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 Polynomials-and-rational-expressions/631467: completely factor the expression 4q^2+27r^4 a. 31q^2+27r^4 b. 27r^4(4q^2+1) c. 4q(q+27r) d. prime If you could please explain I would really appreciate it1 solutions Answer 397596 by jim_thompson5910(28595)   on 2012-07-24 14:28:59 (Show Source): You can put this solution on YOUR website!There are no common factors between the coefficients 4 and 27. There are also no common factors between the variables q^2 and r^4 So the GCF is 1. This means that it's trivial to factor out the GCF (since we get the same thing really after we do) Also, this is a binomial. This means that only the difference of squares rule is used to factor, but we have a sum (and not a difference) of terms. So we can't use that method either. So this expression is prime since it can't be factored. Note: you can also go through the other options and rule them out. For example, choice C) is 4q(q+27r) which distributes to 4q^2 + 108rq, which is NOT the original expression. So choice C is out. You would do the same for the other answer choices. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Polynomials-and-rational-expressions/631460: I need to FRACTOR completely. The following two problems: Problem 1) 78x^2y +48xy^2+8y^3 here is what I got ..Is it right: 72x^2y+48xy^2+8y^3 = 8y ( (3x+y) ^2) = 8y (3x+y)^2 answer: 8y(3x+y)^2 Problem 2) 18x^2-32y^2 here is what I did to this one.. 18x^2-32y^2 =2 (( 3x-4y) (3x+4y )) =2 (3x-4y) (3x+4y) sign of the term will not change. Are my solutions correct?1 solutions Answer 397592 by jim_thompson5910(28595)   on 2012-07-24 14:24:05 (Show Source): You can put this solution on YOUR website!You are 100% correct on both of them. Very nice work.
 Miscellaneous_Word_Problems/631455: Frank bought 20 pounds of sugar for $8. How many pounds of sugar did he get per dollar?1 solutions Answer 397585 by jim_thompson5910(28595) on 2012-07-24 13:50:33 (Show Source): You can put this solution on YOUR website!20 pounds/$8 = (20/8)/(8/8) = (2.5 pounds)/(1 dollar) So he got 2.5 or 2 and a half pounds of sugar per dollar. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Probability-and-statistics/631456: Given a binomial distribution with n = 21 and p = 0.77, would the normal distribution provide a reasonable approximation? Why or why not?1 solutions Answer 397583 by jim_thompson5910(28595)   on 2012-07-24 13:48:49 (Show Source): You can put this solution on YOUR website!Hint: Compute np and n(1-p) If you find that both are greater than 5, then the normal distribution provides a reasonable approximation.
 Equations/631298: 6(5y-2)+3(3+9y)1 solutions Answer 397487 by jim_thompson5910(28595)   on 2012-07-24 00:50:30 (Show Source): You can put this solution on YOUR website! So the answer is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Distributive-associative-commutative-properties/631240: Can you help me solve this question: Simplify the expressions by combining like terms -y+4y and ?1 solutions Answer 397452 by jim_thompson5910(28595)   on 2012-07-23 20:14:29 (Show Source): You can put this solution on YOUR website!-y+4y = -3y since -1+4 = -3 and because we combine like terms 3 and -7 to get 3-7 = -4 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 real-numbers/631228: How many positive integers less than 50 are multiples of 4 but not multiples of 6? I get 6, but the answer is 8. Please explain. Thank you1 solutions Answer 397447 by jim_thompson5910(28595)   on 2012-07-23 19:45:38 (Show Source): You can put this solution on YOUR website!List the positive multiples of 4 (up to 50) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 Then list the positive multiples of 6 (up to 50) 6, 12, 18, 24, 30, 36, 42, 48 ------------------------------------------------------- So go through the first list and erase any elements in that first list that also lie in the second list. So start with the first list 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 and scratch off any numbers you find in the second list (numbers like 12, 24, 36, etc) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 What's left is the following 4, 8, 16, 20, 28, 32, 40, 44 So there are 8 positive integers less than 50 that are multiples of 4 but are not multiples of 6. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
Polynomials-and-rational-expressions/631225: I need to know how to factor this Trinomial.
y^3-15y^2+54y
1 solutions

Answer 397444 by jim_thompson5910(28595)   on 2012-07-23 19:29:31 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF .

