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# Recent problems solved by 'scott8148'

scott8148 answered: 6619 problems
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 Square-cubic-other-roots/140151: Simplify; (8/27)^1/31 solutions Answer 102119 by scott8148(6628)   on 2008-05-05 16:51:15 (Show Source): You can put this solution on YOUR website![8^(1/3)]/[27^(1/3)] __ 2/3
 Angles/140150: both sides of a parallelogram measure 8 cm and 10 cm between them and form an angles of 120 degrees. calculate the length of their diagonal1 solutions Answer 102118 by scott8148(6628)   on 2008-05-05 16:43:51 (Show Source): You can put this solution on YOUR website!let x=diagonal __ using the law of cosines __ x^2=8^2+10^2-(2*8*10*cos(120°)) x^2=64+100-(160(-1/2)) __ x^2=244 __ x=sqrt(244) __ x=2sqrt(61)
 Equations/140152: what is the difference between x-3 and 3-x?1 solutions Answer 102114 by scott8148(6628)   on 2008-05-05 16:36:01 (Show Source): You can put this solution on YOUR website!they are negatives of each other you can get one by multiplying the other by -1 they sum to zero, so they are additive inverses
 Word_Problems_With_Coins/140141: Samantha has a total of one hundred forty-one pennies,nickels and quarters.She has a total of \$15.17. She has fifteen more quarters than pennies and fifteen fewer quarters than nickels. How many of each coin does she have?1 solutions Answer 102106 by scott8148(6628)   on 2008-05-05 16:17:49 (Show Source): You can put this solution on YOUR website!"a total of one hundred forty-one pennies,nickels and quarters" __ 141=p+n+q "She has a total of \$15.17" __ 1p+5n+25q=1517 "fifteen more quarters than pennies" __ q-15=p "fifteen fewer quarters than nickels" __ q+15=n substituting __ 141=(q-15)+n+q __ 156=2q+n substituting __ 156=2q+(q+15) __ 141=3q __ 47=q substituting __ 47+15=n __ 62=n substituting __ 47-15=p __ 32=p
 Exponential-and-logarithmic-functions/140089: Please help me with this. Thanks! Assume that the number of viruses present in a sample is modeled by the exponential function f(t) = 10^t Where t is the elapsed time in minutes. How would you apply logarithms to determine when the sample will grow to 5 billion viruses?1 solutions Answer 102092 by scott8148(6628)   on 2008-05-05 12:34:25 (Show Source): You can put this solution on YOUR website!5000000000=10^t __ taking log __ log(5000000000)=tlog(10) dividing by log(10) __ log(5000000000)/log(10)=t FYI __ this is the American billion, not the British
 Exponential-and-logarithmic-functions/140090: Need help with this. Thanks! A woman deposits \$50,000 in a savings account with 4% continuously compound interest. How many years must she wait until the balance has doubled? 1 solutions Answer 102091 by scott8148(6628)   on 2008-05-05 12:27:45 (Show Source): You can put this solution on YOUR website!the formula you need is A=Pe^(rt) __ A is the Amount after time t __ P is the Principal you start with __ e is Euler's number (the base for natural logarithms) __ r is the rate of interest __ r and t have to use the same time units 100000=50000e^(.04t) __ dividing by 50000 __ 2=e^(.04t) taking natural log __ ln(2)=.04t __ dividing by .04 __ [ln(2)]/.04=t
 Exponential-and-logarithmic-functions/140094: Please help me understand this and solve. Thanks! Maya has deposited \$600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?1 solutions Answer 102090 by scott8148(6628)   on 2008-05-05 12:20:40 (Show Source): You can put this solution on YOUR website!the formula you need is A=Pe^(rt) __ A is the Amount after time t __ P is the Principal you start with __ e is Euler's number (the base for natural logarithms) __ r is the rate of interest __ r and t have to use the same time units 1200=600e^(.0564t) __ dividing by 600 __ 2=e^(.0564t) taking natural log __ ln(2)=.0564t __ dividing by .0564 __ [ln(2)]/.0564=t
