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# Recent problems solved by 'richard1234'

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 Miscellaneous_Word_Problems/540887: In the statement |x+y| less than |x| + |y|, each variable represents any number. Tell whether the statement is true for all, some or no values. If it is true for some or all values, tell which values (positive or negative) makes it true.1 solutions Answer 353902 by richard1234(5390)   on 2011-12-03 10:45:24 (Show Source): You can put this solution on YOUR website!It's true if one of {x,y} is negative or zero. If x and y are both positive or both negative, then they are equal and the statement is not true.
 Complex_Numbers/540721: If arg((z-w)/(z-w^2)) =0,then prove that re(z)=-1/2,where (w and w^2 are non real cube roots of unity)1 solutions Answer 353870 by richard1234(5390)   on 2011-12-03 00:21:26 (Show Source): You can put this solution on YOUR website!If the argument of some complex number is 0, then the number must be a positive real number. Also, the numerator (z - omega) can be set to zero. We have Since we want we set .
 Triangles/540728: Calculate the area of a 30-60-90 triangle with hypotenuse equal to 10.1 solutions Answer 353866 by richard1234(5390)   on 2011-12-03 00:10:36 (Show Source): You can put this solution on YOUR website!The sides of the triangle are 5, 5sqrt(3) and 10. The area is therefore (1/2)(5)(5sqrt(3)) = (25/2)sqrt(3).
 Travel_Word_Problems/540797: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. The question is: Two cyclists, 90 miles apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet in two hours, what is the average speed of each cyclist. 1 solutions Answer 353865 by richard1234(5390)   on 2011-12-03 00:07:13 (Show Source): You can put this solution on YOUR website!If the slower cyclist traveled d miles, then the other cyclist traveled 2d. We therefore have d + 2d = 3d = 90, so d = 30, 2d = 60. Both cyclists took 2 hours to travel 30 and 60 miles respectively, so their average speeds are 15 and 30 mi/h.
 Polynomials-and-rational-expressions/540567: how can you explain the concept of rational expressions in a easier form to someone who doesnt understand?1 solutions Answer 353787 by richard1234(5390)   on 2011-12-02 15:16:22 (Show Source): You can put this solution on YOUR website!A fraction whose numerator and denominator are both polynomials.
 Surface-area/540219: Find the area of the rectangle at the right when x = 4. 1 solutions Answer 353690 by richard1234(5390)   on 2011-12-01 22:49:53 (Show Source): You can put this solution on YOUR website!What rectangle?
 Probability-and-statistics/540384: If the 100th number in the list is x,what is the 103rd number in the list?1 solutions Answer 353686 by richard1234(5390)   on 2011-12-01 22:48:04 (Show Source): You can put this solution on YOUR website!You didn't provide sufficient information about the list.
 Parallelograms/540406: A student asks whether the volume of a prism can ever be the same number as its surface area. How do you answer?1 solutions Answer 353685 by richard1234(5390)   on 2011-12-01 22:47:08 (Show Source): You can put this solution on YOUR website!Numerically, yes. A cube with side length 6 works.
 Quadratic_Equations/540071: How do I translate this into an equation that I can solve? The sum of two numbers is 50. Find the numbers such that their product is a maximum.1 solutions Answer 353592 by richard1234(5390)   on 2011-12-01 17:02:49 (Show Source): You can put this solution on YOUR website!Let a and 50-a be two numbers (their sum must be 50). You want to maximize the product a(50-a), or -a^2 + 50a. You can use calculus or the vertex of a quadratic to do this.
 Sequences-and-series/540072: What would be the next two numbers in this sequence of numbers? 2 6 9 27 30 ____ ____ I tried seeing how much the numbers increased. I added 4 + 3 + 16 + 3. This did not make sense to me. I tried even and odd. This did not make sense. I need help.1 solutions Answer 353591 by richard1234(5390)   on 2011-12-01 16:57:59 (Show Source): You can put this solution on YOUR website!Multiply by 3, add 3, multiply by 3, add 3, etc.
