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Exponents/346214: What is 5 to the power of 15?
1 solutions

Answer 247563 by Fombitz(13828) About Me  on 2010-09-21 14:35:44 (Show Source):


Probability-and-statistics/346137: A game consists of tossing a fair die and then (blindly) selecting a card from a 52 card deck. You win the to prize if the top number on your tossed die is a 1 and you draw a red card. What are the odds against your winning the top prize?
1 solutions

Answer 247561 by Fombitz(13828) About Me  on 2010-09-21 14:30:47 (Show Source):
You can put this solution on YOUR website!
Let's calculate the odds of actually winning first.
P(1 on die)=1%2F6
P(red card)=26%2F52=1%2F2
P(1 and red)=%281%2F6%29%281%2F2%29=1%2F12
So then
P(not(1 and red))+P(1 and red)=1
P(not(1 and red))=1-P(1 and red)
P(not(1 and red))=1-1%2F12
P(not(1 and red))=11%2F12
So the chances of not winning are 11%2F12
In terms of odds, there is 1 chance of winning, 11 chances of not winning.
Odds are 11:1 against winning.



Linear-equations/346208: 2(z + 3)/3 =5 - z answer is 9/5

can anyone give me a full break down on why the answer is 9/5 im getting a totally incorrect answer please help
1 solutions

Answer 247559 by Fombitz(13828) About Me  on 2010-09-21 14:26:44 (Show Source):
You can put this solution on YOUR website!
%282%28z+%2B+3%29%29%2F3+=5+-+z
Multiply both sides by 3.
2%28z%2B3%29=3%285-z%29
2z%2B6=15-3z
Take it from there and solve for z.


Equations/346182: a^3-2a^2-4a-8=0
How would I solve this?
1 solutions

Answer 247558 by Fombitz(13828) About Me  on 2010-09-21 14:24:15 (Show Source):
You can put this solution on YOUR website!
You can graph it to find out how many roots are real.
.
.
.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3-2x%5E2-4x-8%29
.
.
.
There is one real root.
The other two are complex.
I iterated using Newton's method,
x=3.6786
.
.
.
The approximate complex roots are,
x=-0.8393+%2B-+1.2126i%29 from www.wolframalpha.com


Functions/346186: what is the domain for the following functions :
(11x+3)/(x-7)

sqr(8x^2) +12


5(x-1)^5/2
1 solutions

Answer 247557 by Fombitz(13828) About Me  on 2010-09-21 14:17:13 (Show Source):
You can put this solution on YOUR website!
1. All x except those that make x-7=0
2. No restrictions, (-infinity,infinity)
3. No restrictions, (-infinity,infinity)


Polynomials-and-rational-expressions/346204: Compare and contrast, in complete sentences, the difference between the products of y^2y^5 and (y^2)^5. Provide the expanded form and product of each.
*** i dont understand the difference of these

1 solutions

Answer 247556 by Fombitz(13828) About Me  on 2010-09-21 14:15:11 (Show Source):
You can put this solution on YOUR website!
According to the law of exponents,
y%5E2%2Ay%5E5=y%5E%282%2B5%29=y%5E7
%28y%5E2%29%5E5=y%5E%282%2A5%29=y%5E10
In expanded form,
y%5E2=y%2Ay
y%5E5=y%2Ay%2Ay%2Ay%2Ay
y%5E2%2Ay%5E5=y%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay
While,
y%5E2=y%2Ay
%28y%5E2%29%5E5=+%28y%2Ay%29%2A%28y%2Ay%29%2A%28y%2Ay%29%2A%28y%2Ay%29%2A%28y%2Ay%29
%28y%5E2%29%5E5=y%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay


Linear-equations/346196: -2/3 x = 5/9 the answer is -5/6

Im having problems solving linear equations with fractions can anyone give me a full break down as per why the answer is -5/6? i know -2/3 has to get multiplied to both sides for the x to be alone but i'm lost after that.
1 solutions

Answer 247552 by Fombitz(13828) About Me  on 2010-09-21 13:58:47 (Show Source):
You can put this solution on YOUR website!
%28-2%2F3%29x+=+5%2F9+
Multiply both sides by the multiplicative inverse of (-2%2F3) which is (-3%2F2),
%28-3%2F2%29%28-2%2F3%29x+=+%28-3%2F2%29%285%2F9%29+
%28-6%2F-6%29x=-15%2F18
%281%29x=-%285%2A3%29%2F%286%2A3%29
x=-%285%2F6%29%283%2F3%29
x=-%285%2F6%29%281%29
highlight%28x=-5%2F6%29


