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# Recent problems solved by 'ewatrrr'

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 Numbers_Word_Problems/411258: How much less is the sum of all odd digits between 24 and 308 than the sum of all even digits between 23 and 307?1 solutions Answer 289123 by ewatrrr(10682)   on 2011-02-19 09:43:48 (Show Source): You can put this solution on YOUR website! ``` Hi How much 'less' is the sum of all odd digits 'between' 24 and 308 than the sum of all even digits 'between' 23 and 307? 306 = 26 + (n-1)2 306 = 26 + 2n - 2 282 = 2n n = 141 = 23,406 |sum of evens 305 = 25 + 2n-2 141 = n 141/2(50 + 280) = 141/2*330 = 23,265 |sum of odds 23,406 - 23,265 = 141 ```
 Probability-and-statistics/411245: From a standard deck of cards, first two cards are drawn from the deck without replacement. What is the probability that both cards are jacks?1 solutions Answer 289118 by ewatrrr(10682)   on 2011-02-19 09:13:30 (Show Source): You can put this solution on YOUR website! ``` Hi From a standard deck of cards, first two cards are drawn from the deck without replacement. P(both are Jacks) = 4/52*3/51 Note: w/o replacement, on 2nd card, there are 3 Jacks left out of the 51 cards left ```
 Linear-systems/411252: what solution set will satisfy if the system of equation 4x+y=8 a2x=3y+11 are manipulated using substitution? 1 solutions Answer 289117 by ewatrrr(10682)   on 2011-02-19 09:09:52 (Show Source): You can put this solution on YOUR website! ``` Hi Solving system by substition method ('manipulated'...never heard it put quite that way :) 4x+y=8 Or y = (-4x-8) 2x=3y+11 2x =3(-4x-8) + 11 2x = -12x - 24 + 11 14x = -13 x = -13/14 and y = -4*-13/14 - 8 = 52/14 - 112/14 = -60/14 = -30/7 y = -30/7 CHECKING our Answer*** 2x = 3y+11 -13/7 = -90/7 + 77/7 = -13/7 ```
 Age_Word_Problems/411253: nazia is twice old askanwal. if 10 years ago, nazia was 4 times as old as kanwal, then the present ages of nazia and kanwal are?1 solutions Answer 289116 by ewatrrr(10682)   on 2011-02-19 08:53:40 (Show Source): You can put this solution on YOUR website! ``` Hi nazia is twice old as kanwal Let x and 2x represent as Kanwal and Nazia's ages NOW respectively Question states*** 10years ago... 2x-10 = 4(x-10) Solving for x 30 = 2x x = 15, Kania age Now. Nazia is 30. (2*15) CHECKING our Answer*** 20 = 4*5 ```
 Quadratic-relations-and-conic-sections/411152: please help me write an equation for an ellepse with endpoints of the major axis at (4,1) and (-6,1) and endpoints of the minor axis at (-1,3) and (-1,-1).1 solutions Answer 289009 by ewatrrr(10682)   on 2011-02-18 17:23:10 (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 vertices are determined by distance of a and b from center C(-1,1): a = 5 and b = 2 ```
 Quadratic_Equations/411133: Need help solving this, trying to figure out how to get rid of decimals to make quadratic equation easier to solve. -0.3x^2 + 0.1x = -0.021 solutions Answer 289002 by ewatrrr(10682)   on 2011-02-18 16:03:36 (Show Source): You can put this solution on YOUR website!``` Hi -0.3x^2 + 0.1x = -0.02 |multiplying thru by -100 30x^2 - 10x - 2 = 0 15x^2 - 5x - 1 = 0 ```
