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Number-Line/350025: how to write that 4 is less than 1 in a number line
1 solutions

Answer 250248 by Fombitz(13828) About Me  on 2010-09-30 10:17:39 (Show Source):
You can put this solution on YOUR website!
You can't write it on a number line.
Anyways, 4 is not less than 1.
4 is greater than 1 as shown on the number line.
Values to the left of a number are smaller than the number on a number line.
number_line%28600%2C-2%2C5%2C1%2C4%29


Coordinate-system/350008: The profit earned from manufacturing x widgets is .0001x^3 - .21x^2 + 135x - 2000 dollars. Other contraints dictate that at least 200 widegets but no more than 950 widgets be manufactured.
Use your graphing calculator to determine how many widgets should be produced to earn the maximum profit.
1 solutions

Answer 250246 by Fombitz(13828) About Me  on 2010-09-30 10:12:18 (Show Source):
You can put this solution on YOUR website!

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This function has a local maxima of 25500 when x=500


decimal-numbers/350009: Round each number to the stated place value
14. 16.3521 tenths
15. 1.999 tenths
1 solutions

Answer 250245 by Fombitz(13828) About Me  on 2010-09-30 10:06:56 (Show Source):
You can put this solution on YOUR website!
16.3521 =16.4
1.999=2.0


Quadratic_Equations/350129: simplify your answer: 18th root of (-8)^18
i believe the answer would be 8 and -8 due to taking the 18th root of -8^18
1 solutions

Answer 250244 by Fombitz(13828) About Me  on 2010-09-30 10:06:01 (Show Source):
You can put this solution on YOUR website!
Yes, that's correct.
8 and -8.


Points-lines-and-rays/350092: Find the equation of the line joining the points
(─7, 6, ─ 3) and (7, ─ 6, 3).
1 solutions

Answer 250243 by Fombitz(13828) About Me  on 2010-09-30 10:05:03 (Show Source):
You can put this solution on YOUR website!
Using the two sets of points and the parameter t (t=1),
x=-7%2B14t
y=6%2B12t
z=-3%2B6t
Solve each in terms of t.
%28x%2B7%29%2F14=t
%28y-6%29%2F12=t
%28z%2B3%29%2F6=t
The equation of the line is then,
%28x%2B7%29%2F14=%28y-6%29%2F12=%28z%2B3%29%2F6


Quadratic_Equations/350127: (h^4)/(h^16) divide and simplify I divided the 16th exponent by 4 getting four so would the answer b H^4?
1 solutions

Answer 250241 by Fombitz(13828) About Me  on 2010-09-30 09:58:28 (Show Source):
You can put this solution on YOUR website!
No, the law of exponents for division with same base is to subtract exponents.
h%5E4%2Fh%5E16=h%5E%284-16%29=h%5E%28-12%29=1%2Fh%5E12


test/350019: Please help me solve this equation: Find a vertical line x=a that bisects the region bounded by the curve +y=1%2Fx%5E2+, the x-axis and between x=1 and x=8.
1 solutions

Answer 250239 by Fombitz(13828) About Me  on 2010-09-30 09:56:47 (Show Source):
You can put this solution on YOUR website!
I think you mean bisect the area generated by the curve and the x-axis?
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int%28%281%2Fx%5E2%29%2Cdx%2C1%2Ca%29=int%28%281%2Fx%5E2%29%2Cdx%2Ca%2C8%29
int%28%281%2Fx%5E2%29%2Cdx%29=-1%2Fx%2BC
-1%2Fa%2B1=-1%2F8%2B1%2Fa
-2%2Fa=-9%2F8
1%2Fa=9%2F16
a=16%2F9
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highlight%28x=16%2F9%29


Coordinate-system/350012: For the function f(x) = x2 + 5x - 5, find and simplify the difference quotient (f(x)-f(1))/(x-1)
1 solutions

Answer 250237 by Fombitz(13828) About Me  on 2010-09-30 09:50:07 (Show Source):


Quadratic_Equations/350123: i started this question however am unsure if it is correct question: √((a+4)²)
since we are looking for the square root of (a+4)^2 i would think that the answer is just a+4 because squaring it would be a^2+4^2 and the square root of that would be a+4

