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 Linear_Equations_And_Systems_Word_Problems/261381: I visited a beautiful flower garden yesterday and counted 26 flowers. Each flower was either red or yellow, and the flowers were not all the same color. My friend made the following observation: No matter which two flowers you might have picked, at least one was bound to be red. From this can you determine how many were red and how many were yellow?1 solutions Answer 192631 by solver91311(18785)   on 2010-01-26 18:03:53 (Show Source): You can put this solution on YOUR website! 25 red, 1 yellow. John
 Probability-and-statistics/261369: can 8/5 be reduced?1 solutions Answer 192619 by solver91311(18785)   on 2010-01-26 17:50:29 (Show Source): You can put this solution on YOUR website! Do 8 and 5 have any common integer factors? John
 Quadratic_Equations/261422: Maybe I'm thinking too hard. This seems easy enough but the more I think about it, the more I think I'm wrong. The question is: 'Find the equation of a quadratic function with a vertex at the point (-1,-5) that also contains the point (1,3).' My answer is (x+1)^2-5 Am I right or at least close? I don't recall doing a problem like this is class and I haven't found one like it in my textbooks. Thanks for the help guys!1 solutions Answer 192609 by solver91311(18785)   on 2010-01-26 17:28:28 (Show Source): You can put this solution on YOUR website! Not quite. Here's how I know: Substitute -1 for and evaluate: So the point (-1,-5) is on the curve. So far, so good. Now substitute 1 for for and evaluate: and that means that the point (1,3) is NOT on the graph. Back to the drawing board. You are looking for a quadratic function of the form: such that if , then and if , then . Furthermore, since (-1,-5) is specified as the vertex, the -coordinate of the vertex, namely -1, must be equal to . That gives rise to a system of three linear equations: Doing a little tidying up, we get: You should be able to take it from here. John
 Functions/261423: state the domain of the given function. thanks in advance y = x / x-11 solutions Answer 192592 by solver91311(18785)   on 2010-01-26 17:01:28 (Show Source): You can put this solution on YOUR website! The domain of a function is the set of numbers for which the function is defined. For a rational function, the domain is the set of all real numbers except any number(s) that would make a denominator equal zero. John
 Numbers_Word_Problems/261424: three numbers are consecutive even integers first integer 6 so the questionis what are the next two? I said 8 and 10 first integer is -6 need the next two first integer is -90 need the next two first integer is x was not sure if i am doing this right if you could please explain how you got your answer thank you so very much.1 solutions Answer 192589 by solver91311(18785)   on 2010-01-26 16:58:26 (Show Source): You can put this solution on YOUR website! Typically, you count UP from the first one. -6 plus 2 is -4, -4 plus 2 is -2. If your first one is , then the next one is , and the one after that is John
 Conjunction/261272: Write the argument belowin symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q you used. If the koi are swimming in the pond, then the birds are chirping. The koi are not swimming in the pond. The birds are not chirping. I am so confused and need help please.1 solutions Answer 192496 by solver91311(18785)   on 2010-01-26 12:21:21 (Show Source): You can put this solution on YOUR website! Let represent "The koi are swimming in the pond" Let represent "The birds are chirping" Then "If the koi are swimming in the pond, then the birds are chirping" can be represented by either: If then or "The koi are not swimming in the pond" is the negation of statement , or But Material Implication says that is equivalent to But since we are given , is true regardless of the value of . Therefore knowing implies nothing regarding the value of and the argument is invalid. John
 Conjunction/261207: Form the contrpositive: If I do not wash my clothes, then I will have nothing clean to wear. a) If I have nothing clean to wear, I did not wash my clothes. b) If I do not wash my clothes, then I will have something clean to wear c) If i wash my clothes, then I will have something clean to wear. d) If I have something clean to wear, I washed my clothes. e) If I have something clean to wear, I did not wash my clothes. I know b and e doesn't make sense, but the rest all look the same to me.1 solutions Answer 192494 by solver91311(18785)   on 2010-01-26 12:06:02 (Show Source): You can put this solution on YOUR website! Just follow the pattern for creating a contrapositive: Take the opposite of the conclusion and make that the new premise. The original conclusion is "I will have nothing clean to wear" The opposite of that is "I have something clean to wear" and now the premise of the contrapositive is: If I have something clean to wear. Take the opposite of the original premise and make that the new conclusion. The original premise: "If I do not wash my clothes..." The opposite: "I washed my clothes." So the entire contrapositive becomes: If I have something clean to wear, then I washed my clothes. Choice d. John
