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 Surface-area/601053: How do you find the area of a rectangle with these dimensions: 5ft 3in x 6ft?1 solutions Answer 379575 by jim_thompson5910(28536)   on 2012-04-19 15:13:50 (Show Source): You can put this solution on YOUR website!1 ft = 12 inches 5*1 ft = 5*12 inches 5 ft = 60 inches 5 ft 3 in = 5 ft + 3 in = 60 in + 3 in = 63 in So 5 ft 3 in = 63 in ----------------------------------------------------- 1 ft = 12 inches 6*1 ft = 6*12 inches 6 ft = 72 inches So 6 ft = 72 inches ----------------------------------------------------- This means that (5 ft 3 in)*(6 ft) = (63 in)*(72 in) = (63*72)(in*in) = 4536 square inches So the area is 4536 square inches
 Geometry_Word_Problems/600994: A regular 30-sided polygon is inscribed in a circle with a radius of 8. Use the law of cosines to find an exact expression for the length of one of the sides. 1 solutions Answer 379574 by jim_thompson5910(28536)   on 2012-04-19 15:09:05 (Show Source): You can put this solution on YOUR website!c^2 = a^2 + b^2 - 2ab*cos(C) c^2 = 8^2 + 8^2 - 2*8*8*cos(12) c^2 = 64 + 64 - 128*cos(12) c^2 = 128 - 128*cos(12) c = sqrt( 128 - 128*cos(12) )
 Probability-and-statistics/601029: The probability that the children of a certain couple will have red hair is 0.223. If the couple were to have five children, what is the probability that exactly two of them will have red hair?1 solutions Answer 379573 by jim_thompson5910(28536)   on 2012-04-19 15:05:41 (Show Source): You can put this solution on YOUR website!P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x) P(X = 2) = (5 C 2)*(0.223)^(2)*(1-0.223)^(5-2) P(X = 2) = (5 C 2)*(0.223)^(2)*(0.777)^(5-2) P(X = 2) = (10)*(0.223)^(2)*(0.777)^3 P(X = 2) = (10)*(0.049729)*(0.469097433) P(X = 2) = 0.23327746245657 So the probability that exactly two of them will have red hair is approximately 0.233277
 Probability-and-statistics/601044: Two cards are dealt from ordinary pack; Event (A) : both cards are same suit Event (B): both cards are red (i) Which event is more likely. I have attempted this part and I believe I am right in saying that b is more likely with a probability of 0.24509... and A is 0.0588.... (ii) Find the probability that the two cards are either both red or both from the same suit. (iii) Use the definition of p(A given B) to calculate the probability that the two cards are from the same suit, given that they are both red. I am struggling on parts two and three. Thanks 1 solutions Answer 379572 by jim_thompson5910(28536)   on 2012-04-19 14:54:42 (Show Source): You can put this solution on YOUR website!i) Let's say you draw a diamond card. What is the probability of drawing another diamond card? The probability would be 12/51 = 0.23529 (assuming you can't replace the cards). This idea can be done with any suit. So in general, the probability of drawing two cards that are of the same suit is roughly 0.23529 Now let's say you draw a red card. The probability of drawing another red card is 25/51 = 0.490196 So the probability of drawing two red cards is 0.490196 Clearly 0.490196 is larger than 0.23529, which means that event B is more likely. ------------------------------------------------------- ii) P(Both red or same suit) = P(Both red) + P(same suit) - P(Both red and same suit) P(Both red or same suit) = 25/51 + 12/51 - 12/51 P(Both red or same suit) = 25/51 P(Both red or same suit) = 0.49019 ------------------------------------------------------- iii) P(A given B) = ( P(A and B) )/P(B) P(same suit given both red) = ( P(same suit and both red) )/P(both red) P(same suit given both red) = ( 12/51 )/(25/51) P(same suit given both red) = ( 12/51 )*(51/25) P(same suit given both red) = 12/25 P(same suit given both red) = 0.48
