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 Average/714956: the average of 85,86,87 and 82 is?1 solutions Answer 439085 by jim_thompson5910(28598)   on 2013-02-15 18:09:43 (Show Source): You can put this solution on YOUR website!Mean = (Sum of the values)/(Number of values) Mean = (85+86+87+82)/4 Mean = 340/4 Mean = 85
 Angles/714949: I want to know what property(addition, subtraction, substitution, transitive, partition) is used, if x=2 and y=5, then xy=101 solutions Answer 439084 by jim_thompson5910(28598)   on 2013-02-15 18:07:28 (Show Source): You can put this solution on YOUR website!x*y = x*y ... reflexive property (any number is ALWAYS equal to itself) x*y = 2*5 ... substitution property (ie you're replacing x with 2 and y with 5 on the right side) x*y = 10 ... multiplication So it sounds like the answer is substitution
 Parallelograms/714951: If someone draws a parallelogram and measures 120 degrees what is the measure of the three angles1 solutions Answer 439080 by jim_thompson5910(28598)   on 2013-02-15 17:59:00 (Show Source): You can put this solution on YOUR website!The adjacent angle is supplementary to the given angle. So the adjacent angle is 180 - 120 = 60 degrees The angle opposite the 120 degree angle is also 120 degrees. The angle opposite the 60 degree angle is also 60 degrees. So the four angles are: 120, 60, 120, 60 Which means that the given angle is 120, while the other 3 angles are 60, 120, 60
 Sequences-and-series/714941: study the sequence,and find the pattern.then answer the question below. 1,2,4,7,11,16,221 solutions Answer 439058 by jim_thompson5910(28598)   on 2013-02-15 17:10:24 (Show Source): You can put this solution on YOUR website!from 1 to 2 you add 1 from 2 to 4, you add 2 from 4 to 7, you add 3 from 7 to 11, you add 4 from 11 to 16, you add 5 from 16 to 22, you add 6 The values you add to jump from term to term are: 1,2,3,4,5,6 So the term would be 22+7 = 29 and the next term would be 29+8 = 37 and so on...
 Average/714927: For each of the described lines write an equation in point slope form a) passing through (3,2) with the slope 1/5 b) passing through (-12,1) with the slope -2 Can you please help me? Thanks so much in advance1 solutions Answer 439042 by jim_thompson5910(28598)   on 2013-02-15 15:59:37 (Show Source): You can put this solution on YOUR website!a) Plug in the given slope Plug in the given point the line goes through and you're done with part a) --------------------------------------------------------------------------- a) Plug in the given slope Plug in the given point the line goes through Simplify and you're done with part b) ---------------------------------------------------------------------------
 Probability-and-statistics/714861: Given: P(A) = 0.4 P(B) = 0.24 P(A ∪ B) = 0.56 Find P(A ∩ B)1 solutions Answer 439040 by jim_thompson5910(28598)   on 2013-02-15 15:45:14 (Show Source): You can put this solution on YOUR website!P(A ∩ B) = P(A) + P(B) - P(A ∪ B) P(A ∩ B) = 0.4 + 0.24 - 0.56 P(A ∩ B) = 0.08
 Linear-systems/714887: What is the equation of line as a solution for the given pair (2,10) and (1,5)1 solutions Answer 439039 by jim_thompson5910(28598)   on 2013-02-15 15:43:51 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 10 to both sides. Combine like terms. Remove the trailing zero So the equation that goes through the points and is
 test/714899: Graph equation and solve for y y=-2x+11 solutions Answer 439038 by jim_thompson5910(28598)   on 2013-02-15 15:42:44 (Show Source): You can put this solution on YOUR website!Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1 So starting at , go down 2 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Functions/714882: What is the sum of 1,605 + 1,219 + 1,119 + 1,153? 1 solutions Answer 439037 by jim_thompson5910(28598)   on 2013-02-15 15:41:37 (Show Source): You can put this solution on YOUR website!1,605 + 1,219 + 1,119 + 1,153 = 5,096
 test/714926: Write a quadratic equation that opens up and has an axis of symmetry at x=0. Thank You.1 solutions Answer 439036 by jim_thompson5910(28598)   on 2013-02-15 15:40:31 (Show Source): You can put this solution on YOUR website!Anything of the form , where is a positive number and is any real number, fits this the criteria you set. So say a = 3 and b = 5 which gives us The equation has an axis of symmetry at x=0. This is because the axis of symmetry formula is x = -b/2a, but notice how b = 0. So x = -b/2a = 0/2(3) = 0/6 = 0, which shows that x = 0 is the axis of symmetry.
 Inverses/714911: design a polygon that is not a rectangle and has an area of eight square unit. HElP ME PLEASE 1 solutions Answer 439035 by jim_thompson5910(28598)   on 2013-02-15 15:37:59 (Show Source): You can put this solution on YOUR website!Create a parallelogram (that's not a rectangle) with a base of 4 units and a height of 2 units. It will have an area of 4*2 = 8 square units.
 Polynomials-and-rational-expressions/714874: Solve the equation (x-1)(4x+3)=01 solutions Answer 439033 by jim_thompson5910(28598)   on 2013-02-15 15:36:38 (Show Source): You can put this solution on YOUR website!(x-1)(4x+3)=0 x-1=0 or 4x+3=0 x=1 or 4x=-3 x=1 or x=-3/4 The two solutions are x=1 or x=-3/4
Polynomials-and-rational-expressions/714872: Factor the trinomial completely
12x^3-15x^2-18x
1 solutions

