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Parallelograms/375883: How can I prove that opposite angles of a parallelogram are congruent?
1 solutions

Answer 267316 by Fombitz(13828) About Me  on 2010-11-24 15:50:04 (Show Source):
You can put this solution on YOUR website!
Use the argument that when parallel lines are cut by a transversal, alternate interior angles are congruent.


Probability-and-statistics/375889: You rolll two dice, a green one and a red one. What is the probability of getting a sum of 11?
1 solutions

Answer 267315 by Fombitz(13828) About Me  on 2010-11-24 15:49:02 (Show Source):
You can put this solution on YOUR website!
There are 36 possible outcomes for the pair of dice.
(5,6)
(6,5)
Only 2 of them sum to 11.
P%2811%29=2%2F36=1%2F18


Quadratic_Equations/375879: 3x^2 + 9x, find x and y intercepts,range and vertex.
1 solutions

Answer 267314 by Fombitz(13828) About Me  on 2010-11-24 15:48:06 (Show Source):
You can put this solution on YOUR website!
y=3x%5E2%2B9x
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.
Y=intercept:
x=0%7D%7D%0D%0A%7B%7B%7By=3%280%29%2B9%280%29=0
(0,0)
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.
X-intercepts:
3x%5E2%2B9x=0
3x%28x%2B3%29=0
Two solutions:
x=0
(0,0)
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.
x%2B3=0
x=-3
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(-3,0)
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.
.
Convert to vertex form, y=a%28x-h%29%5E2%2Bk by completing the square.
y=3x%5E2%2B9x
y=3%28x%5E2%2B3x%29
y=3%28x%5E2%2B3x%2B9%2F4%29-3%289%2F4%29
y=3%28x%2B3%2F2%29%5E2-27%2F4
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Since a=3%3E0, the parabola opens upwards and the value at the vertex is the function minimum.
Range: (-27%2F4,infinity)
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logarithm/375800: 3 exponent3x = 4 x 10 exponent x, find x
8 exponent3x/24=2730/2( exponent3x-2 ), find x
1 solutions

Answer 267313 by Fombitz(13828) About Me  on 2010-11-24 15:34:31 (Show Source):
You can put this solution on YOUR website!
Use the caret to signify an exponent. 3^(3x)=3%5E%283x%29
3%5E%283x%29=4%2A10%5E%28x%29
log%283%2C%283%5E%283x%29%29%29=log%283%2C%284%2A10%5E%28x%29%29%29
3x=log%283%2C%284%29%29%2Blog%283%2C%2810%5E%28x%29%29%29
3x=log%283%2C%284%29%29%2Bx%2Alog%283%2C%2810%29%29
3x-x%2Alog%283%2C%2810%29%29=log%283%2C%284%29%29
x%283-log%283%2C%2810%29%29%29=log%283%2C%284%29%29
highlight%28x=log%283%2C%284%29%29%2F%283-log%283%2C%2810%29%29%29%29
x=log%2810%2C%284%29%29%2F%283%2Alog%2810%2C3%29-log%2810%2C%2810%29%29%29
x=log%2810%2C%284%29%29%2F%283%2Alog%2810%2C3%29-1%29%29
or approximately,
x=1.3957


Probability-and-statistics/375771: Please explain.
If a probability distribution curve is bell-shaped, then this is a normal distributaion.

1 solutions

Answer 267312 by Fombitz(13828) About Me  on 2010-11-24 15:19:50 (Show Source):
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Not necessarily.
A normal distribution does have a bell shaped curve but there are other requirements that make it a normal distribution.


logarithm/375870: Write the expression in condensed form: 1/2logx - logy + logz
1 solutions

Answer 267311 by Fombitz(13828) About Me  on 2010-11-24 15:18:34 (Show Source):


Linear-equations/375878: plz help. find the slope of the line containing the points (2,5)and (4,9)
1 solutions

Answer 267310 by Fombitz(13828) About Me  on 2010-11-24 15:16:37 (Show Source):
You can put this solution on YOUR website!
Use the formula for slope,
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%289-5%29%2F%284-2%29


Quadratic_Equations/375885: Find a fourth degree polynomial function f(x) having only real coefficients,-1,4, and i as zeros, and f(2)=30
1 solutions

Answer 267309 by Fombitz(13828) About Me  on 2010-11-24 15:15:35 (Show Source):
You can put this solution on YOUR website!
If x=i is a solution, then so is x=-i since complex solutions only come in complex conjuate pairs.
f%28x%29=a%28x-1%29%28x-4%29%28x-i%29%28x%2Bi%29
f%28x%29=a%28x-1%29%28x-4%29%28x%5E2%2B1%29
.
.
f%282%29=a%282-1%29%282-4%29%282%5E2%2B1%29=30
a%281%29%28-2%29%285%29=30
a=-3
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.
.
highlight%28f%28x%29=-3%28x-1%29%28x-4%29%28x%5E2%2B1%29%29