 Inverses/600992: How would you find the additive inverse of 9y 1 solutions Answer 379571 by jim_thompson5910(28536)   on 2012-04-19 14:26:41 (Show Source): You can put this solution on YOUR website!The additive inverse of any number is simply the negative of that number. For example, the additive inverse of 2 is -2. The additive inverse of -3 is -(-3) = 3. So basically the signs flip. So the additive inverse of 9y is -9y
 Percentage-and-ratio-word-problems/600982: Suppose that in 1990, the average plane ticket from New York to San Francisco was $240 but rose to a price of$430 by 2007. Determine the relative change in price from 1990 to 2007, and then refer to the chart to compare this change to the overall rate of inflation according to the CPI. Average Annual Consumer Price Index Year CPI Year CPI 1990 130.7 2000 172.2 1991 136.2 2001 177.1 1992 140.3 2002 179.9 1993 144.5 2003 184.0 1994 148.2 2004 188.9 1995 152.4 2005 195.3 1996 156.9 2006 201.6 1997 160.5 2007 207.3 1998 163.0 2008 215.3 1999 166.6 I got 80%. But I am not sure what else to do.1 solutions Answer 379570 by jim_thompson5910(28536)   on 2012-04-19 14:24:23 (Show Source): You can put this solution on YOUR website!I'm not exactly sure how CPIs work, but my guess is that you're comparing this 80% increase with the percentage increase of the CPIs over this time period. This percentage increase is... Percent Increase = [(New - Old)/Old] * 100 Percent Increase = [(215.3-130.7)/130.7] * 100 Percent Increase = [84.6/130.7] * 100 Percent Increase = 0.647283856159143 * 100 Percent Increase = 64.7283856159143% So in 1990, the CPI was 130.7 and over this entire time period, it increased to 215.3 in 2008. This percentage increase was roughly 64.73% Compare this with the percentage increase of the price of the plane ticket and you can see that the price of the plane ticket clearly grew more.
 Functions/601031: finding the numbers that are not in the domain of the function? f(x)=x/x-7 So i set x-7=0 so x=7 So therefore it can't be 7, it cant be domain so it would be {x|x#7} right? but it keeps telling me i am wrong. what am i doing wrong?? 1 solutions Answer 379568 by jim_thompson5910(28536)   on 2012-04-19 14:02:58 (Show Source): You can put this solution on YOUR website!You are correct in saying that the domain is $\LARGE \{x|x\neq 7\}$ But I think they simply want the number (or numbers) that are not in the domain. Since you've shown that x = 7 causes a division by zero, this would mean that 7 is not in the domain. So the answer is simply 7.
 Equations/600896: Solve the equation. 7(x + 3) = 7x + 211 solutions Answer 379534 by jim_thompson5910(28536)   on 2012-04-19 01:36:23 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Simplify. Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.
Equations/600884: I need to figure out how to solve this problem:

