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 Numeric_Fractions/576497: What is 4/5 x 5/8 in simplest form I tried making it 20/40 and making it 1/2 is that right? Help1 solutions Answer 369873 by jim_thompson5910(28550)   on 2012-02-22 17:26:58 (Show Source): You can put this solution on YOUR website!You are correct and have the correct answer of 1/2. Congratulations.
 Average/576501: 1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes? A. 5/p B. p - 5 C. p + 5 D. p/5 E. 1- p + 51 solutions Answer 369871 by jim_thompson5910(28550)   on 2012-02-22 17:23:01 (Show Source): You can put this solution on YOUR website!1 page = p minutes 1/p pages = 1 minute 1 minute = 1/p pages 5*1 minute = 5*(1/p) pages 5 minutes = 5/p pages So the answer is choice A
 Average/576506: The sales price of a car is \$12,590, which is 20% off the original price. What is the original price? A. \$14,310.40 B. \$14,990.90 C. \$15,290.70 D. \$15,737.50 E. \$16,935.801 solutions Answer 369870 by jim_thompson5910(28550)   on 2012-02-22 17:21:02 (Show Source): You can put this solution on YOUR website!Let x = original price x - 0.2x = 12590 0.8x = 12590 x = 12590/0.8 x = 15737.5 So the original price is choice D) \$15,737.50
 Volume/576466: if a cube has a side length of 1 foot, what is its capacity1 solutions Answer 369868 by jim_thompson5910(28550)   on 2012-02-22 17:16:44 (Show Source): You can put this solution on YOUR website!The capacity is 1*1*1 = 1 cubic foot
 Percentage-and-ratio-word-problems/576490: Jack never pairs his socks after doing laundry. He just throws the socks into the drawer randomly. If the drawer contains 14 white socks and 12 grey socks, what is the probability he will select a pair of grey socks when selecting two socks at random? Give your answer as a decimal rounded to the nearest thousandth. I'm absolutely lost. Thanks for the help.1 solutions Answer 369867 by jim_thompson5910(28550)   on 2012-02-22 17:14:30 (Show Source): You can put this solution on YOUR website!P(2 grey socks) = P(Grey sock AND grey sock) P(2 grey socks) = P(Grey sock)*P(grey sock) P(2 grey socks) = (12/26)*(11/25) P(2 grey socks) = 132/650 P(2 grey socks) = 0.20307 P(2 grey socks) = 0.203 So the answer is 0.203
 Percentage-and-ratio-word-problems/576493: One marble is randomly drawn and then replaced from a jar containing two white marbles and one black marble. A second marble is drawn. What is the probability of drawing a white and then a black? I'm absolutely lost. Thanks for the help!1 solutions Answer 369866 by jim_thompson5910(28550)   on 2012-02-22 17:11:47 (Show Source): You can put this solution on YOUR website!P(White then black) = P(White AND Black) P(White then black) = P(White)*P(Black) P(White then black) = (2/3)*(1/3) P(White then black) = 2/9
 Miscellaneous_Word_Problems/576473: 3(8+x)=301 solutions Answer 369864 by jim_thompson5910(28550)   on 2012-02-22 17:05:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Circles/576486: If my paper says to find the circumference of a circle whose raius is 4 inches, what do I do? I understand that you multiply the 4 by 2, but it also says to use 3.14 for pi. I do not understand what 3.14 has to do with the problem when it wants me to show the solution/formula. This is what I did: 2×4 = 8 inches1 solutions Answer 369863 by jim_thompson5910(28550)   on 2012-02-22 17:04:18 (Show Source): You can put this solution on YOUR website!Circumference: C = 2pi*r C = 2pi*r C = 2(3.14)(4) C = 25.12 So the circumference is roughly 25.12 inches.
test/576488: 6s squared- s-5 factor the trinomial
1 solutions

Answer 369861 by jim_thompson5910(28550)   on 2012-02-22 17:03:00 (Show Source):
You can put this solution on YOUR website!