Systems-of-equations/375882: SOlve using the multiplication principle first, then use the elimination method:
7p+5q=2
8p-9q=17, I came up with p=1, q=1, however I plugged this into a different site to double check my work and was told something different.
1 solutions

Answer 267308 by Fombitz(13828) About Me  on 2010-11-24 15:13:21 (Show Source):
You can put this solution on YOUR website!
A different site?
The quickest and easiest way is to just plug the results into the original equations.
7p%2B5q=2
7%2B5=2
12=2
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.
8p-9q=17
8-9=17
-1=17
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The results are not good.
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1.7p%2B5q=2
2.
103p=103
highlight%28p=1%29
Now use either equation to solve for q.
7p%2B5q=2
7%2B5q=2
5q=-5
highlight%28q=-1%29


Probability-and-statistics/375836: When you add the values 3, 5, 8, 12, and 20 and then divide by the number of values, the result is 9.6. Which term best describes this value: average, mean, median, mode, or standard deviation?
1 solutions

Answer 267307 by Fombitz(13828) About Me  on 2010-11-24 14:30:26 (Show Source):
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Summing the values and dividing by the number of values gives you the average.


Distributive-associative-commutative-properties/375852: The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is, in fact, improved. The remaining 75% believe that this is just hype (the same old thing with no real improvement). Suppose a marketing study consists of a random sample of twelve people who are given a sales talk about a new, improved product.
Compute the mean and standard deviation of this probability distribution.
1 solutions

Answer 267306 by Fombitz(13828) About Me  on 2010-11-24 14:29:19 (Show Source):
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Find the probability for the number of believers from 0 to 12.
P%280%29=1%2A%280.75%29%5E12%2A%280.25%29%5E0=0.03168
P%281%29=12%2A%280.75%29%5E11%2A%280.25%29%5E1=0.12671
P%282%29=66%2A%280.75%29%5E10%2A%280.25%29%5E2=0.23229
P%283%29=220%2A%280.75%29%5E9%2A%280.25%29%5E3=0.25810
P%284%29=495%2A%280.75%29%5E8%2A%280.25%29%5E4=0.19358
P%285%29=792%2A%280.75%29%5E7%2A%280.25%29%5E5=0.10324
P%286%29=924%2A%280.75%29%5E6%2A%280.25%29%5E6=0.04015
P%287%29=792%2A%280.75%29%5E5%2A%280.25%29%5E7=0.01147
P%288%29=495%2A%280.75%29%5E4%2A%280.25%29%5E8=0.00239
P%289%29=220%2A%280.75%29%5E3%2A%280.25%29%5E9=0.00035
P%2810%29=66%2A%280.75%29%5E2%2A%280.25%29%5E10=0.00004
P%2811%29=12%2A%280.75%29%5E1%2A%280.25%29%5E11=0.00000
P%2812%29=1%2A%280.75%29%5E0%2A%280.25%29%5E12=0.00000
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mu=sum%28x%2AP%28x%29%2C0%2C12%29
mu=3
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.
VAR=sum%28%28x-mu%29%5E2%2AP%28x%29%2C0%2C12%29
VAR=2.25
sigma=sqrt%28VAR%29=1.5%29
.
.
.


Mixture_Word_Problems/375857: A farmer wants to mix milk containing 6% butterfat with 2 quarts of cream that is 15% butterfat to obtain a mixture that is 12% butterfat. How much milk containing 6% butterfat must he use?
1 solutions

Answer 267305 by Fombitz(13828) About Me  on 2010-11-24 14:20:02 (Show Source):
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Let A be the amount of milk she adds.
6A%2B15%282%29=12%28A%2B2%29
6A%2B30=12A%2B24
6A=6
highlight%28A=1%29quart


