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Also students, please put parentheses wherever they need to go. For example, if I see something like

5/x-4^2 = 1

I have no idea what it means because there are multiple ways to interpret the question.

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37. Just let the tens digit be x, and the units digit be 2x + 1, and solve.

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It's impossible. Just draw an isosceles triangle and you'll see. Or, you can use the law of sines.

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The midpoint's just the average of the coordinates, or (1/2, 2).

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We have P(3 heads) = (1/2)^3 = 1/8. Likewise P(3 tails) = 1/8, by symmetry. The probability is 1/8 + 1/8 = 1/4.

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It looks like 1 times 4 to me, leaving y = 4 and x = 7/6.

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(1,6), (-7, 6), and (4.65, 6) are three such coordinates.

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Suppose the walk was 15 miles each way (the distance doesn't matter, we can pick x miles if we wish). That means it takes 5 hours to walk there and 3 hours to walk back. You went 30 miles total, so the average speed is (30 miles)/(8 hours) = 3.75 mph.

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In this case, guessing and checking reveals width = 2 ft, length = 5 ft. If guessing and checking doesn't yield an obvious solution, you can solve such a problem using the quadratic formula.

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To find df/dx and df/dy, just assume that y and x are constants respectively (I'm also using d = differential). So,
(by the Product Rule)
Do the same for df/dy. Then you can find the second derivatives by taking the derivative of df/dx, df/dy.

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1.5613 * 10^-5

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Probably 13 but I'm pretty unsure. Keep in mind that 18 is the legal age to vote, hence the term "new votes." However I don't know what 4 has to do with teething, since people teeth much earlier than 4 years (maybe 4 months). I would answer depends on the previous phrase, so the answer would be 13 because a person becomes a teenager at age 13.

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It would probably be

Domain: [-2, 3]
Range: [1, 5]

However I don't see a graph, so the range could be different based on the function.

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We know that torque equals force*radius, or mass*radius since gravity on Earth is constant in this case. If x is the distance from the 48 kg mass to the fulcrum, then
48x = 24(12 - x)
2x = 12 - x
x = 4 m, 12 - x = 8 m

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If the number is 10d + 6, then
60 + d = 2(10d + 6) - 6
60 + d = 20d - 6
54 = 19d
No integer value for d.

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We have
25 = x^2 - 6x + 9
Factoring, we obtain
25 = (x - 3)^2
One such value of x is 8 (the other one is -2).

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If x and 2x - 3 are the width and length of the rectangle, then
2(x + 2x-3) = 42
x + (2x - 3) = 21
Solving, we obtain x = 8, 2x - 3 = 13.

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I think it denotes whether y is strictly greater than something, or greater than or equal to. Usually if there's a dashed line it means strictly greater than (>) and if it's a solid line then y is greater than or equal to (>=).

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Even though I have never taken a statistics course, I'm quite positive the answer is "equal probabilities at all values of x." Mainly because normal distributions do follow a bell curve, and the probability of getting 100/100 heads is definitely not the same as getting 50/50 heads, tails.

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A) E = arccos (.812) + 2n(pi)
B) E = arctan (5/3) + n(pi)
n is some integer, I added a multiple of pi since the cosine and tangent functions are periodic with periods 2pi and pi.

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By definition, if the parallelogram is inscribed in a circle, it is cyclic, and the measures of opposite angles add up to 180 (i.e. A + C = 180, B + D = 180). However, ABCD is a parallelogram, so A + B = 180, B + C = 180, etc. It follows that A = B, B = C, etc, so ABCD is a rectangle, and angle A = 90 degrees.

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I don't think it's possible to insert parentheses to make this a true expression...here's why:

+/- 10 and +/-2 are both congruent to 2 modulo 4, while -8 is 0 modulo 4. The left side becomes 2 + 0 + 2 + 2 = 6 = 2 modulo 4, regardless of where parentheses are placed. However, 4 is 0 modulo 4 so the two expressions must carry different residues and cannot be equivalent.

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Umm it's 0.7? Or were you looking for P(a or b)?

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Best way would be to use the law of sines. The law of cosines also works, but it is more time-consuming.

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If x is a side length, then
4x = 48 cm
x = 12 cm

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I think I have solved this exact same question previously on this website. Here is my solution:
This is equivalent to finding the power series of ln x centered around x = 1. Note that all derivatives of ln x at x = 1 are equal to 1 or -1. Since we have the power series

Adding one to all the x terms produces the given result.

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Take the ln of both sides:
5x - 1 = ln 1 = 0
From this we conclude that x = 1/5.

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Multiplying the left side we get:
3x + 18 = 4x --> x = 18
It's easy to check by plugging x = 18 into the equation:
3(18 + 6) = 4(18)
72 = 72

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I think I found the recursion!
We have 5 - 8 = -3. Take the absolute value of the difference, multiply by 2 to obtain the next term.
8 - 6 = 2, absolute value, multiply by 2 to get 4, etc.
In general, the sequence should be a_n = 2|a_(n-2) - a_(n-1)|. From this, the following term is 16.

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From the first equation we obtain 9y = 19, so y = 19/9. Substituting that into the second equation we get 19/9 = 6x - 3 --> 46/9 = 6x --> x = 23/27.

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Good question. However, the proof requires a little introductory calculus.
In calculus, we define a function called the "derivative," which measures the instantaneous rate of change of a function. Basically, it is the same as finding slope, except that the two points get infinitely close, and it can be evaluated using limits. The derivative is usually denoted f'(x) or .
By the power rule (you'll learn it early in calculus), the derivative of is . The relative minimum or maximum occurs when the derivative is equal to zero, and the slope is positive on one side of that point and negative on the other.
Since the derivative of the quadratic is it is easy to see that this derivative is equal to zero when , therefore it is the vertex.