Answer 439032 by jim_thompson5910(28598)   on 2013-02-15 15:35:39 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24

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

These factors pair up and multiply to .
1*(-24) = -24
2*(-12) = -24
3*(-8) = -24
4*(-6) = -24
(-1)*(24) = -24
(-2)*(12) = -24
(-3)*(8) = -24
(-4)*(6) = -24

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

First NumberSecond NumberSum
1-241+(-24)=-23
2-122+(-12)=-10
3-83+(-8)=-5
4-64+(-6)=-2
-124-1+24=23
-212-2+12=10
-38-3+8=5
-46-4+6=2

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).

 Permutations/714749: Write an expression. A decade is 10 years. How many years are in d decades?1 solutions Answer 438965 by jim_thompson5910(28598)   on 2013-02-15 01:16:53 (Show Source): You can put this solution on YOUR website!1 decade = 10 years d*1 decade = d*10 years d decades = 10d years So there are 10d years in d decades
 Permutations/714748: Write an expression. There are 9 T-shirts. How many T-shirts go in b boxes?1 solutions Answer 438964 by jim_thompson5910(28598)   on 2013-02-15 01:15:55 (Show Source): You can put this solution on YOUR website!The expression is Ex: say you have 3 boxes, then you would have t-shirts per box.
 Equations/714751: 7(p+3)-3p=5+6(p+5)-4p 1 solutions Answer 438963 by jim_thompson5910(28598)   on 2013-02-15 01:10:10 (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. 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
 Probability-and-statistics/714753: According to a recent study, 1 in every 6 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled 25 women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that more than 22 of the women sampled have not been the victim of domestic abuse. Would like to see the formula that gives the answer 0.1886871 solutions Answer 438959 by jim_thompson5910(28598)   on 2013-02-15 00:47:24 (Show Source): You can put this solution on YOUR website!Let X = number of women who have not been the victim of domestic abuse So each trial has a probability of 1 - 1/6 = 5/6 = 0.83333333333333 So p = 0.83333333333333 n = 25 Now compute the following probabilities P(X = 23), P(X = 24), P(X = 25) P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k) P(X = 23) = (25 C 23)*(0.83333333333333)^(23)*(1-0.83333333333333)^(25-23) P(X = 23) = (25 C 23)*(0.83333333333333)^(23)*(0.16666666666667)^(25-23) P(X = 23) = (300)*(0.83333333333333)^(23)*(0.16666666666667)^2 P(X = 23) = (300)*(0.015094938254969)*(0.0277777777777789) P(X = 23) = 0.125791152124747 P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k) P(X = 24) = (25 C 24)*(0.83333333333333)^(24)*(1-0.83333333333333)^(25-24) P(X = 24) = (25 C 24)*(0.83333333333333)^(24)*(0.16666666666667)^(25-24) P(X = 24) = (25)*(0.83333333333333)^(24)*(0.16666666666667)^1 P(X = 24) = (25)*(0.0125791152124741)*(0.16666666666667) P(X = 24) = 0.0524129800519766 P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k) P(X = 