Angles/346197: In triangle ABC, the measure of angle C is four times the measure of angle A, and the measure of angle B is 18° more than the measure of angle C. Find the measure of each angle of the triangle.


how do i get a formula for this?
1 solutions

Answer 247551 by Fombitz(13828) About Me  on 2010-09-21 13:55:32 (Show Source):
You can put this solution on YOUR website!
Since it's a triangle, you know that
A%2BB%2BC=180
From the description,
C=4A
B=18%2BC=18%2B4A
Now you can substitute into the first equation and only have A as a variable.
Solve for A, then go back and solve for B and C.


Radicals/346195: Please explain the steps on how to find the domain of 27x + 1 over the square root of 3 - x.
Thank you
1 solutions

Answer 247550 by Fombitz(13828) About Me  on 2010-09-21 13:53:35 (Show Source):
You can put this solution on YOUR website!
The domain is all of the x values where the function is defined.
The square root is defined only when the argument is not negative.
A function is defined when the denominator is not zero.
So the square root argument can't be zero either.
Solve for
3-x%3E0
x%3C3
That's the only restriction.
The domain of the function is then (-infinity,3).
graph%28300%2C300%2C-10%2C10%2C-100%2C300%2C%2827x%2B1%29%2Fsqrt%283-x%29%29%29


Linear-equations/346152: x + 3y = 2
-x + y = 1
1 solutions

Answer 247548 by Fombitz(13828) About Me  on 2010-09-21 13:50:06 (Show Source):
You can put this solution on YOUR website!
1.x+%2B+3y+=+2
2.-x+%2B+y+=+1
Add the equations together.
x%2B3y-x%2By=2%2B1
4y=3
highlight%28y=3%2F4%29
Then from eq. 2,
-x%2B3%2F4=1
highlight%28x=-1%2F4%29


Travel_Word_Problems/346145: what is the speed of a plane that travels at a rate of 560 mph with a wind of r mph?
1 solutions

Answer 247547 by Fombitz(13828) About Me  on 2010-09-21 13:47:34 (Show Source):
You can put this solution on YOUR website!
By with, you mean the plane and wind are in the same direction?
If so, the plane speed, P, is,
P=560%2Br


Inequalities/346156: Solve.
-9/4x>-1/8
1 solutions

Answer 247546 by Fombitz(13828) About Me  on 2010-09-21 13:46:00 (Show Source):


Polynomials-and-rational-expressions/346162: 6-3x-2y+xy
=3(2-x)-4(2-x)
=(3-4)(2-x)
Is this the correct way to do this problem? Thanks for all your help.
1 solutions

Answer 247545 by Fombitz(13828) About Me  on 2010-09-21 13:44:05 (Show Source):
You can put this solution on YOUR website!
What are you solving for? which variable?


Exponents/346187: Simplify your answers. Assume no denominators are 0.
Show cancelling and factoring.
1. b(2)/5 divided by b
Please help me!!

1 solutions

Answer 247544 by Fombitz(13828) About Me  on 2010-09-21 13:42:09 (Show Source):


Exponents/346190: Solve for the variable in each equation below. Show all your work. Provide a check for each answer. If a solution is undefined, state that in your answer.
b/2 - b/5 =6
CHECK.
Help me please, I'm stuck! Thank you!
1 solutions

Answer 247543 by Fombitz(13828) About Me  on 2010-09-21 13:41:10 (Show Source):
You can put this solution on YOUR website!
b%2F2+-+b%2F5+=6
Multiply both sides by 2%2A5=10.
5b-2b=60
Now you're unstuck.
Finish it and solve for b.


Expressions-with-variables/346188: Simplify your answers. Assume no denominators are 0.
Show cancelling and factoring.
y(2)-49/z(2)+z
DIVIDED BY
y+7/z
HELP ME PLEASE! Thank you!!! :)
1 solutions

Answer 247542 by Fombitz(13828) About Me  on 2010-09-21 13:39:54 (Show Source):
You can put this solution on YOUR website!
Show exponentiation by using the caret, ^.
.
.
Dividing by a fraction is the same as multiplying by its reciprocal.