Now let's try to factor the inner expression

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Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,6,9,18,27,54
-1,-2,-3,-6,-9,-18,-27,-54

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*54 = 54
2*27 = 54
3*18 = 54
6*9 = 54
(-1)*(-54) = 54
(-2)*(-27) = 54
(-3)*(-18) = 54
(-6)*(-9) = 54

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1541+54=55
2272+27=29
3183+18=21
696+9=15
-1-54-1+(-54)=-55
-2-27-2+(-27)=-29
-3-18-3+(-18)=-21
-6-9-6+(-9)=-15

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

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So then factors further to

===============================================================

So completely factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

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If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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 Distributive-associative-commutative-properties/631220: Can you help me use the distributive property to rewrite these expressions without parentheses: (7+2y)(-3) , (-5q-7)4 , -6(s-8) , -x(x+1) , (-p+2)(-5) ?1 solutions Answer 397441 by jim_thompson5910(28595)   on 2012-07-23 19:08:15 (Show Source): You can put this solution on YOUR website!I'll do the first two to get you started # 1 So the answer is -------------------------------------------------------------------- # 2 and the answer for #2 is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 test/631214: 1 solutions Answer 397437 by jim_thompson5910(28595)   on 2012-07-23 18:55:55 (Show Source): You can put this solution on YOUR website!Problem missing. Please repost. Thanks.
 Rational-functions/631215: 4(xy-1)-(x-3)1 solutions Answer 397436 by jim_thompson5910(28595)   on 2012-07-23 18:55:40 (Show Source): You can put this solution on YOUR website! So the answer is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Rational-functions/631213: -3x(x^3+2x^2-x)1 solutions Answer 397433 by jim_thompson5910(28595)   on 2012-07-23 18:51:42 (Show Source): You can put this solution on YOUR website! So the original expression simplifies to -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Money_Word_Problems/631211: a sporting goods store has 39 bicycles. if 2/3 of this quantity are sold, how many bicycles were sold ?1 solutions Answer 397431 by jim_thompson5910(28595)   on 2012-07-23 18:43:27 (Show Source): You can put this solution on YOUR website!2/3 of 39 = (2/3)*(39) 2/3 of 39 = (2/3)*(39/1) 2/3 of 39 = (2*39)/(3*1) 2/3 of 39 = 78/3 2/3 of 39 = 78/3 2/3 of 39 = 26 So the store sold 26 bikes. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Linear-equations/631205: w y - + - = x z1 solutions Answer 397428 by jim_thompson5910(28595)   on 2012-07-23 18:22:02 (Show Source): You can put this solution on YOUR website! So the answer is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Equations/631200: c^-3d^-2/c^-4d^-5=1 solutions Answer 397427 by jim_thompson5910(28595)   on 2012-07-23 18:20:22 (Show Source): You can put this solution on YOUR website! So the answer is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Linear-equations/631204: 4x-1=3x+31 solutions Answer 397426 by jim_thompson5910(28595)   on 2012-07-23 18:18:51 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Linear-systems/631199: which of the following is not a solution to the system of linear eqautions below? 5y=3x+15 6x=10y-30 1 solutions Answer 397424 by jim_thompson5910(28595)   on 2012-07-23 17:58:09 (Show Source): You can put this solution on YOUR website!You didn't provide the answer choices. Please repost. Thanks. All you need to do is plug in the given answer choices to check them. If you get a false equation, then the ordered pair is not a solution.
