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# Recent problems solved by 'richard1234'

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 Probability-and-statistics/567216: A contestant correctly answered 9 of 12 questions correctly. Find the probability of the contestant answering the next question correctly1 solutions Answer 366469 by richard1234(5390)   on 2012-02-02 23:19:58 (Show Source): You can put this solution on YOUR website!Empirical probability would be 9/12 or .75, but the actual probability could be anything between 0 and 1.
 Triangles/566996: If a triangle has a 3 inch side on each side is is a triangle?1 solutions Answer 366468 by richard1234(5390)   on 2012-02-02 23:19:04 (Show Source): You can put this solution on YOUR website!I agree with the other tutor, read your post again. If that second "is" should be "it" then it doesn't take much to determine whether it is a triangle.
 Radicals/566930: Please help me solve this equation:. what i have tried is squaring both sides to where i get the i subtracted the the answer i got was but my teacher said it was wrong he has said the correct answer is what did i do wrong?1 solutions Answer 366464 by richard1234(5390)   on 2012-02-02 23:07:27 (Show Source): You can put this solution on YOUR website!How'd you get x=20 from x^2 - x = 20? You should also subtract the 20, so your equation will look something like , this factors to , so x = 5 or x = -4. Since we have a square root, we should check to make sure our solutions actually work. x = 5 definitely works, x = -4 probably won't since the square root usually denotes only the positive root. The solution 13/12 is wrong.
 Geometry_proofs/567032: how can you write an indirect proof that two obtuse angles cannot form a linear pair?1 solutions Answer 366462 by richard1234(5390)   on 2012-02-02 23:02:43 (Show Source): You can put this solution on YOUR website!Assume that they do form a linear pair. Since both angles' measures are greater than 90 deg, then their sum must be greater than 180 deg. However, angles form a linear pair if and only if their sum is 180 deg, so contradiction.
 Square-cubic-other-roots/567207: in the problem 3m^5-3m why is the answer 3m(m^2+1)(m+1)(m-1) instead of 3m(m+1)(m+1)(m+1)(m-1) ? I can not find any reason to have descending powers in factoring the difference of two squares??1 solutions Answer 366461 by richard1234(5390)   on 2012-02-02 23:00:09 (Show Source): You can put this solution on YOUR website! You must have factored m^2 + 1 as (m+1)(m+1), which is incorrect. m^2 + 1 can't be factored into polynomials with real coefficients.
 Geometry_proofs/567088: Proof the given is angel one and angel two are right angels prove that angel one is congruent To angel two in no less than four steps1 solutions Answer 366460 by richard1234(5390)   on 2012-02-02 22:57:12 (Show Source): You can put this solution on YOUR website!If you want answers for questions about angels, consult your local church or clergy or read the Bible or something. You want "angles" instead. If angles 1 and 2 are right angles, then they must have the same degree (or radian) measure, therefore they are congruent.
 Polynomials-and-rational-expressions/567111: How do you divide and multiply and divide rational expressions? Can you explain it to me in the simplest way possible? 1 solutions Answer 366459 by richard1234(5390)   on 2012-02-02 22:54:17 (Show Source): You can put this solution on YOUR website!It's very similar to multiplying/dividing fractions, that's all you really need to know. Make sure you can multiply polynomials correctly.
 Inequalities/567200: how do i solve the inequality x^2x-15<0 algebraically1 solutions Answer 366458 by richard1234(5390)   on 2012-02-02 22:53:00 (Show Source): You can put this solution on YOUR website!Do you mean (which cannot really be solved algebraically), or , or or even ? Make sure you check for errors or ambiguities before you post.
 Miscellaneous_Word_Problems/566955: Explain how you know a triangle can have side lengths measuring 11, 15 and 21.1 solutions Answer 366457 by richard1234(5390)   on 2012-02-02 22:50:34 (Show Source): You can put this solution on YOUR website!Three positive numbers will uniquely determine a triangle (provided that they satisfy the triangle inequality, which they do in this case).
 absolute-value/567162: If you have a problem like |x-2| + 3 = 5 you would solve it with a positive and negative equation changing the signs of both the 5 and the 3. If you had an inequality |x-2| + 3 > 5 your positive and negative equations would not include changing the sign of the 3. Why is that? |x-2| + 3 = 5 x + 1 = 5 x=4 |x-2| - 3 = -5 x - 5 = -5 x=0 |x-2| + 3 > 5 x + 1 > 5 x>4 |x-2| + 3 < -5 x + 1 < -5 x<-61 solutions Answer 366455 by richard1234(5390)   on 2012-02-02 22:48:20 (Show Source): You can put this solution on YOUR website!I don't know, your solution is a bit flawed. You can't really say that |x-2| + 3 is always equal to x+1, since there are negative solutions involved too. You should move the 3 to the RHS first: Now we can take positive and negative solutions: or , this yields x=4 and x=0. Here, you would change the sign of the 3, but I wouldn't do that; you're more likely to make a mistake this way. For the inequality, we have , this can either be or (since we can have a negative solution -x-2 > 2, multiplying by -1 reverses the direction of the inequality). The solutions are x > 4 and x < 0.
