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 Probability-and-statistics/191415: You are given the probability that event A occurs. Find P (not A), the probability that event A does not occur1 solutions Answer 143640 by jim_thompson5910(28476)   on 2009-04-15 23:51:08 (Show Source): You can put this solution on YOUR website!If , then . In other words, just subtract the given probability from 1 to get the probability that A will NOT occur.
 Permutations/191392: This question is from textbook MATHEMATICS: Structure and Method, Course 2 I DON'T KNOW WHAT TO DO! HELP ME HERE IS THE QUESTION- Philip wishes to check out two books out of his school library. If the library contains 800 books, in how many ways might Philip get his choice of books? PLEASE RESPOND IMMEDIATELY!!!!!!!!!!!IT'S DUE TOMMOROW!!!!!!!!!!!!!!!!!!!!!!!!!1 solutions Answer 143630 by jim_thompson5910(28476)   on 2009-04-15 21:49:28 (Show Source): You can put this solution on YOUR website!For the first selection, you have a choice of 800 books. Once that selection has been made, you now have 799 books left over. So if the order matters, then you simply multiply 800 by 799 to get: 800 x 799 = 639,200 So there are 639,200 different ways to choose two books (where the order of the books matters). ---------------------------------------------- If the order of the books does NOT matter, then simply divide by 2 (since xy is the same as yx) to get 639,200/2=319,600 So there are 319,600 different ways to choose two books if the order does NOT matter.
 Linear-systems/191384: This question is from textbook algebra 1 the question (i have to do 11 of these) is: "Determine whether each system is consistent or inconsistent by solving it graphically and algebraically" { y=-4x+6 { 2y=-8x-8 i tried doing "step 1: 2(-4x+6)=-8x-8 step 2: -8x+12=-8x-8 step 3: 0x+12=-8" and i know it isn't right, could someone explain how you find the answer please. thanks!! 1 solutions Answer 143624 by jim_thompson5910(28476)   on 2009-04-15 21:20:52 (Show Source): You can put this solution on YOUR website!You have the correct steps. Since the equation is NOT true, this means that there are NO solutions. So the system is inconsistent.
 logarithm/191371: Question: Write an exponential function, y=ab^x for a graph that includes points at (1, 12) and (2, 36). I do not understand how to find this. Can you please show me the steps and answer?1 solutions Answer 143618 by jim_thompson5910(28476)   on 2009-04-15 20:49:24 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in and . These are the x and y coordinates to the point (1,12) Simplify Divide both sides by "a". Rearrange the equation ------------------------ Go back to the given equation. Plug in and . These are the x and y coordinates to the point (2,36) Plug in Square to get Multiply Reduce Multiply both sides by "a". Divide both sides by 36. Reduce ----------------------- Go back to the first isolated equation Plug in Reduce So the exponential equation is
 Polynomials-and-rational-expressions/191261: Please help me factorize and state the roots of the following polynomial. Please, I beg you, I need to know how to to this and would really appreciate whatever help I can get. This was a take home assignment. Thanks. P(x)=4x^7+28x^6+27x^5-203x^4-591x^3-431x^2+146x+1201 solutions Answer 143585 by jim_thompson5910(28476)   on 2009-04-15 17:04:37 (Show Source): You can put this solution on YOUR website!Wow, this is as long as it gets (well I hope so anyway...). Here are two ways to do this: Method #1: Use the rational root theorem to find all of the possible roots and test EVERY possible root to see if it is actually a root. Since the degree of the equation is 7, this means that once you find 7 roots, then you don't need to check any more possible roots. Here's where this method gets really tedious: there are A LOT of possible roots (48 in total) But, here's how to find them: Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 120 (the last coefficient): Now let's list the factors of 4 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur Once you have all of the possible rational roots, either plug them in directly or use synthetic division to determine which ones are actually roots. Method #2: Since the first method seems like a lot of busy work (which it is), just use a graphing calculator to find some of the roots, and then use those roots to find other roots (using synthetic division). Eventually, you'll reduce that massive polynomial to a quadratic which you can solve using the quadratic formula. If you're completely stuck, then repost or email me. By the way, the 7 roots are: 3, -1/2, 1/2, -4, -2, -2+i, -2-i Also, completely factors (over the reals) to In other words,
