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# Recent problems solved by 'ewatrrr'

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 Probability-and-statistics/431050: a population of 5,000 test scores are found to be normally distributed with a mean of 50 and a std. deviation of 10 how many students scored above 651 solutions Answer 299263 by ewatrrr(10682)   on 2011-04-04 15:08:24 (Show Source): You can put this solution on YOUR website!mean of 50 and a std. deviation of 10 (score of 65) *Note: z = 15/10 = 1.5 P(above 65) = P(z>1.5) = .0668 area under the graph to the right of green line
 Linear-equations/431042: write an equation in slope-intercept form of the line satisfying the following conditions through point (3,9): perpendicular to x=31 solutions Answer 299262 by ewatrrr(10682)   on 2011-04-04 15:01:02 (Show Source): You can put this solution on YOUR website! ``` Hi Line passing thru point(3,9) perpendicular to x = 3 (Blue) y = 9 (green line) ```
 Probability-and-statistics/431046: a population of 5,000 test scores are found to be normally distributed with a mean of 50 and a std. deviation of 10 what percentage of scores are between 30 and 651 solutions Answer 299260 by ewatrrr(10682)   on 2011-04-04 14:56:37 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: mean of 50 and a std. deviation of 10 z = -20/10 = -2 and z = 15/10 = 1.5 P(between 30 and 65) = P( -2 > z < 1.5) = .9332 - .0228 = .9104 91.04% of them are between 30 and 65 Area under the graph between z = -2 and z = 1.5 ```
 Probability-and-statistics/431031: What is the probablity of getting an IQ score lower than 100 ?1 solutions Answer 299259 by ewatrrr(10682)   on 2011-04-04 14:50:01 (Show Source): You can put this solution on YOUR website! ``` Hi IQ = 100 is the mean score used P(lower than 100) = .5 ```
 Human-and-algebraic-language/431035: the formula for the perimeter of a rectangle is P=2L+2W. If the length, L, is 9 meters and the width, W, is 6 meters find the perimeter, P, of this rectangle.1 solutions Answer 299257 by ewatrrr(10682)   on 2011-04-04 14:46:04 (Show Source): You can put this solution on YOUR website! ``` Hi L = 9m and W =6m P = 18m + 12m = 30m ```
 Complex_Numbers/431038: (9U^2)^5/21 solutions Answer 299255 by ewatrrr(10682)   on 2011-04-04 14:42:19 (Show Source): You can put this solution on YOUR website! ``` Hi If it is: [9(U^2)^5/2] then 9^(5/2)U^5 = 3^5*U^5 = 243U^5 ```
 Linear_Equations_And_Systems_Word_Problems/431025: quantities pand q are always in the same ratio. if p=5 when q=2 what is the value of p when q=51 solutions Answer 299251 by ewatrrr(10682)   on 2011-04-04 14:22:39 (Show Source): You can put this solution on YOUR website! ``` Hi p/q = 5/2 | Cross Multiplying 2p = 25 p = 12.5 CHECKING our answer*** |Cross Multiplying 25 = 25 ```
 Travel_Word_Problems/431022: Max was drove for 3hrs on a freeway, then decreased his speed by 20mph & drove for 3 more hours. If the total trip was 324 miles, what was his speed on the freeway?1 solutions Answer 299249 by ewatrrr(10682)   on 2011-04-04 14:18:35 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent his speed on the freeway & his speed off freeway be(x-20mph) Question states*** reduced speed to (x-20)mph when off the freeway for last 3hrs 3x + 3(x-20mph) = 324 6x = 384 x =64mph, freeway speed ```
 test/430987: Subtract (5a^3-9b^2+3ab) From (9a^3-6b^2-8ab)1 solutions Answer 299244 by ewatrrr(10682)   on 2011-04-04 13:45:55 (Show Source): You can put this solution on YOUR website! ``` Hi (9a^3-6b^2-8ab) -(5a^3-9b^2+3ab) 9a^3-6b^2-8ab -5a^3+9b^2-3ab 4a^3 +3b^2-11ab ```
 Probability-and-statistics/431006: a population of 5,000 test scores are found to be normally distributed with a mean if 50 and a standard deviation of 10. What percentage of scores are below 551 solutions Answer 299241 by ewatrrr(10682)   on 2011-04-04 13:42:05 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: z =(55-50)/10 = 5/10 = .5 P( x <55) = .6915 69.15% of the scores Percentage under the graph to the left of the green line: z=.5 ```
 Evaluation_Word_Problems/430985: The complex expression 2/x/4/x can be written as: 2/x x 4/x 2/x divided by 4/x 2/x - 4/x or 2/x + 4/x1 solutions Answer 299238 by ewatrrr(10682)   on 2011-04-04 13:36:00 (Show Source): You can put this solution on YOUR website! ``` Hi ```
