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 test/384198: Your question goes here. Write clearly! We are not mind readers, so be sure to ask a question that we can understand.1 solutions Answer 272468 by richard1234(5390)   on 2010-12-12 17:23:25 (Show Source): You can put this solution on YOUR website!Also students, please put parentheses wherever they need to go. For example, if I see something like 5/x-4^2 = 1 I have no idea what it means because there are multiple ways to interpret the question.
 Numbers_Word_Problems/385002: The untis digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digit is 10.1 solutions Answer 272465 by richard1234(5390)   on 2010-12-12 17:04:22 (Show Source): You can put this solution on YOUR website!37. Just let the tens digit be x, and the units digit be 2x + 1, and solve.
 Triangles/384945: In an isosceles triangle, if the base is longer than either leg, then would the measure of each base angle be greater than the measure of the vertex angle?1 solutions Answer 272442 by richard1234(5390)   on 2010-12-12 16:00:13 (Show Source): You can put this solution on YOUR website!It's impossible. Just draw an isosceles triangle and you'll see. Or, you can use the law of sines.
 Linear-equations/384948: Find the midpoint of the line segment having the given endpoints. (8, -4) and (-7, 8)1 solutions Answer 272441 by richard1234(5390)   on 2010-12-12 15:50:25 (Show Source): You can put this solution on YOUR website!The midpoint's just the average of the coordinates, or (1/2, 2).
 Probability-and-statistics/384951: An experiment consists of tossing a quarter, a dime, and a nickel. What is the probability that all three coins come up the same (ie all three come up heads or all three come up tails)?1 solutions Answer 272438 by richard1234(5390)   on 2010-12-12 15:42:55 (Show Source): You can put this solution on YOUR website!We have P(3 heads) = (1/2)^3 = 1/8. Likewise P(3 tails) = 1/8, by symmetry. The probability is 1/8 + 1/8 = 1/4.
 Linear_Algebra/384931: solve system of equations: 1x4=y y+6x=111 solutions Answer 272435 by richard1234(5390)   on 2010-12-12 15:39:56 (Show Source): You can put this solution on YOUR website!It looks like 1 times 4 to me, leaving y = 4 and x = 7/6.
 Coordinate-system/384920: A solution to y=6 How do you solve the problem to come up with 3 coordinates?1 solutions Answer 272434 by richard1234(5390)   on 2010-12-12 15:34:13 (Show Source): You can put this solution on YOUR website!(1,6), (-7, 6), and (4.65, 6) are three such coordinates.
 Travel_Word_Problems/384928: You walk fro your home to the post office at an average rate of 3 mph. You then walk back at an average rate of 5 mph. What is the average rate for your entire trip?1 solutions Answer 272432 by richard1234(5390)   on 2010-12-12 15:29:45 (Show Source): You can put this solution on YOUR website!Suppose the walk was 15 miles each way (the distance doesn't matter, we can pick x miles if we wish). That means it takes 5 hours to walk there and 3 hours to walk back. You went 30 miles total, so the average speed is (30 miles)/(8 hours) = 3.75 mph.
 Rectangles/384872: The width of a rectangle is 3 ft less than the lenght. The area is 10 ft square. Find the length and width.1 solutions Answer 272429 by richard1234(5390)   on 2010-12-12 15:23:34 (Show Source): You can put this solution on YOUR website!In this case, guessing and checking reveals width = 2 ft, length = 5 ft. If guessing and checking doesn't yield an obvious solution, you can solve such a problem using the quadratic formula.
 Quadratic_Equations/384886: Hi Please help. Partial differentiate the following, the d's are the 'curly' d's but couldnt get them on here Find df/dx, df/dy, d^2f=dx^2 and d^2f/dy^2 for f(x, y) = e^(x+y).sin(x - y). Thank You1 solutions Answer 272426 by richard1234(5390)   on 2010-12-12 15:20:52 (Show Source): You can put this solution on YOUR website!To find df/dx and df/dy, just assume that y and x are constants respectively (I'm also using d = differential). So, (by the Product Rule) Do the same for df/dy. Then you can find the second derivatives by taking the derivative of df/dx, df/dy.
 Coordinate-system/384924: Express the number in scientific notation. .0000156131 solutions Answer 272425 by richard1234(5390)   on 2010-12-12 15:12:02 (Show Source): You can put this solution on YOUR website!1.5613 * 10^-5
 Miscellaneous_Word_Problems/384742: Admission to a secret and exclusive club is through passwords. When you knock on the door, the doorman says something and you have to respond with a number. The doorman tells the first member, 'New votes'. The member considers this for a moment and replies, '9' and the doorman lets him in. Another member comes to the door and the doorman says, 'Teething'. The response is '18'. He is also let in. A third member comes to the door and the doorman says, 'Teen hero'. The member replies, '4' upon which he is allowed in. Now it is your turn. You knock on the door and the doorman says 'Even for us.' What should be your response? 27 17 11 13????????????// \ its very tuff...1 solutions Answer 272359 by richard1234(5390)   on 2010-12-12 09:21:46 (Show Source): You can put this solution on YOUR website!Probably 13 but I'm pretty unsure. Keep in mind that 18 is the legal age to vote, hence the term "new votes." However I don't know what 4 has to do with teething, since people teeth much earlier than 4 years (maybe 4 months). I would answer depends on the previous phrase, so the answer would be 13 because a person becomes a teenager at age 13.
