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 expressions/639953: How to solve the following: 3x-y =7 when y=2x-4 Thank you1 solutions Answer 402961 by jim_thompson5910(28476)   on 2012-08-22 13:35:01 (Show Source): You can put this solution on YOUR website!Hint: Since y = 2x-4, you can replace the y in the first equation with 2x-4 3x-y =7 3x-(y) =7 3x-(y) =7 3x-(2x-4) =7 3x-(2x-4) = 7 I'll let you take it from here.
 Polynomials-and-rational-expressions/639844: I hope this is the right section. How would I factor x^2 -y^2 +x -y? The answer is (x-y)(x+y+1) However I get 4(y+x)(y-x)(x-1) when I try.1 solutions Answer 402886 by jim_thompson5910(28476)   on 2012-08-22 00:55:52 (Show Source): You can put this solution on YOUR website! So the answer is
 Probability-and-statistics/639646: .... A study is conducted to determine if adults over 50 years old with higher total cholesterol levels are more hostile than those with lower cholesterol levels. A group of 100 adults is randomly selected and their level of hostility as well as their cholesterol levels is recorded. 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 402857 by jim_thompson5910(28476)   on 2012-08-21 20:16:29 (Show Source): You can put this solution on YOUR website!I. What is the population? The set of all 50 year old adults. ------------------------------------------------------- II. What is the sample? The 100 people randomly selected (from the population) for this study ------------------------------------------------------- III. Is the study observational or experimental? Justify your answer. It's an observation because the researchers are simply looking at data and they are NOT manipulating the subjects in any way. They are also NOT splitting the subjects into two groups (the control and experimental group. ------------------------------------------------------- IV. What are the variables? The variables are cholesterol level and hostility level. ------------------------------------------------------- V. For each of those variables, what level of measurement (nominal, ordinal, interval, or ratio) was used to obtain data from these variables? Cholesterol Level: Ratio (since they can be ordered, the differences make sense, and there's a 0) Hostility Level: Ordinal (assuming you have something like "not hostile", "somewhat hostile" and "very hostile")
 Equations/639641: Find an equation of the line containing the given pair of points. (2,1) and (6,4)1 solutions Answer 402841 by jim_thompson5910(28476)   on 2012-08-21 18:08:44 (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 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 1 to both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is
 test/639642: S=a/(1-r)1 solutions Answer 402838 by jim_thompson5910(28476)   on 2012-08-21 18:04:15 (Show Source): You can put this solution on YOUR website!What do you want to do here?
 test/639614: If y = 1, then (x+5)•y=x+5. Which property supports this statement?1 solutions Answer 402836 by jim_thompson5910(28476)   on 2012-08-21 17:32:17 (Show Source): You can put this solution on YOUR website!(x+5)•y=x+5 (x+5)•1=x+5 x+5 = x+5 We're using the multiplicative identity property to go from step 2 to step 3
 Polynomials-and-rational-expressions/639585: 3a-3a^21 solutions Answer 402818 by jim_thompson5910(28476)   on 2012-08-21 16:34:54 (Show Source): You can put this solution on YOUR website!If you want to factor, then
 Square-cubic-other-roots/639577: what is the approximate side lenght of a tabletop with an area of 25ftsq1 solutions Answer 402812 by jim_thompson5910(28476)   on 2012-08-21 16:27:30 (Show Source): You can put this solution on YOUR website!If this table is a square, then the side length is sqrt(25) = 5 feet If it's a rectangle, then it could be a number of side lengths (ex: 1*25, 2*12.5, ... etc etc)
 Complex_Numbers/639579: How do you solve; i^49 ?1 solutions Answer 402809 by jim_thompson5910(28476)   on 2012-08-21 16:24:02 (Show Source): You can put this solution on YOUR website! So
 Functions/639388: Given that a(x)=x^2-5 and b(x)=6x+1 Evaluate (aob)(x) and (boa)(x) I understand that this is (fog)(x) and (gof)(x) So a(b(x)) is how I should insert the functions, but I'm not sure if I'm doing it right? Please help, Thank You1 solutions Answer 402716 by jim_thompson5910(28476)   on 2012-08-21 00:29:04 (Show Source): You can put this solution on YOUR website!The idea is to start with the outer function first. Then replace the input with the inner function. a(x) = x^2-5 a(b(x)) = (b(x))^2-5 ... Replace ALL 'x' terms with b(x) a(b(x)) = (6x+1)^2-5 ... Replace b(x) on the right side with 6x+1 (since b(x) = 6x+1) I'll let you expand and simplify this. ------------------------------------------------------- Now we reverse what we just did b(x)=6x+1 b(a(x))=6(a(x))+1 b(a(x))=6(x^2-5)+1 I'll let you simplify.
