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# Recent problems solved by 'stanbon'

stanbon answered: 57236 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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 logarithm/78798: This question is from textbook algebra & Trigonometrie 2log2-log61 solutions Answer 56552 by stanbon(57304)   on 2007-04-19 18:38:05 (Show Source): You can put this solution on YOUR website!2log2-log6 =log4-log6 =log(4/6) =log(2/3) = -0.17609... ============== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/78788: This question is from textbook Algebra My question is: Mary is three years older than her twin brothers. Next year, the sum of the ages will be exactly 102. How old are they now. The Work I have is: m=3+b m+b+w=102 3+b+b+w=102 3+2b+w=1021 solutions Answer 56548 by stanbon(57304)   on 2007-04-19 18:29:56 (Show Source): You can put this solution on YOUR website!Mary is three years older than her twin brothers. Next year, the sum of the ages will be exactly 102. How old are they now. The Work I have is: m=3+b m+b+b=102 3+b+b+b=102 3+3b=102 3b=99 b=33 (each of the twin brothers is 33) Mary is 33+3=36 =========== Cheers, Stan H.
 Radicals/78759: This question is from textbook I need to find out what the smallest power to which you can raise both sides of the radical equation is so that the radicals are eliminated. the equation is: = 3 I know i need to find a power, but I am not sure how to get it. I don't understand what they mean by so that the radicals are eliminated. I had guessed 3 at first but that is obviously wrong. Can you help me? Thanks.1 solutions Answer 56490 by stanbon(57304)   on 2007-04-19 09:14:25 (Show Source): You can put this solution on YOUR website!The index on the left side is 2---i.e. square root The index on the right side is 3--i.e. cube root To rid the equation of radicals raise both sides to 2*3=6th power ----------- Cheers, Stan H.
 Mixture_Word_Problems/78748: This question is from textbook Elementary Statistics A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interval for the population mean.1 solutions Answer 56485 by stanbon(57304)   on 2007-04-19 08:18:31 (Show Source): You can put this solution on YOUR website!A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interval for the population mean. -------- x-bar = 645 E=1.96[31/sqrt(56)]=8.1194 The 95% confidence interval is 645-8.1194<=mu<=645+8.1194 ========= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/78755: Graph the solution set of x>-4. How do I do this one. I know how to use the number line, but is there a simple way of understanding the graphing system?1 solutions Answer 56484 by stanbon(57304)   on 2007-04-19 08:13:39 (Show Source): You can put this solution on YOUR website!Graph the solution set of x>-4. ---------- Draw a line. Label some point -4 Draw a small circle around that point. Draw an arrow starting at the circle and going to the left. Put a head on the arrow point to the left. That is the graph you want. ============== Cheers, Stan h.
 Linear_Equations_And_Systems_Word_Problems/78756: can you help me with setting up this problem and solve find an equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x=0.5, z=4, and w=5.1 solutions Answer 56483 by stanbon(57304)   on 2007-04-19 08:09:27 (Show Source): You can put this solution on YOUR website!find an equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x=0.5, z=4, and w=5. --------- y=kxz/w^2 You need to find "k". Substitute the given values to get: 20=k*0.5*4/25 500=2k k=250 EQUATION: y = 250xz/w^2 ========== Cheers, Stan H.
 Trigonometry-basics/78648: Graph the problem: y=3sin2x1 solutions Answer 56461 by stanbon(57304)   on 2007-04-18 22:29:06 (Show Source): You can put this solution on YOUR website!Graph the problem: y=3sin2x -------- Draw a sine curve on an xy coordinate system The 2x means the Period is 2(pi)/2= pi instead of 2pi. So put "pi" on the x axis at the end of the 1st period, 2pi at the end of the 2nd period, etc. The 3 means the amplitude is 3 instead of 1. So mark your y-axis accordingly. The curve rises a maximum of 3 and decends a maximum of -3. ============= cheers, Stan H.