 Expressions-with-variables/384684: In the following graph determine the domain and range of the function. The solid dots indicate the end points of the graph. Show your work not just the final answer. End points (-2,5) and (3,1) 1 solutions Answer 272357 by richard1234(5390)   on 2010-12-12 08:56:09 (Show Source): You can put this solution on YOUR website!It would probably be Domain: [-2, 3] Range: [1, 5] However I don't see a graph, so the range could be different based on the function.
 Miscellaneous_Word_Problems/384735: A lever 12m long balances weights of 48kg on one end and 24kg on the other end. Find the lengths of the two arms of the lever.1 solutions Answer 272354 by richard1234(5390)   on 2010-12-12 08:46:10 (Show Source): You can put this solution on YOUR website!We know that torque equals force*radius, or mass*radius since gravity on Earth is constant in this case. If x is the distance from the 48 kg mass to the fulcrum, then 48x = 24(12 - x) 2x = 12 - x x = 4 m, 12 - x = 8 m
 Linear_Equations_And_Systems_Word_Problems/384693: this is actually a digit problem. 1. the units digit of a two digit number is 6. The number with the digit in reverse order is 6 less than twice the original number. Find the number.1 solutions Answer 272353 by richard1234(5390)   on 2010-12-12 08:42:04 (Show Source): You can put this solution on YOUR website!If the number is 10d + 6, then 60 + d = 2(10d + 6) - 6 60 + d = 20d - 6 54 = 19d No integer value for d.
 Quadratic_Equations/384666: Given the quadratic function f(x)=x^2 - 6x + 9 find a value of x such that f(x)= 251 solutions Answer 272300 by richard1234(5390)   on 2010-12-11 23:14:43 (Show Source): You can put this solution on YOUR website!We have 25 = x^2 - 6x + 9 Factoring, we obtain 25 = (x - 3)^2 One such value of x is 8 (the other one is -2).
 Rectangles/384627: The perimeter of a rectangle is 42 ft. The length of the rectangle 3 ft. less than twice the width.Find the length and width of the rectangle.1 solutions Answer 272299 by richard1234(5390)   on 2010-12-11 23:12:46 (Show Source): You can put this solution on YOUR website!If x and 2x - 3 are the width and length of the rectangle, then 2(x + 2x-3) = 42 x + (2x - 3) = 21 Solving, we obtain x = 8, 2x - 3 = 13.
 Graphs/384514: in our algebra worksheet, you graph these lines such as y>2/3x+1, and when you;re done filling in the correct plane, what does "INCLUDES BOUNDARY LINE" mean? thanks1 solutions Answer 272298 by richard1234(5390)   on 2010-12-11 23:10:58 (Show Source): You can put this solution on YOUR website!I think it denotes whether y is strictly greater than something, or greater than or equal to. Usually if there's a dashed line it means strictly greater than (>) and if it's a solid line then y is greater than or equal to (>=).
 Probability-and-statistics/384522: 2.Which of the following is NOT a characteristic of the normal distribution? Answer Symmetric Mean = Median = Mode Bell-shaped Equal probabilities at all values of x 1 solutions Answer 272294 by richard1234(5390)   on 2010-12-11 22:58:48 (Show Source): You can put this solution on YOUR website!Even though I have never taken a statistics course, I'm quite positive the answer is "equal probabilities at all values of x." Mainly because normal distributions do follow a bell curve, and the probability of getting 100/100 heads is definitely not the same as getting 50/50 heads, tails.
 Trigonometry-basics/384428: A) Calculate Angle E if Cos E = 0.812 B) Calculate Angle E if Tan E = 5/31 solutions Answer 272293 by richard1234(5390)   on 2010-12-11 22:50:21 (Show Source): You can put this solution on YOUR website!A) E = arccos (.812) + 2n(pi) B) E = arctan (5/3) + n(pi) n is some integer, I added a multiple of pi since the cosine and tangent functions are periodic with periods 2pi and pi.
 Circles/384558: Parallelogram ABCD is inscribed in circle O. Find the measure of angle A.1 solutions Answer 272289 by richard1234(5390)   on 2010-12-11 22:43:06 (Show Source): You can put this solution on YOUR website!By definition, if the parallelogram is inscribed in a circle, it is cyclic, and the measures of opposite angles add up to 180 (i.e. A + C = 180, B + D = 180). However, ABCD is a parallelogram, so A + B = 180, B + C = 180, etc. It follows that A = B, B = C, etc, so ABCD is a rectangle, and angle A = 90 degrees.
 expressions/384569: 10 – 8 – 10 + 2 = 4 where do I insert the parentheses?1 solutions Answer 272286 by richard1234(5390)   on 2010-12-11 22:39:54 (Show Source): You can put this solution on YOUR website!I don't think it's possible to insert parentheses to make this a true expression...here's why: +/- 10 and +/-2 are both congruent to 2 modulo 4, while -8 is 0 modulo 4. The left side becomes 2 + 0 + 2 + 2 = 6 = 2 modulo 4, regardless of where parentheses are placed. However, 4 is 0 modulo 4 so the two expressions must carry different residues and cannot be equivalent.