 Quadratic_Equations/410250: If a stone is tossed from the top of a 210 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 210, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer1 solutions Answer 288999 by ewatrrr(10682)   on 2011-02-18 15:57:24 (Show Source): You can put this solution on YOUR website! ``` Hi h(t) = -9.8t^2 – 10t + 210, where t is in seconds, and height is in meters when it hits the ground: h(t) = 0 -9.8t^2 – 10t + 210 = 0 |multiplying thru by -10 98t + 100t - 2100 = 0 49t^2 + 50t - 1050 = 0 |tossing out negative solution for time t = 4.15 (rounded to the nearest hundredth's place) ```
 Quadratic_Equations/411127: Completing the square? Can someone show me the steps to completing the square for this please? - 1/5x^2 - 1/2x + 2 = 01 solutions Answer 288997 by ewatrrr(10682)   on 2011-02-18 15:47:43 (Show Source): You can put this solution on YOUR website! ``` Hi Completing the square: - 1/5x^2 - 1/2x + 2 = 0 |Multiplying thru by -10 so as all denominators= 1 2x^2 + 5x -20 = 0 2(x^2 + 5/2) - 20 = 0 2[x + 5/4)^2 -25/16] - 20 = 0 2(x+5/4)^2 - 25/8 - 160/8 = 0 2(x+5/4)^2 - 185/8 = 0 ```
 Linear-systems/411123: Can this problem be done by elimination are subsitution if so can you show me which one and how to do it? y+4x=-5 y+5x=31 solutions Answer 288996 by ewatrrr(10682)   on 2011-02-18 15:41:37 (Show Source): You can put this solution on YOUR website! ``` Hi y+4x=-5 y+5x=3 Sets Up for a simple elimination: -y-4x = 5 |mulitplying 1st Eq thru with -1 to eliminate y y+5x= 3 x = 8 x = 8 and y = -37 (y +5x=3; y = -5*8 + 3) CHECKING our Answer*** y + 4x = -5 -37 +32 = -5 ```
 test/411111: Its been a long time and I'm starting to return to school. How do I calculate this to simple terms? (3/4-2/3) + (1/2+1/3)1 solutions Answer 288986 by ewatrrr(10682)   on 2011-02-18 15:22:22 (Show Source): You can put this solution on YOUR website! ``` Hi simplifying: (3/4-2/3) + (1/2+1/3) 1*(3/4-2/3) + 1*(1/2+1/3) 3/4 -2 /3 + 1/2 + 1/3 |using the common denominator of 12 for each term: 9/12 - 8/12 + 6/12 + 4/12 (9 - 8 + 6 + 4)/12 = 11/12 ```
 Equations/410994: Decide whether or not the ordered pair is a solution of the system. (3,2) 2x+y=4, 4x+2y=81 solutions Answer 288966 by ewatrrr(10682)   on 2011-02-18 13:18:38 (Show Source): You can put this solution on YOUR website! ``` Hi Decide whether or not the ordered pair Pt(3,2) is a solution of the system. 2x+y=4 | 6 + 2 ≠ 4 4x+2y=8 |12 + 4 ≠ 4 NO this ordered pair is NOT the solution for this system of 2 linear equations NOte: These linear equations represent the SAME line: y = -2x + 4 ```
 Miscellaneous_Word_Problems/411069: Please help me with this word problem.... The numerator of a certain fraction is 7 less than its denominator. If 4 is subtracted from the numerator and 1 added to the denominator, the resulting fraction equals 1/3. Find the fraction. 1 solutions Answer 288965 by ewatrrr(10682)   on 2011-02-18 13:08:01 (Show Source): You can put this solution on YOUR website! ``` Hi The numerator of a certain fraction is 7 less than its denominator. Let x and (x-7)represent the denominator and numerator respectively Question states*** [(x-7)-4] / (x+1) = 1/3 Solving for x |cross multiplying to solve for x 3(x-11) = (x+1) 2x = 34 x = 17, the denominator. The numerator is 10. (17-7) Fraction is 10/17 CHECKING our Answer*** 6/18 = 1/3 ```
 Exponential-and-logarithmic-functions/411074: (log base of 3)3+(log base of 3)x=51 solutions Answer 288961 by ewatrrr(10682)   on 2011-02-18 12:58:52 (Show Source): You can put this solution on YOUR website! ``` Hi 3^5 = 3x 81 = x ```
