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Square-cubic-other-roots/582768: What is a rational exponent? How are rational exponents related to radicals? Give an example of how an expression with a rational exponent can be rewritten as a radical expression. Please do not provide the formula, your example should contain numbers/letters.
1 solutions
Answer 372235 by richard1234(5390)   on 2012-03-05 21:47:08 (Show Source):
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Numbers_Word_Problems/582523: 1) I am a 2-digit number less than 90.
2) Three more than my value is an even number.
3) The sum of my digits is a multiple of 8.
1 solutions
Answer 372081 by richard1234(5390) on 2012-03-05 16:19:19 (Show Source):
You can put this solution on YOUR website!2) Three more than my value is an even number.
This is just a "tricky" way of saying "I am an odd number."
3) The sum of my digits is a multiple of 8.
Since we have a 2-digit number, the digit sum must be either 8 or 16 (24 is too large). If it is 8, then we have 71, 53, 35, 17. If it is 16, we have 79 (97 is too large).
Therefore all the possible numbers are 17, 35, 53, 71, and 79.
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Miscellaneous_Word_Problems/582299: Prove by induction that if n distinct dice are rolled, then the number of outcomes where the
sum of the faces is an even integer equals the number of outcomes where the sum of the faces
is an odd integer?
1 solutions
Answer 372080 by richard1234(5390) on 2012-03-05 16:17:13 (Show Source):
You can put this solution on YOUR website!Base case n=1 is obviously true.
Suppose that the statement is true for n dice (n>1). If we add another die that is distinguishable from the other n dice, then for each sequence of n dice rolls  , we can let
 is even if and only if S is even and the (n+1)th roll is even, or if S is odd and the (n+1)th roll is odd. If we look at this from a probabilistic view, we have
P(S even) = 1/2 because there are as many even outcomes as odd outcomes
P((n+1)th roll even) = 1/2 because 2,4,6 are even
Therefore P(S even and (n+1)th roll even) = 1/4. Similarly, P(S odd and (n+1)th roll odd) = 1/4, so P(S + a_(n+1) even) = 1/2, which is half of all the possible outcomes. Hence we are done.
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Polynomials-and-rational-expressions/582095: I need help factoring. I just don't get it.
8x^2y+34xy-84y
1 solutions
Answer 372004 by richard1234(5390) on 2012-03-05 00:06:02 (Show Source):
You can put this solution on YOUR website!First you can factor out 2y:
)
The 4x^2 + 17x - 42 is a bit tricky to factor; the best way to learn is by experience and simply being able to "see" the correct factorization.
4x^2 + 17x - 42 can be factored into a product (ax + b)(cx + d). We want ac = 4, so a,c can equal 2 or 1,4. However, if a = c = +/- 2, the x coefficient will be even, so try a=1, c=4. We can kind of "guess and check" based on the factorization of -42 to obtain the factorization
(4x - 7)) , in which the complete answer would be (4x-7)) .
Again, this takes lots of practice. Another way you could factor it is to find the roots of 4x^2 + 17x - 42 by the quadratic formula:
Then you could factor it as (x + 6)) . However, the leading coefficient is 4 so we can multiply the first term by 4.
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Polynomials-and-rational-expressions/582155: According to Newton's universal gravitation, the attractive force F between two bodies is given by
where m1 and m2 are the mass of the two bodies, r is the distance between the two bodies, and G is the gravitational constant =  newtons meter squared kilogram squared.
Suppose an object is traveling directly from Earth to the moon. The mass of Earth is  kilograms, the mass of the moon is  kilograms, and the mean distance from Earth to the moon is 384000 kilometers. For an object between Earth and the moon, how far from Earth is the force on the object due to the moon greater than the force on the object due to Earth?
Thank you!
1 solutions
Answer 372002 by richard1234(5390) on 2012-03-04 23:55:39 (Show Source):
You can put this solution on YOUR website!Suppose d is the distance between this object and Earth, m_1 is the mass of the object, m_2 and m_3 are the masses of the Earth and moon, respectively. Then r-d or 384000-d is the distance between the object and the Moon. We want the following inequality to be true:
^2})
G and m_1 cancel, leaving
^2} \Rightarrow m_2 (r-d)^2 < m_3 d^2 \Rightarrow m_2 (r-d)^2 - m_3 d^2 < 0)
Since m_2, m_3, and r are known, solve the quadratic in terms of d (you will have to expand, simplify first), replace m_2, m_3, r in, and find the smallest d such that the gravitational force from the Moon is greater than the force from the Earth.
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Probability-and-statistics/581518: There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores are approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean μ = 1509 and standard deviation σ = 321.
Tonya scores 1770 on the SAT. Jermaine scores 28 on the ACT. Assuming that both tests measure the same thing, who has the higher score? Report the z-scores for both students. (Round your answers to two decimal places.)
Tonya's score standardizes to z = .
Jermaine's score standardizes to z = .
Therefore,.......... has the higher score.
1 solutions
Answer 371956 by richard1234(5390) on 2012-03-04 19:16:41 (Show Source):
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Polygons/581522: How many different ways can you find the area of a regular octagon with all sides equal to 3 meters? Describe each method and use it to find the area. Are the answers the same? Should the answers be the same?
1 solutions
Answer 371906 by richard1234(5390) on 2012-03-04 16:04:19 (Show Source):
You can put this solution on YOUR website!Suppose the vertices of the octagon are A,B,C,...,H in counterclockwise order with AB = 3 m, and O is the center.
