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# Recent problems solved by 'ewatrrr'

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 Probability-and-statistics/375965: SAT I scores around the nation tend to have a mean scale score around 500, a standard deviation of about 100 points, and are approximately normally distributed. What SAT I score within the population would have a percentile rank of approximately 97.5? Show all work as to how this is obtained. 1 solutions Answer 267629 by ewatrrr(10682)   on 2010-11-26 10:18:41 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: P = .975 then z = 1.9599 1.9599 = (x - 500) / 100 195.99 = x-500 x = 695.99 Or 696 SAT score ```
 logarithm/375866: how to solve: log2x-log(x-7)=log3 1 solutions Answer 267625 by ewatrrr(10682)   on 2010-11-26 10:08:27 (Show Source): You can put this solution on YOUR website! ``` Hi log2x-log(x-7)=log3 log2x-log(x-7)-log3=0 log(2x/3(x-7) = 0 10 ^0 = 2x/3(x-7) 1 = 2x/3(x-7) 3(x-7)= 2x 3x - 21 = 2x x = 21 ```
 Exponents-negative-and-fractional/376004: a^-2 + a -------- a + 1 complex fraction, answer is a^2 - a+1 --------- a^2 but i do not get this answer1 solutions Answer 267619 by ewatrrr(10682)   on 2010-11-26 09:46:01 (Show Source): You can put this solution on YOUR website! ``` Hi (a^-2 + a) / a + 1 (1 + a^3) / a^2(a + 1) Multiplying numerator and denominator by a^2 (a^3 +1) / a^2(a + 1) (a +1)(a^2 -a +1) / a^2(a + 1) factoring out (a+1) in the numerator (a^2 -a +1) / a^2 Simplifying ```
 Quadratic_Equations/375879: 3x^2 + 9x, find x and y intercepts,range and vertex.1 solutions Answer 267323 by ewatrrr(10682)   on 2010-11-24 16:18:50 (Show Source): You can put this solution on YOUR website! ``` Hi, y = 3x^2 + 9x y intercept shen x = 0 (0,0) the y intercept x-intercepts is when y = 0 0 = 3x^2 + 9x 0 = 3x(x+3) x= 0 x = -3 x-intercepts (0,0) and (-3,0) the vertex form of a parabola, where(h,k) is the vertex y = 3(x^2 + 3x) y = 3[(x+ 3/2)^2 - 9/4] y = 3(x + 3/2)^2 - 27/4 vertex Pt(-3/2,-27/4) Range [-27/4,) ```
 expressions/375816: Solve the equation. If it is an identity (all real numbers) or a contradiction (no solution), so state. x  5 + 6x = -2 + 7x 1 solutions Answer 267288 by ewatrrr(10682)   on 2010-11-24 13:19:48 (Show Source): You can put this solution on YOUR website! ``` Hi, Solving the equation x  5 + 6x = -2 + 7x 7x - 5 = 7x - 2 -5 ≠ -2 There is NO solution ```
 Linear-equations/375832: Please help. Write an eqution of the line containing the given point and parallel to the given line. Express your answer in y = mx+b. (2,4); x +6y=51 solutions Answer 267286 by ewatrrr(10682)   on 2010-11-24 13:16:53 (Show Source): You can put this solution on YOUR website! ``` Hi, the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. Line parallel to the following x +6y=5 Solving for y to put into the slope-intercept form y = -x/6 + 5/6 m = (-1/6) New line parallel to this line has the same slope y = -x/6 + b Using ordered pair Pt(2,4) to solve for b 4 = -2/6 + b 4 + 1/3 = 13/3 = b y = -x/6 + 13/3 ```
 Exponential-and-logarithmic-functions/375848: Explain the differences between solving these two equations:  log3(x - 1) = 4 and log3(x - 1) = log34 1 solutions Answer 267282 by ewatrrr(10682)   on 2010-11-24 13:09:53 (Show Source): You can put this solution on YOUR website! ``` Hi, log3(x - 1) = 4 Using the following Property of Logarithms 3^4 = (x-1) 81 = x-1 82 = x log3(x - 1) = log34 logarithm bases are equal in this example, therefore: (x-1) = 4 x = 5 ```
 Miscellaneous_Word_Problems/375837: A board 21 ft long is cut into two pieces. Five times the length of the shorter piece is 1 ft more than three times the length of the longer piece. Find the length of the two pieces1 solutions Answer 267281 by ewatrrr(10682)   on 2010-11-24 13:04:54 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent length of the shorter piece then (21ft -x) would represent the lomger piece Question states*** 5x = 3(21ft-x) +1ft solving for x 5x = 63ft - 3x + 1ft 8x = 64ft x = 8 ft, the length of the shorter piece Longer piece is 13ft (21ft-8ft) CHECKING our Answer*** 5*8ft = 3*13ft + 1ft = 40ft ```