 Miscellaneous_Word_Problems/411075: Please help me, thank you. Represent the number algebraically whose ten’s digit is h and whose units digit is k 1 solutions Answer 288956 by ewatrrr(10682)   on 2011-02-18 12:52:23 (Show Source): You can put this solution on YOUR website! ``` Hi number whose ten’s digit is h and whose units digit is k algebraically, number would be : 10h + k ```
 Probability-and-statistics/411067: A club has 15 students. Anserw the follow. Show steps. a)How many different 3-member committees could the club form? b) How many different 6-member committees could the club form? c)In how many ways can a club president,vice-president and a secretary be chosen?1 solutions Answer 288953 by ewatrrr(10682)   on 2011-02-18 12:40:50 (Show Source): You can put this solution on YOUR website! ``` Hi Note: nCx = and nPx = A club has 15 students. a)How many different 3-member committees could the club form: 15C3 15C3 = 15*14*13/2*3 = 2730/6 = 455 b) How many different 6-member committees could the club form:15C6 15C6 = 15*14*13*12*11*10/2*3*4*5*6=3603600/144 = 5005 c)In how many ways can a club president,vice-president and a secretary be chosen? 15P3 = 15*14*13 = 2730 ```
 Miscellaneous_Word_Problems/411066: Please help me solve this problem.... The sum of two numbers is S. One of the numbers is n. Represent algebraically 3 times the other number. 1 solutions Answer 288949 by ewatrrr(10682)   on 2011-02-18 12:25:50 (Show Source): You can put this solution on YOUR website! ``` Hi The sum of two numbers is S Let n and (S-n) represent the one and the other number. Represent algebraically 3 times the other number: 3(S-n) ```
 Quadratic-relations-and-conic-sections/410619: what are the intercepts, the foci and the asymptotes for the hyperbola? y^2/9-x^2/4=1.1 solutions Answer 288940 by ewatrrr(10682)   on 2011-02-18 11:45:59 (Show Source): You can put this solution on YOUR website! ``` Hi where Pt(h,k) is a center with vertices 'b' units up and down from center. intercepts: (0,3) and (0,-3) the foci: sqrt(4+9) = sqrt(13)= 3.6056 the asymptotes: y = ± b/a | y = 3/2x and y = -3/2x ```
 Quadratic-relations-and-conic-sections/411041: Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. f(x)=1/4(x+2)^2+11 solutions Answer 288935 by ewatrrr(10682)   on 2011-02-18 11:28:15 (Show Source): You can put this solution on YOUR website! ``` Hi f(x)=1/4(x+2)^2+1 Using the vertex form of a parabola, where(h,k) is the vertex the vertex: Pt(-2,1) the line of symmetry: x = -2 and the maximum or minimum value of f(x): f(-2) = 1 is a minimun |parabola opens upward as a = (1/4)>0 f(x)= -22x^2+2x+6 OR f(x) = -22(x- 1/11)^2 + 64/11 |completing the square ```
 Graphs/411045: Find the Domain and the range of the given relation. Also determine whether the relation is a function? {(6,-1), (-3,2), (0,5), (-2,2)}1 solutions Answer 288931 by ewatrrr(10682)   on 2011-02-18 11:19:48 (Show Source): You can put this solution on YOUR website! ``` Hi Ordered pairs:{(6,-1), (-3,2), (0,5), (-2,2)} Domain {6,-3,0,-2} Function? NO, as ALL domain values do not have an unique range value ```