1. Divide up the octagon into four triangles and five rectangles (draw lines AF, BE, CH, DG). Find the area of each shape using your knowledge about 45-45-90 triangles.
2. Think of the octagon as a square with four right isosceles triangles cut off. Find the area of the square, then subtract off the areas of the triangles.
3. Divide up the octagon into eight congruent isosceles triangles (OAB, OBC, etc.). Use the area formula A = (1/2)ab sin C where a = b = the radius of the circumscribed circle, and C = 45 deg. You may need additional theorems, such as law of sines.
There are many other ways, but most of them are similar to the above three. You should obtain the same answer in each case.
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decimal-numbers/581769: in your lesson "This Lesson (WHAT IS a decimal)" i believe you may have a typo at the very end. 2.2/5=2.2 but i think it should be 2.2/5=2.4 hope this helps and if i'm wrong please email me or even if i'm right that would be cool thanks
1 solutions
Answer 371902 by richard1234(5390) on 2012-03-04 15:58:25 (Show Source):
You can put this solution on YOUR website!Whoops, didn't see the link to the lesson. Yes, 2/5 = .4, not .2. I didn't write that lesson, so you can email the author of the website (who is also the owner of this website) if you wish, at ichudov@algebra.com. Make sure that you are clear with your notation; 2.2/5 is usually interpreted as 2.2 over 5 (or .44), while 2 2/5 means 2 and 2/5 (or 2.4), which is probably what you want.
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Probability-and-statistics/581090: The scatter plot shows the average temperature each month in a particular city. What is a good prediction for the temperature in July if the temperature continues to increase until then?
1 solutions
Answer 371470 by richard1234(5390) on 2012-03-02 00:29:31 (Show Source):
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Quadratic_Equations/580658: 6. Just the Math: Quadratic Function The equation that
you wrote for the area, y=x^2, represents the simplest form of a
quadratic function. A quadratic function is a function of the
form f(x) = ax^2 +bx+c, where a, b, and c are constants with
a=(a line thru the = mark)0. The graph of a quadratic function is a U-shaped graph.
What can you conclude about the rate of change of a quadratic
function? Use a complete sentence in your answer.
7. Identify the values of a, b, and c in each quadratic function
below.
h(x) = x2 - 3x
g(x) = 10 - x^2
f(x) = 2x^2 + 3x+5
f(x) = x^2 - 2x + 8
h(x) =2^2+4x-1
g(x) =x^2 +4
1 solutions
Answer 371384 by richard1234(5390) on 2012-03-01 17:34:50 (Show Source):
You can put this solution on YOUR website!6. The rate of change of a quadratic function  = ax^2 + bx + c) is
 - f(x)}{\Delta x})
You can evaluate it yourself, but if you know the chain rule you can conclude that it is equal to
 = 2ax + b)
7. Easy, a is the coefficient of x^2, b is the coefficient of x, and c is the constant term. For example,
h(x) = x^2 - 3x
has leading coefficient 1, x coefficient -3, and 0 as the constant term. Hence
a = 1
b = -3
c = 0
Try the others the same way.
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Probability-and-statistics/579978: How would you work the problem- what is the probability that a number selected at random from the firs 600 positive integers is divisible by 6 or 9?
1 solutions
Answer 371270 by richard1234(5390) on 2012-02-29 22:37:53 (Show Source):
You can put this solution on YOUR website!Inclusion-exclusion principle. (let n be a number between 1 and 600 inclusive):
 = P(6|n) + P(9|n) - P(18|n))
Note that P(6|n and 9|n) is equivalent to saying P(18|n) since LCM(6,9) = 18.
Out of the integers between 1 and 600 inclusive, there are 100 integers divisible by 6, 66 divisible by 9, and 33 divisible by 18. Therefore,
 = \frac{100}{600} + \frac{66}{600} - \frac{33}{100})
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Probability-and-statistics/579853: For my assignment I am asked to explain what is wrong and why it is wrong. The question reads: If a correlation coefficient of r=0.642 was found between two variables in a sample of paired data that were measured in feet, the value of r would change by a factor of twelve if the data were converted to inches and r was computed again.
I have worked several problems that ask you to switch x and y values to calculate r and in those problems when you switch the x and y values r remains the same and that is clear to me. However, this problem has me stumped.
Thanks for any help or direction you can give me!!
1 solutions
Answer 371083 by richard1234(5390) on 2012-02-28 23:15:18 (Show Source):
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Linear_Algebra/579421: I got this wrong comparing similar triangles - The equation was 9/1 = 8/x My answer was infinite - .88888. . . and wrong. What is the correct answer (9 compared to a length of 1 on similar triangle,same with 8 to x).
1 solutions
Answer 371079 by richard1234(5390) on 2012-02-28 22:33:46 (Show Source):
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Triangles/579529: The length of the hypotenuse of a 30°-60°-90° triangle is 12. Find the perimeter.
1 solutions
Answer 371076 by richard1234(5390) on 2012-02-28 22:27:38 (Show Source):
You can put this solution on YOUR website!Side lengths of a 30-60-90 triangle are in the ratio of 1:sqrt(3):2.
The hypotenuse is 12 so the other side lengths are 6 and 6sqrt(3). Therefore the perimeter is 18 + 6sqrt(3).
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