25) = (25 C 25)*(0.83333333333333)^(25)*(1-0.83333333333333)^(25-25) P(X = 25) = (25 C 25)*(0.83333333333333)^(25)*(0.16666666666667)^(25-25) P(X = 25) = (1)*(0.83333333333333)^(25)*(0.16666666666667)^0 P(X = 25) = (1)*(0.0104825960103951)*(1) P(X = 25) = 0.0104825960103951 ----------------------------------------------------------------------------------------------- To summarize, we found the following P(X = 23)= 0.125791152124747 P(X = 24)= 0.0524129800519766 P(X = 25)= 0.0104825960103951 Now add up the individual probabilities to find P(X > 22) P(X > 22) = P(X = 23)+P(X = 24)+P(X = 25) P(X > 22) = 0.125791152124747+0.0524129800519766+0.0104825960103951 P(X > 22) = 0.18868672818711 So the probability that more than 22 of the women sampled have not been the victim of domestic abuse is roughly 0.18868672818711 If you want to round to 6 decimal places, you would get 0.188687
 Linear_Equations_And_Systems_Word_Problems/714737: Highway bridges often have expansion joints- small gaps between the bridge sections-that allow for the expansion of the bridge when the weather gets hot. Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75°F and that gap increases to 1 inch when the temperature is 50°F . Assume that there is a linear relationship between the width of the gap and the temperature. 1. Write an equation that expresses the width of the gap (W) as a function of the temperature (T). I need HELP!!! Please I BEG OF U PLEASE HELP!!!1 solutions Answer 438953 by jim_thompson5910(28598)   on 2013-02-14 23:47:41 (Show Source): You can put this solution on YOUR website!Let x = gap width in inches and y = temperature in Fahrenheit "Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75°F" means x = 1/2 and y = 75 "and that gap increases to 1 inch when the temperature is 50°F " means x = 1 and y = 50 Let's find the slope of the line through these two points Slope: m = (y2 - y1)/(x2 - x1) m = (50 - 75)/(1 - 1/2) m = (-25)/(1/2) m = -50 So the slope is m = -50 Now use this to find the equation y = mx + b y = -50x + b ... plug in the slope we just found 50 = -50(1) + b ... plug in x = 1 and y = 50 50 = -50 + b 50 + 50 = b 100 = b b = 100 So the equation is y = -50x + 100 Replace x with W since x = gap and y with T because y = temp to get T = -50W + 100 Now solve for W (because we want an equation that expresses the width of the gap (W) as a function of the temperature (T)) So the final answer is
 test/714738: What does x^-1/3 simplify to?1 solutions Answer 438951 by jim_thompson5910(28598)   on 2013-02-14 23:18:07 (Show Source): You can put this solution on YOUR website!x^-1/3 = 1/(x^1/3) = 1/(cube root of x) So the answer is
 Travel_Word_Problems/714725: On a map,5 inches represents 100miles. How many inches would there be between two cities that are 2,500 miles apart?1 solutions Answer 438945 by jim_thompson5910(28598)   on 2013-02-14 22:14:55 (Show Source): You can put this solution on YOUR website!5/100 = x/2500 5*2500 = 100x 12500 = 100x 100x = 12500 x = 12500/100 x = 125 So 125 inches on the map represents 2,500 miles in real life.