9x^2 - 12x +4

Thank you.
1 solutions

Answer 379526 by jim_thompson5910(28536)   on 2012-04-19 00:38:23 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.

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 :
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

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

These factors pair up and multiply to .
1*36 = 36
2*18 = 36
3*12 = 36
4*9 = 36
6*6 = 36
(-1)*(-36) = 36
(-2)*(-18) = 36
(-3)*(-12) = 36
(-4)*(-9) = 36
(-6)*(-6) = 36

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

First NumberSecond NumberSum
1361+36=37
2182+18=20
3123+12=15
494+9=13
666+6=12
-1-36-1+(-36)=-37
-2-18-2+(-18)=-20
-3-12-3+(-12)=-15
-4-9-4+(-9)=-13
-6-6-6+(-6)=-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

Condense the terms.

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

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).

 Circles/600881: THE AREA OF THE CIRCLE IS 676(PIE SIGN) SQUARE CENTIMETERS. FIND THE DIAMETER 1 solutions Answer 379525 by jim_thompson5910(28536)   on 2012-04-19 00:28:06 (Show Source): You can put this solution on YOUR website!A = pi*r^2 676pi = pi*r^2 676pi/pi = (pi*r^2)/pi 676 = r^2 r^2 = 676 r = sqrt(676) r = 26 The radius is 26 cm. So the diameter is d = 2r = 2*26 = 52 cm
 Equations/600874: I need help to solve this problem: x^2(x-3)+7(x-3) Thanks!1 solutions Answer 379524 by jim_thompson5910(28536)   on 2012-04-19 00:23:52 (Show Source): You can put this solution on YOUR website!Factor out the GCF x-3 to get So factors to
 Travel_Word_Problems/600763: Bret is going to the lake with some friends. If the lake is 90 miles away and he is driving at 45 miles per hour, how long with it take to get to the lake1 solutions Answer 379466 by jim_thompson5910(28536)   on 2012-04-18 20:00:52 (Show Source): You can put this solution on YOUR website!d = rt 90 = 45t 90/45 = t 2 = t t = 2 So it will take Bret 2 hours.
 Polynomials-and-rational-expressions/600761: Simplify each radical expression. i don't understand this at all..something to do with a factor tree? completely confused1 solutions Answer 379465 by jim_thompson5910(28536)   on 2012-04-18 19:56:19 (Show Source): You can put this solution on YOUR website!Notice that 243 = 81*3 and that 81 is a perfect square. This is very important as we can simplify the square root of 81 to get 9. So
 Polynomials-and-rational-expressions/600752: Simplify each rational expression. State any excluded values. 6-2x ____ 2x-6 you factor out the top and bottom.. 2(3-x) _____ 2(x-3) is that the problem in simplest form? I'm not sure what the next step would be.1 solutions Answer 379460 by jim_thompson5910(28536)   on 2012-04-18 19:39:51 (Show Source): You can put this solution on YOUR website!Hint: you can factor -1 out of 3-x to get -1(-3+x) which becomes -1(x-3)
 Trigonometry-basics/600742: what is the expression csc x ÷ cot x equivalent to ?1 solutions Answer 379457 by jim_thompson5910(28536)   on 2012-04-18 19:28:13 (Show Source): You can put this solution on YOUR website!csc(x)/cot(x) csc(x)/( 1/tan(x) ) csc(x)*tan(x) (1/sin(x))*(sin(x)/cos(x)) sin(x)/(sin(x)cos(x)) 1/cos(x) sec(x) So csc(x)/cot(x) = sec(x) for all allowed domain values of x.
 absolute-value/600746: Why the absolute value of a/b is not always a/b? 1 solutions Answer 379455 by jim_thompson5910(28536)   on 2012-04-18 19:25:33 (Show Source): You can put this solution on YOUR website!If a/b < 0, then Ex: if a = -6 and b = 3, then a/b = -6/3 = -2. Also, -a/b = -(-2) = 2 So
 Triangles/600743: i have tried but i always get the wrong answer can u show me how to figure this out step by step my question is...... The shorter leg of a 30°-60°-90° triangle measures 8 in. What is the length of the hypotenuse?1 solutions Answer 379453 by jim_thompson5910(28536)   on 2012-04-18 19:21:01 (Show Source): You can put this solution on YOUR website!The hypotenuse is always double the length of the shorter leg in a 30°-60°-90° triangle. So if the shorter leg is 8 inches, then the hypotenuse is 8*2 = 16 inches.
