Alan

10% of 39 is 39*10/100 = 3.9, so if this is subtracted from 39 you have 39 - 3.9 = 35.1

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You can use the calculator here.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{16}}^\circ\right)} = {\mathtt{0.961\: \!261\: \!695\: \!938}}$$

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Looks to me like it's only the 3 that multiplies (x + 1), in which case we have

x + 3x + 3 = 2x

4x + 3 = 2x

Subtract 2x from each side

2x + 3 = 0

Subtract 3 from each side

2x = -3

Divide both sides by 2

x = -3/2 or x  -1.5

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In general cos(2x) = 1 - 2sin²(x) so another way of writing 1 - 2sin²(3a) is cos(6a)

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A 9% grade means 9 vertical units for every 100 horizontal units, so slope = 9/100 = 0.09

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Hmm.  

Suppose there are 1,000,000 items, 700,000 of which are good, 300,000 of which are defective.

The probability that the first one you choose is good is 700,000/1,000,000 = 0.7. 

You now have 699,999 good ones left out of a total of 999,999, so the probability of selecting a second good one is 699,999/999,999 ≈ 0.6999997

You now have 699,998 good ones left out of a total of 999,998, so the probability of selecting a third good one is 699,998/999,998 ≈ 0.6999994

The overall probability is therefore 0.7*0.6999997*0.6999994 ≈ 0.343 ≈ 0.7³

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If h is the height it can be lifted, then we have:

Original circumference = pi*d  where d is diameter of the earth.

New circumference = pi*(d+2h)  since the new diameter is d+2h.

New - Old circumference:  pi*(d + 2h) - pi*d = 1m so that pi*2h = 1m  or h = 1/(2pi) m or h ≈ 0.159m

(xerxes, your next to last line should say "We have ∼0.3197 meters more).

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Mathcad, you might want to note that 31! = 0 mod(31)  not 30 mod(31)  (i.e. it is exactly divisible by 31).

Wilson's theorem says that 30! = 30 mod(31).

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Turn 2 1/3 into an improper fraction.  It becomes 7/3.   

Turn 4 1/3 into an improper fraction.  It becomes 13/3.

The ratio of the two numbers is (2 1/3) divided by (4 1/3).  This ratio is the same if we multiply top and bottom by 3, to get 3*(2 1/3) divided by 3*(4 1/3).  

This is 3*(7/3) divided by 3*(13/3). 

The 3's cancel on the top, leaving 7,  and they cancel on the bottom, leaving 13. So the ratio is 7/13.  

The missing number at the start is therefore 13.

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