 Volume/411043: If the number of square inches in the surafce area of a sphere is equal to the number of cubic inched in the vomlume of the sphere, what is the measure of the radius of the sphere?1 solutions Answer 288928 by ewatrrr(10682)   on 2011-02-18 11:03:46 (Show Source): You can put this solution on YOUR website! ``` Hi r = 12/4 = 3 CHECKING our Answer*** ```
 Percentage-and-ratio-word-problems/411039: 1. The three times the sum of a number and 8 is less than 4 more than the number.Find all such numbers. 2. The conversion from Celsius to Fahrenheit is F = 9 5C + 32. Solve for C to get a conversion formula from Fahrenheit to Celsius. 3. Solve the inequality, giving the solution in interval notation. 2 + 4(x + 3)  2x + 5(x 􀀀 8) 4. The three times the sum of a number and 8 is less than 4 more than the number. Find all such numbers. 21 solutions Answer 288925 by ewatrrr(10682)   on 2011-02-18 10:58:15 (Show Source): You can put this solution on YOUR website! ``` Hi 1) 3(x+8)< x+4 | 2x < -20 OR x < -10 2) OR = (5/9)*-23° = -12.7778°C 3) not clear from the presentation what the Inequality is 4) same as first queston ```
 Polynomials-and-rational-expressions/411026: Hi, I do not understand how to reduce or when to reduce the fraction within the quadratic equation. I came up with this answer. Would you please show me how to reduce for the final answer? Thanks. -x^2+6x-21=0 (-1)-x^2+6x-21=0(-1) x^2+6x-21=0 -6+-sqrt((6)^2-4(1)(-21))/2(1) -6+-sqrt(36+84)/(2) -6+-sqrt(120)/(2) -6+-sqrt(6(20))/(2) -6+-sqrt(6)/(2) -6+- 20 sqrt(6)/(2) -?+- sqrt(6)/(10) (thought we divide -6/20 then divide 2/20) leaves the 6 1 solutions Answer 288921 by ewatrrr(10682)   on 2011-02-18 10:41:59 (Show Source): You can put this solution on YOUR website! ``` Hi As important as correctly using the quadratic formula is starting with the correct quadratic equation to apply it to: -x^2+6x-21=0 |Must multiply ALL terms by -1 to proceed in tha fashion x^2 - 6x + 21 = 0 x^2+6x-21=0 |If... this were the correct quadratic (using as an example) -6+-sqrt(120)/(2) -6+-sqrt(4*30)/(2) -6+-2sqrt(30)/(2) -3+-sqrt(30) |important to take the 'sqrt(4)out front' ```
 Rational-functions/411023: I need help with this equation, log2 9+ log2 a=log2 131 solutions Answer 288917 by ewatrrr(10682)   on 2011-02-18 10:14:19 (Show Source): You can put this solution on YOUR website! ``` Hi log2 9+ log2 a = log2 13 log2 9+ log2 a - log2 13 = 0 log2 9a/13 = 0 2^0= 9a/13 1 = 9a/13 13/9 = a ```
 Miscellaneous_Word_Problems/411027: Suppose you pay \$16 for a shirt that has been discounted 30%. Find the original price of the shirt. Show all of your work and check your answer. 1 solutions Answer 288916 by ewatrrr(10682)   on 2011-02-18 10:10:05 (Show Source): You can put this solution on YOUR website!``` Hi Note: discounted 30% is the same as paying 70% of the value Let x represent the original cost .70*x = \$16 x = \$16/.70 = \$22.86 CHECKING our Answer*** \$22.86 - .30*\$22.86 = \$22.86 - \$6.86 = \$16 ```
 Polynomials-and-rational-expressions/411024: I am having trouble reducing the fraction within the quadratic equation. Would you please check my process to see if I did it right and help me with the ending part? (4x-3)^2=0 (4x-3)(4x-3)=0 16x^2-12x-12x-9=0 16x^2-24x-9=0 -24+- sqrt((24)^2-4(16)(-9))/(2(16)) -24+- sqrt(576+576)/(32) -24+- sqrt(1152)/(32) -24+- sqrt(8(144))/(32) -24+- sqrt(4(2)(144))/(32) -24+- 12(2) sqrt(2)/(32) -24+- 24 sqrt(2)/(32) -1+- sqrt(3(1)/(3) 1 solutions Answer 288915 by ewatrrr(10682)   on 2011-02-18 10:06:15 (Show Source): You can put this solution on YOUR website!``` Hi IF: 16x^2-24x-9=0 THEN: [24 ± 24sqrt(2)]/(32) = 3/4 ± (3/4)sqrt(2) However, in this question: (4x-3)(4x-3)=0 | 16x^2-24x+9=0 x = 3/4 ```
