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# Recent problems solved by 'Deina'

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 Conjunction/484722: If the argument below is valid, name which of the four valid forms of argument is represented. If it is not valid, name the fallacy that is represented. If the water is filtered, then it does not contain lead. The water does not contain lead. Therefore, the water is filtered. Would someone help me please? I'm not sure how to do this completely, because I am not good with these problems. 1 solutions Answer 331606 by Deina(147)   on 2011-08-22 23:52:17 (Show Source): You can put this solution on YOUR website!You can Google "logical fallacies" and find them in any number of places. This particular one, affirming the consequent, is in the category of "Propositional fallacies." From http://en.wikipedia.org/wiki/Affirming_the_consequent Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form: If P, then Q. Q. Therefore, P. An argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false). The name affirming the consequent derives from the premise Q, which affirms the "then" clause of the conditional premise. And bob's your uncle!
 Proportions/484745: A profit of \$2400 is to be divided among three people in a 7:3:2 ratio. How much should each person receive?1 solutions Answer 331605 by Deina(147)   on 2011-08-22 23:34:39 (Show Source): You can put this solution on YOUR website!I'm not sure about the algebraic formula for this, but it's fairly simple. 7 + 3 + 2 = 12 so 2400 / 12 = 200 7 * 200 = 1400 3 * 200 = 600 2 * 200 = 400 and bob's your uncle!
 Mixture_Word_Problems/303128: A Zantac IV has been ordered to run as 2.5 drops/min. It contains 875 mg of Zantac in a total of Zantac in a total of 250 ml. How many milligrams of Zantac will the patient recieve per hour if the set is calibrated to deliver 15 gtts/ml?1 solutions Answer 217264 by Deina(147)   on 2010-05-11 09:59:41 (Show Source): You can put this solution on YOUR website! 2.5 gtt / min = 150 gtt / hr 150 / 15 = 10 ml / hr /*********************************/ 875 mg / 250 = 3.5 mg / ml 3.5 * 10 = 35 mg / hr & bob's your uncle!
Rational-functions/303060: Will someone help me with ths last homework question? Thank you.
Divide if possible, Simplify
10a^9/2 divided by 9a^4/6
1 solutions

Answer 217225 by Deina(147)   on 2010-05-10 23:27:35 (Show Source):
You can put this solution on YOUR website!
If I understand you correctly, we are looking at:

In standard notation it would be: (10a^9/2) / (9a^4/6)
Is that correct?

If so:
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: Graphical form: simplifies to Text form: (10a^9/2)/(9a^4/6) simplifies to 10*a^(5)/3Cartoon (animation) form: For tutors: `simplify_cartoon( (10a^9/2)/(9a^4/6) )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor ,,
It becomes .

Look at .
Remove unneeded parentheses around factor ,,
It becomes .

Look at .
Factors 10 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .

Look at .
Factors 6 and 9 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Multiplied denominator integers
It becomes .

Look at .
Reduce similar several occurrences of to
It becomes .

Look at .
It becomes .
Result:

### Universal Simplifier and Solver

Done!

 Linear_Equations_And_Systems_Word_Problems/303075: use y intercept and slope to graph the line described by the equation y=2/3-11 solutions Answer 217223 by Deina(147)   on 2010-05-10 23:15:21 (Show Source): You can put this solution on YOUR website!I assume you made a typo and you meant: , didn't you? If so: and bob's your uncle!
Human-and-algebraic-language/301697: A zoo keeper has a certain number of cages and a certain number of tigers. If she puts one tiger in each cage, she has one tiger too many. If she puts two tigers in each cage she has one cage too many. How many tigers and how many cages does she have?
1 solutions

Answer 216325 by Deina(147)   on 2010-05-07 12:41:03 (Show Source):
You can put this solution on YOUR website!
Ok,
What do we know?
We have 1 more tiger than we do cages, so

We have 1 more cage than 1/2 of the number of tigers, so

 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are and which are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . Remember that the determinant of the 2x2 matrix is . If you need help with calculating the determinant of any two by two matrices, then check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Once again, remember that the determinant of the 2x2 matrix is To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other solution. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is ==================================================================================== Final Answer: So the solutions are and giving the ordered pair (3, 4) Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.