 Length-and-distance/639380: if 2x-10=20, then x-5=1 solutions Answer 402713 by jim_thompson5910(28476)   on 2012-08-20 23:43:07 (Show Source): You can put this solution on YOUR website! So the answer is 10
 Sequences-and-series/639363: Solve for the next two numbers in the following number sequence: 1728, 1000, 512, 216, _, _.1 solutions Answer 402710 by jim_thompson5910(28476)   on 2012-08-20 23:39:57 (Show Source): You can put this solution on YOUR website!Each number is a perfect cube. Notice how 12^3 = 1728, 1000 = 10^3, 512 = 8^3, 216 = 6^3 So the form is n^3 where 'n' is some integer. But we're only focusing on positive even integers and we're counting down to the next even integer each time. Moreover, we're starting at 12. So 'n' becomes -2n+12 where n starts at n = 0. If you want to start at n = 1, then you have to add 2 to 12 to get -2n+14 So the sequence follows the form (-2n+14)^3 where n is a positive integer and n starts at n = 1 We can see that when n = 1, (-2n+14)^3 = (-2*1+14)^3 = 1728 When n = 2, (-2n+14)^3 = (-2*2+14)^3 = 1000 etc etc all the way up to n = 4, (-2n+14)^3 = (-2*4+14)^3 = 216 The next two terms are n = 5, (-2n+14)^3 = (-2*5+14)^3 = 64 and n = 6, (-2n+14)^3 = (-2*6+14)^3 = 8 ======================================================= Answer: So the updated sequence is 1728, 1000, 512, 216, _64_, _8_
 test/639359: How do I solve this problem: 24-6x^2/2 The ^2 means squared1 solutions Answer 402703 by jim_thompson5910(28476)   on 2012-08-20 22:28:30 (Show Source): You can put this solution on YOUR website! So simplifies to
 test/639354: 18y+5(7+3y) solve please. I'm trying to remember so I can help my 7th grade daughter out.1 solutions Answer 402702 by jim_thompson5910(28476)   on 2012-08-20 22:14:16 (Show Source): You can put this solution on YOUR website!18y+5(7+3y) 18y+5(7)+5(3y) 18y+35+15y 33y+35 So 18y+5(7+3y) simplifies to 33y+35
 Functions/639319: State f(x) and g(x) for which f(x)*g(x)=2x^2+11x-6. How do you go about doing this problem? Thank you!1 solutions Answer 402690 by jim_thompson5910(28476)   on 2012-08-20 21:06:24 (Show Source): You can put this solution on YOUR website!Hint: Factor 2x^2+11x-6 You do this by multiplying 2 and -6 to get -12. Then you find two numbers that multiply to -12 and add to 11. These two numbers are 12 and -1 So 2x^2+11x-6 2x^2+12x-x-6 Now factor by grouping
 Geometry_Word_Problems/639244: How do I find the perimeter of a rectangle with an area of 378 square feet? I know Perimeter is P=2(L+W), but I don't know where to begin to figure out my length & width. Thank you 1 solutions Answer 402686 by jim_thompson5910(28476)   on 2012-08-20 20:53:26 (Show Source): You can put this solution on YOUR website!You know that A = LW 378 = LW But you need more information that connects L and W to find the perimeter.
 real-numbers/639252: is -9/3 a natural whole interger rational or irrational number?1 solutions Answer 402685 by jim_thompson5910(28476)   on 2012-08-20 20:52:18 (Show Source): You can put this solution on YOUR website!-9/3 is a rational number since it is a fraction of two integers.
 real-numbers/639247: I have a fraction which is 9/16 and both of the numbers have the square root sign. can you tell me whether its natural whole interger rational or irrational?1 solutions Answer 402684 by jim_thompson5910(28476)   on 2012-08-20 20:51:46 (Show Source): You can put this solution on YOUR website!, which means that this number is a rational number (since it is a ratio or fraction of two integers).
 test/639228: F(5)1 solutions Answer 402649 by jim_thompson5910(28476)   on 2012-08-20 18:34:28 (Show Source): You can put this solution on YOUR website!You're missing the function.
 real-numbers/639225: is the square root of 11 a natural whole interger rational or irrational number?1 solutions Answer 402647 by jim_thompson5910(28476)   on 2012-08-20 18:33:28 (Show Source): You can put this solution on YOUR website!You CANNOT write 11 in the form of where 'x' is some integer. So it is an irrational number You can see this because approximately, and the decimal digits go on forever without repeating a specific pattern.
 real-numbers/639224: is the square root of 81 a natural whole interger rational or irration number?1 solutions Answer 402646 by jim_thompson5910(28476)   on 2012-08-20 18:29:02 (Show Source): You can put this solution on YOUR website!, which makes it a natural number, whole number, integer, and a rational number.
 Graphs/639213: how do you solve y-13<2 ?1 solutions Answer 402645 by jim_thompson5910(28476)   on 2012-08-20 18:14:03 (Show Source): You can put this solution on YOUR website!Add 13 to both sides to get y-13<2 y-13+13<2+13 y < 15
 Rational-functions/639208: What is the simple expression for 5(3•5-4)1 solutions Answer 402641 by jim_thompson5910(28476)   on 2012-08-20 18:11:45 (Show Source): You can put this solution on YOUR website!5(3•5-4) 5(15-4) 5(11) 55 So 5(3•5-4) = 55
 real-numbers/639209: is the fraction -2/5 a natural whole interger rational or irrational number?1 solutions Answer 402640 by jim_thompson5910(28476)   on 2012-08-20 18:07:30 (Show Source): You can put this solution on YOUR website!-2/5 is a rational number since it is a fraction of two integers.
