Prove that it is impossible to have $4.50 in dimes and quarters with the number of quarters being twice the number of dimes

See Explanation below for proof.

Step-by-step explanation:

Let number of dimes be D

Then number of quarters = 2D  

We then get the following VALUE equation: .1D + .25(2D) = 4.5

.1D + .5D = 4.5

.6D = 4.5

D, or number of dimes = 4.5/.6 = 7.5

There is no such thing as HALF a DIME, so it's NOT POSSIBLE

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours

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