 Mixture_Word_Problems/78632: This question is from textbook Elementary Statistics Assume that the salaries of elementary school teachers in the United States are normally distribured with a mean of \$32,000 and a standard deviation of \$3,000. If a teacher is selected at random, find the probability that he or she makes more than \$36,000.1 solutions Answer 56460 by stanbon(57304)   on 2007-04-18 22:20:09 (Show Source): You can put this solution on YOUR website!Assume that the salaries of elementary school teachers in the United States are normally distribured with a mean of \$32,000 and a standard deviation of \$3,000. If a teacher is selected at random, find the probability that he or she makes more than \$36,000. -------------------- Find the z-score of 36000 z(26000)=(36000-32000)/3000=1.3333... P(x>36000)=P(z>1.333)=0.0913 =============== Cheers, Stan H.
 Equations/78731: x/5 - x+3/x = -3/x some help to solve this pleeeeeease1 solutions Answer 56458 by stanbon(57304)   on 2007-04-18 22:12:27 (Show Source): You can put this solution on YOUR website!x/5 - (x+3)/x = -3/x ------------ the least common multiply of the denominators is 5x. Multiply thru by 5x to get: x^2 - 5(x+3) = -3*5 x^2-5x-15=-15 x^2-5x=0 x(x-5)=0 x=0 or x=5 But x cannot be zero as it is in the denominator or the original problem. So, x=5 is the only answer. Cheers, Stan H. ============== Cheers, Stan H.
 Mixture_Word_Problems/78730: This question is from textbook Elementary Statistics An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows.1 solutions Answer 56456 by stanbon(57304)   on 2007-04-18 22:07:42 (Show Source): You can put this solution on YOUR website!An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows. ----------- It is a binomial problem with n=150, p=0.15, 0<=x<=19 If you have a TI calculator with a stat capability use binomcdf(150,0.15,19)=0.250928... ----------- Cheers, Stan H.
 Complex_Numbers/78732: i equals the square root of negative 1, what would be the location of 5-2i on a plane?1 solutions Answer 56455 by stanbon(57304)   on 2007-04-18 22:01:04 (Show Source): You can put this solution on YOUR website!i equals the square root of negative 1, what would be the location of 5-2i on a plane? --------------- When you plot complex numbers on a plane the x-axis becomes the Real Number axis and the y-axis becomes the Imaginary Number axis. --------------- Your problem has as its Real part the number 5 It has as it Imaginary part the number -2 ---------- So you plot it as the point (5,-2) ============== Cheers, Stan H.
 Radicals/78723: When do slove a radical equation using factoring or completing the square, what do you do when c=0?1 solutions Answer 56446 by stanbon(57304)   on 2007-04-18 20:37:23 (Show Source): You can put this solution on YOUR website!Post an example or two of what you mean. cheers, Stan H.
 logarithm/78709: How do u solve this question? A study monitored the life spans of 129 robins over 4 years. The equation was developed to calculate the number of years y for x percent of the robin population to die. y= 2-log(100-x)/.42 How many robins had died after 6 months? 1 solutions Answer 56444 by stanbon(57304)   on 2007-04-18 20:34:34 (Show Source): You can put this solution on YOUR website!A study monitored the life spans of 129 robins over 4 years. The equation was developed to calculate the number of years y for x percent of the robin population to die. y= 2-log(100-x)/.42 How many robins had died after 6 months? Let y=(1/2) yr and solve for x: 0.5=2-log(100-x)/0.42 -1.5=-log(....)/0.42 log(100-x)=0.63 100-x=10^0.63 100-x=4.2657 x=95.73% ------------- # of robins that died is 0.9573*129=123+ ============ Cheers, Stan H.
 logarithm/78710: How do u solve this problem A top-quality fax-copying machine is purchased for \$5800. After t years its value is given by the exponential function V(t)=5800(.8)to the power of t . The company decides to replace the machine when its value declined to \$500. After how long will the machine be replaced? 1 solutions Answer 56441 by stanbon(57304)   on 2007-04-18 20:22:56 (Show Source): You can put this solution on YOUR website!A top-quality fax-copying machine is purchased for \$5800. After t years its value is given by the exponential function V(t)=5800(.8)to the power of t . The company decides to replace the machine when its value declined to \$500. After how long will the machine be replaced? ----------------- EQUATION: 500=5800(0.8)^t Divide by 5800 to get: 5/58 = (0.8)^t Take the log of both sides: -1.064457 = tlog(0.8) -1.064457 = t(-0.09691) t=10.9839 yrs =================== Cheers, Stan H.
 percentage/78702: Identify the amount in the statement "140 is 28% of 500" I would really appreciate someone's help in explaing this to me.1 solutions Answer 56435 by stanbon(57304)   on 2007-04-18 20:04:37 (Show Source): You can put this solution on YOUR website!"140 is 28% of 500" 140 = (0.28)*500 140 is the interest 0.28 is the rate 500 is the amount ============== Cheers, Stan H.