.
.

.
.

.
.


Vectors/346177: two cars leave a crossroads at the same time. One heads north at 50 km/h and the other heads east at 70 km/h. How far apart are the cars after .5 h? after 2.0 h?
1 solutions

Answer 247540 by Fombitz(13828) About Me  on 2010-09-21 13:35:50 (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
.
.
.
Since they are traveling in perpendicular directions, you can use the Pythagorean theorem to calculate the distance between them (the hypotenuse).
H%5E2=%28R%5B1%5D%2At%29%5E2%2B%28R%5B2%5D%2At%29%5E2
H=sqrt%28%2850t%29%5E2%2B%2870t%29%5E2%29
H=sqrt%282500t%5E2%2B4900t%5E2%29
H=sqrt%287400t%5E2%29
H=10sqrt%2874%29%2At
.
.
.
Now you have the distance as a function of time.
When t=0.5, h=10%2Asqrt%2874%29%2A0.5=5%2Asqrt%2874%29miles
Do the same fo the other times.


Equations/346184: (x+1)(X-2)=4
How would I solve if I set this equation to 0?
1 solutions

Answer 247537 by Fombitz(13828) About Me  on 2010-09-21 13:30:15 (Show Source):
You can put this solution on YOUR website!
Use the FOIL method to expand the left hand side.
Then subtract 4 from both sides of the equation.


Equations/346135: Solve by the elimination method.
2r-7s=-38
7r+2s=79
1 solutions

Answer 247536 by Fombitz(13828) About Me  on 2010-09-21 13:29:25 (Show Source):
You can put this solution on YOUR website!
1.2r-7s=-38
2.7r%2B2s=79
Multiply eq. 1 by 7 and eq. 2 by (-2) and add them together.
14r-49s-14r-4s=-266-158
-53s=-424
highlight%28s=8%29
Then from eq. 1,
2r-56=-38
2r=18
highlight%28r=9%29


Equations/346158: Draw graph that represents a line whose parametric equation are: x = 2t -4 and y = -t + 2
1 solutions

Answer 247533 by Fombitz(13828) About Me  on 2010-09-21 13:23:09 (Show Source):
You can put this solution on YOUR website!
x=2t-4
x%2B4=2t
t=%28x%2B4%29%2F2
Substitute into the y equation,
y=-%28x%2B4%29%2F2%2B2
y=-x%2F2-2%2B2
y=-%281%2F2%29x
.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%2F2%29


Rational-functions/346178: please factor completely
4c^2+9-12c
What do I do first?
1 solutions

Answer 247532 by Fombitz(13828) About Me  on 2010-09-21 13:21:06 (Show Source):
You can put this solution on YOUR website!
4c%5E2-12c%2B9=0
Oops!
You're correct that is the answer.
Sorry for screwing you up there.
(2c-3)(2c-3)=4c^2-6c-6c+9=4c^2-12c+9
I will correct it on the website too.
I could say I was just testing you but I just screwed up.
Good work!
highlight%284c%5E2-12c%2B9=%282c-3%29%5E2%29


Expressions-with-variables/346166: 2/3 (5x-1/6) - 3/4 = 1/4
1 solutions

Answer 247530 by Fombitz(13828) About Me  on 2010-09-21 13:20:20 (Show Source):
You can put this solution on YOUR website!
%282%2F3%29%2A%285x-1%2F6%29+-+3%2F4+=+1%2F4
Multiply both sides by 12.
8%285x-1%2F6%29-9=3
40x-8%2F6=12
Multiply both sides by 6.
240x-8=72
240x=80
highlight%28x=1%2F3%29


Probability-and-statistics/346172: What is the probability that a number selected at random from the first 500 positive integers is (exactly) divisible by 6 or 9?
1 solutions

Answer 247525 by Fombitz(13828) About Me  on 2010-09-21 13:16:07 (Show Source):
You can put this solution on YOUR website!
There are 83 numbers exactly divisible by 6 from 6 to 498.
There are 55 numbers exactly divisible by 9 from 9 to 495.
There are 27 numbers that are exactly divisible by 6 and 9 from 18 to 486, we don't want to double count those.
There are 500 numbers total.
P=83%2F500%2B55%2F500-27%2F500
P=111%2F500


Vectors/346134: Find the cross product of the <2, -1, 4> and <6, -2, 1>. Is the resulting vector perpendicular to given vector?
1 solutions

Answer 247506 by Fombitz(13828) About Me  on 2010-09-21 11:27:46 (Show Source):
You can put this solution on YOUR website!
A=(2,-1,4)
B=(6,-2,1)
A%2AB=2%2A6%2B%28-1%29%28-2%29%2B4%2A1=12%2B2%2B4=18
No, perpendicular vectors have a dot product equal to zero.


