The confidence interval is given by
where
is the sample mean and
is the standard error of the mean. In turn, the standard error of the mean is
where
is sample size.
We have
The endpoints of the confidence interval correspond to the finite endpoints of the rejection region. That is,
for which we can solve for
. We get
which is the critical value for a confidence level of
.
A) Possible outcomes are ...
(1, 3), (1, 4), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)
for a total of 7 out of 36 outcomes that match your requirements.
p(3 < sum ≤ 5) = 7/36
B) Possible outcomes are ...
(6, 1), (6, 3), (6, 5), (1, 6), (3, 6), (5, 6)
for a total of 6 out of 36 outcomes that match your requirements.
p(6 and odd) = 6/36 = 1/6
x² + 10x = 26
x² + 10x + 25 = 26 + 25
x² + 5x + 5x + 25 = 51
x(x) + x(5) + 5(x) + 5(5) = 51
x(x + 5) + 5(x + 5) = 51
(x + 5)(x + 5) = 51
(x + 5)² = 51
x + 5 = ±√(51)
- 5 - 5
x = -5 ± √(51)
x = -5 + √(51) or x = -5 - √(51)
Answer:
B= 90
C= 80
D= 100
Step-by-step explanation:
So let’s start with the bottom angles.
We know that the adjacent angles in a parallelogram add up to 180° so our equation would be 
. So let’s simplify it b and b are both the same variables so we will get 2b and -10 + 10 is 0 so we get the following equation 
.
So now we divide 180 and 2 and we get 90 as b.
So one side will be 100 because of the +10 and the other 90 because of the -10.
Now for the next side.
So we know that b+10 is adjacent to c so 180-100 is 80, so 80 is c.
Now for d.
b-10 is 80 so 180-80 is 100, so d is 100.
PYTHOGOROS THEROEM :-
ITS LIKE:- AC² = AB² + BC²