 Quadratic_Equations/78705: Factor completely 9x^2 + 24xy - 9y^2 I know the GCF is 3, but I don't know what to do with the two different variables. Thank you1 solutions Answer 56433 by stanbon(57304)   on 2007-04-18 20:01:12 (Show Source): You can put this solution on YOUR website!Factor completely 9x^2 + 24xy - 9y^2 =3(3x^2+8xy-3y^2) Think of two numbers whose product is 3*-3=-9 and whose sum is 8 The numbers are +9 and -1 So rewrite the problem putting 9xy-1xy in place of 8xy =3(3x^2+9xy-xy-3y^2) Factor the 1st two and the last two terms separately to get: =3(3x(x+3y)-y(x+3y)) Factor out the common factor to get: =3(x+3y)(3x-y) =========== Cheers, Stan H.
 Human-and-algebraic-language/78671: I need to figure out how can I solve this problems? can any body help to me or any idea? really I need a tutorial to solve this problems. ------------------------------------------------------------------------------ 1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this? ------------------------------------------------------------------------------- 2. A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. (a) Using the Library and other course resources, find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code). (b) Using the latitude found in part a and the formula N(P), find the length of a nautical mile to the nearest foot at that location. (c) Next, use the formula N(P) to find the latitude where the nautical mile is 6051 feet. (d) Name two cities in the Northern Hemisphere and two in the Southern that are close to the latitude found in part c. ------------------------------------------------------------------------------- 3. When graphed using polar coordinates, the center of a regular nonagon is at the origin and one vertex is at (6, 0 degrees) or (6, 0 radians). Find the polar coordinates of the other vertices in both degrees and radians. ******************************************************************************* I traying to use this polar cordination to solve all the problems, but i'am lost I want to learn Trigo. I need hlep. The polar cordination http://www.analyzemath.com/polarcoordinates/polarcoordinates.html1 solutions Answer 56429 by stanbon(57304)   on 2007-04-18 18:32:58 (Show Source): You can put this solution on YOUR website!1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? It has a vertical asymptote at x=90 degrees -------- (b) What are other undefined x values? 90 degrees + and 180n degrees - 180n degrees where n=1,2,3,.... --------------------- (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? They approach infinity from below 90 and approach -infinity as they approach 90 degrees from above. -------------------- (d) How does the graph show this? Asymptotes ------------------------------------------------------------------------------- 2. A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees. (a) Using the Library and other course resources, find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code). Use Google or other search engine. ------------- (b) Using the latitude found in part a and the formula N(P), find the length of a nautical mile to the nearest foot at that location. (c) Next, use the formula N(P) to find the latitude where the nautical mile is 6051 feet. (d) Name two cities in the Northern Hemisphere and two in the Southern that are close to the latitude found in part c. ------------------------------------------------------------------------------- 3. When graphed using polar coordinates, the center of a regular nonagon is at the origin and one vertex is at (6, 0 degrees) or (6, 0 radians). Find the polar coordinates of the other vertices in both degrees and radians. I think a nonagon has nine sides 360/9=40 degrees You have vertices at (6,40 degrees), (6,80 degrees), (6,120 degrees) etc In radians you have (6,40(pi/180), (6,80(pi/180)), etc ******************************************************************************* I traying to use this polar cordination to solve all the problems, but i'am lost I want to learn Trigo. I need hlep. It's pretty tough to learn trigonometry by yourself. Get a good instructor. -------------- The polar cordination http://www.analyzemath.com/polarcoordinates/polarcoordinates.html -------------- cheers, Stan H.
