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 Permutations/470766: Evaluate: 8C3 11 56 24 336 1 solutions Answer 322916 by jim_thompson5910(28598)   on 2011-07-15 19:57:34 (Show Source): You can put this solution on YOUR website! Since order does not matter, we must use the combination formula: Start with the given formula Plug in and Subtract to get 5 Expand 8! Expand 5! Cancel Simplify Expand 3! Multiply 8*7*6 to get 336 Multiply 3*2*1 to get 6 Now divide So 8 choose 3 (where order doesn't matter) yields 56 unique combinations
 Quadratic-relations-and-conic-sections/470768: If P(A or B) = 0.9, P(A) = 0.7 and P(B) = 0.5, determine P(A and B) 0.15 0.25 0.45 0.30 1 solutions Answer 322915 by jim_thompson5910(28598)   on 2011-07-15 19:55:38 (Show Source): You can put this solution on YOUR website!Hint: P(A and B) = P(A) + P(B) - P(A or B)
 Polygons/470599: Find the number of sides. Each interior angle measures: a) 156 degrees1 solutions Answer 322777 by jim_thompson5910(28598)   on 2011-07-15 05:01:45 (Show Source): You can put this solution on YOUR website!Hint: Use the formula where is the measure of each interior angle. In this case, , so
 Square-cubic-other-roots/470600: Help me find the real solutions of the equation by factoring: x to the 3rd power + 2x(square) - 16x - 32 = 01 solutions Answer 322776 by jim_thompson5910(28598)   on 2011-07-15 05:00:14 (Show Source): You can put this solution on YOUR website!First, we must factor. Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Now factor to get (this a difference of squares) So factors to In other words, ------------------------------------------------------------------ So this essentially means that becomes Now we move onto solving Start with the given equation. or , or Use the zero product property or , or Solve for 'x' in each equation. So the three solutions are or , or
 expressions/470588: What Is The Quotient Of The Square Of A Number t And 14?1 solutions Answer 322773 by jim_thompson5910(28598)   on 2011-07-15 04:54:21 (Show Source): You can put this solution on YOUR website!The Square Of A Number t is . So the quotient of this and 14 is basically this number divided by 14. So the whole thing translates to
 Expressions-with-variables/470530: y=1/3x-21 solutions Answer 322772 by jim_thompson5910(28598)   on 2011-07-15 04:53:12 (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 1 and the run is 3. This means that to go from point to point, we can go up 1 and over 3 So starting at , go up 1 unit and to the right 3 units 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
 Conjunction/470593: Hello. I am looking for assistance on this particular problem. ANy help you can give is greatly appreciated. Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. [(~p v ~q) ^ ~q] 1 solutions Answer 322767 by jim_thompson5910(28598)   on 2011-07-15 04:37:27 (Show Source): You can put this solution on YOUR website!If p is true, then ~p is false since ~p is the opposite of p. Note: ~p means "not p" If q is false, then ~q (not q) is NOT false, so ~q is true. So we know that ~p is false and ~q is true. So ~p v ~q is then true because p v q is true if either p or q is true. Finally, (~p v ~q) ^ ~q is true because BOTH ~p v ~q AND ~q are true. Since they are BOTH true, the conjunction is true. So (~p v ~q) ^ ~q is true, which is the final truth value. Note: I noticed that you mentioned r, but it doesn't show up in the expression. Is that a typo?
 Rational-functions/470470: Can you please help me with the following problems? I need the steps worked out using the √ sign in order for me to follow. Thank you in advance √4(x-√9)= simplify and √45(x-√27) Can you please not just say sqrt. I am trying to follow. 1 solutions Answer 322686 by jim_thompson5910(28598)   on 2011-07-14 18:30:44 (Show Source): You can put this solution on YOUR website! Note: and So ===================================================================== So
