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# Recent problems solved by 'ewatrrr'

ewatrrr answered: 10675 problems
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 Permutations/438293: In how many ways can the first 4 places be filled by 10 horses in a race assuming there are no ties?1 solutions Answer 303148 by ewatrrr(10682)   on 2011-04-20 09:38:26 (Show Source): You can put this solution on YOUR website! ``` Hi In how many ways can the first 4 places be filled by 10 horses in a race (assuming there are no ties) Order Important 10P4 = 10!/6! = 5040 ways ```
 Equations/437967: please help me solve this !!! (2r+1)(12r^2+5r-3)=01 solutions Answer 302964 by ewatrrr(10682)   on 2011-04-19 16:42:01 (Show Source): You can put this solution on YOUR website! ``` Hi, Note use of ^ (uppercase 6) (2r+1)(12r^2 +5r-3)=0 |completing the factoring (2r+1)(4r +3)(3r -1) = 0 (2r+1) = 0 r = -1/2 (4r +3)= 0 r = -3/4 (3r -1)= 0 r = 1/3 ```
 Number-Line/437971: How do you put 3 < x < 6 and 9 < x < 12 on the same number line?1 solutions Answer 302962 by ewatrrr(10682)   on 2011-04-19 16:37:09 (Show Source): You can put this solution on YOUR website! ``` Hi shade the portion of the number line between the respective numbers... putting an open circle on the numbers as they are not included. 3 < x < 6 and 9 < x < 12 ```
 Equations/437969: what is the slope and the y intercept of y=-2x+7?1 solutions Answer 302961 by ewatrrr(10682)   on 2011-04-19 16:27:11 (Show Source): You can put this solution on YOUR website! ``` Hi Using the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. y= -2x+7 slope m = -2 y intercept is Pt(0,7) ```
 Number-Line/437961: How do you put this equation: 3 < x < 9 or 6 < x < 12 on a number line?1 solutions Answer 302960 by ewatrrr(10682)   on 2011-04-19 16:24:58 (Show Source): You can put this solution on YOUR website! ``` Hi In both cases shade the portion of the number line between the numbers. Recommend putting an open circle on the numbers as they are not included. 3 < x < 9 6 < x < 12 ```
 Linear-equations/437957: x-intercept=4, m=21 solutions Answer 302958 by ewatrrr(10682)   on 2011-04-19 16:21:07 (Show Source): You can put this solution on YOUR website! ``` Hi Using the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. x-intercept=4, m=2 y = 2x + b |Pt(4,0) on the line: use ordered pair to solve for b 0 = 8 + b -8 = b y = 2x - 8 ```
 Polynomials-and-rational-expressions/437956: (square root of 3x + 1, plus 2)^21 solutions Answer 302957 by ewatrrr(10682)   on 2011-04-19 16:16:44 (Show Source): You can put this solution on YOUR website! ``` Hi F First terms (3x+1) O Outside terms 2 I Inside terms 2 L Last terms 4 3x + 5 + 4 ```
 Equations/437934: the pentagon building in washington D.C is shaped like a regular pentagon.If the length of one side of the pentagon is represented by n+2, its perimeter would be represented by a) 5n+10 b) 5n+2 C) n+10 d)10n1 solutions Answer 302954 by ewatrrr(10682)   on 2011-04-19 16:11:33 (Show Source): You can put this solution on YOUR website! ``` Hi the pentagon building in washington D.C is shaped like a 'regular' pentagon (all five sides of equal length) If the length of one side of the pentagon is represented by n+2 Perimeter = 5(n+2) = 5n+10 ```
 Rational-functions/437944: Find the standard form of the equation of the ellipse with the given characteristics. foci: (1,1), (1,5) endpoints of the major axis: (1,-5), (1,11) I need help with this problem.1 solutions Answer 302952 by ewatrrr(10682)   on 2011-04-19 16:09:07 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously listed 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. endpoints of the major axis: (1,-5), (1,11) C(1,3) foci are along the major axis: need to determine that major axis foci are (1,1), (1,5) F = 2 = 2 ```