 Numbers_Word_Problems/301011: how do you solve 3K-5=7K+71 solutions Answer 215862 by Deina(147)   on 2010-05-05 18:30:10 (Show Source): You can put this solution on YOUR website! Decide which side you want to be negative (not that it matters) I'll have the variable side negative, so Subtract 7K from each side: Now we have: -4K - 5 = 7 Add 5 to each side, giving us: -4K = 12 Now, divide each side by -4: So the answer is K = -3 & bob's your uncle!
 Rectangles/301000: the perimeter of a rectangle is 64 cm. the length is 4 less than twice the width. find the length and width1 solutions Answer 215860 by Deina(147)   on 2010-05-05 18:20:12 (Show Source): You can put this solution on YOUR website!Variables Used p = perimeter l = length w = width What do we know? We know that: p = 64 cm l = 2w - 4 and finally we know that p = 2(l + w) or 2l + 2w so we will substitute 2w - 4 for l in the formula: p = 2(2w - 4) + 2w Now we will distribute: p = 4w - 8 + 2w combine like terms: p = 6w - 8 I like working on the left, so we'll flip-flop (advanced mathematical term) and replace "p" with 64: 6w - 8 = 64 Add 8 to each side: 6w = 72 divide each side by 6: so w = 12 now remember that l = 2w - 4, and substitute 12 for 'w' l = 20 Your answers are Length = 20 cm Width = 12 cm & bob's your uncle!
 real-numbers/300995: 7x+8=781 solutions Answer 215859 by Deina(147)   on 2010-05-05 18:05:06 (Show Source): You can put this solution on YOUR website!7x+8=78 Are you serious? Ok, Subtract 8 from each side: 7x = 70 divide each side by 7 x = 10 & bob's your uncle!
 Parallelograms/300676: how do you measure a parallelogram?1 solutions Answer 215708 by Deina(147)   on 2010-05-04 22:50:36 (Show Source): You can put this solution on YOUR website!It depends on the size. If it's small enough I would use a ruler, but if it's like really huge you might need a measuring tape. If it's that big a friend to hold the end of the tape would be handy, too! & bob's your uncle!
Graphs/299251: what is the solution of the following linear system?
2y + 6x = -24
y - 13x = -12
a)(0,-12)
b)none
c)(0,3)
d) infinite number of solutions
1 solutions

Answer 215105 by Deina(147)   on 2010-05-02 10:23:24 (Show Source):
You can put this solution on YOUR website!
Jim Thompson jim_thompson5910@hotmail.com wrote this great solver invoking Cramer's Rule that explains these problems extremely well!

It looks complicated, but go through it step by step, making sure you understand each step, and it's really pretty simple!
 Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are and which are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . Remember that the determinant of the 2x2 matrix is . If you need help with calculating the determinant of any two by two matrices, then check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Once again, remember that the determinant of the 2x2 matrix is To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other solution. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is ==================================================================================== Final Answer: So the solutions are and giving the ordered pair (0, -12) Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.