 Coordinate-system/470187: I'm being asked to find the x and y-intercepts of various equations. One that has me stumped in y=2x-6. I know that -6 is the y-intercept, but in an equation like this, how do I find the x-intercept? 1 solutions Answer 322521 by jim_thompson5910(28598)   on 2011-07-14 01:30:16 (Show Source): You can put this solution on YOUR website!To find the x-intercept, plug in y=0 and solve for x. y=2x-6 0=2x-6 6=2x 6/2=x 3=x x=3 So the x-intercept is the point (3,0)
 Miscellaneous_Word_Problems/470200: A mini license plate for a toy car must consist of three numbers followed by a letter. Each number must be a 3,6, or 9. Each letter must be a T or R. Repetition of digits is NOT permitted. Construct a tree diagram List the sample space exact probability of creating a mini license plate with a T. Give solution exactly in reduced fraction form I don't know how to construct the tree diagram. I have worked the problems as follows: Sample space is: 369Y,396T,639T,693T,936T,963T AND the same for letter R 12 points so probability is 6/12=1/2 If you can offer help on tree diagram and advise if I have the proper answer. Thanks!1 solutions Answer 322520 by jim_thompson5910(28598)   on 2011-07-14 01:28:10 (Show Source): You can put this solution on YOUR website!The tree diagram will look like the following (of course, you may have it oriented a different way) Sample space: {369T,396T,639T,693T,936T,963T,369R,396R,639R,693R,936R,963R} There are 6 plates with a T in them and there are 12 plates total. So probability is 6/12 = 1/2
 Linear-equations/470204: x + 12 < 41 solutions Answer 322518 by jim_thompson5910(28598)   on 2011-07-14 01:16:12 (Show Source): You can put this solution on YOUR website!x + 12 < 4 x + 12 - 12 < 4 - 12 x + 0 < -8 x < -8
 Distributive-associative-commutative-properties/470182: Simplify the fraction to lowest terms 60,000/150,0001 solutions Answer 322513 by jim_thompson5910(28598)   on 2011-07-13 22:45:46 (Show Source): You can put this solution on YOUR website!60,000/150,000 = 6/15 = 2/5
 Divisibility_and_Prime_Numbers/470176: ((x)/(3)-(y)/(4))/(y)/(5)-(x)/(6)) I'm trying so so so much to solve that and still can not. Please, can you help me?1 solutions Answer 322512 by jim_thompson5910(28598)   on 2011-07-13 22:40:31 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply EVERY term by the inner LCD 60 to clear out all the inner fractions. So
 Circles/470139: This question seems to make no sense to me , at a point i thought i had something but i just cant solve pleasee help me: Two points on the circle given by the equation (x-1)^2+(y+3)^2=100 have x-coordinate -7.what is the y coordinates of those two points? now that i reread this problem im thinking the numbers in the actual equation are irrelevant but im not sure. your help is appreciated thsnk you.1 solutions Answer 322503 by jim_thompson5910(28598)   on 2011-07-13 20:43:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in x=-7. The goal now is to solve for y. Subtract Square -8 to get 64 Subtract 64 from both sides. Subtract Take the square root of both sides. or Break up the "plus/minus" or Take the square root of 36 to get 6. or Subtract 3 from both sides. or Subtract So the y-coordinates are and So the two points are (-7,3) and (-7,-9)
 Graphs/470143: How do I graph 6x-3y=9, if it isn't in y=mx+b form?1 solutions Answer 322502 by jim_thompson5910(28598)   on 2011-07-13 20:39:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. 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 up 2 and over 1 So starting at , go up 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
Polynomials-and-rational-expressions/470120: Use synthetic division to determine which of the following values of "c" is a zero of 4x^3+37x^2+6x-27.
-3,5,-8,8,-4
a.5
b.-4
c.-8
d.-3
e.8