1 solutions

Answer 250235 by Fombitz(13828) About Me  on 2010-09-30 09:46:51 (Show Source):
You can put this solution on YOUR website!
First,
%28a%2B4%29%5E2 does not equal a%5E2%2B4%5E2.
Using the FOIL method,
%28a%2B4%29%5E2=%28a%2B4%29%28a%2B4%29
%28a%2B4%29%5E2=a%5E2%2B4a%2B4a%2B4%5E2
%28a%2B4%29%5E2=a%5E2%2B8a%2B4%5E2
There is a cross product term.
As an example,
%281%2B2%29%5E2=3%5E2=9
If we did it like you showed,
%281%2B2%29%5E2=1%2B4=5+
which is clearly incorrect.
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The answer is %28a%2B4%29 but that may not be the complete answer because -%28a%2B4%29 is also an answer since -%28a%2B4%29%2A%28-%28a%2B4%29%29=%28a%2B4%29%5E2


Quadratic_Equations/350124: factor completley t^3-6t^2-27t or determine if not able to be factored.
1 solutions

Answer 250234 by Fombitz(13828) About Me  on 2010-09-30 09:40:00 (Show Source):


Geometry_Word_Problems/350112: If the area of a right triangle is 24 square inches and the hypotenuse is 12 inches, find the lengths of the legs of the triagle.
1 solutions

Answer 250233 by Fombitz(13828) About Me  on 2010-09-30 09:38:56 (Show Source):
You can put this solution on YOUR website!
Let x and y be the legs of the triangle.
A=%281%2F2%29xy=24
1.xy=48
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2.x%5E2%2By%5E2=12%5E2
Find the intersection points between these two functions.
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From eq. 1,
y=48%2Fx
y%5E2=2304%2Fx%5E2
Substitute into eq. 2,
x%5E2%2B2304%2Fx%5E2=144
x%5E4-144x%5E2%2B2304=0
x%5E4-144x%5E2%2B5184%2B2304=5184
%28x%5E2-72%29%5E2%2B2304=5184
%28x%5E2-72%29%5E2=2880
%28x%5E2-72%29%5E2=64%2A9%2A5
x%5E2-72=0+%2B-+8%2A3%2Asqrt%285%29
x%5E2=72+%2B-+24sqrt%285%29
or approximately,
x1=11.21 and x2=4.28
with corresponding y values of
y1=4.28 and y2=11.21



Probability-and-statistics/350116: A bag contains 4 blue marbles, 3 red marbles, 2 green marbles and a white marble. You reach in and randomly pick one marble, set it aside, and then randomly pick a second marble. What is the probability of picking two blue marbles?
1 solutions

Answer 250223 by Fombitz(13828) About Me  on 2010-09-30 09:10:04 (Show Source):
You can put this solution on YOUR website!
4 blue marbles
3 red marbles
2 green marbles
1 white marble
10 total
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To choose the 1st blue marble,
P%28B%29=4%2F10=2%2F5
To choose the 2nd blue marble,
P%28B%29=3%2F9=1%2F3
The probability of choosing both is,
P%282B%29=%282%2F5%29%281%2F3%29=2%2F15


Graphs/350111: Graph the equation and idenify the y intercept.
y=4x-3
I have unterstood for the most part i just am not understanding how they are getting the points for the variable x
1 solutions

Answer 250221 by Fombitz(13828) About Me  on 2010-09-30 09:04:23 (Show Source):
You can put this solution on YOUR website!
x values are values you choose.
That's the independent variable.
Then once you choose that, the value of y is determined, it's the dependent variable (dependent on your choice of x).
The y-intercept is the value of y when x=0.
It's the value of the function when it crosses the y-axis.
y=4x-3
y=4%280%29-3
y=-3
(0,-3)
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Choose any other x value and calculate y.
Then you'll have two points and you can draw your line.
How about x=2? Again, doesn't matter, it's your choice.
y=4x-3
y=4%282%29-3
y=8-3
y=5
(2,5)
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Now plot the points and connect them with a line.
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Probability-and-statistics/350110: If the probability of a student graduating from college with a 4.0 GPA is 0.008, what is the probability of a student graduating from college with less than a 4.0 GPA?
1 solutions

Answer 250220 by Fombitz(13828) About Me  on 2010-09-30 09:00:43 (Show Source):
You can put this solution on YOUR website!
Assuming that 4.0 is the highest GPA, then all other scores must be less than 4.0.
P(not 4.0)+P(4.0)=1
P(not 4.0)=1-P(4.0)
P(not 4.0)=1-0.008
P(not 4.0)=0.992


test/350018: Please help me solve this equation: Sketch the regions enclosed by the given curves and then find the area of the regions.
a. +y=e%5Ex+ +y=%28x-1%29%5E2+ and +x=2+
b. +y=-7-x%2B3x%5E2+ and +y=2x-x%5E2+
c. +y=1=cosx+ and +y=cosx+ +0%3C=x%3C=pi+
1 solutions

Answer 250218 by Fombitz(13828) About Me  on 2010-09-30 08:58:36 (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-2%2C4%2C-2%2C4%2Ce%5E%28x%29%2C%28x-1%29%5E2%2C2%29
Find the intersection point between y=e%5Ex and y=2
e%5Ex=2
x=ln%282%29
So then the area would be,

Expand the terms, integrate, and simplify to get the final answer.
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graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-7-x%2B3x%5E2%2C2x-x%5E2%29
Same procedure.
Find the two intersection points x1 and x2 by solving,
-7-x%2B3x%5E2=2x-x%5E2
Proceed as above integrating from one intersection point to the other.