 Rational-functions/375844: (x+7)^21 solutions Answer 267280 by ewatrrr(10682)   on 2010-11-24 13:00:11 (Show Source): You can put this solution on YOUR website! ``` Hi, (x+7)^2 (x+7)(x+7) x^2 + 14x + 49 Note:SUM of the inner product(7x) and the outer product(7x) = 14x Checking our answer (x+7)(x+7)= x(x+7) + 7(x+7) = x^2 + 7x + 7x + 49 = x^2 +14x + 49 ```
 test/375843: (x+y)(x-y)1 solutions Answer 267279 by ewatrrr(10682)   on 2010-11-24 12:57:17 (Show Source): You can put this solution on YOUR website! ``` Hi, (x+y)(x-y) x^2 - y^2 Note:SUM of the inner product(x*y) and the outer product(-x*y) = 0 ```
 Miscellaneous_Word_Problems/375838: How many pounds of candy worth \$8 per pound must be mixed with 4lbs of candy worth \$10.50 per pound to create a mixture that costs \$9 per pound?1 solutions Answer 267278 by ewatrrr(10682)   on 2010-11-24 12:54:20 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the pounds of \$8 per pound candy Mixing the candy to create a mixture that cost 9\$ per pound 8x + 10.50*4lb = 9*(x + 4lb) solving for x 8x + 10.50*4lb = 9*x + 9*4lb 1.50*4lb = x 6lb = x, the amount of the pounds of \$8 per pound candy CHECKING our Answer \$8/lb*6lb + \$10.50/lb*4lb = \$48 + \$42 = \$90 = 9/lb*10lb ```
 Linear-equations/375822: PLEASE HELP. I tried this problem but am stumped. Find an equation of the line containing the given pair of points. (1/4, - 1/2) and (3/4, 6). What is the equation of the line? This is what I have so far; -1/3 - 5 ____________ ?? 1/6 - 5/6 Thank you1 solutions Answer 267274 by ewatrrr(10682)   on 2010-11-24 11:43:29 (Show Source): You can put this solution on YOUR website! ``` Hi, Finding an equation of the line containing the given pair of points. The standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. (1/4, - 1/2) and (3/4, 6) Using the points to find the slope m m = (13/2)/(1/2) = 13 y = 13x + b using Pt(3/4,6) to solve for b 6 = 39/4 + b -15/4 = b y = 13x - 15/4 ```
 Age_Word_Problems/375765: The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times older than the age of my youngest grandchild and my eldest grandchilds age is two years more than the ages of my two youngest grandchildren added together. How old is my eldest grandchild?1 solutions Answer 267273 by ewatrrr(10682)   on 2010-11-24 11:30:08 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the age of the youngest, (x + 3), the middle one and 3x the eldest Question states 3x = x + (x+3) + 2 solving for x x = 5, the age of the youngest the eldest gradchild is 15 CHECKING our Answer 15 = 5 +8 + 2 ```
 Age_Word_Problems/375806: mother is 4 times as old as MAy. 5 years ago, she was 7 times as old as may. how old is each 2 years from now.1 solutions Answer 267272 by ewatrrr(10682)   on 2010-11-24 11:22:16 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent May's age. Then the mother's age would be represented by 4x 5 years ago, the mother was 7 times as old as May*** 4x - 5 = 7(x-5) solving for x 4x - 5 = 7x - 35 30 = 3x 10 = x, May's age NOW. the mother is NOW 40 (4*10) how old is each 2 years from now May is 12 and the mother is 42 CHECKING OUR ANSWER 5 years ago, the mother was 7 times as old as May*** 35 = 7*5 ```
 Age_Word_Problems/375807: a man is 32 years old while his son is 8 years old,in how many years so that the man will be twice as old as his son.1 solutions Answer 267270 by ewatrrr(10682)   on 2010-11-24 11:15:23 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the number of years so that the man will be twice as old as his son. Now, the man is 32 years old while his son is 8 years old 32 + x = 2(8 + x) solving for x 32 + x = 16 + 2x 16 = x, the number of years from now that the man will be twice as old as his son CHECKING our Answer 32 + 16 = 2(8 + 16)= 2*24 = 48 ```