 Conjunction/261274: Given p is true, q is true, and r is false, find the truth value of the statement: ~ p (q v ~r). Please show step by step work, so I can do my other problems.1 solutions Answer 192482 by solver91311(18785)   on 2010-01-26 11:44:38 (Show Source): You can put this solution on YOUR website! It depends. Do you mean or If it is the first case, since is true, is false, so false and anything else is false, so the statement is false. In the second case, is true, is false, so is true and you have true or true which is true. Then is false as before, so you have false or true which is true. John
 Miscellaneous_Word_Problems/261279: Dawn is a sefood chef and can stuff a large party of shrimp in 6 hours. If her brother helps her, they can stuff the large party pack of shrimp in 4 hours. If Dawn gets sick, how long would it take her brother to stuff the large party of shrimp himself?1 solutions Answer 192468 by solver91311(18785)   on 2010-01-26 11:22:44 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. You are given that and that the combined time is 4, so: Solve for John
 Conjunction/261270: Determine the truth value of the following statement: Leonhard Euler was a famous mathematician and the sum of any two odd numbers is an even number. Is this true or false?1 solutions Answer 192463 by solver91311(18785)   on 2010-01-26 11:16:54 (Show Source): You can put this solution on YOUR website! In order for a statement consisting of two statements joined by "and" to be a true statement, both of the constituent statements must be true. Let us first examine the second of your two constituent statements. The -th odd number is . The -th odd number is . The sum of these two odd numbers is then: The sum is clearly divisible by 2 and is therefore an even number, hence the second part of the compound statement is true. So, it all comes down to your definition of "famous mathematician." If you believe that Herr Euler was a mathematician and that he was famous, whatever that means, then the first part of the compound statement is true. It is very possible that the statement posed is true for some people and false for others. For example, I would unhesitatingly say that the statement is true, because I believe Leonhard Euler to be not only "a" famous mathematician, but "the" famous mathematician. Other people, deplorably ignorant in my view, have never heard of him and therefore must deny the statement. John
 Distributive-associative-commutative-properties/261252: How can you remember the difference between Distributive, associative, cummutative and remember the difference between factors and terms1 solutions Answer 192456 by solver91311(18785)   on 2010-01-26 11:00:13 (Show Source): You can put this solution on YOUR website! Start with the associative property. Associate means to be together. Addition and multiplication are "binary" operations. That means you can only perform either of them on two quantities at a time. The associative property says that it doesn't matter which of several pairs of quantities you associate first, second, etc., it all comes out the same in the end. That is: and for all values of a, b, and c. Next, the commutative property. Commute means to move from one place to the other. You commute from home to school, your parents commute from home to work. The commutative property allows you to move the order of quantities you add or multiply as in: and for all values of a and b. The distributive property. Distribute means to spread around or pass around. The teacher distributes test booklets, the paperboy distributes newspapers, and so on. The distributive property allows you to distribute a factor across a set of terms. The factor a was distributed across the set of terms b plus c. A product is the result of multiplying two or more numbers called factors. Consider the number 6. It has two non-trivial factors, namely 2 and 3. Consider the number . It has factors of and . The number has 4 factors: and then three factors of Terms are numbers that are elements of a sum, that is they are the individual numbers that are added. Note that I do not include subtraction. There is no such thing as subtraction. If you want the difference of two numbers add the opposite. For example, never think of 6 - 2 as "six minus two" Rather, think of it as "six plus the opposite of two", namely 6 + (-2). In this example, 6 and -2 are terms. This is because the operation of subtraction is NOT commutative. Note that: whereas has three terms, namely , , and I also do not define division. Rather, I always multiply by the reciprocal. That is because the operation of division is not commutative. In general: However, multiplication by the reciprocal, like any other multiplication IS commutative. John