 Quadratic-relations-and-conic-sections/437950: Find the standard form of the equation of the ellipse with the given characteristics. foci: (1,1), (1,5) endpoints of the major axis: (1,-5), (1,11) I need help with this problem.1 solutions Answer 302950 by ewatrrr(10682)   on 2011-04-19 16:06:34 (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. endpoints of the major axis: (1,-5), (1,11) C(1,3) foci are along the major axis: need to determine that major axis foci are (1,1), (1,5) F = 2 = 2 ```
 Rational-functions/437941: Find the center and foci of the ellipse: (x-1)2 + (y+6)2 ------- -------=1 13 49 I think the answer is center (1,-6) and foci (-7,6), (5,6). Is this correct? 1 solutions Answer 302943 by ewatrrr(10682)   on 2011-04-19 15:53:08 (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. C(1,-6) Yes! F = foci are along the major axis: need to determine that major axis foci are (1,0) and (1,-12) ```
 Probability-and-statistics/437858: one million tickets are sold for a lottery in which a single prize will be awarded a) If you purchase a ticket, determine your odds against winning. b) If you purchase 10 tickets, determine your odds against winning.1 solutions Answer 302940 by ewatrrr(10682)   on 2011-04-19 15:40:51 (Show Source): You can put this solution on YOUR website! ``` Hi 1M tickets are sold for a lottery in which a single prize will be awarded a) If you purchase a ticket, determine your odds against winning. 999,999:1 b) If you purchase 10 tickets, determine your odds against winning. P(10/1,000,000)= 1/100,000 99,999:1 ```
 Probability-and-statistics/437942: how many cases can be filled with 9900 cans if each case holds 48 cans 1 solutions Answer 302938 by ewatrrr(10682)   on 2011-04-19 15:37:08 (Show Source): You can put this solution on YOUR website! ``` Hi how many cases can be filled with 9900 cans if each case holds 48 cans 9900/48 = 206.25 cases ```
 Probability-and-statistics/437900: contrator one is twice as likely to win as contractor 3 , contractor two is three times as likely to win as contractor three what are the probabilities of winning for each 1 solutions Answer 302937 by ewatrrr(10682)   on 2011-04-19 15:35:41 (Show Source): You can put this solution on YOUR website! ``` Hi contrator one(2x) is twice as likely to win as contractor 3 (x) contractor two(3x) is three times as likely to win as contractor three(x) what are the probabilities of winning for each P(contractor one) = 2/6 = 1/3 P(contractor two) = 3/6 = 1/2 P(contractor three) = 1/6 Note: 2/6 + 3/6 + 1/6 = 1 ```
 Probability-and-statistics/437925: suppose a data set has a mean of 104 and a standard deviation of 5. Find the z score for a data value of 107 1 solutions Answer 302935 by ewatrrr(10682)   on 2011-04-19 15:30:16 (Show Source): You can put this solution on YOUR website! ``` Hi data set has a mean of 104 and a standard deviation of 5. Find the z score for a data value of 107: z = (107-104)/5 = 3/5 ```
 Probability-and-statistics/437928: how many different three -members teams can be selected from a group of seven students? a)1 b)35 C)210 d)5,0401 solutions Answer 302933 by ewatrrr(10682)   on 2011-04-19 15:28:07 (Show Source): You can put this solution on YOUR website! ``` Hi how many different 3-members teams can be selected from a group of 7 students? 7C3 = 35 different 3-member teams ```
