where n is the number of the term. --- a(100) = 1 + 99*3 a(100) = 1 + 297 a(100) = 298 ===================== Cheers, Stan H =====================
 Triangles/428582: Factor completely. factor the GCF as the first step. 45xyz^2 + 5x^2yz^2 + 100yz^2 In the middle set x is to the power of 2 not 2yz1 solutions Answer 297864 by stanbon(57219)   on 2011-03-29 10:51:32 (Show Source): You can put this solution on YOUR website!45xyz^2 + 5x^2yz^2 + 100yz^2 --- GCD: 5yz^2 --- = 5yz^2[9xz+x^2+20] =========== Cheers, Stan H. ==============
 Money_Word_Problems/428591: Tammys weekly salary is 120% more than wandas weekly salary. Both salaries combined equals \$165. What is wandas weekly salary..1 solutions Answer 297862 by stanbon(57219)   on 2011-03-29 10:47:08 (Show Source): You can put this solution on YOUR website!Tammys weekly salary is 120% more than wandas weekly salary. Both salaries combined equals \$165. What is wandas weekly salary.. --- Let Wanda's salary be "x": Then Tammy's salary is "1.20x": ---- Equation: x + 1.2x = 165 2.2x = 165 x = \$75 ----- Cheers, Stan H. =======
 Linear-systems/428587: Solve for x and what is the common denominator? There should be a line under each top number. Thank you 1 + 3 = 2 4x 2x x+1 1 solutions Answer 297861 by stanbon(57219)   on 2011-03-29 10:43:29 (Show Source): You can put this solution on YOUR website! 1/(4x) + 3/(2x) = 2/(x+1) --- lcd = 4x(x+1) --- Multiply thru by lcd to get: x+1 + 3*2(x+1) = 2*4x) ----- x + 1 + 6x+6 = 8x x = 7 ---- Cheers, Stan H. =============
 Probability-and-statistics/428590: Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 29 dollars and a standard deviation of 6 dollars. What interest payment is exceeded by only 21% of the bank's Visa cardholders??1 solutions Answer 297860 by stanbon(57219)   on 2011-03-29 10:40:01 (Show Source): You can put this solution on YOUR website!Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 29 dollars and a standard deviation of 6 dollars. What interest payment is exceeded by only 21% of the bank's Visa cardholders?? ---- Draw the picture of a normal curve with mean = 29 --- Find the z-value with a right-tail of 0.21 --- invNorm(0.79) = 0.8064 --- Find the corresponding payment: x = zs+u x = 0.8064*6+29 x = \$33.84 ================ Cheers, Stan H. ===================
 Numeric_Fractions/428589: How do we solve problems using the principles together such as -9/2+4=91/21 solutions Answer 297859 by stanbon(57219)   on 2011-03-29 10:34:43 (Show Source): You can put this solution on YOUR website!How do we solve problems using the principles together such as -9/2+4=91/2 ---------------- (-9/2) + 4 --- (-9/2) + (8/2) --- = -1/2 ======================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/428548: Can you please help me with these problems. I need to know how to work it out, not just the answer, so I can figure out others. 1: Plans to build a park include a circular fountain. The outline of the fountain can be modeled with the equation (x-4)^2+(y+5)^2=50, where the units are meters and the graph is on a grid map of the park. Find the coordinates of the center of the fountain AND find the circumference of the fountain. 2: Bill is making a graphic design on the computer using a coordinate grid. He starts with a circle with center (0,0). He then draws a congruent circle with the equation x^2+y^2+12x+4y+5=0. What was the radius of the first circle and what translation did he make to draw the second circle? Thank you!1 solutions Answer 297854 by stanbon(57219)   on 2011-03-29 08:36:07 (Show Source): You can put this solution on YOUR website!1: Plans to build a park include a circular fountain. The outline of the fountain can be modeled with the equation (x-4)^2+(y+5)^2=50, where the units are meters and the graph is on a grid map of the park. Find the coordinates of the center of the fountain AND find the circumference of the fountain. ----- The center is at (4,-5) The radius = sqrt(50) = 5sqrt(2) ----- Circum = 2(pi)r = 2(pi)5sqrt(2) = 10(pi)sqrt(2) ================================ 2: Bill is making a graphic design on the computer using a coordinate grid. He starts with a circle with center (0,0). He then draws a congruent circle with the equation x^2+y^2+12x+4y+5=0. What was the radius of the first circle and what translation did he make to draw the second circle? --- Complete the square: x^2+12x+a + y^2+4y+b = -5+a+b --- x^2+12x+36 + y^2+4y+4 = -5+36+4 --- (x+6) + (y+2) = 35 -- Center at (-6,-2); radius = sqrt(35) --- Radius of the 1st circle was sqrt(35) Translation: He moved the 1st circle 6 to the left and 2 down. ================== Cheers, Stan H. ==================
 Age_Word_Problems/428549: carmen is twice tom's age.3 years ago carmen was 3 times as old as tom.how old is carmen?how old is tom?1 solutions Answer 297852 by stanbon(57219)   on 2011-03-29 08:28:58 (Show Source): You can put this solution on YOUR website!carmen is twice tom's age.3 years ago carmen was 3 times as old as tom.how old is carmen?how old is tom? ---- Equations: c = 2t (c-3) = 3(t-3) --- Substitute for "c" and solve for "t": (2t-3) = 3t-9 t = 6 (tom's age now) --- Solve for "c": c = 2t c = 12 (camen's age now) =========================== Cheers, Stan H.