 Word_Problems_With_Coins/411020: IQ scores are normally distributed with a mean score of 100 and a standard deviation of 15. What is the probability that a person selected at random will have an IQ larger than 125?1 solutions Answer 288912 by ewatrrr(10682)   on 2011-02-18 09:38:21 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: z = 25/15 = 1.6667 P( z > 1.6667) = .0478 ```
 Percentage-and-ratio-word-problems/409800: the shot in mens shot put has a volume of about 905 cubic centimeters. Find the radius of the shot. (hint use the formula v=4/3pie r^3 for the volume of a sphere.)1 solutions Answer 288911 by ewatrrr(10682)   on 2011-02-18 09:31:07 (Show Source): You can put this solution on YOUR website! ``` Hi OR = 6.0015 cm ```
 Percentage-and-ratio-word-problems/410864: 2 open pipes fill a tank together in 6min. one pipe alone fills a tank in 9min. find time for second pipe alone.1 solutions Answer 288910 by ewatrrr(10682)   on 2011-02-18 09:24:46 (Show Source): You can put this solution on YOUR website! ``` Hi 2 open pipes fill a tank together in 6min. one pipe alone fills a tank in 9min. find time for second pipe alone. Let x represent the time for second pipe alone Question states*** per min the Equalizer 1/9 + 1/x = 1/6 Solving for x by mulitplying thru with 54x, so as all denominators= 1 6x + 54 = 9x 54 = 3x x = 18min, the time for second pipe alone CHECKING our Answer*** 2/18 + 1/18 = 3/18 = 1/6 ```
 Percentage-and-ratio-word-problems/411016: Attendance at a concert was 480. The ratio of adults to students was 5 to 3. How many adults attended? How many students attended 1 solutions Answer 288909 by ewatrrr(10682)   on 2011-02-18 09:20:19 (Show Source): You can put this solution on YOUR website! ``` Hi Attendance at a concert was 480 Let x and (480-x) represent the number of adults and children respectively Question states***Sets up the Proportion |cross multiplying to solve for x Solving for x 3x = 5(480-x) 8x = 2400 x = 300, # if adults attending. The # of children was 180. (480-120) CHECKING our Answer*** 300/180 = 5/3 ```
 Evaluation_Word_Problems/409096: Trevor launched a rocket in the soccer field. it landed 22 feet above the ground in a tree. if the rocket and trevor are 25 feet apart, what is the distance between trevor and the tree?1 solutions Answer 288908 by ewatrrr(10682)   on 2011-02-18 09:04:51 (Show Source): You can put this solution on YOUR website! ``` Hi Trevor launched a rocket in the soccer field, landing 22 feet above the ground in a tree if the rocket and trevor are 25 feet apart, find distance between trevor and the tree Let x represent distance between trevor and the tree Using the Pythagorean Theorem x^2 = 25^2 - 22^2 x = sqrt(141)= 11.8743 ft ```
 Evaluation_Word_Problems/410145: 168 pieces of fruit 1/3 are not necturines what is the equation to figure how many are not necturines?1 solutions Answer 288907 by ewatrrr(10682)   on 2011-02-18 09:00:16 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent how many are not necturines Question states*** (1/3)168 = x or 56 are not necturines ```