logarithm/375867: how to solve:
log(2x+3)+log(x-2)=2logx
1 solutions

Answer 267304 by Fombitz(13828) About Me  on 2010-11-24 14:18:39 (Show Source):
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log%28%282x%2B3%29%29%2Blog%28%28x-2%29%29=2log%28%28x%29%29
log%28%282x%2B3%29%28x-2%29%29=log%28%28x%5E2%29%29
%282x%2B3%29%28x-2%29=x%5E2
2x%5E2-x-6=x%5E2
x%5E2-x-6=0
%28x-3%29%28x%2B2%29=0
Two solutions:
x-3=0
x=3
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.
.
x%2B2=0
x=-2
Verify the solutions.
log%28%282x%2B3%29%29%2Blog%28%28x-2%29%29=2log%28%28x%29%29
log%28%282%283%29%2B3%29%29%2Blog%28%283-2%29%29=2log%28%283%29%29
log%28%289%29%29%2Blog%28%281%29%29=2log%28%283%29%29
log%28%289%29%29=log%28%289%29%29
.
.
.
log%28%282x%2B3%29%29%2Blog%28%28x-2%29%29=2log%28%28x%29%29
log%28%282%28-2%29%2B3%29%29%2Blog%28%28-2-2%29%29=2log%28%28-2%29%29
This solution is not allowed since the log function requires a positive argument.
.
.
.
highlight%28x=3%29


Linear_Algebra/375869: what is the solution set of (4x-3)+2>11
1 solutions

Answer 267303 by Fombitz(13828) About Me  on 2010-11-24 14:14:41 (Show Source):


Probability-and-statistics/375868: if odds against an event occurring are 2:7,what is the probability of the event occurring?
1 solutions

Answer 267302 by Fombitz(13828) About Me  on 2010-11-24 14:13:47 (Show Source):
You can put this solution on YOUR website!
Odds are given as outcomes against to outcomes for.
Probability is given as outcomes for divided by total outcomes.
P=7%2F9


logarithm/375823: e^x-2=(1/e^6)^x+4
1 solutions

Answer 267301 by Fombitz(13828) About Me  on 2010-11-24 14:12:33 (Show Source):


Geometry_Word_Problems/375849: If the area of a rectangle is 128cm, what is the parameter if the length is twice the width?
1 solutions

Answer 267300 by Fombitz(13828) About Me  on 2010-11-24 14:07:38 (Show Source):
You can put this solution on YOUR website!
A=L%2AW
A=%282W%29%2AW=128
W%5E2=64
W=8cm
L=2W=16cm
I think you mean perimeter,
P=2L%2B2W
P=16%2B32
highlight%28P=48%29cm


Probability-and-statistics/375774: Please explain:
Because the tails of the normal distribution curve are infinitely long, the total area under the curve is also infinite. 0

1 solutions

Answer 267298 by Fombitz(13828) About Me  on 2010-11-24 14:05:31 (Show Source):
You can put this solution on YOUR website!
False, the area under the curve of a normal distribution curve equals 1.


Equations/375865: Is there an equation in algerbra for the number of days in a year. My wife says there is but don't remember it. If there are 365 days in a year, 52 weeks in a year and 7 days in one week then 7 x 52 = 364. Where does the other day come from.
Thanks
Hugh
1 solutions

Answer 267297 by Fombitz(13828) About Me  on 2010-11-24 14:02:33 (Show Source):
You can put this solution on YOUR website!
30 days hath September,
April, June and November,
All the rest have 31,
Excepting February alone.
Which only has but 28 days clear
And 29 in each leap year
.
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.
N=4%2A30%2B28%2B7%2A31=120%2B28%2B217=365
N%5Bleap%5D=366


Quadratic_Equations/375858: Hi, Totally Stuck here, not sure if the lecturer has skiped over this part,
Find dy=dx as a function of x and y when:
(a) y - x sin y - 3x^2 - 1 = 0
(b) x^2y^3 - x^2 + 3y - 3 = 0
(c) (1 - x^2) tan^-1 y = 3
Thanks
1 solutions

Answer 267296 by Fombitz(13828) About Me  on 2010-11-24 13:58:32 (Show Source):
You can put this solution on YOUR website!
Use implicit differentiation, treat each terms as if it is differentiable (other than constants). Use the product rule, etc. to simplify. Gather up all of the dy and dx terms and then form the quotient, dy/dx.
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I'll do one, you do the rest.
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y+-+x%2Asin%28y%29+-+3x%5E2+-+1=0
dy-%28x%2Acos%28y%29dy%2Bsin%28y%29%2Adx%29-6xdx=0
dy-x%2Acos%28y%29dy=6xdx%2Bsin%28y%29dx
dy%281-x%2Acos%28y%29%29=%286x%2Bsin%28y%29%29dx
highlight%28dy%2Fdx=%286x%2Bsin%28y%29%29%2F%281-x%2Acos%28y%29%29%29


test/375862: Find the maximum value of f ( x ) = 4 x + y given the feasible region.

1 solutions

Answer 267294 by Fombitz(13828) About Me  on 2010-11-24 13:53:50 (Show Source):
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No feasible region given.