 Linear_Algebra/431005: the graph of f(x) resembles the graph of g(x)=x^2, but has been flipped over the x-axiz and shifted down 4 units and left 1 unit. write the the equation of f(x).1 solutions Answer 299236 by ewatrrr(10682)   on 2011-04-04 13:27:29 (Show Source): You can put this solution on YOUR website! ``` Hi y = x^2 (Green) y = -(x+1)^2 -4 (Blue) Vextex(-1,-4) ```
 Graphs/431000: What type of line should be used when graphing 2x-3y is less than or equal to 6.1 solutions Answer 299233 by ewatrrr(10682)   on 2011-04-04 13:23:18 (Show Source): You can put this solution on YOUR website! ``` Hi 2x-3y ≤ 6 (2/3)x-2 ≤ y y ≥ (2/3)x-2 I. graph y = (2/3)x-2 II. Shade area above/including the line ```
 logarithm/430997: solve for x: ln x =9 ???1 solutions Answer 299227 by ewatrrr(10682)   on 2011-04-04 13:15:51 (Show Source): You can put this solution on YOUR website! ``` Hi ln x =9 e^9 = x 8103.0839 = x |Calculator makes short work of finding x ```
 Polynomials-and-rational-expressions/430986: Factor the following polynomials. (1) 9-x^2 (2) 4x^2+81-36x (3) 4y^2+16y+16 (4) x^2-25/x+5 1 solutions Answer 299226 by ewatrrr(10682)   on 2011-04-04 13:10:33 (Show Source): You can put this solution on YOUR website! ``` Hi Recommend for 1-3 to multiply the factors using FOIL to verify those factors F First terms O Outside terms I Inside terms L Last terms (1) 9-x^2 (3-x)(3+x) (2) 4x^2-36x+81 (2x-9)(2x-9) (3) 4(y^2+4y+4) 4(y+2)(y+2) (4) ```
 Radicals/430988: h=-16t^2+96t+1121 solutions Answer 299225 by ewatrrr(10682)   on 2011-04-04 13:00:21 (Show Source): You can put this solution on YOUR website! ``` Hi, You did not state the exact nature of your Question: h=-16t^2+96t+112 |Represents a parabola opening downward h= -16(t-3)^2 + 144 + 160 |completing Square to find Vertex the vertex form of a parabola, where(h,k) is the vertex Vertex(3,304) h reaches a maximum of 304 when t = 3 ```
 Numbers_Word_Problems/430990: what number is twice the orginal number when you times by 3 then add 41 solutions Answer 299224 by ewatrrr(10682)   on 2011-04-04 12:52:40 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the number Question states*** 3n+4 = 2n n = -4 CHECKING our answer*** 3*-4 + 4 = 2*-4 = -8 ```
 logarithm/430992: solve for x: e^x=12 ????1 solutions Answer 299223 by ewatrrr(10682)   on 2011-04-04 12:50:32 (Show Source): You can put this solution on YOUR website! ``` Hi e^x = 12 ln12 = x |calculator makes short work of this 2.4849 = x ```
 Probability-and-statistics/430954: starting salaries of marketing majors are normally distributed with a mean of 42,000 and a standard deviation of 3900. what is the probability that a randomly selected marketing major will receive a starting salary between 40,000 and 50,000?1 solutions Answer 299222 by ewatrrr(10682)   on 2011-04-04 12:47:27 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: z = -2000/3900 = -.5128 and z = 8000/3900 = 2.0513 P(between 40,000 and 50,000) = P(-.5128 < z < 2.0513) = .6758 ```
 test/430983: Add (8x^2-3y^2-5xy) + (-12x^2-6y^2+9xy1 solutions Answer 299221 by ewatrrr(10682)   on 2011-04-04 12:35:13 (Show Source): You can put this solution on YOUR website! ``` Hi Add 1*(8x^2-3y^2-5xy) +1*(-12x^2-6y^2+9xy) |applying distributive Principle 8x^2-3y^2-5xy -12x^2-6y^2+9xy |combining Like terms -4x^2-9y^2+4xy or -(4x^2-4xy+ 9y^2) ```
 test/430980: Multiply (3x-4)^21 solutions Answer 299220 by ewatrrr(10682)   on 2011-04-04 12:30:01 (Show Source): You can put this solution on YOUR website! ``` Hi Multiply (3x-4)^2 = (3x-4)(3x-4) = 9x^2 -24x +16 F First terms 9x^2 O Outside terms -12x I Inside terms -12x L Last terms 16 ```
 Travel_Word_Problems/430975: The trip takes 5 hours for a car moving at 26 mph . What is the speed of a car that makes the trip in 2 hours?1 solutions Answer 299219 by ewatrrr(10682)   on 2011-04-04 12:27:01 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent speed of a car making the trip in 2hr D = 5hr*26mph = 130mi 2hr*x = 130mi x = 65mph ```
 test/430977: Multiply (4a-5)(2a+3)1 solutions Answer 299218 by ewatrrr(10682)   on 2011-04-04 12:18:47 (Show Source): You can put this solution on YOUR website! ``` Hi Multiply (4a-5)(2a+3) 8a^2 +2a -15 F First terms 8a^2 O Outside terms 12a I Inside terms -10a L Last terms -15 ```
