Answer:
0.1274
Step-by-step explanation:
Let X be the random variable that measures the number of children who get their own coat.
Then, the expected value of X is
E[X] = 1P(X=1) + 2P(X=2)+3P(X=3)+...+10P(X=10)
The probability that a child gets her or his coat is
P(X=1) = 1/10
To compute the probability that 2 children get their own coat, we notice that there are 10! possible permutations of coats. The two children can get their coat in only one way, the other 8 coats can be arranged in 8! different positions, so the probability that 2 children get their own coat is
P(X=2) = 8!/10! = 1/(10*9) and
2P(X=2) = 2/(10*9)
Similarly, we can see that the probability that 3 children get their own coat is
P(X=3) = 7!/10! = 1/(10*9*8) and
3P(X=3) = 3/(10*9*8*7)
and the expected value of X would be
E[X] = 1/10 + 2/(10*9) + 3/(10*9*8)+...+10/10! = 0.1274
If you're rolling a single cube, then ...
-- There are 6 possible out comes.
-- One of them (5) is a multiple of 5 .
-- The probability of rolling it is (1/6) = <em>16-2/3 %</em> .
If everything is acting perfectly random, then ion 100 rolls,
you'd expect to succeed 16 or 17 times.
If you're rolling a pair of cubes, then ...
-- There are (6 x 6) = 36 possible outcomes.
-- There are seven ways to get a multiple of 5.
(1+4), (4+1), (2+3), (3+2), (4+6), (6+4), (5+5)
-- The probability of rolling one of those is
(7/36) = <em>19-4/9 %</em> .
If everything is acting perfectly random, then in 100 rolls,
you'd expect to succeed 19 or 20 times.
<h3>
Answer: 180 degrees</h3>
note: it doesn't matter if its clockwise or counterclockwise when it comes to 180 degree rotations.
========================================
Explanation:
The rule for 180 degree rotations is
(x,y) ---> (-x, -y)
So the x and y coordinates flip in sign from positive to negative, or vice versa.
Point D ' (-3, 5) rotates to D ' (3, -5) following this rule
-----------------
A further detailed break down might look like this
x = -3 becomes -x = -(-3) = 3
y = 5 becomes -y = -5
(-3, 5) ----> (3, -5)
Answer:
y = |x + 2|
Step-by-step explanation:
given the straight shape, it must be a linear function, but the "bend" in it indicates that an absolute value is being used.
So to start we can say: y = |x|
But that's not sufficient, as it would show that bend being at 0, 0. Instead, we need to translate it two units to the left, giving us:
y = |x + 2|
Answer:
16x - 31
Step-by-step explanation:
Write the full equation:
5(8x - 3) +4(-6x - 4)
Distribute:
40x - 15 - 24x - 16
Combine Like Terms:
16x - 15 - 16
Your answer is:
16x - 31
