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# Recent problems solved by 'stanbon'

stanbon answered: 57304 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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 Graphs/390775: write the equation so that y is a function of x: 4(y-6x)=121 solutions Answer 277109 by stanbon(57377)   on 2011-01-04 19:29:14 (Show Source): You can put this solution on YOUR website! write the equation so that y is a function of x: 4(y-6x)=12 Divide by 4 to get: y-6x = 3 Add 6x to both sides to get: y = 6x+3 ================ cheers, stan H.
 test/390774: One number is three less than the other. Their sum is 21. find the numbers.1 solutions Answer 277108 by stanbon(57377)   on 2011-01-04 19:27:06 (Show Source): You can put this solution on YOUR website!One number is three less than the other. Their sum is 21. find the numbers. Equations: x+y = 21 x = y-3 --- Rearrange: x + y = 21 x - y = -3 ---- Add and solve for "x": 2x = 18 x = 9 ---- Since x+y = 21, y = 12 ---- Cheers, Stan H. ==============
 Proportions/390772: a/40=30/100 i tried and i got 12. i dont know if its the right answer can you explain it to me?1 solutions Answer 277107 by stanbon(57377)   on 2011-01-04 19:24:18 (Show Source): You can put this solution on YOUR website!a/40=30/100 ---- Multiply both sides by 40 to get: a = 40(30/100) --- a = 40(3/10) a = 120/10 a = 12 --- You are correct. Cheers, Stan H.
 percentage/390767: I am trying to teach my child how to find 70% of 120, but have forgotten myself! 1 solutions Answer 277106 by stanbon(57377)   on 2011-01-04 19:22:18 (Show Source): You can put this solution on YOUR website!find 70% of 120 ----------------------- 70% = 70/100 ---- 70% of 120 = (70/100)(120) = (7/10)(120) = 7*12 = 84 ================ Cheers, Stan H. ===========
 Rational-functions/390759: Write 3x-6y= -14 in polar form. Round to the nearest degree. Thank you so much for all of your help!!!!! God Bless!!!!!1 solutions Answer 277104 by stanbon(57377)   on 2011-01-04 19:19:45 (Show Source): You can put this solution on YOUR website!Write 3x-6y= -14 in polar form. --- x = r*cos(theta) y = r*sin(theta) ----- Converting the equation: 3rcos(theta) - 6rsin(theta) = -14 rcos(theta) - 2rsin(theta) = -14/3 r = (-14/3)/(cos(theta)-2sin(theta)) ================ Cheers, Stan H.
 Finance/390755: hello I just have a question I have been struggling with and was wonderinf if somebody could please help me with it. The question is determine the time it takes to double an investment in an account that pays an interest of 4% per annum, compounded quarterly. Thankyou so much!1 solutions Answer 277103 by stanbon(57377)   on 2011-01-04 19:10:42 (Show Source): You can put this solution on YOUR website!determine the time it takes to double an investment in an account that pays an interest of 4% per annum, compounded quarterly. ====== Let's say you invest "x" dollars at 4%. Doubling will give you "2x" dollars. --- Formula: 2x = x(1+(0.04/4))^(4t) where t is the number of years. --- 2 = (1+0.01)^4t --- Take the log of both sides and solve for "t": 4t*log(1.01) = log2 --- 4t = log(2)/log(1.01) --- 4t = 69.66 --- t = 17.42 years ======================= Cheers, Stan H. ================
 Linear-equations/390541: A family has two cars. The first carf has a fuel efficiency of 28 miles per gallon of gas and the second has a fuel efficiency of 34 miles per gallon of gas. During one particular week, the two cars went a combined total of 2100 miles, for a total gas consumption of 85 gallons. How many gallons were consumed by each of the two cars that week?1 solutions Answer 277046 by stanbon(57377)   on 2011-01-04 16:41:18 (Show Source): You can put this solution on YOUR website!A family has two cars. The first car has a fuel efficiency of 28 miles per gallon of gas and the second has a fuel efficiency of 34 miles per gallon of gas. During one particular week, the two cars went a combined total of 2100 miles, for a total gas consumption of 85 gallons. How many gallons were consumed by each of the two cars that week? --- Equation: Gas Equation: x + y = 85 gallons Distance Eq: 28x+34y = 2100 miles ----- Multiply thru the gas eq by 28 to get: 28x + 28y = 28*85 --- Subtract that from the distance Eq. and solve for "y": 6y = -280 y = 46 2/3 gallons (amt. consumed by the 34 mpg car) --- x = 85-46 2/3 = 38 1/3 gallons (amt. consumed by the 28 mpg car) ========================= Cheers, Stan H.