 Probability-and-statistics/437924: A deli has five types of meat,two types of cheese,and three types of bread.how many different sandwiches,consisting of one type of meat,one type of cheese,and one type of bread ,does the deli serve/ a)10 b)25 c)30 d)75 1 solutions Answer 302932 by ewatrrr(10682)   on 2011-04-19 15:26:34 (Show Source): You can put this solution on YOUR website! ``` Hi A deli has 5 types of meat,2 types of cheese,and 3 types of bread. different sandwiches,consisting of one type of meat,one type of cheese, and one type of bread ,does the deli serve = 5*2*3 = 30 different sandwiches ```
 Probability-and-statistics/437932: how many dfferent 4-letter arrangements can be formed using the letters of the word JUMP if each letter is used only once? a) 24 B)16 c)12 D) 41 solutions Answer 302928 by ewatrrr(10682)   on 2011-04-19 15:19:43 (Show Source): You can put this solution on YOUR website! ``` Hi how many different 4-letter arrangements can be formed using the letters of the word JUMP if each letter is used only once? 4! = 24 different 4-letter arrangements can be formed ```
 Geometry_Word_Problems/437920: a trapezoid has an area of 120 inches squared. it's altitude measures 8 in. give a possible pair lengths for the bases of the trapezoid.1 solutions Answer 302926 by ewatrrr(10682)   on 2011-04-19 15:17:55 (Show Source): You can put this solution on YOUR website! ``` Hi Area(trapezoid) = trapezoid has an area of 120in^ and h = 8" = 15" or = 30" 12" and 18" would be possible lengths for the bases of the trapezoid ```
 Linear-systems/437873: Solve the system of equations then classify the system. y=-x-11 3x-2y=-181 solutions Answer 302917 by ewatrrr(10682)   on 2011-04-19 14:44:19 (Show Source): You can put this solution on YOUR website! ``` Hi Solve the system of equations then classify the system. y = -x-11 3x -2y = -18 3x -2(-x-11) = -18 3x + 2x+22 = -18 5x = -40 x = -8 and y = -3 (y = -(-8) - 11 = -3) Ordered pair(-8,-3) the solution for this Independent system CHECKING our Answer*** 3x -2y = -18 3*-8 + 2*3 = -18 A consistent system has at least one solution. An inconsistent system has no solutions. An independent system has exactly one solution. A dependent system has infinitely many solutions. ```
 Exponential-and-logarithmic-functions/437822: Combine 2log(base8)x - 2(over)3log(base8)x + 4log(base8)x 2(over)3 is a fraction as in two-thirds1 solutions Answer 302914 by ewatrrr(10682)   on 2011-04-19 14:30:04 (Show Source): You can put this solution on YOUR website! ``` Hi log_8(x^6/x^(2/3)) = log_8(x^(16/3)) |Note: x^(18/3-2/3)= x^(16/3) become familiar with the Properties ```
 Exponential-and-logarithmic-functions/437892: combine 2log(base8)x - 2/3log(base8)x + 4log(base8) not sure how to combine with the fraction.1 solutions Answer 302911 by ewatrrr(10682)   on 2011-04-19 14:22:52 (Show Source): You can put this solution on YOUR website! ``` Hi In reply: yes, that x was not shown. See below had it been. log_8(x^6/x^(2/3)) = log_8(x^(16/3)) |Note: x^(18/3-2/3)= x^(16/3) become familiar with the Properties ```
 Exponential-and-logarithmic-functions/437891: solve for x log(base5)(x+3) - log(base5)x = 21 solutions Answer 302907 by ewatrrr(10682)   on 2011-04-19 14:08:15 (Show Source): You can put this solution on YOUR website! ``` Hi 5^2 = (x+3)/x 25x = x+3 24x = 3 x = 1/8 ```
 Proportions/437885: last question----- The NUFOne Communications COmpany must run a telephone line between two poles at opposite ends of a lake.the length and the width of the lake are 75 feet and 30 feet respectively.What is the distance between the two poles ,to the nearest foor? a) 105 b)81 c)69 d)45 1 solutions Answer 302905 by ewatrrr(10682)   on 2011-04-19 14:04:51 (Show Source): You can put this solution on YOUR website! ``` Hi Rectangular lake: L=75' and W=30' two poles at opposite ends of a lake applying the Pythagorean Theorem: answer to the nearest foot D(between poles) = = 81' ```