 Trigonometry-basics/600739: what is the co-function to secant1 solutions Answer 379452 by jim_thompson5910(28536)   on 2012-04-18 19:19:34 (Show Source): You can put this solution on YOUR website!The co-function to secant is cosine.
 Trigonometry-basics/600740: if A is a positive acute angle and tan A = cot 30 then what is the value of tan A1 solutions Answer 379451 by jim_thompson5910(28536)   on 2012-04-18 19:18:51 (Show Source): You can put this solution on YOUR website!tan(A) = cot(30) tan(A) = cos(30)/sin(30) tan(A) = (sqrt(3)/2)/(1/2) tan(A) = (sqrt(3)/2)*(2/1) tan(A) = sqrt(3) Answer: tan(A) = sqrt(3)
 Exponential-and-logarithmic-functions/600735: Evaluate the expression below at t=2, P=$400, and r= -7%. Round your answer to two decimal places. Do not include units in your answer. A(t)= P*e^rt1 solutions Answer 379450 by jim_thompson5910(28536) on 2012-04-18 19:16:17 (Show Source):  Average/600727: Hello. my problem is a^8-b^8 or a to the eighth minus b to the eighth. Please help me learn how to work this.1 solutions Answer 379449 by jim_thompson5910(28536) on 2012-04-18 19:14:23 (Show Source): You can put this solution on YOUR website! So completely factors to test/600724: 2x^2 -21x +40 1 solutions Answer 379446 by jim_thompson5910(28536) on 2012-04-18 18:44:11 (Show Source): You can put this solution on YOUR website! It looks like you want to factor here. 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 : 1,2,4,5,8,10,16,20,40,80 -1,-2,-4,-5,-8,-10,-16,-20,-40,-80 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*80 = 80 2*40 = 80 4*20 = 80 5*16 = 80 8*10 = 80 (-1)*(-80) = 80 (-2)*(-40) = 80 (-4)*(-20) = 80 (-5)*(-16) = 80 (-8)*(-10) = 80 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First NumberSecond NumberSum 1801+80=81 2402+40=42 4204+20=24 5165+16=21 8108+10=18 -1-80-1+(-80)=-81 -2-40-2+(-40)=-42 -4-20-4+(-20)=-24 -5-16-5+(-16)=-21 -8-10-8+(-10)=-18 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).  test/600718: 3y = 101 solutions Answer 379444 by jim_thompson5910(28536) on 2012-04-18 18:35:59 (Show Source): You can put this solution on YOUR website! So the solution is Polynomials-and-rational-expressions/600707: I am having problems understanding my math home work. It says to Factor completely. Remember to look first for a common factor and to check by multiplying. If a Polynomial is prime,state this. -36a^2 -96ab -64b^2 Can you show me how to work this problem step by step and then show me how to check it as well. I am a little lost on how to do this. 1 solutions Answer 379443 by jim_thompson5910(28536) on 2012-04-18 18:34:20 (Show Source): You can put this solution on YOUR website! Start with the given expression. 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 coefficient is . Now multiply the first coefficient by the last coefficient 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 : 1,2,3,4,6,8,9,12,16,18,24,36,48,72,144 -1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72,-144 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*144 = 144 2*72 = 144 3*48 = 144 4*36 = 144 6*24 = 144 8*18 = 144 9*16 = 144 12*12 = 144 (-1)*(-144) = 144 (-2)*(-72) = 144 (-3)*(-48) = 144 (-4)*(-36) = 144 (-6)*(-24) = 144 (-8)*(-18) = 144 (-9)*(-16) = 144 (-12)*(-12) = 144 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First NumberSecond NumberSum 11441+144=145 2722+72=74 3483+48=51 4364+36=40 6246+24=30 8188+18=26 9169+16=25 121212+12=24 -1-144-1+(-144)=-145 -2-72-2+(-72)=-74 -3-48-3+(-48)=-51 -4-36-4+(-36)=-40 -6-24-6+(-24)=-30 -8-18-8+(-18)=-26 -9-16-9+(-16)=-25 -12-12-12+(-12)=-24 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 Condense the terms. -------------------------------------------------- So then factors further to =============================================================== Answer: 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). Check: So this verifies the answer.  