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# Recent problems solved by 'robertb'

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 Miscellaneous_Word_Problems/452667: A gasoline tank is 7/8 full. After 12 gallons have been used, it is half full. How many gallons does the tank hold when it is full? 1 solutions Answer 311519 by robertb(4012)   on 2011-05-24 03:00:28 (Show Source): You can put this solution on YOUR website!Let x = # of gallons of gasoline when tank is full. ==> ==> ==> ==> gallons.
 Sequences-and-series/453400: compute e^0.3 using the infinite series for e^x1 solutions Answer 311517 by robertb(4012)   on 2011-05-24 02:41:08 (Show Source): You can put this solution on YOUR website! +... . Using only the first five terms of this series to approximate , we get 1.3498375, which is actually correct to the 4th decimal place.
 Money_Word_Problems/453339: if you invest money into an account that receives a steady annual interest rate of 3.5%, how many years will it take to double your investment? 1 solutions Answer 311515 by robertb(4012)   on 2011-05-24 02:03:35 (Show Source): You can put this solution on YOUR website! <==> ==> ==> years, to the nearest tenth.
 Mixture_Word_Problems/453055: solution A is 40% acid. Solution B is 80% acid. How much of each is needed to make 120 liters of a solution that is 50% acid?1 solutions Answer 311511 by robertb(4012)   on 2011-05-24 01:30:44 (Show Source): You can put this solution on YOUR website!0.40*x + 0.80*(120 - x) = 0.50*120 ==> 0.4x + 96 - 0.8x = 60 ==> -0.4x = -36 ==> x = 90 liters of 40% acid, and 120 - x = 30 liters 80% acid.
 Equations/453079: y = 4 x^2 - 2 x - 3 find zeros1 solutions Answer 311509 by robertb(4012)   on 2011-05-24 01:24:28 (Show Source): You can put this solution on YOUR website! ==> 2x - 3 = 0 ==> 2x = 3 ==> x = 3/2. ==> 2x + 1 = 0 ==> 2x = -1 ==> x = -1/2.
 Exponential-and-logarithmic-functions/453373: log3 x- log3(x-2)=11 solutions Answer 311507 by robertb(4012)   on 2011-05-24 00:59:54 (Show Source): You can put this solution on YOUR website! ==> ==> ==> x = 3(x-2) x = 3x - 6 ==> -2x = -6 ==> x = 3.
 Age_Word_Problems/453287: Find a two-decimal-place number between 0 and one such that the sum of its digits is 9 and such that if the digits are reversed the number is increased by 0.271 solutions Answer 311505 by robertb(4012)   on 2011-05-24 00:51:22 (Show Source): You can put this solution on YOUR website!The number is 0.36. Let x be the tens place, y the ones place. Then x + y = 9, and 10x + y + 27 = 10y + x ==> 27 = 9y - 9x <==> y - x = 3 y - x = 3 y + x = 9 ==> 2y = 12 y = 6 ==> x = 3. The decimal number is 0.36.
 Quadratic-relations-and-conic-sections/453348: What type of conic is y^2-6x+3y-2=0?1 solutions Answer 311496 by robertb(4012)   on 2011-05-23 23:38:51 (Show Source): You can put this solution on YOUR website!A parabola.
 Equations/453316: If -4x=4(x-8) than what is x?1 solutions Answer 311481 by robertb(4012)   on 2011-05-23 21:56:35 (Show Source): You can put this solution on YOUR website!-4x = 4x - 32 ==> -8x = -32 ==> x = -32/-8 = 4.
 Miscellaneous_Word_Problems/453325: The volume of this rectangular prism is 792 cubic meters. Its width is 11 meters, and its height is 12 meters. What is its depth?1 solutions Answer 311478 by robertb(4012)   on 2011-05-23 21:54:16 (Show Source): You can put this solution on YOUR website!11*12*d = 792 ==> 132d = 792 ==> d = 6 meters, the depth of the rectangular prism.