 Probability-and-statistics/384644: if p(a and b)=0.7, p(a)=0.3 and p(b)=0.8 determine p(a and b)1 solutions Answer 272283 by richard1234(5390)   on 2010-12-11 22:33:43 (Show Source): You can put this solution on YOUR website!Umm it's 0.7? Or were you looking for P(a or b)?
 Geometric_formulas/384573: If you know the length of two sides of a triangle and the measure of each of the angles, how do you figure out the length of the third side?1 solutions Answer 272279 by richard1234(5390)   on 2010-12-11 22:24:36 (Show Source): You can put this solution on YOUR website!Best way would be to use the law of sines. The law of cosines also works, but it is more time-consuming.
 Rectangles/384639: the perimeter of a square picture frame is 48 cm. Find the length of each side of the frame.1 solutions Answer 272277 by richard1234(5390)   on 2010-12-11 22:21:27 (Show Source): You can put this solution on YOUR website!If x is a side length, then 4x = 48 cm x = 12 cm
 Sequences-and-series/384386: Hi Please help, Obtain the Maclaurin series expansion about the point 0 for the function ln(x+1) as ln(x + 1) = x-x^2/2+x^3/3+(1)^n+1x^n/n + ...    Note that we cannot find a Maclaurin expansion of the function ln x since ln x does not exist at x = 0 and so cannot be differentiated at x = 0. Thank You in advance Matt 1 solutions Answer 272140 by richard1234(5390)   on 2010-12-11 09:37:31 (Show Source): You can put this solution on YOUR website!I think I have solved this exact same question previously on this website. Here is my solution: This is equivalent to finding the power series of ln x centered around x = 1. Note that all derivatives of ln x at x = 1 are equal to 1 or -1. Since we have the power series Adding one to all the x terms produces the given result.
 logarithm/384358: e^(5x-1)=11 solutions Answer 272089 by richard1234(5390)   on 2010-12-11 00:39:26 (Show Source): You can put this solution on YOUR website!Take the ln of both sides: 5x - 1 = ln 1 = 0 From this we conclude that x = 1/5.
 real-numbers/384370: 3(x + 6)= 4x I need to solve this and show a check.1 solutions Answer 272088 by richard1234(5390)   on 2010-12-11 00:37:05 (Show Source): You can put this solution on YOUR website!Multiplying the left side we get: 3x + 18 = 4x --> x = 18 It's easy to check by plugging x = 18 into the equation: 3(18 + 6) = 4(18) 72 = 72
 Sequences-and-series/384316: Find the missing number: 5, 8, 6, 4, 4, 0, 8, ? I tried 3n-1. I started with n=2,then n=3, but it failed at n=4. I also tried the multiple of the difference of the numbers. the difference between 5&8 is 3, then multiply that by the difference between 8&6 which is 2; so (5-8)* (8-6)= 6. Then (8-6) * (6-4)=4, then (6-4) * (4-4)=0 That's where it failed. I also tried 2n-1 starting with n=3, but that failed also. I looked for a pattern in the difference between the numbers, like the triangular numbers or Fibonacci numbers but no luck. I don't know what else to try.1 solutions Answer 272087 by richard1234(5390)   on 2010-12-11 00:31:51 (Show Source): You can put this solution on YOUR website!I think I found the recursion! We have 5 - 8 = -3. Take the absolute value of the difference, multiply by 2 to obtain the next term. 8 - 6 = 2, absolute value, multiply by 2 to get 4, etc. In general, the sequence should be a_n = 2|a_(n-2) - a_(n-1)|. From this, the following term is 16.
 Expressions-with-variables/384337: 5y+4y=19 y=6x-3 Could somebody solve this and show the steps, using elimination, substitute method.1 solutions Answer 272086 by richard1234(5390)   on 2010-12-11 00:22:43 (Show Source): You can put this solution on YOUR website!From the first equation we obtain 9y = 19, so y = 19/9. Substituting that into the second equation we get 19/9 = 6x - 3 --> 46/9 = 6x --> x = 23/27.
 Rational-functions/384359: In the function f(x) = ax 2 + bx + c, the minimum or maximum value occurs where x is equal to -b/(2a). How is that value derived? 1 solutions Answer 272085 by richard1234(5390)   on 2010-12-11 00:20:19 (Show Source): You can put this solution on YOUR website!Good question. However, the proof requires a little introductory calculus. In calculus, we define a function called the "derivative," which measures the instantaneous rate of change of a function. Basically, it is the same as finding slope, except that the two points get infinitely close, and it can be evaluated using limits. The derivative is usually denoted f'(x) or . By the power rule (you'll learn it early in calculus), the derivative of is . The relative minimum or maximum occurs when the derivative is equal to zero, and the slope is positive on one side of that point and negative on the other. Since the derivative of the quadratic is it is easy to see that this derivative is equal to zero when , therefore it is the vertex.