Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have 
and 
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of 
are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
It would take 19.31 full containers to fill the fish tank.
There is 1000 ml in a L making it 5000 ml needed to fill the tank.
Divide the 5000 ml by 259 ml to get your answer.
Step-by-step explanation:
The equation of a line with slope m and y-intercept b is y = m x + b.
This line goes through the point ( 0 ,0 ), so the y-intercept is zero.
We are given the slope as − 2 / 3.
The equation of the line is y= – 2 / 3 x + 0 = – 2 / 3 x
y = – 2 / 3 x
<h3>
Answer: Choice B</h3>
With matrix subtraction, you simply subtract the corresponding values.
I like to think of it as if you had 2 buses. Each bus is a rectangle array of seats. Each seat would be a box where there's a number inside. Each seat is also labeled in a way so you can find it very quickly (eg: "seat C1" for row C, 1st seat on the very left). The rule is that you can only subtract values that are in the same seat between the two buses.
So in this case, we subtract the first upper left corner values 14 and 15 to get 14-15 = -1. The only answer that has this is choice B. So we can stop here if needed.
If we kept going then the other values would be...
row1,column2: P-R = -33-16 = -49
row1,column3: P-R = 28-(-24) = 52
row2,column1: P-R = 42-25 = 17
row2,column2: P-R = 35-(-30) = 65
row2,column3: P-R = -19-36 = -55
The values in bold correspond to the proper values shown in choice B.
As you can probably guess by now, matrix addition and subtraction is only possible if the two matrices are the same size (same number of rows, same number of columns). The matrices don't have to be square.
Answer:
see below
Step-by-step explanation:
If x represents the number of dimes, then 2x will represent twice the number of dimes. This is the number of quarters, since there are twice as many quarters as dimes.
There are 6 more nickels than dimes, so the number of nickels is 6 more than x. It is (x+6).
If we use the monetary values in cents, then the total of all coins is ...
25(2x) +10(x) + 5(x+6) = 485 . . . . . . matches choice D