 Polynomials-and-rational-expressions/428559: (3x^2+5x+2)/(2x+1) Please help me and show me how did you get it, step by step. Thank you.1 solutions Answer 297851 by stanbon(57219)   on 2011-03-29 08:23:57 (Show Source): You can put this solution on YOUR website!The following site shows a good example of how to do long division with polynomials. -- Other sites can be viewed if you use Google to search for "algbra long division". --- http://www.sosmath.com/algebra/factor/fac01/fac01.html ---- Cheers, Stan H.
 Polynomials-and-rational-expressions/428558: (5x + 1)(x + 2)1 solutions Answer 297849 by stanbon(57219)   on 2011-03-29 08:19:48 (Show Source): You can put this solution on YOUR website!(5x + 1)(x + 2) ---- (5x)(x+2) + 1(x+2) --- 5x^2 + 10x + x + 2 --- 5x^2+11x+2 ----------- Cheers, Stan H.
 Systems-of-equations/428560: I NEED TO SEE HOW THIS PROBLEM IS WORKED OUT I KNOW THE ANSWER IS 15X+15Y 6(2X+3Y)+3(X-Y)1 solutions Answer 297848 by stanbon(57219)   on 2011-03-29 08:16:50 (Show Source): You can put this solution on YOUR website!6(2X+3Y)+3(X-Y) 12x+18y+3x-3y --- 15x+15y =========== Cheers, Stan H.
 Probability-and-statistics/428532: i need to find the z values for a normal distribution were the mean is 75 and standard deivation is 21 - the probability that exceeds 19%1 solutions Answer 297847 by stanbon(57219)   on 2011-03-29 08:14:45 (Show Source): You can put this solution on YOUR website! i need to find the z values for a normal distribution where the mean is 75 and standard deivation is 21 - the probability that exceeds 19% ----- Find the z with a left tail of 0.19 invNorm(0.19) = -0.8779 --- Any z-value greater than -0.8779 will have a left tail exceeding 19% ======================== Cheers, Stan H.
 Probability-and-statistics/428557: It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average?1 solutions Answer 297846 by stanbon(57219)   on 2011-03-29 08:10:33 (Show Source): You can put this solution on YOUR website!It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average? ---- z(19) = (19-18.2)/1.7 = 0.4706 P(x< 19) = P(z< 0.4706) = 0.6810 ------------- So 68.1% will last up to 19 mths. So 0.3190 will fail in that period. Jolt can expect to replace 0.319*500 = 160 units. Cheers, Stan H. ==============
 Miscellaneous_Word_Problems/428422: need the answer for time .80 mile i ran a .99 mile in a time of 5:121 solutions Answer 297787 by stanbon(57219)   on 2011-03-28 21:08:29 (Show Source): You can put this solution on YOUR website!need the answer for time .80 mile I ran .99 mile in a time of 5:12 ------ rate = distance/time = 0.99 mi/(5 1/5)hr --- = 0.99/(6/5) --- = 0.825 mph ------------- Your Problem: time = distance/rate --- time = 0.80 mi/0.825 mph = 0.97 hr = 58.18 minutes ==================================================== Cheers, Stan H. =============
 Permutations/428425: There is just room for 5 more people to go on a trip, but 7 people want to go. In how many ways can 5 people be chosen for the trip?1 solutions Answer 297785 by stanbon(57219)   on 2011-03-28 21:00:26 (Show Source): You can put this solution on YOUR website!There is just room for 5 more people to go on a trip, but 7 people want to go. In how many ways can 5 people be chosen for the trip? ---- ans: 7C5 = 7C2 = (7*6)/(1*2) = 21 =================================== Cheers, Stan H. ==========
 Polynomials-and-rational-expressions/428371: On planet ZOG, colored coins are used as money. 12 white, 9 red, 8 yellow, 4 blue, and no greens can be exchanged for 2 white, 1 red, no yellows, 1 blue, and 1 green. Suppose that 1 green=n blues, 1 blue=n yellows, 1 yellow=n reds, and 1 red=n whites. What is the whole number exchange rate for these coins? Is one exchange rate possible? Okay, so I started work and hit a dead end. My work is as follows. therefore We also know that g=bn, b=ny, y=nr, and r=nw. Therefore or by subtracting everything to one side and dividing everything by w. The problem is this: I am in Algebra I. We haven't learned how to solve 4th degree polynomials, which makes me think that there is an easier way to solve this problem that I didn't pick up on. Please help. I don't necessarily want the answer, just an Algebra I way to solve this problem. Thanks in advance. 