 Linear-equations/261139: How to write y-x=5 in slope intercept form1 solutions Answer 192375 by solver91311(18785)   on 2010-01-26 00:10:28 (Show Source): You can put this solution on YOUR website! Add to both sides. John
 expressions/261140: ( x- 3) + 5x - 11 how do you figure out X1 solutions Answer 192373 by solver91311(18785)   on 2010-01-26 00:08:46 (Show Source): You can put this solution on YOUR website! You don't. You don't have an equation -- there is no equal sign -- so there is no way to do anything with this other than simplify it to . John
 Equations/261118: Solve the formula for the specified variable. I=nE/nr+R Solve for n. Ok, so I know I have to get "n" to one side, but when there are no numbers involved, it's a little confusing. How do I go about solving this for n?1 solutions Answer 192372 by solver91311(18785)   on 2010-01-26 00:05:17 (Show Source): You can put this solution on YOUR website! I presume you mean: Multiply both sides by Add to both sides: Multiply by -1 Factor out an Multiply by John
 Money_Word_Problems/261062: I need help setting up this problem please. Tickets to a recital cost $2.00 for children,$5.00 for adults and $3.00 for seniors citizens. After the recital, the organizers find that 570 people attended, and$1,950 was earned from ticket sales.However,they are unable to find a record of exactly how many children,adults,and senior citizens attended. All they can find is a cryptic note from the theater manager stating that three-fourths as many senior citizens as children attended1 solutions Answer 192325 by solver91311(18785)   on 2010-01-25 21:11:38 (Show Source): You can put this solution on YOUR website! Let represent the number of children Let represent the number of adults Let represent the number of seniors We know that: We also know that: And finally we know that: Solve the system. I would use the substitution method initially to reduce the system to two equations in two variables. John
 Rectangles/261056: The perimeter of an equalateral triangle is 45 inches. A rectangle whose width is 1/3 its length has a perimeter of 48 inches. Which figure has the longest side? explain im lost1 solutions Answer 192321 by solver91311(18785)   on 2010-01-25 21:00:30 (Show Source): You can put this solution on YOUR website! An equilateral triangle has three sides of equal measure. The perimeter is the distance around the figure, so divide 45 by 3 to get the measure of one side of the equilateral triangle. A rectangle perimeter is given by: But you know that the width is one third of the length, which is to say that the length is 3 times the width, and you know the perimeter to be 48 so you can write: Solve the above for then multiply by 3 to determine the length of the rectangle. Then solve for the measure of the side of the equilateral triangle by dividing 45 by 3. Which is longer? John
 Linear-equations/261057: How do you change y+4=-3/4(x-1) to standard form?1 solutions Answer 192318 by solver91311(18785)   on 2010-01-25 20:54:50 (Show Source): You can put this solution on YOUR website! Do whatever you need to do to make it look like: I would multiply both sides by 4, distribute the -3, add 3x to both sides, then add -16 to both sides. But that's not the only way it could be done. John
 Polynomials-and-rational-expressions/261059: The office jet printer can copy Maria's dissertation in 14 minutes. The laser jet printer can copy the same document in 12 minutes. If the two machines work together how long would they take to copy the dissertation. I thought that I should do this: Office Jet = 1/14 Laser Jet = 1/12 1/14+1/12, but the result is 13/84 of a minute, I know this is not correct, can someone help me to find the correct formula please?1 solutions Answer 192316 by solver91311(18785)   on 2010-01-25 20:51:37 (Show Source): You can put this solution on YOUR website! You are soooo close. If printer A can do the whole job in 14 minutes, then it can do 1/14 of the job in 1 minute. Likewise printer B can do 1/12 of the job in 1 minute. So when you add 1/14 of the job to 1/12 of the job, you get that both machines working together can do 13/84 of the job in one minute, therefore they can go the whole job in 84/13 minutes, just under 6 and a half minutes. John
 Evaluation_Word_Problems/261060: Find sqrt( 1-a^2)x b when a = 0.28 and b = 10 I tried sqrt( 1 - (0.28)^2) x 10 = 9.6 is that right?1 solutions Answer 192313 by solver91311(18785)   on 2010-01-25 20:46:02 (Show Source): You can put this solution on YOUR website! Presuming that your represents multiplication and your is not under the square root radical, then yes, you are correct. John
 test/261034: Solve for x to the nearest tenth: 1 solutions Answer 192312 by solver91311(18785)   on 2010-01-25 20:43:25 (Show Source): You can put this solution on YOUR website! Take the natural log (or base 10 log if you like -- doesn't matter) of both sides: Use to write: Multiply both sides by Add 1 to both sides: Multiply both sides by Use to write: A little calculator work and a round-off should get you the answer you need. John