 Exponents/639206: (3^-1-3^3)^21 solutions Answer 402638 by jim_thompson5910(28476)   on 2012-08-20 18:01:00 (Show Source): You can put this solution on YOUR website!(3^-1-3^3)^2 (1/3^1-3^3)^2 (1/3-3^3)^2 (1/3-27)^2 (1/3-81/3)^2 (-80/3)^2 ((-80)^2)/3^2 6400/9 So (3^-1-3^3)^2 = 6400/9
 Numeric_Fractions/639193: I don't know how to solve: 3/4 - 1/2 I'd like to know how to solve that. 1 solutions Answer 402630 by jim_thompson5910(28476)   on 2012-08-20 17:33:04 (Show Source): You can put this solution on YOUR website!3/4 - 1/2 3/4 - (1/2)(2/2) 3/4 - 2/4 (3-2)/4 1/4 ------------------------------------------------------- Answer: 3/4 - 1/2 = 1/4
 Equations/639197: blank + blank + blank = 21 lb. How do I solve?1 solutions Answer 402627 by jim_thompson5910(28476)   on 2012-08-20 17:31:53 (Show Source): You can put this solution on YOUR website!x+x+x = 21 3x = 21 x = 21/3 x = 7 So 7+7+7 = 21
 Equations/639200: how to show the work to this problem 9/5 x 8/31 solutions Answer 402626 by jim_thompson5910(28476)   on 2012-08-20 17:30:53 (Show Source): You can put this solution on YOUR website!9/5 x 8/3 (9*8)/(5*3) 72/15 24/5 ------------------------------------------------------- So 9/5 x 8/3 simplifies to 24/5
 test/639189: 3(s-t)21 solutions Answer 402617 by jim_thompson5910(28476)   on 2012-08-20 17:06:48 (Show Source): You can put this solution on YOUR website!3(s-t)^2 3(s-t)(s-t) 3(s(s-t)-t(s-t)) 3(s^2-st-ts-t^2) 3(s^2-st-st-t^2) 3(s^2-2st-t^2) 3s^2-6st-3t^2 So 3(s-t)^2 simplifies to 3s^2-6st-3t^2
 Sequences-and-series/639183: Find a set of at least 5 data values that has a mean of 20 and a standard deviation of 6.1 solutions Answer 402616 by jim_thompson5910(28476)   on 2012-08-20 17:05:18 (Show Source): You can put this solution on YOUR website!Start with the set 20,20,20,20,20 That has a mean of 20, but a standard deviation of 0. Then increase one value to get 21, but decrease another value (to balance things out) to get 19. So we might have 19, 20, 20, 20, 21 Now find the standard deviation. It will be roughly 0.70710678 (use a calculator here). Repeat the last 3 steps to find another standard deviation. We can keep going and do this by trial and error, but there's a much easier way This way involves using the definition of sample standard deviation. sigma = sqrt(sum((x-mu)^2)/(n-1)) 6 = sqrt(sum((x-mu)^2)/(n-1)) 6^2 = sum((x-mu)^2)/(n-1) 36 = sum((x-mu)^2)/(n-1) 36 = sum((x-mu)^2)/(5-1) 36 = sum((x-mu)^2)/4 36*4 = sum((x-mu)^2) 144 = sum((x-mu)^2) sum((x-mu)^2) = 144 (x1-mu)^2+(x2-mu)^2+(x3-mu)^2+(x4-mu)^2+(x5-mu)^2 = 144 (x1-20)^2+(x2-20)^2+(x3-20)^2+(x4-20)^2+(x5-20)^2 = 144 (20-x-20)^2+(20-20)^2+(20-20)^2+(20-20)^2+(20+x-20)^2 = 144 (20-x-20)^2+(0)^2+(0)^2+(0)^2+(20+x-20)^2 = 144 (-x)^2+0+0+0+(x)^2 = 144 x^2 + x^2 = 144 2x^2 = 144 x^2 = 144/2 x^2 = 72 x = sqrt(72) x = 8.48528137423857 So the data set of 20,20,20,20,20 becomes 20-8.48528137423857,20,20,20,20+8.48528137423857 11.5147186257614,20,20,20,28.48528137423857 So the data set 11.5147186257614,20,20,20,28.48528137423857 has a mean of 20 and a standard deviation of (roughly) 6 ------------------------------------------------ If you want to be exact, then the data set 20-sqrt(72), 20, 20, 20, 20+sqrt(72) has a mean of 20 and a standard deviation of exactly 6
 Inequalities/639182: 2x-1/3x-2 less than or equal to 11 solutions Answer 402612 by jim_thompson5910(28476)   on 2012-08-20 16:41:22 (Show Source): You can put this solution on YOUR website!Hint: Graph both y = (2x-1)/(3x-2) (in green) and y = 1 (in blue) using a graphing calculator Then look for the interval(s) where the green curve is below the blue line.