1 solutions Answer 297784 by stanbon(57219)   on 2011-03-28 20:52:15 (Show Source): You can put this solution on YOUR website!On planet ZOG, colored coins are used as money. 12 white, 9 red, 8 yellow, 4 blue, and no greens can be exchanged for 2 white, 1 red, no yellows, 1 blue, and 1 green. Suppose that 1 green=n blues, 1 blue=n yellows, 1 yellow=n reds, and 1 red=n whites. What is the whole number exchange rate for these coins? Is one exchange rate possible? Okay, so I started work and hit a dead end. My work is as follows. therefore We also know that g=bn, b=ny, y=nr, and r=nw. Therefore or by subtracting everything to one side and dividing everything by w. The problem is this: I am in Algebra I. We haven't learned how to solve 4th degree polynomials, which makes me think that there is an easier way to solve this problem that I didn't pick up on. Please help. I don't necessarily want the answer, just an Algebra I way to solve this problem. Thanks in advance. ============================== 1st of all: There is a solution less than 10. 2nd: Let n = some value like n = 10. You might get a positive value. Let n = some value like n = -10. You might get a negative value. ---- That mean there is a solution between n = -10 and n = 10. --- Use that idea to pin the solution between 2 values. Keep pinning it till you find the solution. ====================== By the way, you have done a find job with the problem. Congratulations. Cheers, Stan H. ================
 Polynomials-and-rational-expressions/428399: solve |4x-2|=61 solutions Answer 297779 by stanbon(57219)   on 2011-03-28 20:36:14 (Show Source): You can put this solution on YOUR website!solve |4x-2|=6 ----- 4x-2 = 6 or 4x-2 = -6 4x = 8 or 4x = -4 x = 2 or x = -1 ------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/428394: Please help me figure out the following: A countertop will have a hole drilled in it to hold a cylindrical container that will function as a utensil holder. The area of the entire countertop is given by 5x squared plus 12x plus 7. The area of the hole is given by x squared plus 2x plus 1. Write an expression for the area in factored form of the countertop that is left after the hole is drilled. Thanks!1 solutions Answer 297778 by stanbon(57219)   on 2011-03-28 20:33:37 (Show Source): You can put this solution on YOUR website!A countertop will have a hole drilled in it to hold a cylindrical container that will function as a utensil holder. The area of the entire countertop is given by 5x squared plus 12x plus 7. The area of the hole is given by x squared plus 2x plus 1. Write an expression for the area in factored form of the countertop that is left after the hole is drilled. ------ Remaining area = (5x^2+12x+7)-(x^2+2x+1) = 4x^2+10x+6 --- Factor: 4x^2+10x+6 = 2(2x^2+5x+3) ---- = 2(2x^2+4x+x+2) --- = 2(2x(x+2)+(x+2)) --- = 2(x+2)(2x+1) ==================== Cheers, Stan H. ============
 Miscellaneous_Word_Problems/428387: Soybean meal is 12% protein, cornmeal is 6% protein, how many pounds of each should be mixed together in order to get 240 pound mixture that is 10% protein? I have tried to solve this at least a dozen times and only get part of it right. Can you please explain how?1 solutions Answer 297774 by stanbon(57219)   on 2011-03-28 20:25:03 (Show Source): You can put this solution on YOUR website!Soybean meal is 12% protein, cornmeal is 6% protein, how many pounds of each should be mixed together in order to get 240 pound mixture that is 10% protein? -------- Equation: protein + protein = protein 0.12x + 0.06(240-x) = 0.10*240 --- Multiply thru by 100 to get: 12x + 6*240-6x = 10*240 6x = 4*240 x = (2/3)*240 --- x = 160 lbs. (amt of Soybean needed) --- 240-x = 80 lbs. (amt of Cornmenal needed) ================================================ Cheers, Stan H. =============