 Coordinate-system/78694: How do you find percent of increase or decrease?1 solutions Answer 56428 by stanbon(57304)   on 2007-04-18 17:58:26 (Show Source): You can put this solution on YOUR website!Let's say price = \$20 Price is increased to \$35 Subtract the original price from the new price to get \$15 Divide that difference by original price: 15/20= 75% increase ========================= Let original price be \$20 Price is decreased to \$5 Subtrace the original price from the new price to get -\$15 Divide that difference by original price to get -15/20=-0.75= 75% decrease --------------- Cheers, Stan H.
 Reduction-of-unit-multipliers/78696: CONVERT 15 MILES PER HOUR TO X FEET PER MINUTE.1 solutions Answer 56427 by stanbon(57304)   on 2007-04-18 17:50:26 (Show Source): You can put this solution on YOUR website!CONVERT 15 MILES PER HOUR TO X FEET PER MINUTE. -------- 15(mi/hr)(60/1)*min/hr(5280/1)ft/mi = [15*60*5280] ft/min = 4,752,000 ft/min ==================== Cheers, Stan H.
 Linear-equations/78667: Define a variable, write an inequality, and solve each problem. A number decreased by 17 is less than -131 solutions Answer 56410 by stanbon(57304)   on 2007-04-18 14:11:49 (Show Source): You can put this solution on YOUR website!A number decreased by 17 is less than -13 x-17<-13 x<=4 ================ Cheers, Stan H.
 Numeric_Fractions/78659: I can't seem to figure out what to do with this equation 5/8n = 3 3/4 How do I figure out n?1 solutions Answer 56409 by stanbon(57304)   on 2007-04-18 14:09:15 (Show Source): You can put this solution on YOUR website!5/8n = 3 3/4 (5/8)n = 15/4 Multiply both sides by 8/5 to get: n=(15/4)(8/5) n= 6/5 ============== Cheers, Stan H.
 Functions/78662: Factors for Loan qualification: 1.Front-end ratio should not exceed Conventional VA FHA 0.28 N/A 0.29 2.Back-end ratio should not exceed 0.36 0.41 0.41 3.Credit Score should be 650 or higher. Suppose a family has a gross monthly income of \$2229. What is the maximum monthly debt payment that would meet the back-end ratio qualification for a conventional loan? A)\$646.41 B)\$913.89 C)\$802.44 D)\$624.121 solutions Answer 56407 by stanbon(57304)   on 2007-04-18 13:57:24 (Show Source): You can put this solution on YOUR website!max month debt payment = (back-end ratio)*(gross monthly income) mmdp = 0.36*2229= \$802.44 =========== Cheers, Stan H.
 Linear-equations/78665: Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither. 3x-7y=1,7x+3y=4 1 solutions Answer 56406 by stanbon(57304)   on 2007-04-18 13:47:26 (Show Source): You can put this solution on YOUR website!Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither. 3x-7y=1 slope is 3/7 ------------- 7x+3y=4 slope is -7/3 ----------- Therefore the graphs are perpendicular. Cheers, Stan H.
 Radicals/78628: Can someone please help me solve these 3 problems....I'm still lost. Thanks:) 1) For a home that has a roof that is 7m from peak to eave and the attic space is 3m high at the peak, how long does each of the pieces of insulation need to be? Round to the nearest tenth. 2) Find the distance between each pair of roots. (-3, 0) and (4, 0) 3) Use the Pythagorean theorem to determine the length of each line segment. Where appropriate, round to the nearest hundredth. (3,2) (1,-2) 1 solutions Answer 56404 by stanbon(57304)   on 2007-04-18 13:03:49 (Show Source): You can put this solution on YOUR website!1) For a home that has a roof that is 7m from peak to eave and the attic space is 3m high at the peak, how long does each of the pieces of insulation need to be? Round to the nearest tenth. -------- Draw the picture. I assume you want to put the insulation horizontally on the floor of the attic. The horizontal distance = sqrt(7^2-3^2)= sqrt40 = 2sqrt10 ft. 2sqrt10= 6.32 ft ---------------------- 2) Find the distance between each pair of roots. (-3, 0) and (4, 0) d=sqrt[(0-0)^2+(4--3)^2 = sqrt[49]=7 ------------------------- 3) Use the Pythagorean theorem to determine the length of each line segment. Where appropriate, round to the nearest hundredth. (3,2) (1,-2) d=sqrt[(-2-2)^2 + (1-3)^2] = sqrt[16+4]=sqrt20=2sqrt5 =================== Cheers, stan H.