 Linear-equations/390647: If you are finding the line perpendicular to x + 3y = 5, what is the slope of the line?1 solutions Answer 277043 by stanbon(57377)   on 2011-01-04 16:26:43 (Show Source): You can put this solution on YOUR website!If you are finding the line perpendicular to x + 3y = 5, what is the slope of the line? ========== Slope of the given line: 3y = -x+5 y = (-1/3)x + (5/3) ---- slope = -1/3 ---- Slope of a perpendicular line: 3 ====================================== Cheers, Stan H.
 logarithm/390652: how do i solve (log base 4 (x+3))+(log base 4 (x-3))=2?1 solutions Answer 277042 by stanbon(57377)   on 2011-01-04 16:23:11 (Show Source): You can put this solution on YOUR website!log base 4 (x+3))+(log base 4 (x-3))=2 ---- log4(x+3) + log4(x-3) = 2 ------- log4[x^2-9] = 2 --- base = 4 exponent = 2 result = x^2-9 --- Write in exponential form: x^2-9 = 4^2 --- x^2 = 16+9 --- x^2 = 25 --- Positive solution: x = 5 ======================= Cheers, Stan H.
 logarithm/390653: how do i solve 3(log base 2 (x))=6?1 solutions Answer 277040 by stanbon(57377)   on 2011-01-04 16:19:35 (Show Source): You can put this solution on YOUR website! 3(log base 2 (x))=6 Divide both sides by 3 to get: log2(x) = 2 --- base = 2 exponent = 2 result = x --- Write in exponential form: x = 2^2 x = 4 ===================== Cheers, Stan H.
 Systems-of-equations/390655: Need help on answering this math problem please help. Thanks! f(x)=10²+5= 1 solutions Answer 277039 by stanbon(57377)   on 2011-01-04 16:17:42 (Show Source): You can put this solution on YOUR website!f(x)=10²+5 ---- 10^2 means 10*10 = 100 ---- Your Problem: f(x) = 100+5 f(x) = 105 ============== Cheers, Stan H.
 Miscellaneous_Word_Problems/390649: The sum of these two numbers are 31. The product of these two numbers are 150, what are the numbers?1 solutions Answer 277038 by stanbon(57377)   on 2011-01-04 16:15:12 (Show Source): You can put this solution on YOUR website!The sum of these two numbers are 31. The product of these two numbers are 150, what are the numbers? -------- Equations: x + y = 31 xy = 150 ----- Modify: x = 31-y --- Substitute: (31-y)y = 150 --- Solve: -y^2+31y-150 = 0 y^2-31y+150 = 0 --- Factor: y^2- 25y-6y + 150 = 0 y(y-25)-6(y-25) = 0 (y-25)(y-6) = 0 -------------- y = 25, then x = 6 OR y = 6, then x = 25 ====================== Cheers, Stan H.
 Numeric_Fractions/390650: 3/6 divided by 9/161 solutions Answer 277035 by stanbon(57377)   on 2011-01-04 16:09:05 (Show Source): You can put this solution on YOUR website!3/6 divided by 9/16 --------------- [3/6]/[9/16] --- Invert the denominator and multiply: --- [3/6] --- Cancel any factor common to a numerator and a denominator: [1/1] = 8/9 ================ Cheers, stan H.
 Functions/390648: Which of the following is NOT a function? A. {(4,0), (0,-1), (2,0), (1,1), (3,0)} B. {(1,3), (2,3), (3,6), (4,6), (5,8)} C. {(3,1), (3,2), (6,3), (6,4), (8,5)} D. {(6,4), (7,6), (8,4), (9,6), (5,4)} 1 solutions Answer 277034 by stanbon(57377)   on 2011-01-04 16:05:27 (Show Source): You can put this solution on YOUR website!Which of the following is NOT a function? --- Look for 2 or more occurences of an x value with 2 different y values. -------------------------- A. {(4,0), (0,-1), (2,0), (1,1), (3,0)} x's are all different so it is a function. ------------------- B. {(1,3), (2,3), (3,6), (4,6), (5,8)} x's are all different so it is a function. ------------------------------- C. {(3,1), (3,2), (6,3), (6,4), (8,5)} x = 3 is repeated and has 2 different y values Not a function. -------------------------------------- D. {(6,4), (7,6), (8,4), (9,6), (5,4)} x's are all different so it is a function. ========================================== Cheers, stan H.