1 solutions

Answer 322495 by jim_thompson5910(28598)   on 2011-07-13 19:53:15 (Show Source):
You can put this solution on YOUR website!
Checking -3:
 -------------------------------------- -3 | 4 37 6 -27 | -12 -75 207 4 25 -69 180

Since the last entry in the last row is NOT a 0, -3 is NOT a zero

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

Checking 5:

 -------------------------------------- 5 | 4 37 6 -27 | 20 285 1455 4 57 291 1428

Since the last entry in the last row is NOT a 0, 5 is NOT a zero

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

Checking -8:

 -------------------------------------- -8 | 4 37 6 -27 | -32 -40 272 4 5 -34 245

Since the last entry in the last row is NOT a 0, -8 is NOT a zero
================================================================

Checking 8:

 -------------------------------------- 8 | 4 37 6 -27 | 32 552 4464 4 69 558 4437

Since the last entry in the last row is NOT a 0, 8 is NOT a zero
================================================================

Checking -4:

 -------------------------------------- -4 | 4 37 6 -27 | -16 -84 312 4 21 -78 285

Since the last entry in the last row is NOT a 0, -4 is NOT a zero

 Graphs/470118: How do you graph 4x=3y, since it isn't in y=mx+b form?1 solutions Answer 322492 by jim_thompson5910(28598)   on 2011-07-13 19:47:15 (Show Source): You can put this solution on YOUR website!Solve for y: 4x=3y 3y = 4x y = 4/3x So we now have . Add on a +0 (it doesn't change anything) to get . So the equation is now in y=mx+b form where and
 Functions/470114: If "f" is a one-to-one function and f(6)=-8,f(-8)=-7, and f(-7)=6, find f^-1(-7) a. -6 b. -8 c. -7 d. 6 e. 7 1 solutions Answer 322484 by jim_thompson5910(28598)   on 2011-07-13 19:38:14 (Show Source): You can put this solution on YOUR website! ... Start with the given equation ... Apply to both sides. ... Since f is one-to-one, (ie f and f inverse cancel each other out) So
Polynomials-and-rational-expressions/470107: Use synthetic division to divide 5x^3-x^2-3x+1 by x+4
a. 5x^2-21x+81
b. 5x^2-x-3
c. 5x^2+19x-87+(325/x+4)
d. 5x^2-x-3+(1/x+4)
e. 5x^2-21x+81-(323/x+4)
1 solutions

Answer 322475 by jim_thompson5910(28598)   on 2011-07-13 19:21:39 (Show Source):
You can put this solution on YOUR website!
Perform synthetic division, to get

 -------------------------------------- -4 | 5 -1 -3 1 | -20 84 -324 5 -21 81 -323