 Equations/539813: 64x + 5 = 133 64 * x + 5=133 64 * x +5 -133=0 64 * x + -128 64/64 64/128 x=2 I am not understanding why the 133 became a negative number nor do I understand why the answer is a positive answer. I understand how I got the answer but I am not understanding how the positive/negative works:/ Thank you in advance1 solutions Answer 353560 by richard1234(5390)   on 2011-12-01 08:30:54 (Show Source): You can put this solution on YOUR website!Because you are subtracting 133 from both sides of the equation. Alternatively, you can subtract 5 from both sides to get 64x = 133 - 5 = 128, x = 2.
 Volume/539222: how can you find out whether a contaier is a square or cylinder?1 solutions Answer 353517 by richard1234(5390)   on 2011-11-30 23:50:55 (Show Source): You can put this solution on YOUR website!Containers can't be squares. Squares are two-dimensional. If you meant "cube" or "rectangular prism" then it really depends; cubes and prisms could be defined as cylinders, but cylinders are often defined as having circular or elliptical bases.
 Probability-and-statistics/539694: I need a little boost on this one to refresh my memory! Please! A coin is weighted so that tails is twice as likely as heads to occur. What probability should we assign to heads? to tail? Thank you so much!1 solutions Answer 353514 by richard1234(5390)   on 2011-11-30 23:09:57 (Show Source): You can put this solution on YOUR website!Let the probability of obtaining a head be p. Then the probability of getting a tail is 2p. They add up to 1 (disjoint, either must happen), so p + 2p = 1, p = 1/3 and 2p = 2/3.
 Miscellaneous_Word_Problems/539695: A woman asks,"How much for one?" The Vendor says, "30 cents" The woman asks, "How much for 15?" The Vendor says, "60 cents" The woman says, "I need 615." The Vendor says, "That will be 90 cents." Show your work and explain how you solved the problem. This is on my 2nd graders homework. So far we have 1=30, 15=60, 615=90. Can anyone help us solve this?1 solutions Answer 353512 by richard1234(5390)   on 2011-11-30 23:03:22 (Show Source): You can put this solution on YOUR website!She is probably buying house numbers, birthday candles, or something else where each digit costs 30 cents.
 Subset/539701: Let A = {1, 2, 3} and B = {{1,2}, 3} then A U B IS?? 1 solutions Answer 353511 by richard1234(5390)   on 2011-11-30 23:00:00 (Show Source): You can put this solution on YOUR website!If the set {1,2} is an element of B, then A union B is {1,2,3,{1,2}}.
 Complex_Numbers/539691: Suppose z=a+bi is a complex number, and w=x+yi is another complex number such that z+w is a real number and zw is also a real number. Show that w must be the conjugate of z.1 solutions Answer 353510 by richard1234(5390)   on 2011-11-30 22:51:13 (Show Source): You can put this solution on YOUR website!If z+w is real then (here, Im(z) stands for the imaginary part of z), so b = -y. Also, if zw is real, then . We can replace y with -b. Since a = x and y = -b, z and w are conjugates of each other.
 Linear-equations/539660: What does the -.1 and -300 in the equation means P(x) =-.1x^ + 50x - 3001 solutions Answer 353500 by richard1234(5390)   on 2011-11-30 21:30:55 (Show Source): You can put this solution on YOUR website!They are simply coefficients.
 Volume/538709: The area of a circular lid to a tank is 550 sq ft. Find the radius of the lid (rounded to the nearest hundredths)1 solutions Answer 353235 by richard1234(5390)   on 2011-11-29 19:09:45 (Show Source): You can put this solution on YOUR website!We have
 Geometry_proofs/538702: how would you answer a proof if they give u a shape of a rhombus and put a number in each corner1 solutions Answer 353234 by richard1234(5390)   on 2011-11-29 19:07:24 (Show Source): You can put this solution on YOUR website!State the whole question, please. I take a rhombus and put numbers in each vertex, now what?
 Distributive-associative-commutative-properties/538699: Can you please help me to understand the associative and commutative property? 1 solutions Answer 353231 by richard1234(5390)   on 2011-11-29 19:03:59 (Show Source): You can put this solution on YOUR website!Consider a binary operation * (such as addition, subtraction, multiplication). The operation * is associative if a*(b*c) = (a*b)*c for all a,b,c. In other words, the order of which operation is done first does not matter. The operation * is commutative if a*b = b*a. This means that the order of your arguments (a,b) does not matter. Addition and multiplication are both associative and commutative. Note that associativity and commutativity are not limited to addition and multiplication (other operations, like vector dot products, are commutative).