 Miscellaneous_Word_Problems/140083: Hi, I need your help in solving this problem. I find it hard and I can't come up with a better solution. Thank you. It takes John 5 hours to paint a house. It takes Bob 3 hours to paint the same house. How long will it take to paint the house if both of them work together? 1 solutions Answer 102089 by scott8148(6628)   on 2008-05-05 12:00:05 (Show Source): You can put this solution on YOUR website!when people work together to complete a task, __ each person completes some fraction of the task based on their individual rate for example __ if Mike can build a shed in 10 hours, __ when he works with a group that can build it in 3 hrs; Mike does 3/10 or 30% of the job the individual fractions sum to 1, the whole task let x=time together __ x/5+x/3=1 __ multiplying by 15 __ 3x+5x=15 __ 8x=15 dividing by 8 __ x=15/8 __ x=1.875
 Probability-and-statistics/140091: HELP! I have tried several different ways to set up this problem, but I can't get it right! I don't know what formula to use in order to solve it. Melinda’s lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color? Thank you!1 solutions Answer 102088 by scott8148(6628)   on 2008-05-05 11:39:37 (Show Source): You can put this solution on YOUR website!not sure about a formula __ this is like a thought experiment she needs a pair of each color, so what is the BEST case? __ she picks 3 pairs, one of each color but with no lights, she has to pick enough to be SURE she has one of each color __ so what's the WORST case? __ she picks 5 pairs, all white __ then she picks 3 more pairs, all red __ finally, she picks a black pair so, to be SURE, she has to pick 9 pairs
 Exponential-and-logarithmic-functions/140096: I don't understand this question. A computer is infected with the Sasser viruse. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another 5 minutes, etc. How long until 100 million computers are infected? 1 solutions Answer 102087 by scott8148(6628)   on 2008-05-05 11:27:30 (Show Source): You can put this solution on YOUR website!every 5 minutes, the number of infected computers is MULTIPLIED by 20 __ 1...20...400...8000...etc __ how long until 100 million? let t="time in minutes" __ 100M=1(20)^(t/5) taking log __ log(100M)=(t/5)(log(20)) dividing by log(20) __ log(100M)/log(20)=t/5 multiplying by 5 __ 5[log(100M)/log(20)]=t
 Quadratic-relations-and-conic-sections/139712: I am working on a math homework sheet. I am having trouble with some problems. Can someone please help me figure these out. Find the equation of the parabola by the given information. 13.) Vertex at the origin, focus at (0,3).1 solutions Answer 102033 by scott8148(6628)   on 2008-05-04 19:09:36 (Show Source): You can put this solution on YOUR website!a general equation for a parabola is (x-h)^2=4p(y-k) (h,k) is the vertex, and p is the distance from the vertex to the focus substituting __ (x-0)^2=4(3-0)(y-0) __ x^2=12y
 Word_Problems_With_Coins/139995: In a collection of coins there are 7 less dimes than there are quearters.If the value of the collection is \$3.85, then how many quaters are there?1 solutions Answer 102030 by scott8148(6628)   on 2008-05-04 18:45:30 (Show Source): You can put this solution on YOUR website!let x="number of quarters "there are 7 less dimes than there are quearters" __ x-7 "the value of the collection is \$3.85" __ x(.25)+(x-7)(.10)=3.85 distributing and multiplying by 100 __ 25x+10x-70=385 adding 70 __ 35x=455 dividing by 35 __ x=13
