Answer:
a) 0.75
b) 0.0625
c) 0.1875
d) 0.375
Step-by-step explanation:
Let's start by first finding the probability a teacher orders 6 boxes. Since it is a four sided dice, the probability of getting a 1 is going to be 0.25.
Similarly, for any other number on the dice, the teacher orders 2 boxes. We can think of this as NOT rolling a 1. Using our previous answer, this comes out to be: 1 - 0.25 = 0.75
It should be remembered in the following answers that teachers ordering 6 or 2 boxes are not influenced by the results of other teachers. These are statistically independent events.
a) As given above, this probability is 0.75
b) The probability that both teachers order 6 boxes will be their individual probabilities multiplied. This comes out to be: 0.25 x 0.25 = 0.0625
c) Like in part (b), this is both of their probabilities multiplied:
0.25 x 0.75 = 0.1875
d) This is nearly the same as part (c), but with a little twist. The order matters. There are two scenarios:
- First teacher gets 6 boxes, and the second gets 2.
- First teacher gets 2 boxes, and the second gets 2.
Both of these events have a probability of 0.1875, as shown in (c). To get the total probability of this event happening, we must add these together:
0.1875 + 0.1875 = 0.375
Area ≈ 12.57
Circumference ≈ 12.57
Answer:
there would have been 12 crackers on the plate at the start
Step-by-step explanation:
So 1/3 +1/4 = 7/12
Therefore 5/12 left on the plate …ie 5.
So total to start with
5/5×12=12
Ans 12
Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
The equation of a circumference is 2
r. Since we know that r=17, we plug that into the formula, and get an answer of C. 34