 Money_Word_Problems/299163: in a recent election between an incumbent and one opponent, the incumbent won by a ratio of 7 to 6. If the opponent won 30594 votes, how many votes did the incumbent win? thanks for all your help1 solutions Answer 215078 by Deina(147)   on 2010-05-02 00:49:12 (Show Source): You can put this solution on YOUR website!divide 30594 by 6 then multiply that result by 7 & bob's your uncle!
 Probability-and-statistics/299209: Select a company of your choice and collect the financial statements of that company for past 3 years.Calculate the ratios which are relevant to the working capital management of that company.1 solutions Answer 215075 by Deina(147)   on 2010-05-02 00:31:01 (Show Source): You can put this solution on YOUR website!I'll meet you half way: I'll select the company, and you collect the financial statements. Let me know when you get the past three years worth of financials for, say, Halliburton? If Halliburton is too difficult, I suppose we could settle for Blackwater. As I recall, this particular problem has popped up several times here in the past few weeks, so either it's quite a popular problem, or you've been putting off tackling it in hopes that someone else would do the work for you. Perhaps you should start on it before you lose any more time. I'm sure your professor would be happy to help you if you're having trouble understanding the assignment.
 Equations/299198: one canned juice drink is 30% orange juice; another is 10% orange juice.How many liters of each should be mixed together in order to get 20L that is 15% orange juice?1 solutions Answer 215074 by Deina(147)   on 2010-05-02 00:25:53 (Show Source): You can put this solution on YOUR website!one canned juice drink is 30% orange juice; another is 10% orange juice.How many liters of each should be mixed together in order to get 20L that is 15% orange juice? let x = number of liters of 30% juice 30x - 10x + 200 = 300 20x = 100 x = 5 5 L of 30% 15 L of 10% & bob's your uncle!
 Linear-equations/298726: what is 35x y =1751 solutions Answer 214817 by Deina(147)   on 2010-04-30 11:23:35 (Show Source): You can put this solution on YOUR website!35x y =175 Depending on your graphing software you may need to move everything but y to one side, which would give you: Then your graph would look something like: & bob's your uncle!
 Percentage-and-ratio-word-problems/298693: Write as a percent. \$108 out of \$900 was spent on textbooks.1 solutions Answer 214780 by Deina(147)   on 2010-04-30 01:12:26 (Show Source): You can put this solution on YOUR website! Multiply 0.12 * 100 to convert it to percent 12% of the \$900 was spent on books, the remainder went for pizza & beer & bob's your uncle!
 Numeric_Fractions/298654: A 2/3 cup mix of lemon juice and olive oil makes a good cleaner for wood. If 1/4 cup of the mixture is lemon juice, how much of the cleaner is olive oil?1 solutions Answer 214778 by Deina(147)   on 2010-04-30 01:08:24 (Show Source): You can put this solution on YOUR website!Total volume is cup cup of that is lemon juice, so the remainder is olive oyl. first, convert the fractions to the same denominator: 4 * 3 = 12 giving us: cups of olive oyl & bob's your uncle!
 Graphs/298678: please help graph y is = to or < -5x-5 and y = to or > x+4 the proper notation is: y <= -5x-5 and y >= x+4 1 solutions Answer 214777 by Deina(147)   on 2010-04-30 00:59:39 (Show Source): You can put this solution on YOUR website! & bob's your uncle!
 Graphs/298251: An ice cube that measures 3 centimeters on each side contains how many cubic centimeters of ice? Include correct units with your solution. 1 solutions Answer 214615 by Deina(147)   on 2010-04-29 09:28:42 (Show Source): You can put this solution on YOUR website!Find out what it means to "cube" a number & bob's your answer! Hurry, before your problem melts away!
 Surface-area/298247: Find the area of a square if one side measures 11 centimeters. Include correct units with your solution. 1 solutions Answer 214614 by Deina(147)   on 2010-04-29 09:25:44 (Show Source): You can put this solution on YOUR website!Find out what 11 cm squared is & bob's your uncle!
 Finance/298246: A train has traveled 150 miles toward its destination. This distance represents 30% of the total trip. What will the total mileage be? 1 solutions Answer 214613 by Deina(147)   on 2010-04-29 09:23:53 (Show Source): You can put this solution on YOUR website!Asked & answered. See Proportions/298232 BTW: this is not a Finance question!