 Radicals/191291: This question is from textbook I need some help with a problem that states I need to rationalize the denominator. The problem is (square(3)-square(4))/(square(3)+square(4)). I did the steps that it said to, but my answer does not match the answer in the book. When I solved the problem I got (square(3)-square(4)(square(3)+square(4) with a - 1 for the denominator? What am I doing wrong? Any help would be greatly appreciated!1 solutions Answer 143582 by jim_thompson5910(28476)   on 2009-04-15 16:46:51 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply both the numerator and denominator by Note: is the conjugate of the denominator . Multiplying these two expressions yields a rational expression FOIL the denominator (use the difference of squares formula) FOIL the numerator (use the perfect square formula) Square each term Combine and multiply the roots. Combine like terms. Simplify to get Multiply Reduce So
 expressions/191309: (7-2)/51 solutions Answer 143579 by jim_thompson5910(28476)   on 2009-04-15 16:35:13 (Show Source): You can put this solution on YOUR website! So
 Equations/191305: X+3/x-1=x+4/x-5 (x+3)(x-5)=(x-1)(x+4) x^2+3x-15=x^2-x-4 x^2+4x+11=x^21 solutions Answer 143578 by jim_thompson5910(28476)   on 2009-04-15 16:34:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Cross multiply FOIL (this is where you made a mistake) Get everything to the left side Combine like terms. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is .
 Polynomials-and-rational-expressions/191271: Convert the number to scientific notation. 1,934,000,0001 solutions Answer 143550 by jim_thompson5910(28476)   on 2009-04-15 14:00:06 (Show Source): You can put this solution on YOUR website!Take the decimal point and place it in between the 1 and the 9. Take note that you have to move the decimal point 9 places to the right. So the exponent is 9 So this means that:
 decimal-numbers/191258: Write the number without exponents. 2.78x10^101 solutions Answer 143546 by jim_thompson5910(28476)   on 2009-04-15 13:38:00 (Show Source): You can put this solution on YOUR website!Simply move the decimal point 10 spots to the right to get:
 Complex_Numbers/191251: This question is from textbook algebra and trigonometry structure and method book 2 Find the number of times r is a root of P(x)=0. P(x)= x^4+4x^3-16x-16; r=-2 i found the depressed eruation twice but the numbers were all messed up. please help and explain.1 solutions Answer 143544 by jim_thompson5910(28476)   on 2009-04-15 13:12:17 (Show Source): You can put this solution on YOUR website!First, perform synthetic division where -2 is the test zero (let me know if you need help with synthetic division) -2 | 1 4 0 -16 -16 | -2 -4 8 16 ------------------------ 1 2 -4 -8 0 Since the last number in the bottom row is zero, this means that the remainder is 0. So -2 is a root of The first 4 numbers form the depressed polynomial . This means that ================================= Now perform synthetic division on using the same test zero: -2 | 1 2 -4 -8 | -2 0 8 ------------------ 1 0 -4 0 Notice how the last number in the bottom row is 0. So -2 is a root of . So far, r=-2 is a root of multiplicity 2 (ie -2 is a root twice). The first 3 numbers in the bottom row form the new polynomial . This tells us that So ================================= Now perform synthetic division on the polynomial -2 | 1 0 -4 | -2 4 ------------ 1 -2 0 So -2 is a root of . So this means that r=-2 is a root of multiplicity 3 (ie -2 is a root three times). The first two numbers in the bottom row form the new polynomial: Now because -2 is NOT a root of , this means that we can stop looking for more roots of -2. So Or in other words, Notice how the factor is repeated 3 times, this supports our conclusion that r=-2 is a root of multiplicity 3
 Equations/191248: Can someone tell me why 3.14 and 1/6 are irrational numbers? Thank You!1 solutions Answer 143534 by jim_thompson5910(28476)   on 2009-04-15 11:23:34 (Show Source): You can put this solution on YOUR website!They aren't irrational numbers (unless you've made a typo somewhere). Since and can both be represented by a fraction of whole numbers, this means that and are both rational numbers.
 Polynomials-and-rational-expressions/191192: 4 x+20/x^2+5x=1 solutions Answer 143494 by jim_thompson5910(28476)   on 2009-04-14 23:38:59 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where or
 Equations/191061: This question is from textbook saxon algebra2 solve. 3x/x^2-1=5/x I worked it out to: 2(x-5)(x+1) Is this correct?1 solutions Answer 143449 by jim_thompson5910(28476)   on 2009-04-14 15:41:00 (Show Source): You can put this solution on YOUR website!I'm assuming that the equation is . Start with the given equation Cross multiply Distribute and multiply Subtract from both sides Combine like terms. Divide both sides by -2 Reduce Take the square root of both sides or Break up the "plus/minus" to form 2 separate equations. or Simplify the square root. So the solutions are or
Polynomials-and-rational-expressions/191090: factor by grouping
5x^2-12x+7
1 solutions