 Polynomials-and-rational-expressions/261009: I know this is a large problem,but I have no clue how to get started on it. Can someone please help me understand also? Thank you Mareellen 4. A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 12 feet across and 8 feet tall (see figure). How long should the pieces of PVC plumbing pipe be? 1 solutions Answer 192297 by solver91311(18785)   on 2010-01-25 20:10:19 (Show Source): You can put this solution on YOUR website! That is a lot of work. Write back and I'll give you a price for the entire problem with complete explanations. John
 Quadratic_Equations/260990: t^5-256t=0 I took a t out and got: t(t4-256)=0 what do i do now?1 solutions Answer 192275 by solver91311(18785)   on 2010-01-25 19:37:54 (Show Source): You can put this solution on YOUR website! Well, one of your roots is obviously . Now you can then say that: Let Then you can say: So or but since which means that or which means that Giving us the expected 5 roots for the initial quintic equation. John
 Linear-equations/260975: What is the slope of a line with the equation 4x + 12y = 6?1 solutions Answer 192266 by solver91311(18785)   on 2010-01-25 19:22:12 (Show Source): You can put this solution on YOUR website! Solve the equation for in terms of . That is, manipulate the equation so that is by itself with a coefficient of 1 on one side of the equation and everything else is on the other side. The resulting coefficient on will be the slope of the line represented by the equation. John
 Linear-systems/260987: Help !! "solve each of the equations" -2x+3y =-9 y= ?????1 solutions Answer 192263 by solver91311(18785)   on 2010-01-25 19:18:47 (Show Source): You can put this solution on YOUR website! All you can do is solve the equation for one of the variables in terms of the other. Here you are asked to solve for so: Add to both sides, then multiply both sides by John
 Rectangles/260985: The length of a rectangle is four times the width. the perimeter is ninety cm. what is the width and length.1 solutions Answer 192258 by solver91311(18785)   on 2010-01-25 19:15:17 (Show Source): You can put this solution on YOUR website! The perimeter of a rectangle is given by: But we are given that: and the perimeter is 90, so: Just solve for John
 Human-and-algebraic-language/260981: A bicyle shop has bicycles with 2 wheels and tricycles with 3 wheels. They have 15 different cycles for sale. The 15 cycles have 34 wheels. How many bicycles and tricycles does the shop have for sale?1 solutions Answer 192255 by solver91311(18785)   on 2010-01-25 19:12:13 (Show Source): You can put this solution on YOUR website! Let represent the number of 2 wheeled cycles. Let represent the number of 3 wheeled cycles. Since the shop had 15 cycles and they are all either 2 wheeled or 3 wheeled, then: The number of wheels on two-wheeled cycles must be . The number of wheels on three-wheeled cycles must be . And the sum of the wheels is 34, so: Just solve the system of equations and you have your answer. John
 Linear-equations/257091: how do you solve x-4y=81 solutions Answer 189066 by solver91311(18785)   on 2010-01-14 19:58:01 (Show Source): You can put this solution on YOUR website! You don't. If you have two variables and only one equation, then there are an infinite number of elements in the solution set. John
 Rectangles/257079: what is the width of a triangle that has a preimeter of 58 inches1 solutions Answer 189049 by solver91311(18785)   on 2010-01-14 19:30:32 (Show Source): You can put this solution on YOUR website! What do you mean by the 'width' of a triangle? Not that it makes much difference. The perimeter of a polygon is the sum of the measures of all of the sides. Unless you have some other information about the polygon, trying to determine one of the dimensions from the value of the perimeter is impossible. John
 Miscellaneous_Word_Problems/257063: please and thank you how do you solve this problem this is the problem: At Monroe High the sophomore class has 60 more students then the freshman class. the junior class has 50 fewer students then twice the students in the freshman class. the senior class is three times as large as the freshman class. if there are a total of 1,424 students at monroe high,how many students are in the freshman class? i know this is theway to solve but i have no idea how to get the answer o=f+60 j=2f-50 e=3f f+o+j+e=14241 solutions Answer 189042 by solver91311(18785)   on 2010-01-14 19:14:18 (Show Source): You can put this solution on YOUR website! You have a perfectly good beginning. Now all that you need to do is a little substitution. Since , we can write: and following the same logic, with the other two equations we can end up with: Now all you need to do is collect like terms and solve for . You then need to calculate the size of the other three classes and see if they sum to 1424 in order to check your work. John