 Functions/538280: What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance in which a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs 1 solutions Answer 353155 by richard1234(5390)   on 2011-11-29 08:37:04 (Show Source): You can put this solution on YOUR website!All linear equations are functions, except those in the form x = C (C is constant) because one of the qualifications of a function is that each x (or independent variable) map to at most one y (here, one x maps to infinitely many y). A non-linear function is simply a function that is not linear. For example, y = x^2 is non-linear.
 test/538139: Describe a situation that the expression 10n can model.1 solutions Answer 353153 by richard1234(5390)   on 2011-11-29 08:33:40 (Show Source): You can put this solution on YOUR website!For example, if a meal costs \$10, and you buy n meals,...
 Geometry_Word_Problems/538307: What is the most Geometry problems for third year first and second grading period ?1 solutions Answer 353152 by richard1234(5390)   on 2011-11-29 08:32:32 (Show Source): You can put this solution on YOUR website!What kind of geometry are you learning? And use proper grammar next time ("What are" instead of "What is").
 Graphs/537538: State the domain of the function y = 3x + 11 solutions Answer 352910 by richard1234(5390)   on 2011-11-28 00:02:21 (Show Source): You can put this solution on YOUR website!Depends on what domain you limit it to. If y maps a real number to a real number, then the domain is the set of all real numbers.
 Problems-with-consecutive-odd-even-integers/537097: what are some integer equations that equal 281 solutions Answer 352908 by richard1234(5390)   on 2011-11-27 23:56:38 (Show Source): You can put this solution on YOUR website!Ask someone what the second perfect number is; you should get 28 as an answer.
 Complex_Numbers/537309: Classify the given numbers as real and rational, real and irrational, or complex. (4)^1/2 + 21 solutions Answer 352907 by richard1234(5390)   on 2011-11-27 23:55:10 (Show Source): You can put this solution on YOUR website!Assuming (as opposed to ), this number is equal to 2+2, or 4. This is a real and rational number. Technically, it is also considered a complex number because it can be graphed on the complex plane (or written as 4+0i).
 Rational-functions/536950: If the random variable z is the standard normal score and a > 0, is it true that P(z > -a) = P(z < a)? Why or why not? 1 solutions Answer 352906 by richard1234(5390)   on 2011-11-27 23:51:36 (Show Source): You can put this solution on YOUR website!Yes, the standard normal curve is assumed to be symmetric.
 Rational-functions/537107: Given the function y=f(x), such that the entire graph of the function lies above the x-axis. Why does the equation f(x)=0 have no real solutions?1 solutions Answer 352905 by richard1234(5390)   on 2011-11-27 23:50:36 (Show Source): You can put this solution on YOUR website!Because f(x) = 0 would mean that there exists some x such that (x,0) (an x-intercept) is on the graph. Since the entire graph is above the x-axis, this is impossible.
 Polynomials-and-rational-expressions/537512: Essay. List the terms, coefficients, and degree of the following polynomial: 5x8 + 3x6 – 2x + 4/51 solutions Answer 352904 by richard1234(5390)   on 2011-11-27 23:46:28 (Show Source): You can put this solution on YOUR website!I wonder why this question intends for an essay... Terms: 5x^8, 3x^6, -2x, 4/5 Coefficients: 5, 3, -2, 4/5 Degree: 6 (highest exponent)
 Number-Line/537521: Where would 18 and 20 be on a number line between -1 and 1?1 solutions Answer 352903 by richard1234(5390)   on 2011-11-27 23:44:42 (Show Source): You can put this solution on YOUR website!Outside the boundaries.
 Miscellaneous_Word_Problems/537561: The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C=200x/500-5x What is the cost to remove 75% of the pollutant? Show how you arrived at the answer. 1 solutions Answer 352902 by richard1234(5390)   on 2011-11-27 23:39:33 (Show Source): You can put this solution on YOUR website!Replace x with 75 and simplify the expression.