Rate-of-work-word-problems/346096: A strong man takes two minutes to make one cut through a log. How long will he need to cut a ten-foot long log into four equal pieces?
1 solutions

Answer 247505 by Fombitz(13828) About Me  on 2010-09-21 11:26:09 (Show Source):
You can put this solution on YOUR website!
1 cut yields 2 pieces.
3 cuts will yield 4 pieces.
1 cut takes 2 minutes.
3 cuts take 3(2) or 6 minutes.


test/346095: Graph each equation. Check your work.
-2x+5y=-10
1 solutions

Answer 247504 by Fombitz(13828) About Me  on 2010-09-21 11:24:39 (Show Source):
You can put this solution on YOUR website!
Find the intercepts.
To find the x-intercept, set y=0 and solve for x.
+-2x%2B5y=-10
-2x%2B5%280%29=-10
-2x=-10
x=5
(5,0)
.
.
.
To find the y-intercept, set x=0+and solve for y.
-2x%2B5y=-10
-2%280%29%2B5y=-10
5y=-10
y=-2
(0,-2)
.
.
.
Plot the points and connect them with a line.
.
.
.


Distributive-associative-commutative-properties/346133: state the name of the property illustrated
(x+4)+[-(x+4)]=0
1 solutions

Answer 247503 by Fombitz(13828) About Me  on 2010-09-21 11:20:38 (Show Source):
You can put this solution on YOUR website!
Additive inverse property


Equations/346097: (1/y-1)/[2+(1/y-1)]
please show how you got your answer thank you
1 solutions

Answer 247502 by Fombitz(13828) About Me  on 2010-09-21 11:20:15 (Show Source):
You can put this solution on YOUR website!
%281%2F%28y-1%29%29%2F%282%2B%281%2F%28y-1%29%29%29
Multiply numerator and denominator by %28y-1%29

%281%2F%28y-1%29%29%2F%282%2B%281%2F%28y-1%29%29%29=+1%2F%282y-2%2B1%29
%281%2F%28y-1%29%29%2F%282%2B%281%2F%28y-1%29%29%29=+highlight%281%2F%282y-1%29%29


Percentage-and-ratio-word-problems/346112: You have $10,000 to invest. Some was invested at 6% and the other at 11% for one year. If you made $800, how much was invested at each percentage?
1 solutions

Answer 247499 by Fombitz(13828) About Me  on 2010-09-21 11:16:13 (Show Source):
You can put this solution on YOUR website!
Let A be the amount at 6%, B the amount at 11%.
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1.A%2BB=10000
2.6A%2B11B=80000
Multiply eq. 1 by (-6) and add to eq. 2,
-6A-6B%2B6A%2B11B=-60000%2B80000
5B=20000
highlight%28+B=4000%29
Then from eq. 1,
A%2B4000=10000
highlight%28A=6000%29
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$6000 at 6% and $4000 at 11%.


Quadratic_Equations/346130: How do i solve this quadratic equation?
x=^-b+√b^2-4ac
2a
1 solutions

Answer 247498 by Fombitz(13828) About Me  on 2010-09-21 11:12:51 (Show Source):
You can put this solution on YOUR website!
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
That's not a quadratic equation, it's the quadratic formula.
It's the solution to the quadratic equation,
ax%5E2%2Bbx%2Bc=0


Quadratic_Equations/346128: How do I solve this quadratic equation?
x^2-5x-14=0
1 solutions

Answer 247497 by Fombitz(13828) About Me  on 2010-09-21 11:10:35 (Show Source):
You can put this solution on YOUR website!
Factor,
x%5E2-5x-14=0
%28x-7%29%28x%2B2%29=0
Two solutions:
x-7=0
highlight%28x=7%29
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x%2B2=0
highlight%28x=-2%29