Answer 143448 by jim_thompson5910(28476)   on 2009-04-14 15:30:04 (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 :
1,5,7,35
-1,-5,-7,-35

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

These factors pair up and multiply to .
1*35
5*7
(-1)*(-35)
(-5)*(-7)

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

First NumberSecond NumberSum
1351+35=36
575+7=12
-1-35-1+(-35)=-36
-5-7-5+(-7)=-12

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 .

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

Polynomials-and-rational-expressions/191092: factor by grouping
4x^2-4x-3
1 solutions

Answer 143447 by jim_thompson5910(28476)   on 2009-04-14 15:28:19 (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 :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

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

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

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

First NumberSecond NumberSum
1-121+(-12)=-11
2-62+(-6)=-4
3-43+(-4)=-1
-112-1+12=11
-26-2+6=4
-34-3+4=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

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

So factors to .

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

 Graphs/190944: A Line parallel to -3x + 2y = 9 and contains points (-2,1) How do I set this up??1 solutions Answer 143362 by jim_thompson5910(28476)   on 2009-04-13 19:39:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. We can see that the equation has a slope and a y-intercept . Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is . Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 1 to both sides. Combine like terms. So the equation of the line parallel to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the parallel line (green) through the point .
 Geometry_Word_Problems/190946: I have a homework problem that I could use some help with-thank you. What is another measure for an angle that measures 283 degrees? _________ degrees.1 solutions Answer 143359 by jim_thompson5910(28476)   on 2009-04-13 19:30:32 (Show Source): You can put this solution on YOUR website!Just add 360 degrees to the angle to get 283+360=643. So another angle measure is 643 degrees. Note: adding 360 to an angle makes the angle wrap around one full revolution and come back to the same location as the original angle.
1 solutions

Answer 143354 by jim_thompson5910(28476)   on 2009-04-13 19:11:48 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor?

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 :
1,3
-1,-3

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

These factors pair up and multiply to .
1*(-3)
(-1)*(3)

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

First NumberSecond NumberSum
1-31+(-3)=-2
-13-1+3=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 .

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

 Graphs/190927: This question is from textbook saxon algebra 2 4x^3-36x=0 4x(x^2-9)=0 4x(x-3)(x+3) Is this finished?1 solutions Answer 143347 by jim_thompson5910(28476)   on 2009-04-13 18:23:37 (Show Source): You can put this solution on YOUR website!You should have . Now set each factor equal to zero: , , or and solve for "x" to get , or
 Trigonometry-basics/190819: Can you help me complete this identity? 1)secx - 1/sec x=? 1 solutions Answer 143336 by jim_thompson5910(28476)   on 2009-04-13 16:14:45 (Show Source): You can put this solution on YOUR website! ... Start with the given expression ... Replace each secant with Multiply the second fraction by the reciprocal ... Multiply the second term by Multiply Subtract the fractions Replace with So Note: you can rewrite as and then rewrite as (using the identity ) So this also means that
 expressions/190842: This question is from textbook Intermediate Algebra an Applied Approach We are working on logarithms. This was added to our prefinal homework. I am so confused at this point. Given F(x) = 3x-2, evaluate the following. a. F(-4) b. F(-1) c. F(0) Here is what i've done so far after several attempts I keep doing it different and confusing myself. I need to understand as finals are next week. Thank you for any help. f(F,x)=3^(x-2),F(-4) Evaluate F(-4) by replacing x with -4 in the function. F(-4)=3^((-4)-2) F(-4)=(1)/(729) ((1)/(729)) 1 solutions Answer 143332 by jim_thompson5910(28476)   on 2009-04-13 16:00:22 (Show Source): You can put this solution on YOUR website!Is the function ??? Evaluating f(-4): Start with the given function Plug in Subtract Rewrite the right side with a positive exponent by writing the reciprocal of the base. Raise 3 to the 6th power to get 729 ---------------------------- Evaluating f(-1): Start with the given function Plug in Subtract Rewrite the right side with a positive exponent by writing the reciprocal of the base. Raise 3 to the 3rd power to get 27 ---------------------------- Evaluating f(0): Start with the given function Plug in Subtract Rewrite the right side with a positive exponent by writing the reciprocal of the base. Square 3 to get 9 ----------------------------
 Square-cubic-other-roots/190860: Can you please help me solve this? I have to rationalize (the square root of 5) over (the square root of 5)-(1)1 solutions Answer 143324 by jim_thompson5910(28476)   on 2009-04-13 15:44:35 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply both the numerator and the denominator by FOIL the denominator using the difference of squares formula Square each term Combine like terms. Distribute Multiply So
 absolute-value/190867: Homework - absolute value abs(x^2-3) = 2x I know in absolute value you work it twice once + then -, but im not sure what to do with this one. Thanks1 solutions Answer 143321 by jim_thompson5910(28476)   on 2009-04-13 15:39:29 (Show Source): You can put this solution on YOUR website!If you have the equation , to find "x", you simply solve the two equations or So in this case, to solve , you'll need to solve (you'll get two solutions here) and you'll need to solve (you'll get two more solutions here) Once you have the four possible solutions, you need to check them. If any possible solutions do not satisfy the original equation , then they are not a solution. Let me know if this makes sense. If not, then repost or email me.
 Polynomials-and-rational-expressions/190873: Factor by grouping 25x^4-15x^2+10x^2-61 solutions Answer 143315 by jim_thompson5910(28476)   on 2009-04-13 15:24:15 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor the GCF from the first group Factor the GCF from the second group Combine like terms. So factors to