 Linear-equations/453249: find the x- and the y- intercept of 3x-y=6. 1 solutions Answer 311477 by robertb(4012)   on 2011-05-23 21:52:25 (Show Source): You can put this solution on YOUR website!Write the equation in intercept form. Divide both sides by 6, to get , or . Hence the x-intercept is 2 and the y-intercept is -6.
 Sequences-and-series/453308: I am stumped on this one. I have been working it for hours but cannot seem to get the right formula to do it. Any help would be much appreciated. Thanks Write the nth term of the following sequence in terms of the first term of the sequence. a, a + 4, a + 8, . . .1 solutions Answer 311467 by robertb(4012)   on 2011-05-23 21:20:00 (Show Source): You can put this solution on YOUR website!The nth term of an arithmetic sequence is given by . Here, , and d = 4. Now substitute these values into the general formulas.
 Sequences-and-series/453310: I am stumped on this one too. I have been working it for hours but cannot seem to get the right formula to do it. Any help would be much appreciated. Thanks Write the nth term of the following sequence in terms of the first term of the sequence. 10, 20, 40, . . .1 solutions Answer 311465 by robertb(4012)   on 2011-05-23 21:17:14 (Show Source): You can put this solution on YOUR website!The nth term of a geometric sequence is given by . , and r = 2. Now substitute these values into the general formula.
 Equations/453299: If 4x+6=2x+10 than what is x?1 solutions Answer 311463 by robertb(4012)   on 2011-05-23 21:13:57 (Show Source): You can put this solution on YOUR website!4x + 6 = 2x + 10 4x - 2x = 10 - 6 2x = 4 x = 2.
 Probability-and-statistics/453289: If the probability of a certain team winning is 3/4, what is the probability that this team will win its first three games and lose the fourth? I'm not sure where to begin given my basic understanding of probability. Can you help?1 solutions Answer 311462 by robertb(4012)   on 2011-05-23 21:10:47 (Show Source):
 Equations/453302: Please help me solve the equation 30d^2+33d+9=0 1 solutions Answer 311458 by robertb(4012)   on 2011-05-23 21:05:17 (Show Source): You can put this solution on YOUR website!Divide both sides by 3, to give ==>d = -3/5, -1/2.
 Sequences-and-series/453276: evaluate the series to the given term 1. 256 + 192 + 144 + ...; S7 2. 1 – 3 + 9 – 27 + ...; S10 3. –14 + (–7) + 0 + 7 + ...; S101 solutions Answer 311454 by robertb(4012)   on 2011-05-23 21:01:16 (Show Source): You can put this solution on YOUR website!the sum of the first n terms of a geometric series is given by the formula , where = the first term of the series, and r = common ratio. 1. , r = 3/4. ==> 2. , r = -3. 3. This is an arithmetic series, so .
 Probability-and-statistics/453265: If you pick four values at random from a normal distribution, what is the probability that all four values will be more than one standard deviation above the mean?1 solutions Answer 311451 by robertb(4012)   on 2011-05-23 20:48:02 (Show Source): You can put this solution on YOUR website!From the empirical, or 68-95-99.7 rule, the probability that one value will be more than 1 standard deviation above the mean is . Assuming independence of the values, the probability that all four values will be more than one standard deviation above the mean is
 Polynomials-and-rational-expressions/452949: One root of the polynomial equation 0=x^3-4x^2+9x-10 is 1-2i. Find an additional root. A.-2+i B.-1-2i C.2+i D.1+2i 1 solutions Answer 311245 by robertb(4012)   on 2011-05-23 01:22:20 (Show Source): You can put this solution on YOUR website!The complex conjugate of the given root, 1 + 2i, is also a root. So the answer is d.