Linear-equations/600712: y=1/5x+21 solutions Answer 379442 by jim_thompson5910(28536) on 2012-04-18 18:31:38 (Show Source): You can put this solution on YOUR website!I'm assuming you want to graph this. 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 5. This means that to go from point to point, we can go up 1 and over 5 So starting at , go up 1 unit and to the right 5 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  Exponential-and-logarithmic-functions/600711: Please Rewrite The Equation In Exponential Form. 1 solutions Answer 379441 by jim_thompson5910(28536) on 2012-04-18 18:30:47 (Show Source): You can put this solution on YOUR website! converts to  Permutations/600714: Find the number of ways in which each commitee can be selected. -3 people from a group of 51 solutions Answer 379440 by jim_thompson5910(28536) on 2012-04-18 18:30:00 (Show Source): You can put this solution on YOUR website!C(n,r) = (n!)/(r!(n-r)!) C(5,3) = (5!)/(3!*(5-3)!) C(5,3) = (5!)/(3!*2!) C(5,3) = (5*4*3!)/(3!*2!) C(5,3) = (5*4)/(2!) C(5,3) = (5*4)/(2*1) C(5,3) = (20)/(2) C(5,3) = 10 So there are 10 ways (assuming order doesn't matter)  Trigonometry-basics/600688: hey please help me with this problem,and if possible can you show me the work that leads to the answer. thank you very much if cot x = 5/12 and cos x > 0 find csc1 solutions Answer 379433 by jim_thompson5910(28536) on 2012-04-18 17:46:19 (Show Source): You can put this solution on YOUR website!cot(x) = 5/12 cot^2(x) = (5/12)^2 cot^2(x) = 25/144 ------------------- Now use the identity 1+cot^2(x) = csc^2(x) 1+cot^2(x) = csc^2(x) 1+25/144 = csc^2(x) 169/144 = csc^2(x) csc^2(x) = 169/144 csc(x) = sqrt(169/144) ... See note below csc(x) = sqrt(169)/sqrt(144) csc(x) = 13/12 Note: Because cos(x) > 0 and cot(x) = cos(x)/sin(x), this means that sin(x) > 0 as well (to keep cot(x) positive). This forces csc(x) > 0 (because csc(x) = 1/sin(x)) ========================================================================== Answer: So the answer is csc(x) = 13/12  percentage/600685: If I start out with$103 in my bank account yesterday and today I have \$78 by what percent did the money in my account decrease?1 solutions Answer 379432 by jim_thompson5910(28536)   on 2012-04-18 17:40:30 (Show Source): You can put this solution on YOUR website!Percent Decrease = [(Old - New)/Old] * 100 Percent Decrease = [(103-78)/103] * 100 Percent Decrease = [25/103] * 100 Percent Decrease = 0.242718446601942 * 100 Percent Decrease = 24.2718446601942%
 Polynomials-and-rational-expressions/600686: what are the coefficents of the given equation including any missing terms x^5-3x^4+3.5^2-16x1 solutions Answer 379431 by jim_thompson5910(28536)   on 2012-04-18 17:39:41 (Show Source): You can put this solution on YOUR website!The coefficients are the numbers that sit in front of the variable term. Coefficient of x^5: 1 (since x^5 = 1x^5) Coefficient of x^4: -3 (-3 is the number in front of the x^4 term) Coefficient of x^3: 0 (there is no x^3, so we denote it as 0x^3) Coefficient of x^2: 3.5 (assuming you made a typo and meant to say 3.5x^2) Coefficient of x^1 or x: -16 Coefficient of x^0 or constant term: 0
 test/600681: A roulette wheel contains slot numbers 1-36 and a 0 and 00. 18 slots are red and 18 are black. The 0 & 00 are green. Find the probability that the ball lands on red. 1 solutions Answer 379430 by jim_thompson5910(28536)   on 2012-04-18 17:34:13 (Show Source): You can put this solution on YOUR website!There are 36+2 = 38 slots and 18 of them are red. So the probability is 18/38 = 9/19