 Age_Word_Problems/375808: 3 years ago, larry was twice as old as ben. three years from now hewill be 1 1/2 times as old as ben. how old is each? 1 solutions Answer 267268 by ewatrrr(10682)   on 2010-11-24 11:09:56 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x be ben's age now and y represent larry's age now. y - 3 =2(x -3)=2x - 6 3 years ago, larry was twice as old as ben y + 3 =(3/2)(x + 3)=(3/2)x + (9/2) three years from now he will be 1 1/2 times as old as ben y - 3 =2x - 6 y + 3 =(3/2)x + (9/2) Solving for x by eliminating y y - 3 =2x - 6 -y - 3 =-(3/2)x - (9/2) subtracting second equation from the first -6 = x/2 - 21/2 9/2 = x/2 9 = x, ben's age now. Substituting for x to solve for y, larry's age now y - 3 = 2x - 6 y = 2x -3 y =2*9 - 3 = 15, larry's age now checking our answer 3 years ago, larry was twice as old as ben 12 = 2*6 ```
 Age_Word_Problems/375809: in four years, cindy's age will be the same as tina's age now. in 2 year,tina will be twie as old as cindy. find the age of cindy in 3 years.1 solutions Answer 267260 by ewatrrr(10682)   on 2010-11-24 10:53:11 (Show Source): You can put this solution on YOUR website! ``` Hi, in four years, cindy's age will be the same as tina's age now Let x represent tina's age now, than cindy's is (x-4) tina is an always will be 4 years older than cindy. x = 2(x-4) in two years x = 2x - 8 8 = x, tina's age in two years, tina is now 6 and cindy is 2 (6-4) the age of cindy in 3 years is 2 + 3 = 5 ```
 Polynomials-and-rational-expressions/375783: Find the x-intercepts for the graph of the equation y=x^2-3x-4. The x-intercepts are _________ help?1 solutions Answer 267231 by ewatrrr(10682)   on 2010-11-24 09:37:48 (Show Source): You can put this solution on YOUR website! ``` Hi Finding the x-intercepts for the graph of the equation y=x^2-3x-4 (y=0 when the graph crosses the x-axis) 0 = x^2-3x-4 solving by factoring (x-4)(x+1)=0 Note:SUM of the inner product(-4x) and the outer product(1*x) = -3x (x-4)=0 x=4 (x+1)=0 x = -1 ```
 Polynomials-and-rational-expressions/375772: solve: x^2+6x-4=0 help?1 solutions Answer 267227 by ewatrrr(10682)   on 2010-11-24 09:32:49 (Show Source): You can put this solution on YOUR website!``` Hi, solving x^2+6x-4=0 Using the Quadratic formula ```
 Polynomials-and-rational-expressions/375773: factor: 21-10a+a^2 help?1 solutions Answer 267225 by ewatrrr(10682)   on 2010-11-24 09:29:00 (Show Source): You can put this solution on YOUR website! ``` Hi, factoring 21-10a+a^2 a^2-10a + 21 factoring (a-7)(a-3)Note:SUM of the inner product(-7a) and the outer product(-3a) = -10a ```
 Polynomials-and-rational-expressions/375778: solve: c^2+3c-54=0 help?1 solutions Answer 267223 by ewatrrr(10682)   on 2010-11-24 09:26:57 (Show Source): You can put this solution on YOUR website! ``` Hi, solving c^2+3c-54=0 factoring (c+9)(c-6)=0 Note:SUM of the inner product(9c) and the outer product(-6c) = 3c (c+9)=0 c = -9 (c-6)=0 c = 6 ```
 Polynomials-and-rational-expressions/375775: solve: a^2-6a-27=0 help?1 solutions Answer 267222 by ewatrrr(10682)   on 2010-11-24 09:24:22 (Show Source): You can put this solution on YOUR website! ``` Hi solving a^2-6a-27=0 factoring (a-9)(a+3)= 0 Note:SUM of the inner product(-9a) and the outer product(3a) = -6a (a-9)=0 a = 9 (a+3)= a = -3 ```
 Probability-and-statistics/375737: Adult Intelligence Quotient scores have been demonstrated to be normally distributed with a mean of 100 and a standard deviation of 15. Suppose that nine adults are chosen at random and their Intelligence Quotients are measured. Determine the probability that the mean Intelligence Quotient score of the nine adults is greater than or equal to 118.1 solutions Answer 267220 by ewatrrr(10682)   on 2010-11-24 09:08:27 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: z = 18/5 = 3.6 P(z ≥ 3.6) = 1 - .9998 =.00016 ```