 Linear-equations/390646: Write the equation y - 2 = 2(x - 3) in standard form.1 solutions Answer 277033 by stanbon(57377)   on 2011-01-04 16:01:41 (Show Source): You can put this solution on YOUR website!Write the equation y - 2 = 2(x - 3) in standard form. y - 2 = 2x-6 y = 2x-4 ---- Standard form: 2x-y = 4 ------------------- Cheers, Stan H.
 Triangles/390578: can a triangle have lenths of 17,19, and 35?1 solutions Answer 276982 by stanbon(57377)   on 2011-01-04 13:05:44 (Show Source): You can put this solution on YOUR website!can a triangle have lengths of 17,19, and 35? ---- Since 17+19 > 35, the answer is yes. Cheers, stan H.
 Trigonometry-basics/390579: If sin A>0 and tan A<0, then A is in what quadrant?1 solutions Answer 276980 by stanbon(57377)   on 2011-01-04 13:03:33 (Show Source): You can put this solution on YOUR website!If sin A>0 and tan A<0, then A is in what quadrant? ------------ Since sin = y/r and r is always positive, y is + is sin is +. So, sin>0 A must be in I or II. ---- Since tan = y/x, if tan<0 and y is positive, x must be negative. So, tan<0 A must be in II. =========================== Cheers, Stan H.
 Polygons/390576: a regular polygon has 12 sides... what is the measurements of each interiot angle? please show all your work1 solutions Answer 276976 by stanbon(57377)   on 2011-01-04 12:48:37 (Show Source): You can put this solution on YOUR website!a regular polygon has 12 sides... what is the measurement of each interior angle? --- There are 12 equal exterior angles. Fact: The sum of the exterior angles = 360 degrees. --- Ans: 360/12 = 30 degrees. ============= Cheers, Stan H.
 Probability-and-statistics/390557: Assume that in a hypothesis test with null hypothesis 0 μ H : = 13.0 at a = 0.05, that a value of 11.0 for the sample mean results in the null hypothesis not being rejected. That corresponds to a confidence interval result of A) The 95% confidence interval for the mean does not contain the value 13.0 B) The 95% confidence interval for the mean contains the value 11.0 C) There is insufficient information to conclude whether the 95% confidence interval for the mean contains or does not contain the value 13.0 D) The 95% confidence interval for the mean contains the value 13.0 Nationwide, the average waiting time until electric utility customer service representative answers a call is 300 seconds per call. The Gigantic Kilowatt Energy Company took a sample of 35 calls and found that, on the average, they answered in 240 seconds per call with a standard deviation of 50. Can the company claim that they are faster than the average utility? A) No, because –0.20 falls in the critical region B) Yes, because –7.10 falls in the critical region C) No, because –1.20 falls in the critical region D) Yes, because –0.20 falls in the critical region If the observed value is 4, the expected value is 5, and the standard error is 4, then the test value used for the z test is equal to A) –1.00 B) 0.25 C) –0.25 D) 1.00 What is the critical t-value for a right-tailed test when a = .025and d.f. = 12? A) 0.695 B) 2.179 C) 2.831 D) 2.201 1 solutions Answer 276974 by stanbon(57377)   on 2011-01-04 12:46:19 (Show Source): You can put this solution on YOUR website!Assume that in a hypothesis test with null hypothesis Ho: u = 13.0 at a = 0.05, that a value of 11.0 for the sample mean results in the null hypothesis not being rejected. That corresponds to a confidence interval result of A) The 95% confidence interval for the mean does not contain the value 13.0 B) The 95% confidence interval for the mean contains the value 11.0 C) There is insufficient information to conclude whether the 95% confidence interval for the mean contains or does not contain the value 13.0 D) The 95% confidence interval for the mean contains the value 13.0 --- Answer: A =================== Nationwide, the average waiting time until electric utility customer service representative answers a call is 300 seconds per call. The Gigantic Kilowatt Energy Company took a sample of 35 calls and found that, on the average, they answered in 240 seconds per call with a standard deviation of 50. Can the company claim that they are faster than the average utility? Ho: u = 300 Ha: u < 300 (claim) t(240) = (240-300)/[50/sqrt(35)] = -7.10 A) No, because –0.20 falls in the critical region B) Yes, because –7.10 falls in the critical region C) No, because –1.20 falls in the critical region D) Yes, because –0.20 falls in the critical region Answer: B ========================================== If the observed value is 4, the expected value is 5, and the standard error is 4, then the test value used for the z test is equal to: z(4) = (4-5)/4 = -1/4 --- A) –1.00 B) 0.25 C) –0.25 D) 1.00 Ans: C ========================================== What is the critical t-value for a right-tailed test when a = .025and d.f. = 12? A) 0.695 B) 2.179 C) 2.831 D) 2.201 Ans: B ================= Cheers, Stan H. --------------------------------------------------------------------------------