 Linear-equations/437878: can you please help me with this problem if line j is perpendicular to line k.If the slope of line j is 5/2,what is the slope of line k 1 solutions Answer 302902 by ewatrrr(10682)   on 2011-04-19 13:59:06 (Show Source): You can put this solution on YOUR website! ``` Hi line j is perpendicular to line k slope of line j = 5/2 slope of line k = -2/5 Note: slopes of perpendicular lines are negative reciprocals of one another that is: 5/2*-2/5 = -1 ```
 Rational-functions/435518: how do you graph y= x^2/2 -5? 1 solutions Answer 302900 by ewatrrr(10682)   on 2011-04-19 13:56:23 (Show Source): You can put this solution on YOUR website! ``` Hi Using the vertex form of a parabola, where(h,k) is the vertex y= .5x^2 -5 1) Parabola 2)Parabola with vertex Pt(0,-5) 3) y-axis the line of symmetry 4) Parabola Opens Upward a = .5 >0 5) x-intercepts(when y = 0) are x = ± ```
 Rational-functions/437874: what conic does the equation x^2/16+ y^2/4=1 represent? hyperbola,circle,parabola, or ellipse 1 solutions Answer 302894 by ewatrrr(10682)   on 2011-04-19 13:47:39 (Show Source): You can put this solution on YOUR website! ``` Hi Re: reply 4X^2+4Y^2=16 x^2 + y^2 = 4 | II. circle: C(0,0) radius 2 x^2/16+ y^2/4=1 Ellipse Need to be familiar with various standard forms: I.The standard form of a Parbola is II.Standard Form of an Equation of a Circle is III. Standard Form of an Equation of an Ellipse is IV.Standard Form of an Equation of an Hyperbola is OR ```
 sets-and-operations/437865: I need Venn diagram of this problem Soft Drink Taste Test A soft drink company wishes to introduce a new soft drink. The company is considering two flavors, lemon lime and cherry cola. In a sample of 125 people, it was found that • 80 liked lemon lime. • 68 liked cherry cola. • 42 liked both types c) How many liked either one or the other or both? d) How many did not like either flavor? 1 solutions Answer 302891 by ewatrrr(10682)   on 2011-04-19 13:40:41 (Show Source): You can put this solution on YOUR website! ``` Hi, unable to do Venn diagrams here: Chart may be useful to guide You. sample of 125 people Total one /both/neither LLIME 80 -42 38 COLA 68 -42 26 BOTH 42 Neither 19 Total 125 c) How many liked either one or the other or both? 106 d) How many did not like either flavor? 19 ```
 Geometry_Word_Problems/437824: two supplementary angles are in the ratio 7 to 2. find the number of degrees in the smaller angle.1 solutions Answer 302859 by ewatrrr(10682)   on 2011-04-19 11:46:37 (Show Source): You can put this solution on YOUR website! ``` Hi two supplementary angles are in the ratio 7 to 2. Let x and (180°-x)represent the smaller and larger of these supplementary angles. |Cross Multiplying 7x = 2(180°-x) 9x = 360° x = 40°, the smaller angle ```
 Trigonometry-basics/437811: Will you please solve the following equation and find all solutions? And provide an explanation? I am not sure whether to write it this way: or this way: 2sin^2(x) + 3sin(x) +1 = 0 Thank you1 solutions Answer 302857 by ewatrrr(10682)   on 2011-04-19 11:29:40 (Show Source): You can put this solution on YOUR website! ``` Hi 2sin^2(x) + 3sin(x) +1 = 0 factoring (2sinx +1)(sinx + 1) =0 (2sinx +1)= 0 sinx = -1/2 (sinx + 1) =0 sinx = -1 See following (cosx,sinx) summary for the corresponding solutions for the above ```
 Probability-and-statistics/437799: A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 2 pieces of candy at random. Find the probability that you have 2 lemon candies.1 solutions Answer 302856 by ewatrrr(10682)   on 2011-04-19 11:21:39 (Show Source): You can put this solution on YOUR website! ``` Hi 11 candies (6 cherry, 3 orange, 2 lemon) You reach in and take 2 pieces of candy at random. P (2 lemon) = 2/11*1/10 = 2/110 = 1/55 ```