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graph%28300%2C300%2C-1%2C4%2C-3%2C3%2C1%2Bcos%28x%29%2C1-cos%28x%29%2Ccos%28x%29%29
I'm not sure if the first function is 1%2Bcos%28x%29 or 1-cos%28x%29
If it's 1%2Bcos%28x%29, then the integration is straightforward since
1%2Bcos%28x%29-cos%28x%29=1
Integrating that over x=0 to x=pi would give you A=%28pi-0%29=pi
If it's 1-cos%28x%29, then find the intersection point x1 again where,
1-cos%28x%29=cos%28x%29
Then you have to modify the area because at this point the functions cross.
A=int%28%281-2cos%28x%29%29%2Cdx%2C0%2Cx1%29%2Bint%28%282cos%28x%29-1%29%2Cdx%2Cx1%2Cpi%29


Equations/350031: x = {(a1 * b1) + (a2 * b2)} / (a1 * a2)
How to express a2 in algebraic term?
1 solutions

Answer 250214 by Fombitz(13828) About Me  on 2010-09-30 08:41:31 (Show Source):
You can put this solution on YOUR website!
x=%28a%5B1%5Db%5B1%5D%2Ba%5B2%5Db%5B2%5D%29%2F%28a%5B1%5Da%5B2%5D%29
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a%5B1%5Da%5B2%5Dx=a%5B1%5Db%5B1%5D%2Ba%5B2%5Db%5B2%5D
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a%5B1%5Da%5B2%5Dx-a%5B2%5Db%5B2%5D=a%5B1%5Db%5B1%5D
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a%5B2%5D%28a%5B1%5Dx-b%5B2%5D%29=a%5B1%5Db%5B1%5D
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highlight%28a%5B2%5D=%28a%5B1%5Db%5B1%5D%29%2F%28a%5B1%5Dx-b%5B2%5D%29%29


absolute-value/350016: |2x-1|+1>6
1 solutions

Answer 250212 by Fombitz(13828) About Me  on 2010-09-30 08:38:33 (Show Source):
You can put this solution on YOUR website!
abs%282x-1%29%2B1%3E6
abs%282x-1%29%3E5
%282x-1%29%3E5 and -%282x%2B1%29%3E5
2x%3E6 and 2x%2B1%3C-5
x%3E3 and 2x%3C-4
x%3E3 and x%3C-2
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(-infinity,-2)U(3,infinity)
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Graphical verification: Look for regions where the red line is above the green line.
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Exponents/350017: (3m^-1n^4)^-2 (2m^3n^-5)^4
1 solutions

Answer 250210 by Fombitz(13828) About Me  on 2010-09-30 08:33:53 (Show Source):
You can put this solution on YOUR website!

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test/350079: Please help me solve this equation: Determine the sum for the following series:
(a) 100+10+1+...
(b) 27-9+3-1+...
1 solutions

Answer 250209 by Fombitz(13828) About Me  on 2010-09-30 08:28:48 (Show Source):
You can put this solution on YOUR website!
(a) 100+10+1+0.1+0.01+...=111.11111, repeating
1%2F9=0.11111 repeating.
Multiply both sides by 1000.
1000%2F9=111.1111
Sum=highlight%281000%2F9%29
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(b)27-9+3-1+...=


Exponents/350086: p2*p5*p/p6
1 solutions

Answer 250205 by Fombitz(13828) About Me  on 2010-09-30 08:03:26 (Show Source):


Matrices-and-determiminant/350085: suppose A is a 2 x 2 matrix as follows
A = [56
34]
how do i decide whether A is invertible? and if it is find A^-1
1 solutions

Answer 250204 by Fombitz(13828) About Me  on 2010-09-30 08:02:34 (Show Source):
You can put this solution on YOUR website!
A 2x2 matrix needs 4 elements.
You only have 2 elements.
Please repost.