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 :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

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

These factors pair up and multiply to .
1*(-30) = -30
2*(-15) = -30
3*(-10) = -30
5*(-6) = -30
(-1)*(30) = -30
(-2)*(15) = -30
(-3)*(10) = -30
(-5)*(6) = -30

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

First NumberSecond NumberSum
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=1

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

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

Answer:

So 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).

 Probability-and-statistics/576412: Please help me solve this problem: Jillene wrapped 5 gifts for her 5 cousins. If she gives them out randomly, what is the probability that every cousin gets the right present? 1 solutions Answer 369844 by jim_thompson5910(28550)   on 2012-02-22 15:39:06 (Show Source): You can put this solution on YOUR website!There are 5! = 5*4*3*2*1 = 120 different ways to hand out gifts, but only one way to hand them out such that every cousin gets the right present. So the probability is 1/120 which in decimal form is 0.00833333 (so about a 0.833% chance)
 Linear-equations/576405: I need step by step instructions on how to solve the following: x + 2y - 2z + 4w = 1 y + z - w = 4 2z + 2w = -12 3w = 6 (x,y,z,w) = ?1 solutions Answer 369838 by jim_thompson5910(28550)   on 2012-02-22 15:28:49 (Show Source): You can put this solution on YOUR website!3w = 6 w = 6/3 w = 2 -------------- 2z + 2w = -12 2z + 2(2) = -12 2z+4 = -12 2z = -12-4 2z = -16 z = -16/2 z = -8 ----------------------- y + z - w = 4 y + (-8) - 2 = 4 y - 10 = 4 y = 4 + 10 y = 14 ------------------------------------------ x + 2y - 2z + 4w = 1 x + 2(14) - 2(-8) + 4(2) = 1 x + 28 + 16 + 8 = 1 x + 52 = 1 x = 1-52 x = -51 So the solution is (-51, 14, -8, 2)
 Polynomials-and-rational-expressions/576389: I am trying to help my daughter Ember in her algebra class. 3^(10/3) change to as a radical expression? Explain. Secondly, simplify the resulting expression if possible. 1 solutions Answer 369836 by jim_thompson5910(28550)   on 2012-02-22 15:23:03 (Show Source): You can put this solution on YOUR website!Use the identity to get Optionally, you can evaluate to get 59049, which would mean that You can then further simplify to get
 Systems-of-equations/576354: 4w-2(1-w)=-381 solutions Answer 369821 by jim_thompson5910(28550)   on 2012-02-22 14:33:04 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/576305: If you could lay this out for me. solve 4k+5-2k=3k+11 solutions Answer 369794 by jim_thompson5910(28550)   on 2012-02-22 12:02:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/576152: solve 7x + 5 =21 solutions Answer 369790 by jim_thompson5910(28550)   on 2012-02-22 11:58:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Equations/576267: what are the steps for solving this type of question????? 6x-7=-7x+161 solutions Answer 369789 by jim_thompson5910(28550)   on 2012-02-22 11:49:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Equations/576272: 2( x + 4) = 301 solutions Answer 369788 by jim_thompson5910(28550)   on 2012-02-22 11:48:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/576276: x -9 = -6x + 51 solutions Answer 369787 by jim_thompson5910(28550)   on 2012-02-22 11:48:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/576290: 7x+3=3x+111 solutions Answer 369786 by jim_thompson5910(28550)   on 2012-02-22 11:47:40 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Exponents/576116: x^2-2x=1 solutions Answer 369742 by jim_thompson5910(28550)   on 2012-02-22 00:42:26 (Show Source): You can put this solution on YOUR website!x^2-2x=x(x-2)