 Linear_Algebra/714641: What's 5+r+71 solutions Answer 438926 by jim_thompson5910(28598)   on 2013-02-14 19:53:01 (Show Source): You can put this solution on YOUR website!The like or common terms are 5 and 7. They add to 5+7 = 12 So 5+r+7 is the same as r+12
 Expressions-with-variables/714427: please help us solve this: 5(1-3x)=-4 thanks1 solutions Answer 438798 by jim_thompson5910(28598)   on 2013-02-14 02:10:13 (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
 Expressions-with-variables/714344: My question is: Use substitution to solve this- y=2x-5 & 3y-x=5 i tried adding them together then dividing it by 2, but it came out wrong.1 solutions Answer 438778 by jim_thompson5910(28598)   on 2013-02-13 20:49:43 (Show Source): You can put this solution on YOUR website!3y-x=5 3(2x-5)-x=5 ... plug in y = 2x-5 (ie replace y with 2x-5, we can do this because y and 2x-5 are the same) 6x - 15 - x = 5 5x - 15 = 5 I'll let you finish. You need to solve that equation for x. Once you have x, you can use that value of x, along with y = 2x - 5, to find y.
 Subset/714308: I am having trouble with subsets can you help me and tell me if i am on the right track?: list all the subsets of Q={2,4,6,8,10,12} here is what I have so far: {2} {2,4} {4} {2,6} {6} {2,8} {8} {2,10} {10} {2,12} {12}1 solutions Answer 438769 by jim_thompson5910(28598)   on 2013-02-13 20:32:17 (Show Source): You can put this solution on YOUR website!List all the subsets that have 0 elements, 1 element, 2 elements, 3 elements, etc until you reach 6 like so List of Subsets with Six Elements: Empty Set {} List of Subsets with One Element: {2}, {4}, {6}, {8}, {10}, {12} List of Subsets with Two Elements: {2, 4}, {2, 6}, {2, 8}, {2, 10}, {2, 12}, {4, 6}, {4, 8}, {4, 10}, {4, 12}, {6, 8}, {6, 10}, {6, 12}, {8, 10}, {8, 12}, {10, 12} List of Subsets with Three Elements: {2, 4, 6}, {2, 4, 8}, {2, 4, 10}, {2, 4, 12}, {2, 6, 8}, {2, 6, 10}, {2, 6, 12}, {2, 8, 10}, {2, 8, 12}, {2, 10, 12}, {4, 6, 8}, {4, 6, 10}, {4, 6, 12}, {4, 8, 10}, {4, 8, 12}, {4, 10, 12}, {6, 8, 10}, {6, 8, 12}, {6, 10, 12}, {8, 10, 12} List of Subsets with Four Elements: {2, 4, 6, 8}, {2, 4, 6, 10}, {2, 4, 6, 12}, {2, 4, 8, 10}, {2, 4, 8, 12}, {2, 4, 10, 12}, {2, 6, 8, 10}, {2, 6, 8, 12}, {2, 6, 10, 12}, {2, 8, 10, 12}, {4, 6, 8, 10}, {4, 6, 8, 12}, {4, 6, 10, 12}, {4, 8, 10, 12}, {6, 8, 10, 12} List of Subsets with Five Elements: {2, 4, 6, 8, 10}, {2, 4, 6, 8, 12}, {2, 4, 6, 10, 12}, {2, 4, 8, 10, 12}, {2, 6, 8, 10, 12}, {4, 6, 8, 10, 12} List of Subsets with Six Elements: {2, 4, 6, 8, 10, 12} If you count up the individual sets, you'll find that there are 64 different sets. You can also use the formula 2^n to get 2^6 = 64 So again, there are 64 different possible subsets of {2, 4, 6, 8, 10, 12}
test/714312: Basic factoring of x^2+2x-48
1 solutions