Expressions-with-variables/375846: if a and b are positive integers and (a^(1/2) * b^(1/3)) = 432, what is the value of ab?
1 solutions

Answer 267293 by Fombitz(13828) About Me  on 2010-11-24 13:51:17 (Show Source):
You can put this solution on YOUR website!
a%5E%281%2F2%29%2A+b%5E%281%2F3%29+=+432
Square both sides.
a%5E%283%2F2%29%2Ab=432%5E3
Cube both sides.
a%5E3b%5E2=432%5E6
Look at factors of 432,
a%5E3b%5E2=%282%5E4%2A3%5E3%29%5E6
a%5E3b%5E2=2%5E24%2A3%5E18
Two solutions:
a%5E3=2%5E24, highlight%28+a=2%5E8%29
b%5E2=3%5E18, highlight%28b=3%5E9%29
or
a%5E3=3%5E18, highlight_green%28a=3%5E6%29
b%5E2=2%5E24, highlight_green%28b=2%5E12%29


Square-cubic-other-roots/375825: Can someone please help me this makes no sense to me. I have tried everything and nothing is working. Square rootx-3-3=4
1 solutions

Answer 267290 by Fombitz(13828) About Me  on 2010-11-24 13:21:43 (Show Source):


Circles/375826: Find the center of the circle defined by the equation 4x^2+ 4y^2+24x-56y
+168=0
1 solutions

Answer 267289 by Fombitz(13828) About Me  on 2010-11-24 13:20:12 (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B+4y%5E2%2B24x-56y%2B168=0
x%5E2%2B+y%5E2%2B6x-14y%2B42=0
%28x%5E2%2B6x%29%2B+%28y%5E2-14y%29%2B42=0
%28x%5E2%2B6x%2B9%29%2B+%28y%5E2-14y%2B49%29%2B42=9%2B49
%28x%2B3%29%5E2%2B+%28y-7%29%5E2=16
Compare to the equation of a circle centered at (h,k) with radius R,
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
h=-3
k=7


Linear-equations/375828: Write y = x + 6 in standard form using integers.
1 solutions

Answer 267287 by Fombitz(13828) About Me  on 2010-11-24 13:17:36 (Show Source):


Linear-equations/375832: Please help.
Write an eqution of the line containing the given point and parallel to the given line. Express your answer in y = mx+b.
(2,4); x +6y=5
1 solutions

Answer 267285 by Fombitz(13828) About Me  on 2010-11-24 13:16:45 (Show Source):
You can put this solution on YOUR website!

A parallel line would have the same left hand side, different right hand side.
Use the point to determine the new right hand side.
x%2B6y=2%2B6%284%29=2%2B24=26
.
.
.
x%2B6y=26
6y=-x%2B26
highlight%28y=-%281%2F6%29x%2B13%2F3%29


Probability-and-statistics/375834: how many different four character passwrods can be formed from the numerals 0-9 and the lower case letters of the alphabet

1 solutions

Answer 267284 by Fombitz(13828) About Me  on 2010-11-24 13:14:57 (Show Source):
You can put this solution on YOUR website!
Each of the 4 positions has 36 possible values.
N=36%2A36%2A36%2A36=1679616


Exponential-and-logarithmic-functions/375847: for all non zero r,t,z values 12r5tz7 / -4rt5z3 =? please note that the numbers 5, 7, 5, and 3 are exponents to the letters
1 solutions

Answer 267283 by Fombitz(13828) About Me  on 2010-11-24 13:13:36 (Show Source):


Probability-and-statistics/375544: Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Supposing that the probability distribution of y is as follows below, determine the mean value of z = the number of unbroken eggs.
μz = ?
y 0 1 2 3 4
p(y) .65 .20 .12 .02 .01
1 solutions

Answer 267269 by Fombitz(13828) About Me  on 2010-11-24 11:11:05 (Show Source):


Polynomials-and-rational-expressions/375540: Without performing and mathematical calculations explain why there cannot be any solutions to the equation.
√2x^2-4 + 2√3-4x +1= -6
1 solutions

Answer 267267 by Fombitz(13828) About Me  on 2010-11-24 11:08:33 (Show Source):
You can put this solution on YOUR website!

sqrt%282x%5E2-4%29%2B2%2Asqrt%283-4x%29%2B1=-6
.
.
.
The assumption here is that only the positive square root for each function will be used.
The square root functions only provide non-negative results.
Adding two non-negative results to 1 will never provide a negative sum.


expressions/375815: Solve using the multiplication principle.
4b = -76

1 solutions

Answer 267266 by Fombitz(13828) About Me  on 2010-11-24 11:00:45 (Show Source):