 Quadratic_Equations/139966: A parabola passes through (-2,0),(4,0) and (5,14). Find the equation of the axis of symmetry. Find the equation of the line perpendicular to the Y-axis that passes through exactly one point of the parabola. find the equation of the parabola. I just do not know where to start, what to look for first. Please help. Thankyou. 1 solutions Answer 102014 by scott8148(6628)   on 2008-05-04 15:03:56 (Show Source): You can put this solution on YOUR website!the first two points have the same y-coordinate, so the axis of symmetry is a vertical line (x=?) midway between them __ x=(-2+4)/2 __ x=1 the y value of the first two points is zero, so these are the roots of the quadratic equation __ if -2 and 4 are roots, then x+2 and x-4 are factors __ there may also be a constant factor that is related to the shape of the graph y=k(x+2)(x-4) __ using the 3rd point __ 14=k(5+2)(5-4) __ 2=k __ so y=2(x+2)(x-4) the line through one point passes through the vertex, which lies on the axis of symmetry __ substituting __ y=2(1+2)(1-4) __ y=-18
 Quadratic-relations-and-conic-sections/139709: Please help me with this problem. I have asked for hrlp before but could not find the answer to it. Thank you for your help. This problem is from a homework sheet. Write the series in summation notation. Use the index i and let i begin at 1 in each summation. 3.) 9 + 14 + 19 + 24 + 291 solutions Answer 101832 by scott8148(6628)   on 2008-05-02 10:22:02 (Show Source):
 Geometric_formulas/139701: Hello, I need to have and understand a formula for finding the midpoint between two points on the arc of a circle. I understand how in a cartesian coordinate system and the intersecting chords rule. However, I can't make it any further than that. How can I make a midpoint formula?! Sincerely, John1 solutions Answer 101830 by scott8148(6628)   on 2008-05-02 10:10:35 (Show Source): You can put this solution on YOUR website!if I understand your problem correctly, a line through the center of the circle and the midpoint of the chord connecting the two points on the circumference __ will intersect the circle at the circumferential midpoint
 Quadratic_Equations/139614: What is the equation of the circle having a diameter with endpoints (-4,4) and (2,8)? Please help:)1 solutions Answer 101811 by scott8148(6628)   on 2008-05-01 22:54:34 (Show Source): You can put this solution on YOUR website!the center is midway between the two points at [(-4+2)/2,(4+8)/2] or (-1,6) the radius is the distance from the center to one of the endpoints __ r=sqrt[(-1-2)^2+(6-8)^2] __ r=sqrt(9+4) __ r=sqrt(13) the equation is (x-(-1))^2+(y-6)^2=[sqrt(13)]^2 __ (x+1)^2+(y-6)^2=13
 Quadratic_Equations/139613: Write in general form the equation of the circle given center (4,-1) and radius 10. Please help:)1 solutions Answer 101810 by scott8148(6628)   on 2008-05-01 22:44:59 (Show Source): You can put this solution on YOUR website!(x-4)^2+(y-(-1))^2=10^2 __ (x-4)^2+(y+1)^2=100
 Triangles/139624: Please help me to solve this word problem. A portion of a roller coaster is supported by two steel beams. A cable runs from the top of each beam to the bottom of the other. if one steel beam is 40 feet tall and the other beam is 30 feet tall how high above teh ground do the cables intersect. I have drawn a picture and added in the information from the problem and proved that the triangles fromed were similar, but i dont know what to use to set up the proportion please help.1 solutions Answer 101809 by scott8148(6628)   on 2008-05-01 22:39:49 (Show Source): You can put this solution on YOUR website!picture both beams standing on the x-axis, with the 40 footer running up the y-axis __ and the 30 footer some distance d in the positive x direction let d="distance between beams" __ y=mx+b 1st cable __ y=(-40/d)x+40 2nd cable __ y=(30/d)x+0 __ yd/30=x substituting __ y=(-40/d)(yd/30)+40 __ y=(-4y/3)+40 __ 7y/3=40 __ 7y=120 __ y=120/7 __ a little over 17 ft.
