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# Recent problems solved by 'sophxmai'

 Polynomials-and-rational-expressions/619242: (12w^4- 6w³+w²)/3w²1 solutions Answer 389568 by sophxmai(60)   on 2012-06-09 23:57:45 (Show Source): You can put this solution on YOUR website!(12w^4- 6w³+w²)/3w² can be rewritten as 12w^4/3x^2 - 6w^3/3w^2 + w^2/3w^2 So just simplify the fractions. 12w^4/3x^2 - 6w^3/3w^2 + w^2/3w^2 =4w^2-2w+1/3
 Linear-systems/619345: Factor the trinomial 18r^3-39r^2+20r1 solutions Answer 389566 by sophxmai(60)   on 2012-06-09 23:54:17 (Show Source): You can put this solution on YOUR website!18r^3-39r^2+20r Factor out an r r(18r^2-39r+20) =r(3r-4)(6r-5)
 logarithm/619317: Solve the logarithmic equation: log(x+1)+log(x-1)=log31 solutions Answer 389563 by sophxmai(60)   on 2012-06-09 23:48:18 (Show Source): You can put this solution on YOUR website!Using the rule loga+logb=logab log(x+1)+log(x-1)=log3 log[(x+1)*(x-1)]=log3 log(x^2-x+x-1)=log3 log(x^2-1)=log3 10^[log(x^2-1)]=10^log3 x^2-1=3 x^2=4 x=sqrt4 x=+2,-2
 Expressions-with-variables/619347: if it cost \$78.86 to buy 3 tickets in japan plus 2 tickets in switzerlan. 3 tickets in switzerland plus 2 tickets in japan cost \$74.84. how much does an average movie ticket cost in each country?1 solutions Answer 389562 by sophxmai(60)   on 2012-06-09 23:45:45 (Show Source): You can put this solution on YOUR website!x=Japan y=Switzerland 3x+2y=78.86 2x+3y=74.84 Find x and y Multiply each equation to cancel one of the variables out. 3x+2y=78.86 x2 6x+4y=157.72 2x+3y=74.84 x3 6x+9y=224.52 Now the two equations have 6x, and if you subtract one from the other, you can cancel out one of the variables. 6x+4y=157.72 6x+9y=224.52 -5y=-66.8 y=-66.8/-5 y=13.36 Now you have y, substitute y into an equation to find x. 2x+3y=74.84 2x+3(13.36)=74.84 2x+40.08=74.84 2x=34.76 x=34.76/2 x=17.38 So tickets in Japan cost \$17.38 and tickets in Switzerland cost \$13.36
 Probability-and-statistics/619296: If 11 coins are tossed what is the probability of getting EXACTLY 2 heads?1 solutions Answer 389561 by sophxmai(60)   on 2012-06-09 23:37:06 (Show Source): You can put this solution on YOUR website!If 11 coins are tossed what is the probability of getting EXACTLY 2 heads? Use P(x=k)=nCk*p^k*q^(n-k) Where p=probability of success and q=1-p, probability of failure So P(x=2)=(11C2)(1/2)^2(1/2)^(11-2) =(11C2)(1/4)(1/512) =(11C2)(1/2048) =0.0269
 Probability-and-statistics/619298: A 5-card hand is dealt from a deck of 52 cards. What is the probability that a.) none are queens? b.) all are queens?1 solutions Answer 389560 by sophxmai(60)   on 2012-06-09 23:31:28 (Show Source): You can put this solution on YOUR website!There are only 4 queens in a deck of cards. P(a)= probability that event A occurs = (total number of desired outcomes)/(total number of possible outcomes) Use combinatorics. The total number of possible outcomes in a) and b) is 52C5 = 2598960 The total number of desired outcomes in a) is 48C5 = 1712304 It's 48 because you don't want any queens, and there are 4 queens in a deck of 52 The total number of desired outcomes in b) is 0 because there are only 4 queens in a deck of 52, but you want your 5 card hand to be all queens. So a)P(no queens in a 5 card hand)=1712304/2598960=0.659 b)P(all queens in a 5 card hand)=0/2598960=0
 Graphs/619250: find the slope of the line containing (3,5) and (1,8) 1 solutions Answer 389559 by sophxmai(60)   on 2012-06-09 23:18:21 (Show Source): You can put this solution on YOUR website!Your points are (3,5) and (1,8) Use the slope formula: m=(y2-y1)/(x2-x1) m=(8-5)/(1-3) m=3/-2 m=-3/2
 Probability-and-statistics/619301: A 5-card hand is dealt from a deck of 52 cards. What is the probability that exactly one card is a king?1 solutions Answer 389558 by sophxmai(60)   on 2012-06-09 23:03:43 (Show Source): You can put this solution on YOUR website!Probability is (total number of desired outcomes)/(total number of possibly outcomes) Desired outcome: you want 1 king, and 4 other cards To get that, you use combinatorics: 4C1 x 48C4 = 778320 Total outcome: 5 card hand To get that, you do 52C5 = 2598960 Then the probability is P(1 king in a 5 card hand)= 778320 / 2598960 = 0.299
 Exponents-negative-and-fractional/614754: can you please help me with this? (8 + 5)^0 => => is it 1 because anything with an exponent of zero is 1 am i correct? 1 solutions Answer 386686 by sophxmai(60)   on 2012-05-25 04:51:52 (Show Source): You can put this solution on YOUR website!Yes that's right, anything to the power of 0 is 1.