 logarithm/375535: solve 1 solutions Answer 267065 by ewatrrr(10682)   on 2010-11-23 16:25:06 (Show Source): You can put this solution on YOUR website! ``` Hi, solve x(x+9) = 10^1 x^2 + 9x = 10 x^2 + 9x - 10 = 0 factoring (x+ 10)(x-1)=0 (x+10) = 0 x = -10 This is an Extraneous solution (x-1)= 0 x = 1 ```
 Quadratic_Equations/375527: 2. x2  2x  11 = 0 Use the Quadratic Formula to solve each equation. 1 solutions Answer 267063 by ewatrrr(10682)   on 2010-11-23 16:18:07 (Show Source): You can put this solution on YOUR website! ``` Hi Use the Quadratic Formula to solve x^2  2x  11 = 0 x = 4.464 x = -2.464 ```
 Linear_Equations_And_Systems_Word_Problems/375526: A student scored 71, 83, and 96 on threee algebra test. what must he score on the forth test in order to have an average grade of at least 85?1 solutions Answer 267059 by ewatrrr(10682)   on 2010-11-23 16:10:11 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the score on the forth test (71 + 83 + 96 + x)/4 ≥ 85 (71 + 83 + 96 + x) ≥ 340 250 + x ≥ 340 x ≥ 90 he must score a least a 90 on his fourth test ```
 Probability-and-statistics/375516: 2. A random sample of 10 children at a particular elementary school had their hearing tested and received the following scores. 51, 50, 49, 43, 56, 46, 45, 32, 52, 58. If the average score for normal hearing youngsters is 52, is there reason to believe that on the average, children at this school do not have normal hearing? 1 solutions Answer 267058 by ewatrrr(10682)   on 2010-11-23 16:05:30 (Show Source): You can put this solution on YOUR website! ``` Hi, *Note: Formula for the test statistic is In this case n = 10 Entering the Data into an Excel worksheet column and applying the Data Analysis tool found and for this sampling. = -3.8/2.328 = -1.632 P(t < -1.632) can be found using the NORMSDIST(-1.632)function in Excel or by looking at an usual standard normal table. P(t < -1.632) = .05134 or 5.1% The test results show that this sampling is in the low range of normal hearing ```
 Probability-and-statistics/375517: An investigator chooses 5 rats random from the colony of rats maintained by the psychology department of the university. After special training to delay response, the reaction times in tenths of seconds to a signal were recorded and found to be 5, 3, 6, 4, 10. Test the hypothesis that the mean reaction time for rats of this type is 4 tenths of a second. 1 solutions Answer 267057 by ewatrrr(10682)   on 2010-11-23 15:55:55 (Show Source): You can put this solution on YOUR website! ``` Hi, *Note: Formula for the test statistic is In this case n = 5 Entering the Data into an Excel worksheet column and applying the Data Analysis tool found and for this sampling. = -.02/.086 = -.2326 P(t < -.2326) = .4080 Or 40.80% The test results would show that this sampling is well within the average of mu = .4sec ```
 Quadratic_Equations/375463: 4. x2 + 144 = 0 (1 point) a. 12 b. ±12i c. 12 d. ±12 1 solutions Answer 267017 by ewatrrr(10682)   on 2010-11-23 14:37:11 (Show Source): You can put this solution on YOUR website! ``` Hi, x2 + 144 = 0 x^2 = -144 x = ± 12i Answer b. would be the proper selection ```
 Quadratic_Equations/375468: factor quadratic expression 1. 8x2 + 321 solutions Answer 267015 by ewatrrr(10682)   on 2010-11-23 14:33:09 (Show Source): You can put this solution on YOUR website! ``` Hi, factoring quadratic expression 8x2 + 32 -8(x^2 - 4) -8(x+2)(x-2) Note:SUM of the inner product(2x) and the outer product(-2x) = 0 ```
 Miscellaneous_Word_Problems/375449: Please put this so I can understand it. I am lost. Why is it necessary to study the order of operations and the laws of operations before you begin solving equations?1 solutions Answer 267014 by ewatrrr(10682)   on 2010-11-23 14:29:29 (Show Source): You can put this solution on YOUR website! Hi, Why is it necessary to study the order of operations and the laws of operations before you begin solving equations? the order of operations and the laws of operations are important as a 'roadmap' or 'recipe' so to speak, as to the way to proceed to solve the equation and reach the correct solution.