 Mixture_Word_Problems/78631: This question is from textbook Elementary Statistics Determine the probability distribution's missing value. The probability that a tutor will see 0, 1, 2, 3, or 4 students. x | 0 | 1 | 2 | 3 | 4 p(x) |0.01 | 0.04 | 0.37 | 0.34 | ? 1 solutions Answer 56403 by stanbon(57304)   on 2007-04-18 12:54:14 (Show Source): You can put this solution on YOUR website!The probabilities must add up to one. Add the ones you have and subtract their sum from one to get the missing probability. ------------ Cheers, Stan H.
 Travel_Word_Problems/78653: This question is from textbook intermediate algebra w/appl an insurance representative traveled 735 mi by commercial jet and then an additional 105 mi by helicopter. The rate of the jet was four times the rate of the helicopter. the entire trip took 2.2 hours. Find the rate of the jet.1 solutions Answer 56402 by stanbon(57304)   on 2007-04-18 12:50:11 (Show Source): You can put this solution on YOUR website!an insurance representative traveled 735 mi by commercial jet and then an additional 105 mi by helicopter. The rate of the jet was four times the rate of the helicopter. the entire trip took 2.2 hours. Find the rate of the jet. --------- Jet DATA: distance=735 mi ; rate = 4x mi/hr ; time=d/r = 735/4x hrs ------------------ Helicopter DATA: distance= 105 mi ; rate = x mi/hr ; time=d/r= 105/x hrs ============== EQUATION: time + time = 2.2 hrs Note: 2.2(10/10)=22/10 735/4x + 105/x = 22/10 Note: the least common multiple of 4x, x, and 10 is 20x. Multiply thru by 20x to get: 5*735 + 2100 = 44x x=131.25 mph (speed of helicopter) 4x=525 mph (speed of jet) ================ Cheers, Stan H.
 logarithm/78651: find a so that the graph of f(x) =LOGA ^ XCONTAINS THE POINT (21,4) A=1 solutions Answer 56401 by stanbon(57304)   on 2007-04-18 12:43:10 (Show Source): You can put this solution on YOUR website!find a so that the graph of f(x) =LOGA ^ XCONTAINS THE POINT (21,4) y=log(base a)x This means: x=a^y Substituting (21,4) you get: 21=a^4 a= 21^(1/4)=2.140695143... Cheers, Stan H.
 Numeric_Fractions/78652: I have a question about how you simplify fractions with variables. Here is a problem with its solution. Why is the answer not simplified into a mixed number? 3 over 10q plus 9 over 10 q equals 6 over 5 q? 1 solutions Answer 56400 by stanbon(57304)   on 2007-04-18 12:38:53 (Show Source): You can put this solution on YOUR website!3/10q + 9/10q = 6/5q ----------- The lcm of the denominators is 10q Multiply thru by 10q to get: 3 + 9 = 12 12= 12 ------------- This means the eqation is true for all values of q. However q cannot be zero because q is in the denominator. ------------- cheers, Stan H.
 Inequalities/78640: The square root of (6-x) + The square root of (5x + 6) = 61 solutions Answer 56392 by stanbon(57304)   on 2007-04-18 11:00:22 (Show Source): You can put this solution on YOUR website! square root of (6-x) + The square root of (5x + 6) = 6 Square both sides to get: (6-x)+2sqrt[(6-x)(5x+6)]+5x+6 = 36 2sqrt[......] =24-4x sqrt[....]=12-2x Square both sides again to get: -(5x+6)(x-6)=[-2(x-6)]^2 -[5x^2-24x-36] = 4[x^2-12x+36] -5x^2+24x+36 = 4x^2-48x+144 -9x^2+72x-108=0 x^2-8x+12=0 (x-6)(x-2)=0 x=6 or x=2 Checking the answers for extraneous roots: If x=6 the original equation is true If x=2 the original equation is true ================= cheers, Stan H.