 Exponential-and-logarithmic-functions/614548: Solve for x: 1 solutions Answer 386601 by sophxmai(60)   on 2012-05-24 15:22:04 (Show Source): You can put this solution on YOUR website!take the log of both sides and then separate the 2(3^x) by the log(m)+log(n)=log(mn) rule. log(2(3^x))=log(7(5^x)) log(2)+log(3^x)=log(7)+log(5^x) log(2)+xlog(3)=log(7)+xlog(5) xlog(3)-xlog(5)=log(7)-log(2) x(log(3)-log(5))=log(7)-log(2) x=(log(7)-log(2))/(log(3)-log(5)) x=-2.452427 <--i used a calculator x=(log(7)-log(2))/(log(3)-log(5)) can be rewritten using the rule log(m)-log(n)=log(m/n) x=log(7/2)/log(3/5)
 Linear-systems/614544: 2x – 5y = -1 x – 3y = -3 1 solutions Answer 386597 by sophxmai(60)   on 2012-05-24 15:14:45 (Show Source): You can put this solution on YOUR website!2x–5y=-1 x–3y=-3 You first want to get rid of one of the variables. There are two different ways of doing this. The first way is to solve the 2nd equation for x, and then plug it into the 1st equation to solve for y. The second way is to multiply the 2nd equation by 2, and then subtract this new equation from the 1st equation so that x cancels out. Left with y, you solve for it. The first way. 2x–5y=-1 x–3y=-3 Solve the 2nd equation for x x-3y=-3 x=3y-3 Substitute x into the first equation 2x-5y=-1 2(3y-3)-5y=-1 Simplify and solve for y 2(3y-3)-5y=-1 6y-6-5y=-1 y=5 Plug y back into an equation with x in it. x=3y-3 x=3(5)-3 x=15-3 x=12 The second way. 2x–5y=-1 x–3y=-3 Multiply the 2nd equation by 2 x–3y=-3 (x-3y=-3)x2 2x-6y=-6 Subtract the new equation from the first equation. 2x–5y=-1 2x-6y=-6 -------------- y=5 Plug y into an equation with x in it. x–3y=-3 x-3(5)=-3 x-15=-3 x=12
 Equations/614535: Find the choice below which gives a first step in solving the given system of equations by the addition method. 2x -3 y= 7 X-4y = 2 Do you; multiply the first equation by 3 and the second by 4 - multiply the first equation by -4 and the second by -2 -Multiply the second equation by 2 - Multiply the first equation by 4 1 solutions Answer 386592 by sophxmai(60)   on 2012-05-24 15:04:30 (Show Source): You can put this solution on YOUR website! The first step is to multiply the 2nd equation by 2. This is because in order to solve it, you must cancel out one of the variables. By multiplying the 2nd equation by 2, you can subtract the new equation (from multiplying the 2nd equation by 2) from the 1st equation, and get 0x. This leaves you with only y. You can then solve for y, and then plug y back into an equation with x and find x. Multiply the 2nd equation by 2 ()x2 Subtract this from the first equation ------- Solve for y Plug y back into an equation with x
 Miscellaneous_Word_Problems/609683: there are 340 tickets and three kids the mom wants to split them where james has 40 less than ashley and ashley gets 80 less than amanda how many tickets does each kid get1 solutions Answer 383898 by sophxmai(60)   on 2012-05-10 18:33:24 (Show Source): You can put this solution on YOUR website!Let: x=James's tickets y=Ashley's tickets z=Amanda's tickets Write your equations x+y+z=340 x+40=y y+80=z Now solve your system... x+40=y x-y=-40 x+y+z= 340 x-y =-40 2y+z= 380 z= 380-2y y+80=z y+80=380-2y y+2y=380-80 3y=300 y=100 z=380-2y z=380-2(100) z=380-200 z=180 x+40=y x+40=100 x=60 Check: x+y+z=340 60+100+180=340 James has 60 tickets. Ashley has 100 tickets. Amanda has 180 tickets.