 Exponents/567073: im knew to algebra, and i don't know how to attack it, do u think u can help me out. 1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number? A. ZY - V B. Z/V - 3 - Y C. Z/3 - V - Y D. 3V- Z - Y E. V- Z - Y 1 solutions Answer 366452 by richard1234(5390)   on 2012-02-02 22:41:29 (Show Source): You can put this solution on YOUR website!Let X be the remaining number. Since the average of X,Y,Z is V, we have Subtract Y+Z from both sides to isolate X. This is the same as answer choice D.
 Probability-and-statistics/567102: A student is to select 3 classes for next semester. If this student decides to randomly select one course from each of 5 economics classes, 9 math classes, and 5 conputer classes, how many sifferent outcomes are possible. Please explain.1 solutions Answer 366451 by richard1234(5390)   on 2012-02-02 22:39:37 (Show Source): You can put this solution on YOUR website!5 choices for the first class, 9 choices for the second class, 5 for the third. Number of outcomes = 5*9*5 = 225
 Geometry_proofs/567156: How would you solve this? I'm in ninth grade in Geometry 1 Honors: "Find the sum of the first 80 odd integers. Make your own term and value chart. Label the top row, 'number of odd integers' and the bottom 'Sum'.1 solutions Answer 366443 by richard1234(5390)   on 2012-02-02 22:04:51 (Show Source): You can put this solution on YOUR website!Let S_n be the sum of the first n odd (positive) integers (e.g. S_n = 1+3+...+(2n-1)) n---S_n 1 1 2 4 3 9 4 16 k k^2 80 80^2 = 6400 It can be proved using induction that the sum of the first k odd integers is k^2.
 Sequences-and-series/566625: Given the sequence 1331, 1000, 729, x, y, z, 125, . . . , what is the sum of x, y, z? Please show me the steps.1 solutions Answer 366310 by richard1234(5390)   on 2012-02-02 08:37:42 (Show Source): You can put this solution on YOUR website!1331 = 11^3 1000 = 10^3 729 = 9^3 . . . 125 = 5^3 Therefore, x,y,z = 8^3, 7^3, 6^3 or 512, 343, 216. Their sum is 512+343+216 = 1071.
 Probability-and-statistics/566380: If you have 12 $1.00 bills, 5$2.00 bills, 2 $20.00 bills, and 1$50.00, make a probability distribution table and find the expected value.1 solutions Answer 366226 by richard1234(5390)   on 2012-02-01 21:09:09 (Show Source): You can put this solution on YOUR website!20 bills in total $1--12/20$2--5/20 $20-2/20$50-1/20
 Surface-area/566449: how do i find the surface area of prisms and pyramids?1 solutions Answer 366225 by richard1234(5390)   on 2012-02-01 21:05:26 (Show Source): You can put this solution on YOUR website!Find the sum of the areas of the faces; add them up.
 Numbers_Word_Problems/566491: GIVEN THIS CONJECTURE; ANY TWO CONSECUTIVE SQUARE NUMBERS IS AN EVEN NUMBER. FIND THE COUNTER EXAMPLE1 solutions Answer 366224 by richard1234(5390)   on 2012-02-01 21:03:27 (Show Source): You can put this solution on YOUR website!You shouldn't type in all caps. Also, your question is ambiguous; "any two consecutive square numbers" cannot be one even number. If you stated something like "Any two consecutive square numbers *are* even numbers" then there would be infinitely many counterexamples (since the statement cannot be true), e.g. 4 and 9.
 Travel_Word_Problems/566382: what is an object's change in position relative to a reference point called1 solutions Answer 366223 by richard1234(5390)   on 2012-02-01 20:59:11 (Show Source): You can put this solution on YOUR website!Displacement Note that distance is not the same thing as displacement, as distance represents the total distance travelled by a path, while displacement represents only the change in position (e.g. the shortest possible distance between two points).
 Divisibility_and_Prime_Numbers/566460: Hey I am having problems with this just Prime Numbers what are all the prime numbers?1 solutions Answer 366221 by richard1234(5390)   on 2012-02-01 20:57:02 (Show Source): You can put this solution on YOUR website!Any integer greater than 1 that is only divisible by 1 and itself. E.g. 2, 3, 5, 7, 11, 13, 17, ..., infinitely many primes.
 test/566475: What is the slope of the line that passes through the pair of points? Do not include fractions or decals in your slope. 7/8,-2/9),(7/10,-2)1 solutions Answer 366220 by richard1234(5390)   on 2012-02-01 20:55:51 (Show Source): You can put this solution on YOUR website! Who said that the slope cannot contain fractions or decimals? I'll let you figure out a way to write 640/63 without using fractions/decimals.