 Money_Word_Problems/576101: deposited \$2800 in a savings account that pays you 4% annual interest. How much interest did you earn the first year? 1 solutions Answer 369741 by jim_thompson5910(28550)   on 2012-02-22 00:41:31 (Show Source): You can put this solution on YOUR website!You earned 2800*0.04 = 112 dollars in interest in the first year.
 Equations/576083: Solve -11 – (x + 30) = -41 – 2(5x – 18). 1 solutions Answer 369739 by jim_thompson5910(28550)   on 2012-02-22 00:40:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Exponents/576118: x^2 + 6x=1 solutions Answer 369738 by jim_thompson5910(28550)   on 2012-02-22 00:39:19 (Show Source): You can put this solution on YOUR website!x^2 + 6x= x(x+6)
 Numeric_Fractions/576138: what is 5% of \$3000.00 ?1 solutions Answer 369737 by jim_thompson5910(28550)   on 2012-02-22 00:38:21 (Show Source): You can put this solution on YOUR website! 5% of \$3000.00 = 0.05*3000 = 150 So 5% of \$3000.00 is \$150
 test/576108: 2|x|-4=101 solutions Answer 369724 by jim_thompson5910(28550)   on 2012-02-21 22:33:54 (Show Source): You can put this solution on YOUR website!2|x|-4=10 2|x|=10+4 2|x|=14 |x|=14/2 |x|=7 x = 7 or x = -7 So the solutions are x = 7 or x = -7
 test/576009: 3x+2=11 what's the value of x1 solutions Answer 369723 by jim_thompson5910(28550)   on 2012-02-21 22:33:02 (Show Source): You can put this solution on YOUR website!3x+2=11 3x+2-2=11-2 3x = 9 3x/3 = 9/3 x = 3 So the solution is x = 3
 Probability-and-statistics/576097: Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x 1 2 3 4 P(x) 0.01 7/12 1/12 1/4 (B) x 3 6 8 P(x) 0.24 3/5 0.135 (C) x 20 30 40 50 P(x) 0.33 0.02 -0.04 0.69 1 solutions Answer 369721 by jim_thompson5910(28550)   on 2012-02-21 22:24:24 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started A) If the sums of all the individual probabilities add to 1 and each probability is positive (and less than 1), then this is a valid probability distribution. So let's add up the individual probabilities P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) 0.01 + 7/12 + 1/12 + 1/4 0.926666667 So the probabilities all add to 0.926666667, which is NOT 1. So this is NOT a valid probability distribution.
 Probability-and-statistics/576093: 2. A hospital conducts a study of heart-attack victims entering their ER: Half of the patients are given a clot-busting drug, while the other half receive angioplasty. The survival rates are determined, and any side effects are noted. I. What is the population? II. What is the sample? III. Is the study observational or experimental? Justify your answer. IV. What are the variables? V. For each of those variables, what level of measurement (nominal, ordinal, interval, or ratio) was used to obtain data from these variables? 1 solutions Answer 369719 by jim_thompson5910(28550)   on 2012-02-21 22:13:57 (Show Source): You can put this solution on YOUR website!I. The population is the set of all heart attack victims. II. The sample is the set of patients undergoing the study. III. This is an experiment because the sample is broken up into two groups where one group is given treatment of the drug being tested (while the other is given the status quo treatment, or control treatment). IV. The variables are the survival rates and the side effects. V. Survival rates are measure in years, so this is a ratio level measurement. Side effects are a nominal measurement since they list out symptoms and such (in verbal detail).