 Numbers_Word_Problems/609617: Find five consecutive even integers with a sum of -2101 solutions Answer 383888 by sophxmai(60)   on 2012-05-10 18:18:22 (Show Source): You can put this solution on YOUR website!(x)+(x+2)+(x+4)+(x+6)+(x+8)=-210 x+x+2+x+4+x+6+x+8=-210 5x+20=-210 5x=-230 x=-46 Check: (-46)+(-44)+(-42)+(-40)+(-38) =-46-44-42-40-38 =-90-120 =-210
 Exponential-and-logarithmic-functions/609663: Solve 1 solutions Answer 383886 by sophxmai(60)   on 2012-05-10 18:13:48 (Show Source): You can put this solution on YOUR website!Solve . First, take the log of both sides Then move the exponent to the front of the log (it's a rule). Now isolate the x. That's the answer, unless you're allowed a calculator. If so, punch that into your calculator and you should get x=0.357
 Age_Word_Problems/609678: Danny is twice as old as Kevin. Danny and Corey are the same age. Write an equation showing this.1 solutions Answer 383883 by sophxmai(60)   on 2012-05-10 18:07:42 (Show Source): You can put this solution on YOUR website!d=2k d=c c=2k k=d/2 k=c/2
 Rectangles/607684: The perimeter of a rectangle is 48 cm. The length is 6 cm less than twice the width. Which system would model this situation, and what are the length and the width?1 solutions Answer 382836 by sophxmai(60)   on 2012-05-06 16:35:01 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 48 cm. The length is 6 cm less than twice the width. Which system would model this situation, and what are the length and the width? Let x=length and y=width Solve the 2nd equation for x or y (whichever is more convenient) and then plug into the 1st equation. Substitute y into a previous equation to solve for x. The length is 14cm and the width is 10cm.
 Geometry_Word_Problems/607666: The perimeter of a rectangular rose garden is 400 M. The length is 3 M more than twice the width. Find the length and width.1 solutions Answer 382830 by sophxmai(60)   on 2012-05-06 16:27:52 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangular rose garden is 400 M. The length is 3 M more than twice the width. Find the length and width. Let x=length, y=width Solve the 2nd equation for x or y, and then substitute it into the first equation. Now substitute y into a previous equation and solve for x. or depending how you want your answer
 Expressions-with-variables/607676: how do you simplify 3 + x/2?1 solutions Answer 382819 by sophxmai(60)   on 2012-05-06 16:13:34 (Show Source): You can put this solution on YOUR website!Make it so that x is not a fraction = =
 Miscellaneous_Word_Problems/607220: 1 solutions Answer 382563 by sophxmai(60)   on 2012-05-05 03:27:55 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 4 inches longer than twice its width. The area of the rectangle is 96 square inches. What is the length and width of the rectangle? Let x=length and y=width Solve the first equation for y and substitute it into the 2nd equation Reject x=-8 because the length cannot be a negative number So x=6 Substitute x to find y
 Quadratic_Equations/607269: x^3+16x^21 solutions Answer 382561 by sophxmai(60)   on 2012-05-05 02:38:50 (Show Source): You can put this solution on YOUR website!Factor out the = If it says to solve, equate it to 0 and solve for x and
 Numeric_Fractions/607279: can you show me how to divde 4 7/8 by 1/2?1 solutions Answer 382560 by sophxmai(60)   on 2012-05-05 02:36:28 (Show Source): You can put this solution on YOUR website!You want to divide 4 7/8 by 1/2 First make the 4 7/8 into an improper fraction (4*8+7)/8=39/8 Now you have (39/8) divide by (1/2) Flip the fraction after the divide sign and change the sign into a multiply sign (39/8) x (2/1) Now multiply them together (39/8) x (2/1) =(39/4) If it says to make it into a proper fraction again, do so 39/4= 9 3/4
 Surface-area/607280: the perimeter of a college athletic field is 92 meters and the length is 12 m more than the width. find the length and width.1 solutions Answer 382559 by sophxmai(60)   on 2012-05-05 02:32:56 (Show Source): You can put this solution on YOUR website!the perimeter of a college athletic field is 92 meters and the length is 12 m more than the width. find the length and width. Let x=length and y=width 2x+2y=92 x-12=y Substitute the 2nd equation into the first one 2x+2y=92 2x+2(x-12)=92 2x+2x-24=92 4x=116 x=116/4 x=29 Substitute x into one of the original equations x-12=y 29-12=y 17=y the length is 29m, the width is 17m