 Problems-with-consecutive-odd-even-integers/390571: 1) find three positive consecutive odd integers such that the largest decreased by twice the second is equal to 10 less than the smallest. 2) find three consecutive even integers such that twice the sum of the first and second is 10 more than three times the third. 3) find three consecutive odd integers such that twice the sum of the second and third is 43 more than three times the first. 4) find four consecutive odd integers such that the sum of the first three exceeds twice the fourth by 5.1 solutions Answer 276973 by stanbon(57377)   on 2011-01-04 12:31:50 (Show Source): You can put this solution on YOUR website!1) find three positive consecutive odd integers such that the largest decreased by twice the second is equal to 10 less than the smallest. --- 1st: 2x-1 2nd: 2x+1 3rd: 2x+3 ------ Equation: 2x+3 - 2(2x+1) = 2x-1-10 2x+3-4x-2 = 2x-11 -4x= -12 x = 3 1st: 2x-1 = 5 2nd: 2x+1 = 7 3rd: 2x+3 = 9 ========================= 2) find three consecutive even integers such that twice the sum of the first and second is 10 more than three times the third. 1st: 2x-2 2nd: 2x 3rd: 2x+2 --- Equation: 2[2x-2+2x] = 3(2x+2)+10 2(4x-2) = 6x+16 8x-4 = 6x+16 2x = 20 x = 10 --- 1st: 2x-2 = 18 2nd: 20 3rd: 22 ======================= Use the same procedure to solve the following two problems. ======== Cheers, Stan H. ======== 3) find three consecutive odd integers such that twice the sum of the second and third is 43 more than three times the first. 4) find four consecutive odd integers such that the sum of the first three exceeds twice the fourth by 5.
 test/390546: The equation y=461.19x+3492 represents the value of a work of art from 1964 to 2005. what does the number 461.19 represent?1 solutions Answer 276971 by stanbon(57377)   on 2011-01-04 12:25:25 (Show Source): You can put this solution on YOUR website!The equation y=461.19x+3492 represents the value of a work of art from 1964 to 2005. what does the number 461.19 represent? ----- "x" is the number of years after 1064 When "x" increases by one year, y increases by 461.19. --- Mathematically speaking, 461.19 is the slope of the linear expression used to state the value of the work of art. ---- Cheers, Stan H.
 Rational-functions/390548: I dont get how to solve equations by graphing. Could you please show step by step how to do this? -x^3 -3x-2=0 x^4+2x^2-1=0 y=-x^4+4x^3+3=0 -x^3+3x+4=0 x^4+2x-3=0 -x^3 +2x^2 +1=0 Any help you can give wuld be greatly appreciated Thank you1 solutions Answer 276965 by stanbon(57377)   on 2011-01-04 10:57:26 (Show Source): You can put this solution on YOUR website!I dont get how to solve equations by graphing. Could you please show step by step how to do this? --- You would have to plot enough points to see where the curve crosses the x-axis. ---- -x^3 -3x-2=0 If x = 0, y = -2 giving (0,-2) If x = -1, y = 1+3-2 = 2 giving (-1,2) Note: Since the y-value changed from negative to positive, there must be a root between x = -1 and x = 0 Try x = -1/2: If x = -1/2, y = -(-1/8)-(-1/2)-2 = (1/8)+(4/8)-2 = -1 3/8 giving you (-1/2,-11/8) Keeping up this process you can get closer and closer to the solution which is -0.596072... ========================================= Cheers, Stan H. ========
 Geometry_Word_Problems/390551: What is the length of a diagonal of a sqaure with a perimeter of 28 centimeters?1 solutions Answer 276964 by stanbon(57377)   on 2011-01-04 10:40:01 (Show Source): You can put this solution on YOUR website!What is the length of a diagonal of a square with a perimeter of 28 centimeters? --- Perimeter of a square = 4s where s is the length of each side. ------------------ 4s = 28 s = 7 cm (length of each side) ---- Note: diagonal^2 = side^2 + side^2 ----------------- d^2 = 2s^2 d^2 = 2*49 d = 7*sqrt(2) cm ================== Cheers, Stan H. ========
 Polynomials-and-rational-expressions/390550: solve: 2/x+1 + 3/x-1 = 5/x^2-11 solutions Answer 276963 by stanbon(57377)   on 2011-01-04 10:36:35 (Show Source): You can put this solution on YOUR website!solve: 2/x+1 + 3/x-1 = 5/x^2-1 --- Multiply thru by x^2-1 to get: 2(x-1) + 3(x+1) = 5 5x+1 = 5 5x = 4 x = 4/5 ============ Cheers, Stan H.
