You set up the equation to solve for a.

75 = 3000/(2(15) + a)

a = 10

You then set up the formula again for each movie costing $20, s(20) = 3000/(2(20) + 10), and solve for x, the number sold, giving you 60.

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

We are told that x&y = (x – y)^xy . 

–1&2 = (–1 – 2)^(–1)(2) = (–3)^–2 

To simplify this, we can make use of the property of exponents which states that a^–b = 1/(a^b ).

(–3)^–2 = 1/(–3)² = 1/9

The answer is 1/9.

We need to rewrite this problem in mathematic terms.

8 less than 32 can be written as 32 – 8

so we will get the equation

18 – w = 32 – 8.

Now, we need to solve for w. 

–w = 32 – 8 – 18

–w = 6

w = –6

Find the value of the given expression, , by plugging in –6 for w.

Note that x must be greater than y and that y must be greater than 0. This means that x and y are different, positive integers. In addition, the sum, x² + y² must equal to 100. If we list squares beginning from the square of the first integer greater than 0 (1²) up to the square of the greatest integer less than 100 (9²) we will get:

1, 4, 9, 16, 25, 36, 49, 64, 81

We must observe that the only two numbers that will add up to 100 are 36 and 64.

Remember that x > y > 0 and that x² + y² =100.

This means that x must be  and y must be

When we solve for x and y we get:

x = 8

and y = 6.

Therefore, x + y can only be 14.

Plug in numbers for each alternative. If both sides of the inequality are multiplied by 2, the result is the original inequality, . The other options fail (if confused, try plugging in  as a positive,  as a negative).

Assume the first section equals  inches, then the second(or the middle section) must be equal to  and the third piece must be equal to .

 and now you solve for  which equals 10.  Hence the middle piece must be equal to 20 inches and the third piece is only 6 inches long.

By testing the answers, it can be seen that the only equation to satisfy all cases in the table above is

Fred has $100 in quarters and nickels initially.  We are also told that he has 260 quarters.  This is worth $65.  Thus Fred initially has $35 in nickels or 700 nickels.

Fred now exchanges some of his nickels for the dimes of a friend.  He ends up with 650 coins.  We know that Fred started with 960 coins (700 nickels + 260 quarters).  He ends up with 650 coins.  The number of quarters remains unchanged, meaning he now has 390 nickels and dimes.  These must have the same value as the initial 700 nickels, though, since he didn't lose any money.

Now we can finally set up our solution:

Thus Fred has 80 nickels and 310 dimes.

An alternative solution step is to notice that turning nickels into dimes always occurs in exactly one way: 2 nickels to 1 dime.  Every time you do this conversion, you will lose exactly one coin.  We then notice that the number of coins drops from 960 to 650, or drops by 310 coins.  We thus need to get rid of 310 coins.  Since we're only allowed to change nickels into dimes (and lose 1 coin each time), we simply do this 310 times to reach the requisite number of coin losses.  We are left with the proper number of coins with the proper value immediately.  Since every replacement replaced 2 nickels, we also lost  nickels.  Our final number of nickels is thus  nickels.