 Age_Word_Problems/607031: The sum of the ages of a man and his wife is 80 years. 10 years ago, the ages of the wife was exactly two-third the age of the man. Find the present ages of the man and his wife.1 solutions Answer 382353 by sophxmai(60)   on 2012-05-04 04:00:36 (Show Source): You can put this solution on YOUR website!The sum of the ages of a man and his wife is 80 years. 10 years ago, the ages of the wife was exactly two-third the age of the man. Find the present ages of the man and his wife. Let: man's age = x wife's age = y x+y=80 <--sum of their age y-10=2/3x <--10 years ago, the age of the woman was 2/3 of the man's current age y=2/3x+10 <--solve the 2nd equation for y x+2/3x+10=80 <--plug above into 1st equation 5/3x=70 <--simplify and solve x=42 <--plug back into original equation to find y 42+y=80 y=80-42 y=38 Since x=42 and y=38 The man's age is 42 and the wife's age is 38
 Permutations/607044: 1 solutions Answer 382352 by sophxmai(60)   on 2012-05-04 03:52:53 (Show Source): You can put this solution on YOUR website!From a group of eight boys amd two girls a boy and a girl will be selected to attend a conference. In how many ways can the selection be made? First choose your boy: 8C1 Then choose your girl: 2C1 Now multiply them together 8C1 x 2C1 So now you get 8x2 which = 16
 Age_Word_Problems/607061: please help me solve this problem. Eva is 2 years older than Julienne. The sum of their ages is 20. Find their present ages.1 solutions Answer 382350 by sophxmai(60)   on 2012-05-04 03:35:53 (Show Source): You can put this solution on YOUR website!Eva is 2 years older than Julienne. The sum of their ages is 20. Find their present ages. Let: Eva's age = x Julienne's age = y x+y=20 <--the sum of their ages is 20 x-2=y <--Eva is 2 years older than Julienne You can solve this system by either adding/subtracting or substituting. Adding/Subtracting: x+y=20 x-2=y Rearrange the 2nd equation x-2=y becomes x-y=2 So now we have x+y=20 x-y=2 Now add the equations, you will get 2x=22 Now solve... 2x=22 x=11 Now that you have x, plug it into one of the equations to solve for y x-y=2 11-y=2 11-2=y 9=y Since x=11 and y=9 Eva's age is 11 and Julienne's age is 9 Substituting: x+y=20 x-2=y Since the 2nd equation is already arranged in a way that a variable = something... substitute it into the 1st equation. x+y=20 x+(x-2)=20 x+x-2=20 2x-2=20 2x=22 x=11 Now that you have 11, plug x into your 2nd equation x-2=y 11-2=y 9=y Since x=11 and y=9 Eva's age is 11 and Julienne's age is 9
 Equations/606860: Solve the system: x^2+y^2=100 y-x=21 solutions Answer 382293 by sophxmai(60)   on 2012-05-03 18:38:04 (Show Source): You can put this solution on YOUR website!Solve the system Solve the 2nd equation for y So now you have Now substitute the 2nd equation into the 1st one Now expand and group like terms Now factor and solve
 Functions/379447: I need to evaluate the function at each specified value of the independent variable and simplify. f(x) = the square root of (x+9) + 6 (the six is on the outside of the square root) f(-9) f(7) f(x-9)1 solutions Answer 269381 by sophxmai(60)   on 2010-12-01 22:22:41 (Show Source): You can put this solution on YOUR website! f(-9)=6 f(7)=10 f(x-9)=
 Quadratic_Equations/379457: Wright a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0 The solutions are -7,1 1 solutions Answer 269379 by sophxmai(60)   on 2010-12-01 22:16:42 (Show Source): You can put this solution on YOUR website!x=-7, 1 0=(x+7)(x-1)
 Graphs/379389: how do you put the two ponits (5,-5) (0,8) into slope intersept form1 solutions Answer 269363 by sophxmai(60)   on 2010-12-01 21:19:50 (Show Source): You can put this solution on YOUR website!The points that are given to you are (5,-5) and (0,8). The equation is y=mx+b. What you need to find is the slope, m and the y-intercept, b. To find the slope, m, you use the formula: So, Now from y=mx+b, we have To find the y-intercept, we can substitute one of the points in for x and y, and solve for b. (0,8) Now from y=mx+b, we have