So for this one you'll want to write the equation as follows.
In other words $16 times the number of scented candles, plus $28 times the total number of sold candles, minus the scented ones sold. We write both as a function of x (x and 28-x) to easily solve it.
After this you factor out the "10(28-x)" part which is 10*28+10*x and solve for X. Below I'll post the full equation
Check it's correct by 20*16+(28-20)*10=400
Hope it helps
Let P be the midpoint of diagonal BD. Then by the trangle inequality, MP + PN > MN. Also, BP + PN > BN and DP + PM > DM. Then 2DP + 2PN > BC and 2MP + DP > AD. Subtracting these inequalities, we get 2PN - 2MP > BC - AD. Putting this together with the inequality MP + PN > MN gives you MN < (AB + CD)/2.
If MN = (AB + CD)/2, then everything must be parallel, so ABCD is a rectangle.
The answer is 286. It comes from the following sum:
1+3+6+10+15+21+28+35+45+55+66 = 286.
It is the number of ordered partitions of 10 as the sum of four numbers taken from the set 0, 1, 2, 3, ..., 10 . If we write these partitions as 4-tuples such as (3, 2, 0, 5), and take the coordinates to mean, say,
(3 units to the right, 2 units up, no movement to the left, 5 units down), then each partition would be uniquely associated with a lattice point in the plain (or is that plane?!). I have carefully counted the number of such ordered partitions and have a list of them, but am too tired at the moment to list them.
So the answer is 286.
- There are 4 questions with 5 choices each which means that he's got a 1 in 5 chance or 20% chance of getting the answer correct pr.question.
There's a 1 in 20 choice or 5% choice in the pool in total...
But in total there's a total of 4 correct answers out of 20 possible choices.
That is a 4 in 20 or a 1 in 5 chance or 20% chance in total.
Alternatively, on a test with 40 questions there is a 1 in 4 or 25% chance that he gets either question Nr.37., Nr.38., Nr.39. or Nr.40. correct.
Hope that helped?