Alan

Note that log 4 is log 2², which is 2log 2, Hence the log 2 terms cancel.

Also, (1/2) log 3 is log 3^1/2

Hence x = 3 ^1/2

Press the 2nd key first; the sin key will then read asin.

If x = 1 then the left hand side is 8x1 → 8 and the right hand side is 4(1 + 1) → 8, so the left hand side is not greater than the right hand side.

I'm in agreement with Guest#4 on this one!

120dB is the level you might experience at a rock concert!

You need to double the I value:

L = 10log(2*I/Io) 

L = 10log(I/Io) + 10log(2) → 60 + 3.01 ≈ 63dB

12x² -7x+1=0  →  (4x - 1)(3x - 1)

Note that the constants must both be +1 or -1, and since the  -7x term is negative they must both be -1.  Also the factors of 12 must sum to 7.  This means only 3 and 4 will do.

The solutions are therefore given by 4x -1 = 0  or x = 1/4  and  3x - 1 = 0 or x = 1/3

You could do it by entering:  round(2/3*100)/100

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As follows:

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I think the question is ambiguous.  Does "any" mean "all", or does it mean "at least one"?

I've done some MonteCarlo simulations using 10^7 trials.  

(1) Assuming "any" means "at least one", I get a probability of 0.889 (to 3 significant figures).  

     Melody found 8/9 ≈ 0.889

(2) Assuming "any" means "all", I get a probability of 0.111 (to 3 significant figures).

     1/9 ≈ 0.111.

The logic of my MonteCarlo simulation is as follows:

1. Randomly permute the integers 1 to 15.

2. Test the integer in the ninth position against those in the first eight positions.

3. If the ninth integer is less than one or more of the first eight, score 1 for the "at least" sum; if it is less than all of the first eight, score 1 for the "all" sum.

4. Repeat steps 1 to 3 10^7 times.

5. Divide the sums by 10^7 to get the probabilities.

The adjacent length is 5 and the hypotenuse is √(5²+6²) → √61

The point is in the third quadrant so the cosine is negative: -5/√61 → -5√61/61