CPhill

We need to convert the 17 minutes into a decimal.....since there are 60 minutes in one degree, we have

17 minutes *  1 degree/60 minutes  =  17/60 degree  =  .2833333333333333 degrees   (Note how the minutes "cross-cancelled" leaving just degrees !!)

So...we are evaluating...

sin (34.2833333333333333°) ≈ .5633

One terabyte = 10¹² bytes....so........

5 million * 10¹² =

[5 *10⁶ * 10¹² ] =  5 * 10¹⁸ bytes =   5,000,000,000,000,000,000 bytes

Or, using the US definition of this.....five quintillion bytes-......

I rounded up to $62.52, but a penny isn't worth quibbling about!!

I'm always impressed with your ability to use LaTex, heureka !!!   ......I wish I could learn that, but I'm probably too old !!!!

I'm an idiot, Jedithious,  because I CAN'T READ !!!   Ignore my stupid answrs to 3b  and 3c !!!!

First add the quarts = 2+ 1 = 3....(if this answer would have been 4 or greater we would have converted it to gallons and quarts....for example: 3qts + 3 qts = 6 qts = 1 gallon and 2 qts.

Now, add the gallons = 5 + 6 =  11

So, we have 11 gallons and 3 qts.

Melody's first answer is correct....here's a graph of the solution....

As for the second question, we have........ log₅(2x-1) = 2.........in exponential form, we have

5² = 2x-1

25 = 2x -1     subtract 1 from both sides

26 = 2x         divide by 2

13 = x

And there you go......

zegroes answer is good.......if we wanted to express it as a fraction, note that we could cancel the "5" with the "10" before we multiplied, giving us

(1/4) * (9/2) = 9/8   (which = 1.125, just as zegroes said !!!)

Good job, Melody......you're exactly correct with the nultiplication........

Note that it is easy to remember how to find a paricular element in matrix multiplication. To find element a_ij in the resultant matrix, we just multiply the "ith" row of the first matrix times the "jth" column of the second!!

I'm not great at these kinds of problems, but I always like to give 'em a try!!!.........

Let A be the probabilty of one side showing "red".......and let B be the probabilty that both sides are red.

We already know that the double-sided white card doesn't matter, since we already have a card showing "red."

So we have

(Probability of Two sides Red l One side is Red) = P(A and B) /  P(A)

P(BlA) = [(1/2) * (1/2)] / (1/2)  =    (1/2)

Another way of looking at this is that we either have the double-sided red card, or we don't !!!

That's my two cents worth, anyway !!!