So

 Distributive-associative-commutative-properties/470073: perform the indicated operation 6+2 times 8=1 solutions Answer 322468 by jim_thompson5910(28598)   on 2011-07-13 19:08:17 (Show Source): You can put this solution on YOUR website!6+2*8 = 6+16 = 22
 Graphs/470076: How do I graph x+2y=-6, since it isn't in y=mx+b form?1 solutions Answer 322467 by jim_thompson5910(28598)   on 2011-07-13 19:06:38 (Show Source): You can put this solution on YOUR website!Solve for y: x+2y=-6 2y=-x-6 y = -1/2x-6/2 y = -1/2x-3 Equation is now in the form y = mx+b where m=-1/2 and b=-3
 Expressions-with-variables/470058: what is the value of x? 6x-10=3x+81 solutions Answer 322463 by jim_thompson5910(28598)   on 2011-07-13 18:07:48 (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. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/470061: please help!! solve using the principle of zero products (5w+3)(2w-6)=01 solutions Answer 322462 by jim_thompson5910(28598)   on 2011-07-13 18:06:36 (Show Source): You can put this solution on YOUR website!(5w+3)(2w-6)=0 5w+3=0 or 2w-6=0 5w=-3 or 2w=6 w=-3/5 or w=6/2 w=-3/5 or w=3
 Probability-and-statistics/470004: Shortly after the World Trade Center towers were destroyed by terrorists, America Online ran a poll of its Internet subscribers and asked this question: “Should the World Trade Center towers be rebuilt?” Among the 1,304,240 responses, 768,731 answered yes, 286,756 answered no, and 248,753 said that it was too soon to decide. Given that this sample is extremely large, can the responses be considered to be representativeof the population of the United States? Explain. 1 solutions Answer 322461 by jim_thompson5910(28598)   on 2011-07-13 18:05:25 (Show Source): You can put this solution on YOUR website!Even though you have a large sample, this doesn't necessarily mean that this sample is representative. You have to ask yourself: how was the sample drawn? Was it done in a truly random fashion? Also, you have to keep in mind that ONLY AOL internet subscribers were sampled. So people who did not have internet or did not subscribe with AOL were left out. Since many people fit in either category, this means that this sample is NOT representative.
 Polynomials-and-rational-expressions/470043: put the equation in the form ax2+bx+c=0 x^2-3=3x^2+8x 1 solutions Answer 322460 by jim_thompson5910(28598)   on 2011-07-13 17:45:27 (Show Source):
 Graphs/469782: Is [(1,1), (2,1), (2,2) an (1,2)] a function?1 solutions Answer 322269 by jim_thompson5910(28598)   on 2011-07-12 23:48:20 (Show Source): You can put this solution on YOUR website!No, because the x-coordinate of 1 is paired with the y-coordinates 1 and 2. You can't have a function that has one input mapping to 2 different outputs. So it's not a function.
 Inequalities/469683: I need to know how to solve this equation. (x+18)(x-12)(x+3)>0. If anyone can help, I would appreciate it, thanks in advance.1 solutions Answer 322219 by jim_thompson5910(28598)   on 2011-07-12 18:13:42 (Show Source): You can put this solution on YOUR website!First, find the zeros of . (x+18)(x-12)(x+3)=0 x+18=0 or x-12=0 or x+3=0 x=-18, x=12, or x=-3 In ascending order, the zeros are: -18,-3,12 Now in the interval , (x+18)(x-12)(x+3) is negative. Simply plug in any negative number less than -18 to see this (eg: plug in x=-20 to get (-20+18)(-20-12)(-20+3)=-1088) In the interval , (x+18)(x-12)(x+3) is positive. Simply plug in any number in the interval to see this (eg: plug in x=-5 to get (-5+18)(-5-12)(-5+3)=442) In the interval , (x+18)(x-12)(x+3) is negative. Simply plug in any number in the interval to see this (eg: plug in x=0 to get (0+18)(0-12)(0+3)=-648) Finally, in the interval , (x+18)(x-12)(x+3) is positive. Simply plug in any number greater than 12 to see this (eg: plug in x=50 to get (50+18)(50-12)(50+3)=136952) So the following intervals make (x+18)(x-12)(x+3) positive: and So combine them with a union symbol to get the final answer: Here's a graph to visually confirm this
Polynomials-and-rational-expressions/469410: Use the remainder theorem to find P(7) for P(x)=7x^3-9x^2-4x+3
a.2,817
b.-1,929
c.121,593
d.2,811
e.1935
1 solutions

Answer 322053 by jim_thompson5910(28598)   on 2011-07-11 23:19:15 (Show Source):
You can put this solution on YOUR website!
Use synthetic division to get

 -------------------------------------- 7 | 7 -9 -4 3 | 49 280 1932 7 40 276 1935

Since the last entry is 1935, the remainder is 1935. So this means that P(7) = 1935

Note: let me know if you need any help with synthetic division

 Probability-and-statistics/469391: I am not wanting someone to do my work for me on this question that is why I didn't post any data. I am just not sure how to convert to the z-score. With 25 subjects, how do I convert each age and height into a z-score? 1 solutions Answer 322048 by jim_thompson5910(28598)   on 2011-07-11 22:46:07 (Show Source): You can put this solution on YOUR website!Use the formula where is the population mean and is the population standard deviation.
 Quadratic_Equations/469331: \sqrt{10-x} + x=-21 solutions Answer 321977 by jim_thompson5910(28598)   on 2011-07-11 19:10:54 (Show Source): You can put this solution on YOUR website! or or Perform the check to find that only works. So the solution is