X/49 = 21/x
x^2 = 21(49) = 1029
x = √1029 = 32.1
x = 32.1
Answer:
n=206
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by
and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that
, we can use as prior estimate of p 0.5, since we don't have any other info provided, and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=206
-5 - 12 = -17
Starts at -5 degrees, then it drops another 12, so you subtract 12 from -5.
Answer: 
Step-by-step explanation:
By definition, an Isosceles triangle has two equal sides and its opposite angles are congruent.
Observe the figure attached, where the isosceles triangle is divided into two equal right triangles.
So, in this case you need to use the following Trigonometric Identity:

In this case, you can identify that:

Substituting values, and solving for "x", you get:

Therefore, the length of BC rounded to nearest tenth, is:

<4 and <2 corresponding angles
<6 and <3 alternate interior angles
<4 and <5 alternate exterior angles
<6 and <7 interior angles on the same side of transversal