Answer:
A. 55°
Step-by-step explanation:
Complementary angles are angles that add up to give us 90°.
Since <A and <B are complementary angles, it implies that:
m<A + m<B = 90°
If m<A = 35°, therefore:
35° + m<B = 90°
Subtract 35° from each side
m<B = 90° - 35°
m<B = 55°
Answer:
last option
Step-by-step explanation:
It converts sin, π and cos.
The answer is the last option.
Answer:
See the proof below.
Step-by-step explanation:
For this case we just need to apply properties of expected value. We know that the estimator is given by:

And we want to proof that 
So we can begin with this:

And we can distribute the expected value into the temrs like this:

And we know that the expected value for the estimator of the variance s is
, or in other way
so if we apply this property here we have:

And we know that
so using this we can take common factor like this:

And then we see that the pooled variance is an unbiased estimator for the population variance when we have two population with the same variance.
Answer:
c. 12x; 111 cm
Step-by-step explanation:
The regular dodecagon has 12 sides. Each side has a length of x=9.25 cm, and we know that the perimeter of the figure is the sum of the lengths of all the sides: Therefore, since we have 12 sides, the perimeter will be given by the product between the length of each side, x, and the number of sides, 12:

and if we substitute x = 9.25 cm, we find

Let the length be l
Then,
l *(l-3)= 88
l²-3l =88
l²-3l-88=0
l²-11l +8l -88 =0
l(l-11) + 8(l-11) =0
(l+8)(l-11)=0
As, l can't be negative, length=11cm and width=(l-3)=11-3 =8 cm