 Mixture_Word_Problems/631197: the rising cost of attending college. According to College Board, the cost to attend a college or university increased by 80% from 1994 to 2012. If the cost in 2012 is estimated at $18000, find the cost in 1994.1 solutions Answer 397423 by jim_thompson5910(28595) on 2012-07-23 17:38:58 (Show Source): You can put this solution on YOUR website!Let x = cost in 1994 (in thousands of dollars) So if it costs 18 thousand dollars now (in 2012) and it has "increased by 80% from 1994 to 2012", this means that (Cost in 1994) + (80% of cost in 1994) = Cost in 2012 x + 80% of x = 18 x + 0.8x = 18 1.8x = 18 x = 18/1.8 x = 10 Remember that x is in thousands of dollars. So the average cost to attend college in 1994 is$10,000 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Mixture_Word_Problems/631193: At the 2012 State of the Union address, President Obama highlighted the rising cost of attending college. According to College Board, the cost to attend a college or university increased by 80% from 1994 to 2012. If the cost in 2012 is estimated at $18000, find the cost in 1994.1 solutions Answer 397418 by jim_thompson5910(28595) on 2012-07-23 17:36:05 (Show Source): You can put this solution on YOUR website!Let x = cost in 1994 (in thousands of dollars) So if it costs 18 thousand dollars now (in 2012) and it has "increased by 80% from 1994 to 2012", this means that (Cost in 1994) + (80% of cost in 1994) = Cost in 2012 x + 80% of x = 18 x + 0.8x = 18 1.8x = 18 x = 18/1.8 x = 10 Remember that x is in thousands of dollars. So the average cost to attend college in 1994 is$10,000 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Inequalities/631124: Please show me how to solve and write in interval notaion: 3 is < or equal to 2x-1<71 solutions Answer 397415 by jim_thompson5910(28595)   on 2012-07-23 17:31:57 (Show Source): You can put this solution on YOUR website! So the answer is which in interval notation is $\huge [2,4\left)\right.$ -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Probability-and-statistics/631182: Americans watch an average of 3.5 hours of television per person per day. If the standard deviation for the number of hours of television watched per day is 3.9 and a random sample of 266 Americans is selected, the mean of this sample belongs to a sampling distribution. (a) What is the shape of this sampling distribution? (1)skewed right normal (2)symmetrical (3)skewed left (4)uniform (b) What is the mean of this sampling distribution? (Give your answer correct to one decimal place.) (c) What is the standard deviation of this sampling distribution? (Give your answer correct to two decimal places.)1 solutions Answer 397406 by jim_thompson5910(28595)   on 2012-07-23 16:45:13 (Show Source): You can put this solution on YOUR website!(a) What is the shape of this sampling distribution? (1)skewed right normal (2)symmetrical (3)skewed left (4)uniform Answer choice marked in red. This is because the distribution will approach a normal distribution (ie become more like it) as you increase the sample size. Remember that normal distributions are symmetrical. The other choices that involved the word "skewed" are incorrect because skewed is the opposite of symmetrical. So that's out. Also, it's not uniform because the more extreme cases (eg: those who watch barely any TV or those who watch too much TV) will not have the same proportion as those who watch the average amount of TV ----------------------------------------------------------------------------------------------------------------- (b) What is the mean of this sampling distribution? (Give your answer correct to one decimal place.) The mean of the sampling distribution is equal to the population mean. So the mean of this sampling distribution is 3.5 hours. ----------------------------------------------------------------------------------------------------------------- (c) What is the standard deviation of this sampling distribution? (Give your answer correct to two decimal places.) The standard deviation of the sampling distribution with population standard deviation and size is $\LARGE \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$ Plug in and and simplify... $\LARGE \sigma_{\bar{x}} = \frac{3.9}{\sqrt{266}}$ $\LARGE \sigma_{\bar{x}} \approx \frac{3.9}{16.3095}$ $\LARGE \sigma_{\bar{x}} \approx 0.23912$ So the standard deviation of this sampling distribution is approximately 0.24 (rounded to two decimal places). -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------