Answer 438766 by jim_thompson5910(28598)   on 2013-02-13 20:25:08 (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 :
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48

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

These factors pair up and multiply to .
1*(-48) = -48
2*(-24) = -48
3*(-16) = -48
4*(-12) = -48
6*(-8) = -48
(-1)*(48) = -48
(-2)*(24) = -48
(-3)*(16) = -48
(-4)*(12) = -48
(-6)*(8) = -48

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

First NumberSecond NumberSum
1-481+(-48)=-47
2-242+(-24)=-22
3-163+(-16)=-13
4-124+(-12)=-8
6-86+(-8)=-2
-148-1+48=47
-224-2+24=22
-316-3+16=13
-412-4+12=8
-68-6+8=2

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

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

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).

Polynomials-and-rational-expressions/714299: I've been trying to factor this all night but cannot figure it out. Please help...16z^2-54z+35 I've tried AC=560, factors 40 and 14 but that doesn't account for the -54, it's positive 54.
1 solutions

Answer 438750 by jim_thompson5910(28598)   on 2013-02-13 19:50:55 (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 :
1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
-1,-2,-4,-5,-7,-8,-10,-14,-16,-20,-28,-35,-40,-56,-70,-80,-112,-140,-280,-560

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

These factors pair up and multiply to .
1*560 = 560
2*280 = 560
4*140 = 560
5*112 = 560
7*80 = 560
8*70 = 560
10*56 = 560
14*40 = 560
16*35 = 560
20*28 = 560
(-1)*(-560) = 560
(-2)*(-280) = 560
(-4)*(-140) = 560
(-5)*(-112) = 560
(-7)*(-80) = 560
(-8)*(-70) = 560
(-10)*(-56) = 560
(-14)*(-40) = 560
(-16)*(-35) = 560
(-20)*(-28) = 560

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

First NumberSecond NumberSum
15601+560=561
22802+280=282
41404+140=144
51125+112=117
7807+80=87
8708+70=78
105610+56=66
144014+40=54
163516+35=51
202820+28=48
-1-560-1+(-560)=-561
-2-280-2+(-280)=-282
-4-140-4+(-140)=-144
-5-112-5+(-112)=-117
-7-80-7+(-80)=-87
-8-70-8+(-70)=-78
-10-56-10+(-56)=-66
-14-40-14+(-40)=-54
-16-35-16+(-35)=-51
-20-28-20+(-28)=-48

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

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

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).

 Rational-functions/714238: Hello, I am working with functions just substituting and solving problems. The given is f(x)=5x^2+4x-3 and what I am trying to solve is f(x+1) put into the equation. I understand that to substitute the problem would be f(x+1)=5(x+1)^2+4(x+1)-3 I am just unsure of how to solve. If you could help that would be great.1 solutions Answer 438736 by jim_thompson5910(28598)   on 2013-02-13 18:06:36 (Show Source): You can put this solution on YOUR website!f(x)=5x^2+4x-3 f(x+1)=5(x+1)^2+4(x+1)-3 ... so far, so good Now you expand, distribute, and combine like terms to simplify f(x+1)=5(x+1)(x+1)+4(x+1)-3 f(x+1)=5(x^2+2x+1)+4(x+1)-3 f(x+1)=5x^2+10x+5+4x+4-3 f(x+1)=5x^2+14x+6 So the answer is f(x+1)=5x^2+14x+6
 Probability-and-statistics/714240: Without dividing find the decimal equivalent of 6/25. Explain how you found your answer1 solutions Answer 438728 by jim_thompson5910(28598)   on 2013-02-13 17:46:09 (Show Source): You can put this solution on YOUR website!Multiply top and bottom by 4 to get 24/100. Why 4? Because 25*4 = 100. So 24/100 = 0.24 because 0.24 means 24 hundredths (ie 24 out of a 100) So 6/25 = 0.24
 Polynomials-and-rational-expressions/714242: What is (4r+s)+(8-2s)?1 solutions Answer 438727 by jim_thompson5910(28598)   on 2013-02-13 17:44:55 (Show Source): You can put this solution on YOUR website!(4r+s)+(8-2s) 4r+s+8-2s 4r-s+8
 Linear-systems/714193: Using linear combinations, how would you solve: m+3n=2 -m+2n=31 solutions Answer 438724 by jim_thompson5910(28598)   on 2013-02-13 16:42:29 (Show Source): You can put this solution on YOUR website!Add the equations to get m+3n=2 -m+2n=3 -------- 0m+5n=5 5n = 5 n = 5/5 n = 1 Now use this to find m m+3n=2 m+3(1)=2 m + 3 = 2 m = 2 - 3 m = -1 So the solutions are m = -1 and n = 1