 Geometry_Word_Problems/390549: If perimeter of parallelogram is 60cm and the ratio between its dimensions is 2:3 then the length of each is........... , ........... cm 1 solutions Answer 276962 by stanbon(57377)   on 2011-01-04 10:34:33 (Show Source): You can put this solution on YOUR website!If perimeter of parallelogram is 60cm and the ratio between its dimensions is 2:3 then the length of each is........... , ........... cm --- Let the dimensions be 2x and 3x. --- Perimeter = 2(2x + 3x) = 10x --- Equation: 10x = 60cm x = 6 cm ---- 2x = 12 cm (one of the dimensions) 3x = 18 cm (the other dimension) ============= Cheers, Stan H. ==========
 Linear-equations/390547: Dear tutors, i don`t understand how to find the matrix inverse, please if you can help to me. it is a matrix 3x3 -4 3 2 1 -32 1 6 -2 -1 Help me once again please, it is very important for me!!!!1 solutions Answer 276961 by stanbon(57377)   on 2011-01-04 10:31:49 (Show Source): You can put this solution on YOUR website!The process is complicated for this site. --- Please use a Google search for "inverting a matrix". There you will see worked examples. ------------------ Cheers, Stan H.
 Linear-systems/390482: x+2y-z=-7 2x-2y-z=6 x+y-2z=-61 solutions Answer 276864 by stanbon(57377)   on 2011-01-03 22:01:22 (Show Source): You can put this solution on YOUR website!x+2y-z=-7 2x-2y-z=6 x+y-2z=-6 ------------------ Use any method you know to get: x = 1 y = -3 z = 2 ========= Cheers, Stan H.
 Word_Problems_With_Coins/390480: How do I solve this problem: Royce has 1.30 in dimes and quarters. he has one fourth as many quarters as dimes. How many of each does he have?1 solutions Answer 276863 by stanbon(57377)   on 2011-01-03 21:58:16 (Show Source): You can put this solution on YOUR website!Royce has 1.30 in dimes and quarters. he has one fourth as many quarters as dimes. ---------------- Value Equation: 10d + 25q = 130 cents Quantity Eq:::: q = 1/4 d --------------------------------- Modify: d = 4q --- Substitute for "d" and solve for "q": 10(4q)+25q = 130 65q = 130 q = 2 (# of quarters) ---- Since d = 4q, d = 8 (# of dimes) ==== Cheers, Stan H.
 Permutations/390478: There are 2 girls and 7 boys in a math club. A team of four persons must be chosen for a tournament, and there must be at least 1 girl on the team. In how many ways can this be done?1 solutions Answer 276861 by stanbon(57377)   on 2011-01-03 21:54:10 (Show Source): You can put this solution on YOUR website! There are 2 girls and 7 boys in a math club. A team of four persons must be chosen for a tournament, and there must be at least 1 girl on the team. In how many ways can this be done? ----- P(at least one girl on the team) = 1 - P(no girls on the team) --- = 1 - 7C4/9C4 = 1 - 0.278 = 0.722 =============== Cheers, Stan H.
 Travel_Word_Problems/390477: if you are traveling 1 kilometer in 12 seconds, how fast are you traveling? 1 solutions Answer 276858 by stanbon(57377)   on 2011-01-03 21:50:29 (Show Source): You can put this solution on YOUR website! if you are traveling 1 kilometer in 12 seconds, how fast are you traveling? --- (1 km/12 sec)(3600 sec/1 hr) --- = (3600/12)kph === = 300 km/hr ================= Cheers, Stan H. =================