 Linear-equations/430965: I need help understanding the answer to this linear equation. ((x)/(x^2-1))-((x+3)/(x^2-x))= ((-3)/(x^2+x)) I know the solution is -6 I just can't seem to get there on my own. Any help would be greatly appreciated. Thank you! 1 solutions Answer 299217 by ewatrrr(10682)   on 2011-04-04 12:15:51 (Show Source): You can put this solution on YOUR website! ``` Hi |multiplying thru by x(x-1)(x+1) x^2 -(x+3)(x+1) = -3(x-1) x^2-x^2-4x-3 = -3x+3 -6 = x ```
 Human-and-algebraic-language/430869: 40% of the students in the class are boys. There are 18 less boys than girls in the class. How many students are in the class total?1 solutions Answer 299214 by ewatrrr(10682)   on 2011-04-04 12:07:38 (Show Source): You can put this solution on YOUR website! ``` Hi 18 less boys than girls Let x and (x+18) represent th enumber of boys and girls respctively Question states*** .40(x + (x+18) = x .40(2x + 18) = x 7.2 = .2x x = 36, the number of boys. Number of girls is 54. Total of 90 students CHECKING our answer*** .40*90 = 36 ```
 Polynomials-and-rational-expressions/430953: Simplify by removing factors of 1. q^2-49/ q^2-14q+491 solutions Answer 299197 by ewatrrr(10682)   on 2011-04-04 11:20:32 (Show Source): You can put this solution on YOUR website! ``` Hi q^2-49/ q^2-14q+49 ```
 Percentage-and-ratio-word-problems/430949: The ratio of men to women working at a factory Smythe Manufacturing Plant is 4:5. If there are 36 men, how many women are there?1 solutions Answer 299195 by ewatrrr(10682)   on 2011-04-04 11:15:38 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the number of women Note: ratios Set Up Proportions! 4/5 = 36/x | Cross Multiplying 4x = 5*36 x = 5*36/4 x = 45 CHECKING our Answer*** 4/5 = 36/45 ```
 Quadratic-relations-and-conic-sections/430947: identify the foci,of the following ellipse. sketch each. 1. (x-1)^2/25 + (y+2)^2/16 = 1 1 solutions Answer 299194 by ewatrrr(10682)   on 2011-04-04 11:13:02 (Show Source): You can put this solution on YOUR website! ``` Hi Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center and a and b are the respective vertices distances from center. (x-1)^2/25 + (y+2)^2/16 = 1 | a = 5 and b = 4 C(1,-2) f = sqrt(25-16) = 3 (foci are located 3 each side of center along major axis) |foci are (-2,-2) and (4,-2) ```
 Polynomials-and-rational-expressions/430943: The problem: one-half of a number is 25 more than one-third of the same number. I got 150 but i need to show a check on it and don't know how1 solutions Answer 299191 by ewatrrr(10682)   on 2011-04-04 11:02:14 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the number Question states*** (1/2)n = (1/3)n + 25 |Multipying thru by 6 so as all denominators = 1 3n = 2n + 150 n = 150 CHECKING our Answer*** 75 = 50 + 25 ```
 Length-and-distance/430942: If one 30 - 60 - 90 triangle has a short leg 8 inches long, and another has a short leg 24 inches long, find the areas of each triangle, and compare their sizes. Why do you think the areas have the ratio that they do? What would that ratio be if the two triangles had short legs 5 and 20 inches long?1 solutions Answer 299189 by ewatrrr(10682)   on 2011-04-04 10:56:59 (Show Source): You can put this solution on YOUR website! ``` Hi Note: 30-60-90 triangle, sides have a ratio 1:sqrt(3):2 Area[short leg = 8in] = (1/2)*8*8sqrt(3) = 32sqrt(3) Area[short leg = 24in] = (1/2)*24*24sqrt(3) = 288sqrt(3) ratio of the areas is 32/288 = 1/9 or 1:9 Why 1:9 because 1:3^2 is 1:9 larger triangle: shortest leg of that is 3 times the smaller's shortest leg What would be the ratio of the areas of two triangles with short legs 5 and 20 inches long? 1:4^2 or 1:16 ```
 Miscellaneous_Word_Problems/430937: How do I go about solving this word problem: A jeweler has three small solid speres made of gold, of radius 2mm, 3mm, and 4mm. She decides to melt these down and make just one spere out of them. What will the radius of this larger spere be?1 solutions Answer 299187 by ewatrrr(10682)   on 2011-04-04 10:45:20 (Show Source): You can put this solution on YOUR website! ``` Hi Volume(Sphere) = 4/3pir^3 and r = 4/3pi2^3 + 4/3pi3^3 + 4/3pi4^3 = 4/3*99pi = r = r = = 4.63 mm (to nearest hundredth of a mm) ```