 Polynomials-and-rational-expressions/139660: Can some one please help me with this problem: Factor completely: x3 – 3x2 + 6x – 18 Thank you 1 solutions Answer 101808 by scott8148(6628)   on 2008-05-01 22:18:36 (Show Source): You can put this solution on YOUR website!finding a root (a value of x that makes the expression zero) is a good way to start testing the factors of -18 shows that 3 is a root __ this means that x-3 is a factor factoring out x-3 leaves x^2+6, which is not factorable so the factors are (x-3)(x^2+6)
 Money_Word_Problems/139661: A cab company charges customers 5\$ the first mile and \$1.25 the following additional miles. One third of the drivers' pays goes to the cab company. If a driver has 12 fares and drives 84 miles in one day, how much money does the driver earn, not including tips? My teacher said the answer was \$100, but I really don't understand how she solved it. If you could help, me, that would be great.1 solutions Answer 101806 by scott8148(6628)   on 2008-05-01 22:08:38 (Show Source): You can put this solution on YOUR website!if the driver had 12 fares, the driver charged \$5 twelve times for 12 first miles __ and took in (\$5)(12) or \$60 for the other 72 mi (84-12), the driver took in (\$1.25)(72) or \$90 the driver's total take was \$90+\$60 or \$150 __ but 1/3 (\$150/3 or \$50) went to the cab company, leaving the driver with \$100
 Polynomials-and-rational-expressions/139659: Find n to be a perfect square trinomial x^2+20x+n I have looked inside of my algebra book in the index and in sections on perfect square trinomials, and I found absolutely no problems like this in my textbook. So please help me on this problem I am just confused. thank you so much for your time, it really means alot to me. 1 solutions Answer 101805 by scott8148(6628)   on 2008-05-01 21:58:11 (Show Source): You can put this solution on YOUR website!think about factoring a quadratic the factors of the constant term (n) have to add to the coefficient of the x term (20) for the quadratic to be a perfect square, the factors have to be the same __ if f is a factor, then 2f=20 so f=10 __ and f^2=n=100 x^2+20x+100=(x+10)^2
 Geometric_formulas/139490: What is the volume of a sphere, when the radius equals 3?1 solutions Answer 101745 by scott8148(6628)   on 2008-05-01 13:28:33 (Show Source): You can put this solution on YOUR website!the formula you need is v=(4/3)(pi)(r^3)
 Quadratic-relations-and-conic-sections/139350: i need help figuring this one out.. thanks Write an equation of an ellipse with the given characteristics. center(-1,5), vertex (3,5), co-vertex(-1,7) thank you!1 solutions Answer 101726 by scott8148(6628)   on 2008-05-01 11:58:00 (Show Source): You can put this solution on YOUR website!the center is the midpoint between the vetices and also the co-vertices __ this means that the length of the major axis is twice the distance from the center to a vertex __ and the length of the minor axis is twice the distance from the center to a co-vertex [(x+1)^2/8^2]+[(y-5)^2/4^2]=1 __ multiplying by 64 __ (x+1)^2+4(y-5)^2=64
 Quadratic_Equations/139518: hello....I am stumped...hope you can help...Question: Assume Joe Ball hits a major league pop-up (straight upward) on a Johnny Bench 90mph pitch. The function that describes the ball's height (in feet/second) is: h(t) = -16t^2+132t h(t) is height, t = is seconds...How many seconds for the ball to go up and back down? How high does the ball go? I came up with answers 4.125 for ball to go up and down and 272.25 feet for how high ball goes up (correct??)...but here's the stumper: it's now asking to repeat problem using planet Mercury. How do I complete this? (FYI, Mercury is 38% of Earth)....Hope you can help and show me the correct formula and answers..Thank you1 solutions Answer 101711 by scott8148(6628)   on 2008-05-01 10:41:23 (Show Source): You can put this solution on YOUR website!the 4.125 is time up and time down, so "time of flight" is 8.25 on Mercury, the gravitational acceleration (twice the coefficient of the x^2 term) is 38% of Earth __ so just replace the -16 with (38%)(-16) FYI: (the real) Johnny Bench was a catcher, not a pitcher