Graphs/350095: What is 6(x-2)-2(x+3)>0? I need answer and graph please.
1 solutions

Answer 250203 by Fombitz(13828) About Me  on 2010-09-30 08:01:32 (Show Source):


Probability-and-statistics/350096: If a fair die is tossed one time, find the probability of getting a number less than 3 or an odd number.
thank-you
1 solutions

Answer 250202 by Fombitz(13828) About Me  on 2010-09-30 08:00:16 (Show Source):
You can put this solution on YOUR website!
P(1)=1%2F6
P(2)=1%2F6
P(odd)=3%2F6=1%2F2
P(<3 or odd)=1%2F6%2B1%2F6%2B1%2F2-1%2F6=2%2F3
1%2F6 is subtracted since the value of 1 is counted twice, once as an odd and once as a value less than 3.


Probability-and-statistics/350098: If the odds in favor of your winning a bet are 3 to 8, what are the odds against winning the bet?
1 solutions

Answer 250201 by Fombitz(13828) About Me  on 2010-09-30 07:57:24 (Show Source):
You can put this solution on YOUR website!
Odds for winning are given as outcomes for winning to outcomes against winning.
So the odds against winning would be the reverse or 8 to 3.


Functions/349941: A function is given below. Determine the average rate of change of the function between x = -5 and x = -1.
h(x) = x 2 + 8x
1 solutions

Answer 250158 by Fombitz(13828) About Me  on 2010-09-29 23:42:06 (Show Source):


Exponents-negative-and-fractional/349958: n%5E+-4%2Ft%5E1
1 solutions

Answer 250156 by Fombitz(13828) About Me  on 2010-09-29 23:38:02 (Show Source):


Polynomials-and-rational-expressions/349988: The question said perform the indicated operation and simplify:
6x+9/3x-15 * x-5/4x+6
1 solutions

Answer 250155 by Fombitz(13828) About Me  on 2010-09-29 23:37:16 (Show Source):


Exponents-negative-and-fractional/349997: 4 to negatice 3 power
1 solutions

Answer 250151 by Fombitz(13828) About Me  on 2010-09-29 23:33:45 (Show Source):


Probability-and-statistics/349911: A coin is tossed five times. Find the probability that the sixth toss is a tail, given that the first five tosses were all tails.
If a die is rolled one time, find the probability of getting a number greater than five.
If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade.
A pet supplier has a stock of parkeets of which thirty percent are blue parakeets. A pet store orders three parakeets from this supplier. If supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?
A university has 10,000 students of which 4000 are male and 6000 are female. If a class of 30 students is chosen at random from university population, find the mean and variance of the number of male students.


1 solutions

Answer 250073 by Fombitz(13828) About Me  on 2010-09-29 20:12:13 (Show Source):
You can put this solution on YOUR website!
I'll do 4 of the problems.
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a) P(T)=P(H)=1/2, it's independent of previous tosses if the coin is fair.
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b) P(6)=1/6
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c) P(Ace)=4/52=1/13
P(King of Hearts)=1/52
P(Spade)=4/52=1/13
P(Ace or K Hearts or Spade)=P(Ace)+P(K Hearts)+P(Spade)-P(Ace of Spades)
So we don't double count the Ace of Spades as an Ace and a Spade.
P(Ace of Spades)=1/52
P(Ace or K Hearts or Spade)=4/52+1/52+13/52-1/52=17/52
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d) P(B,NB,NB)=0.3(0.7)(0.7)
P(NB,B,NB)=0.7(0.3)(0.7)
P(NB,NB,B)=0.7(0.7)(0.3)
P(1 B)=3(0.3)(0.7)(0.7)=0.441


Divisibility_and_Prime_Numbers/349858: what is 9/28 divided by 27/35 in simplest form
1 solutions

Answer 250069 by Fombitz(13828) About Me  on 2010-09-29 20:05:41 (Show Source):
You can put this solution on YOUR website!
Dividing by a fraction is like multiplying by its reciprocal.
%289%2F28%29%2F%2827%2F35%29=%289%2F28%29%2835%2F27%29
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%289%2F28%29%2F%2827%2F35%29=%281%2F4%29%285%2F3%29
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%289%2F28%29%2F%2827%2F35%29=5%2F12


Exponents/349867: I figured out the answer but I cannot do the equation. here is the problem.
A 2000L tank containing 550L of water is being filled with water at the rate of 75L per minute from a full 1600L tank. How long will it be before the two tanks have the same amount of water?
Thank you.
1 solutions

Answer 250067 by Fombitz(13828) About Me  on 2010-09-29 20:03:36 (Show Source):
You can put this solution on YOUR website!
Find the amount of water in tank 1 (2000 L):A1=550%2B75t
Find the amount of water in tank 2 (1600 L):A2=1600-75t
When does A1=A2???
Find t.
A1=A2
550%2B75t=1600-75t
Take it from there to solve for t.