 Proportions/298232: A train has traveled 150 miles toward its destination. This distance represents 30% of the total trip. What will the total mileage be?1 solutions Answer 214612 by Deina(147)   on 2010-04-29 09:19:52 (Show Source): You can put this solution on YOUR website!30% = 150 100% = x & bob's your uncle! 500 MILES Peter, Paul & Mary If you miss the train I'm on, you will know that I am gone You can hear the whistle blow a hundred miles, a hundred miles, a hundred miles, a hundred miles, a hundred miles, You can hear the whistle blow a hundred miles. Lord I'm one, Lord I'm two, Lord I'm three, Lord I'm four, Lord I'm 500 miles from my home. 500 miles, 500 miles, 500 miles, 500 miles Lord I'm five hundred miles from my home. Not a shirt on my back, not a penny to my name Lord I can't go a-home this a-way This a-away, this a-way, this a-way, this a-way, Lord I can't go a-home this a-way. If you miss the train I'm on you will know that I am gone You can hear the whistle blow a hundred miles.
 Distributive-associative-commutative-properties/298181: 35 - 15 ÷ (-5)(-3)^2 + 4 = ? PLEASE HELP FINAL EXAM NEED HELP THANKS!!!!! 1 solutions Answer 214600 by Deina(147)   on 2010-04-29 08:26:49 (Show Source): You can put this solution on YOUR website!Remember to follow the order of operations: Please Excuse My Dear Aunt Sally - PEDMAS Parenthesis Exponents Division Multiplication Addition Subtraction Then work your way from left to right & bob's your uncle!
 Finance/298144: a pharmacist mixed some 110% saline solution with some 15% saline solution to obtain 100mL of a 12% salnine solution. How much of the 10% saline solution did the pharmacist use in the mixture 1 solutions Answer 214555 by Deina(147)   on 2010-04-28 23:07:59 (Show Source): You can put this solution on YOUR website!He couldn't have used any, since there's no such thing as 110% saline. This question has already been answered at Mixture_Word_Problems/298146: & bob's your uncle!
 Mixture_Word_Problems/298146: a pharmacist mixed some 10% saline solution with some 15% saline solution to obtain 100mL of a 12% saline solution. How much of the 10% saline solution did the pharmacist use in the mixture 1 solutions Answer 214552 by Deina(147)   on 2010-04-28 23:03:36 (Show Source): You can put this solution on YOUR website!10x + 15(100-x) = 12(100) 10x + 1500 - 15x = 1200 -5x + 300 = 0 Add 5x to each side: 300 = 5x divide both sides by 5 so 60 = x x = 60 ml of the 10% solution & bob's your uncle!
 Angles/297943: What is the least common multiple of 4, 8, and 2?1 solutions Answer 214498 by Deina(147)   on 2010-04-28 18:26:24 (Show Source): You can put this solution on YOUR website!What is the smallest number that can be divided evenly by all three numbers? 2 can be divided by itself, but not by 4 or 8 4 can be divided by 2 and 4, but not 8 6 can be divided by 2, but not by 4 or 8 8 can be divided by all three, so the answer is 8 & bob's your uncle!
 Mixture_Word_Problems/297963: 5 fl. oz. of a 2% alcohol solution was mixed with 11 fl. oz. of a 66% alcohol solution. Find the concentration of the new mixture?1 solutions Answer 214496 by Deina(147)   on 2010-04-28 18:19:39 (Show Source): You can put this solution on YOUR website!5 oz + 11 oz = 16 oz 5(2) + 11(66) = 16(x) 10 + 726 = 736 = 16x 46 = x The new mixture is 16 fl oz of 46% solution & bob's your uncle!
 Linear-equations/297953: I am SO confused about my math homework. I'm in middle school and I'm working on linear equations and I am lost. This is the problem: 58.5=3.5x-6. Can you please show me the steps to understand this? THANK YOU SO MUCH!!! :)1 solutions Answer 214495 by Deina(147)   on 2010-04-28 18:11:17 (Show Source): You can put this solution on YOUR website!Linear-equations/297953 (2010-04-28 17:37:52): I am SO confused about my math homework. I'm in middle school and I'm working on linear equations and I am lost. This is the problem: 58.5=3.5x-6. Can you please show me the steps to understand this? THANK YOU SO MUCH!!! :) Ok, as far as I'm concerned, the first step is optional, but it may make it easier for you Multiply both sides by 10 to clear decimals: becomes add 60 to each side: becomes Divide both sides by 35: So, x equals (I'll let you convert it to lowest terms) (Exact answer) Or x equals 18.428571 (Approximate answer) & bob's your uncle!
 Age_Word_Problems/297903: Sofia is 5 times as old as her cousin. Four years from now she will be 3 times as old as her cousin. Whats the ages of both Sofia and her cousin?1 solutions Answer 214487 by Deina(147)   on 2010-04-28 17:44:10 (Show Source): You can put this solution on YOUR website!Variables Used S = Sarah c = cousin What do we know? We know that: S = 5c S + 4 = 3(c + 4) Substitute "5c" for S in the second equation: 5c + 4 = 3(c + 4) Distribute: 5c + 4 = 3c + 12 Subtract 3c from each side: 5c -3c + 4 = 12 Subtract 4 from each side: 2c = 8 Divide both sides by 2 and find that c = 4 Substitute "4" for "c" in the 1st equation: S = 5(4) and we find that Sarah is 20 years old and her cousin is 4 years old & bob's your uncle!
 Equations/297562: please help me solve this equation/ -3x+2=-71 solutions Answer 214269 by Deina(147)   on 2010-04-27 23:54:42 (Show Source): You can put this solution on YOUR website!-3x+2=-7 Subtract 2 from each side: -3x = -9 Divide each side by (-3): x = 3 & bob's your uncle!