 Quadratic_Equations/139466: Find the value of b for which the equation has exactly one real root. (Hint- think discriminate0 x^2+bx+36=01 solutions Answer 101680 by scott8148(6628)   on 2008-04-30 22:32:49 (Show Source): You can put this solution on YOUR website!if b is twice the square root of the constant term, then the quadratic is a perfect square (one real root) b=2sqrt(36) __ b=2(+- 6) __ b=+- 12 if the discriminant equals zero, then there is one real root b^2-4ac=0 __ b^2=4ac __ b=+- sqrt(4ac) __ b=+- sqrt(4*1*36) __ b=+- sqrt(144) __ b=+- 12
 Quadratic_Equations/139465: The base of a triangle is 2 m less than the height. The area of the triangle is 36m^2 . Determine the height of the triangle. h=____ Please help I have no clue how to do this ,1 solutions Answer 101678 by scott8148(6628)   on 2008-04-30 22:21:57 (Show Source): You can put this solution on YOUR website!area equals 1/2 base times height 36=(1/2)(h-2)(h) __ multiplying by 2 __ 72=h^2-2h __ subtracting 72 __ 0=h^2-2h-72 use quadratic formula to find h __ h=[2 +- sqrt(4+288)]/2
 Exponential-and-logarithmic-functions/139456: Find the solution of the exponential equation: 2^(2x+5) = 3^(x−48) in terms of logarithms. THANKS TO ANYONE WHO COULD HELP!!1 solutions Answer 101677 by scott8148(6628)   on 2008-04-30 22:08:41 (Show Source): You can put this solution on YOUR website!taking log __ (2x+5)log(2)=(x-48)log(3) distributing __ 2xlog(2)+5log(2)=xlog(3)-48log(3) subtracting xlog(3)+5log(2) __ 2xlog(2)-xlog(3)=-48log(3)-5log(2) factoring __ x[2log(2)-log(3)]=-48log(3)-5log(2) dividing by 2log(2)-log(3) __ x=[-48log(3)-5log(2)]/[2log(2)-log(3)]
 Graphs/139413: Can anyone help me w/this? Write the equation of the line passing through these two points: (3,4), (-3,2) 1 solutions Answer 101674 by scott8148(6628)   on 2008-04-30 21:50:22 (Show Source): You can put this solution on YOUR website!first, find the slope (m) __ the y change (rise) divided by the x change (run) m=(2-4)/(-3-3) __ m=(-2)/(-6) __ m=1/3 using point-slope __ y-4=(1/3)(x-3) __ distributing __ y-4=(1/3)x-1 adding 4 __ y=(1/3)x+3
 Rate-of-work-word-problems/139424: Since there is a topic for this, it must be a very popular subject. My two questions have to do with painting and pool filling. I haven't had algebra in 38 years and am studying for an Asset placement test. Can figure most things out except these two. Susan can paint a house in 4 hours. John can paint a house in 6 hours. If they work together, how long will it take them to paint the house. The answer is 2 hours 24 minutes, but I need to know how to get to that answer. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? Same process here, but can't remember the equation(s). Any assistance you can give me is appreciated. I have a BS in computer science from 25 years ago, but I still have to take the math placement test to get retraining after losing my job. 1 solutions Answer 101669 by scott8148(6628)   on 2008-04-30 21:33:29 (Show Source): You can put this solution on YOUR website!a task ( painting, pool filling, etc.) that is completed by multiple "inputs" (people, pipes, etc.) __ is a whole made up of fractions __ the fractions sum to 1 (the whole) an input's fraction is found by dividing the combined time by the individual time __ e.g. if A can do a job in 5 hrs, but only takes 3 hours when working with B; __ A does 3/5 of the job and B does the other 2/5 __ B does 2/5 in 3 hrs, so it would take him 3/(2/5) or 15/2 hr alone painting: let x="time together" __ (x/4)+(x/6)=1 __ multiplying by 12 __ 3x+2x=12 __ 5x=12 __ x=12/5=2.4=2hr 24min filling: letx="time together" __ (x/30)+(x/45)+(x/90)=1 __ multiplying by 90 __ 3x+2x+x=90 __ 6x=90 __ x=15 good luck with retraining
 Complex_Numbers/139451: X^4-61x^2=-9001 solutions Answer 101661 by scott8148(6628)   on 2008-04-30 21:01:38 (Show Source): You can put this solution on YOUR website!adding 900 __ x^4-61x^2+900=0 factoring __ (x^2-36)(x^2-25)=0 factoring __ (x+6)(x-6)(x+5)(x-5)=0 x= 6, -6, 5, -5