 Linear_Algebra/576079: Please help solve the following. The instructions read "Solve each system by triangularizing the augmented matrix and using back-substitution. If the system is linearly dependent, give the solution in terms of a parameter. If the system has coincident dependence, answer in set notation. x + 3y +5z = 20 2x + 3y +4z = 16 x + 2y +3z = 12 I listed the matrix as 1 3 5 20 2 2 4 16 1 2 3 12 I used the row operation -2R1 + R2 > R2 to get the matrix to 1 3 5 20 0 -3 -6 -24 1 2 3 12 I then used row operation -1R1 + R3 > R3 to get the matrix to 1 3 5 20 0 -3 -6 -24 0 -1 -2 -8 I then used -1/3R2 + R3 > R3 to get the matrix to 1 3 5 20 0 -3 -6 -24 0 0 0 0 I know the system is linearly dependent but do understand how to solve from here. Please provide detail. Thank you. (also please let me know if I have made a mistake so far. I was given the answer of (p-4, -2P+8, p) but do not know how to come up with the answer with what I have so far.1 solutions Answer 369716 by jim_thompson5910(28550)   on 2012-02-21 22:07:37 (Show Source): You can put this solution on YOUR website!You're doing great. I'm going to finish up. Row 2 has the values 0 -3 -6 -24, which means that -3y -6z = -24. Solve for y to get -3y -6z = -24 -3y = 6z -24 y = (6z)/(-3) -24/(-3) y = -2z + 8 Now if you let z = P (ie let z be the free variable), then y = -2P + 8. So that explains why the second coordinate is -2P+8 and the third is P Now that you know that z = P and y = -2P+8, you can use this to find x in terms of the free variable P (or z). So use the first equation (you can use any equation that has x in it) x + 3y +5z = 20 x + 3(-2P+8) +5P = 20 x -6P+24 +5P = 20 x -P+24 = 20 x -P = 20-24 x -P = -4 x = P-4 So the solutions are x = P-4, y = -2P+8, and z = P which form the ordered triple (P-4, -2P+8, P)
 Graphs/576073: 3a+3-6a > 15 1 solutions Answer 369712 by jim_thompson5910(28550)   on 2012-02-21 21:53:54 (Show Source): You can put this solution on YOUR website!3a+3-6a > 15 -3a+3 > 15 -3a > 15 - 3 -3a > 12 a < 12/(-3) ... Keep in mind that the sign flips when dividing both sides by a negative number a < -4 So the solution is a < -4
 Probability-and-statistics/576057: 8.The probability function for the number of insurance policies John will sell to a customer is given by f(x) .5 - (x/6) for x = 0, 1, or 2 a.Is this a valid probability function? Explain your answer. b.What is the probability that John will sell exactly 2 policies to a customer? c.What is the probability that John will sell at least 2 policies to a customer? d.What is the expected number of policies John will sell? e.What is the variance of the number of policies John will sell? 1 solutions Answer 369711 by jim_thompson5910(28550)   on 2012-02-21 21:51:46 (Show Source): You can put this solution on YOUR website!a) It's only a valid probability function if all the individual probabilities add to one. f(0) = 0.5 - 0/6 = 0.5, so f(0) = 0.5 or f(0) = 1/2 f(1) = 0.5 - 1/6 = 1/3, so f(1) = 1/3 f(2) = 0.5 - 2/6 = 1/6, so f(2) = 1/6 Now add up the individual probabilities: f(0) + f(1) + f(2) = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = (3+2+1)/6 = 6/6 = 1 Since they all add to 1, this is a valid probability function ============================================================ b) P(X = 2) = 1/6 = 0.1667 and this was found in part a) ============================================================= c) P(At least 2) = 1 - P(None) P(At least 2) = 1 - 1/2 P(At least 2) = 1/2 P(At least 2) = 0.5 So the probability of selling at least two policies to a customer is 0.5 ( which is 50% chance) =========================================================== d) Expected number = Expected value = Sum of values*probabilities = (0)*(1/2)+(1)*(1/3)+(2)*(1/6) = 2/3 = 0.667 So the expected number is 0.667, which means that he expects to sell somewhere between 0 and one policy (with more weight/chance towards selling 1 policy) =========================================================== e) E(X^2) = Sum(X^2*probability) E(X^2) = (0^2)*(1/2) + (1^2)*(1/3) + (2^2)*(1/6) E(X^2) = 0 + 1/3 + 2/3 E(X^2) = 1 Variance sigma^2 = E(X^2) - (E(X))^2 sigma^2 = 1 - (2/3)^2 sigma^2 = 1 - 4/9 sigma^2 = 5/9 sigma^2 = 0.556 So the variance of the number of policies John will sell is roughly 0.556