 Sequences-and-series/566162: The question is: what is the sum of 4+11+18+....+4001 I have been taught to add the first and last number, so i get 4005. Then I usually divide by half of the last number, which would be 2000.5 However, I know this only works if the numbers go up by one, not seven. This is where I get lost.1 solutions Answer 366160 by richard1234(5390)   on 2012-02-01 16:11:31 (Show Source): You can put this solution on YOUR website!Let S = the sum you want. Then, we have S = 4 + 11+18+...+4001 S = 4001+3994 + ... + 4 If we add them up, we get 2S = 4005 + 4005 + ... + 4005. Now we have to count the number of "4005s" there are, which is equal to the size of the set {4, 11, 18, ..., 4001}. This is equal to the size of the sets {7, 14, 21, ..., 4004} and {1, 2, 3, ..., 572} (we are just adding or multiplying numbers in the sets by a fixed number; this does not change the size of the set). Therefore, there are 572 "4005s." Hence, 2S = 572*4005, S = 572*4005/2 = 1145430.
 Linear-equations/566239: y=5+3x (1,8)1 solutions Answer 366159 by richard1234(5390)   on 2012-02-01 16:06:43 (Show Source): You can put this solution on YOUR website!What do you want to do with that? (1,8) lies on the line y=5+3x.
 Linear-systems/566238: trying to figure out the problem for the solution 3h +4t =12. I have no idea how to figure this out. the teacher said to make your best attempt but I don't even know where to begin.1 solutions Answer 366157 by richard1234(5390)   on 2012-02-01 16:04:36 (Show Source): You can put this solution on YOUR website!3h+4t = 12 cannot be solved for a unique solution because you have two variables and one equation, and this will yield infinitely many solutions. You can, however, solve for each variable. Suppose we want to solve for h. Then, Similarly, if we want to solve for t,
 Proofs/566235: Prove that the sum of any pair of rational numbers is a rational number.1 solutions Answer 366155 by richard1234(5390)   on 2012-02-01 16:02:30 (Show Source): You can put this solution on YOUR website!Let and be two rational numbers, where a,b,c,d are integers. Then, Since integers are closed under addition and multiplication, the numerator and denominator will both be integers. Hence, the sum of two rational numbers is a rational number. We can also say that rational numbers are closed under addition.
 Functions/565931: give an example of three f,g, and h (none of which is a constant function) such that fog=foh, but g is not equal to h.1 solutions Answer 366021 by richard1234(5390)   on 2012-01-31 23:22:00 (Show Source): You can put this solution on YOUR website!Let f(x) = x^2 g(x) = x h(x) = -x Then f(g(x)) = x^2 and f(h(x)) = (-x)^2 = x^2.
 Functions/565454: HOW DO YOU DETERMINE THE TURNING POINTS OF A GRAPH GIVEN THE FUNCTION: F(X)=2(X-3)(X^2+4)^3 1 solutions Answer 366020 by richard1234(5390)   on 2012-01-31 23:20:54 (Show Source): You can put this solution on YOUR website!Take the derivative of f with respect to x (I used the product rule): Set it equal to zero and find all real x that satisfy. Once you have done this, check to make sure that the sign of f'(x) actually changes.
 Word_Problems_With_Coins/565611: what 4 coins make 90 cents1 solutions Answer 366019 by richard1234(5390)   on 2012-01-31 23:16:50 (Show Source): You can put this solution on YOUR website!half dollar, quarter, dime, nickel
 Polynomials-and-rational-expressions/565600: Essay: Show all work. The area of a rectangular swimming pool is given by . One side length of the pool is given by 2x + 5 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer.1 solutions Answer 366018 by richard1234(5390)   on 2012-01-31 23:16:13 (Show Source): You can put this solution on YOUR website!What is the area of the swimming pool? You didn't post that.
 Geometry_proofs/565708: Two circles meet at points P and Q, and diameters P A and P B are drawn. Show that the line AB goes through the point Q. (Probably it is easier to think of drawing the lines AQ and QB and then showing that they are actually the same line.)1 solutions Answer 366017 by richard1234(5390)   on 2012-01-31 23:15:06 (Show Source): You can put this solution on YOUR website! The easiest solution is probably to draw the segment connecting the centers of the circles (denote Y,Z), as well as segment PQ: Since PY = (1/2)PA and PZ = (1/2)PB, triangles YPZ and APB are similar with a 1:2 ratio. Additionally, PR = (1/2)PQ (this can be proven by symmetry). Since R lies on YZ, Q must lie on AB. Or, another way you can prove it is show that the pairs of triangles PRY/PQA and PRZ/PQB are similar. Then, you may let angle PRY = m, angle PQA = m, it follows that angle PRZ = angle PQB = 180-m. Hence, angles PQA + PQB = 180, so A,Q,B are collinear.
 Equations/565743: m + 5=m-3 my sons homework cant help him out or find a page that will show how to find the answer1 solutions Answer 366014 by richard1234(5390)   on 2012-01-31 22:47:11 (Show Source): You can put this solution on YOUR website!No solutions. If there is a solution, then you can subtract m from both sides to obtain 5 = -3, which is obviously not true.
 Complex_Numbers/565901: x+5=12 How do i solve this?1 solutions Answer 366013 by richard1234(5390)   on 2012-01-31 22:42:19 (Show Source): You can put this solution on YOUR website!Subtract 5 from both sides of equation x = 7