Answer:
1024
Step-by-step explanation:
you can plug 10 to the explicit formula. f(n)= a times r to the power of n minus 1. A is the first term, r is the common ratio and n is the nth term. 2 times 2 to the power of 10 minus 1. 2 times 2 to the power of 9 is 1024. Hope this helps!
Answer:
2
Step-by-step explanation:
The slope of a line is found by using
m = (y2-y1)/(x2-x1)
(10-4)/(1--2)
6/(1+2)
6/3
2
Trigonometry can be used to find angles and sides of simple triangles. If an 18-foot ladder touches a building 14 feet up the wall then the angle can be deduced by trigonometry. In this case, the ladder defines the hypotenuse (H) of the triangle and the wall defines the opposite (O) side of the triangle. Therefore we can use the equation theta=sin^-1(O/H) . This yields an angle of 51 degrees.
Answer:
D. Confidence interval decreases.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation ![s = \sqrt{\frac{p(1-p)}{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
When sample size increases:
The standard deviation of the sample mean is:
![s = \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
That is, it is inversely proportional to the sample size, so if the sample size incerases, the standard deviation decreases, and so does the confidence interval.
This means that the correct answer is given by option D.