 Probability-and-statistics/452695: The following table lists the probability distribution of the number of refrigerators owned by all families in a city. Study the distribution and answer the questions. x 0 1 2 3 P(x) .02 .28 .61 .09 The probability that a family owns: a. Exactly 3 refrigerators is: _______ b. At least 2 refrigerator is: _____ c. Fewer than 3 refrigerators is: _____ d. The mean of the distribution is  = ______ e. The standard deviation of the distribution is  = _____ 1 solutions Answer 311244 by robertb(4012)   on 2011-05-23 01:17:24 (Show Source): You can put this solution on YOUR website!a. 0.09 b. 0.61 + 0.09 = 0.70 c. 1 - 0.09 = 0.91 d. = E(X) = 0*0.02 + 1*0.28 + 2*0.61 + 3*0.09 = 1.77 e. variance = ==> standard deviation =
 Trigonometry-basics/452918: Find the exact value of the expression. sin195 degrees1 solutions Answer 311243 by robertb(4012)   on 2011-05-23 00:47:43 (Show Source): You can put this solution on YOUR website!sin195 = sin(135 + 60) = sin135*cos60 + cos135*sin60 = = =
 Quadratic-relations-and-conic-sections/452926: parabola with foci at (4,6) and directrix at x=81 solutions Answer 311240 by robertb(4012)   on 2011-05-23 00:36:50 (Show Source): You can put this solution on YOUR website!Under the given conditions, the vertex will be at the point (6,6). a = 6 - 4 = 2, and the standard equation would be , or .
 Quadratic-relations-and-conic-sections/452810: Write an equation of an ellipse with the given characteristics: Center: (3,3) Vertex: (3, -1) Co Vertex: (1,3)1 solutions Answer 311239 by robertb(4012)   on 2011-05-23 00:27:38 (Show Source): You can put this solution on YOUR website!Semi-major axis is 3--1 = a = 4. Semi-minor axis is 3 - 1 = b = 2. ==> standard form of the equation is , or
 Evaluation_Word_Problems/452837: Use a half-angle identity to find the exact value of the expression. sin 112.5 degrees1 solutions Answer 311236 by robertb(4012)   on 2011-05-22 22:24:56 (Show Source):
 Trigonometry-basics/452834: Find the value of the trigonometric expression. cos 150degrees cos 120 degrees - sin 150 degrees sin 120 degrees1 solutions Answer 311232 by robertb(4012)   on 2011-05-22 22:09:15 (Show Source): You can put this solution on YOUR website!cos(150 + 120) = cos 150* cos 120 - sin 150*sin 120 = cos 270 = 0.
 Exponential-and-logarithmic-functions/452885: Hi. How would I solve the problem log2 (x^2-9)=4 Would I factor out the (x^3-9) to make its (x+3) (x-3) Then go from there?1 solutions Answer 311230 by robertb(4012)   on 2011-05-22 22:06:10 (Show Source): You can put this solution on YOUR website! <==> ==> ==> x = -5, 5. Both values satisfy the original equation, and so are the final answers.
 Trigonometry-basics/452828: Simplify the trigonometric expression. tanOcotO1 solutions Answer 311223 by robertb(4012)   on 2011-05-22 21:55:01 (Show Source):
 Sequences-and-series/452871: Please help! I have been working on this problem night and I'm not going anywhere with it! Consider the sequence -7, -5.6, -4.2, -2.8,-1.4,... A. Write an explicit formula for the sequence (I know its An=A1+(n-1)d but I don't know where the 'D' comes from) B. Write a recursive formula for the sequence. C. Suppose you need to find the 50th term of the sequence. List which formula you should use. D. Which term is the number 103.6 Sorry it's so much thats just all one number on my homework! please please help1 solutions Answer 311221 by robertb(4012)   on 2011-05-22 21:50:30 (Show Source): You can put this solution on YOUR website!A. , d = 1.4 ==> B. C. D. ==> n = 80.
 Pythagorean-theorem/452846: What's the area of an equilateral triangle with sides measuring 6 meters?1 solutions Answer 311219 by robertb(4012)   on 2011-05-22 21:40:31 (Show Source): You can put this solution on YOUR website!The altitude of the equilateral triangle would be . The area of the triangle is then square meters.
 Exponential-and-logarithmic-functions/451905: Evaluate. log4(256)1 solutions Answer 310720 by robertb(4012)   on 2011-05-19 23:29:31 (Show Source):