The answer is 3. 3 unit distance.
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval estimate for the mean number of calories for servings of breakfast cereals is (195.3, 215.7).
<h3>What is a t-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm t\frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.- t is the critical value.
- n is the sample size.
- s is the standard deviation for the sample.
From the sample and the significance level of 0.05, we have that the parameters are given by:
![\overline{x} = 205.5, s = 14.2, n = 10, t = 2.2622](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%3D%20205.5%2C%20s%20%3D%2014.2%2C%20n%20%3D%2010%2C%20t%20%3D%202.2622)
Hence:
![\overline{x} - t\frac{s}{\sqrt{n}} = 205.5 - 2.2622\frac{14.2}{\sqrt{10}} = 195.3](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20-%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20205.5%20-%202.2622%5Cfrac%7B14.2%7D%7B%5Csqrt%7B10%7D%7D%20%3D%20195.3)
![\overline{x} + t\frac{s}{\sqrt{n}} = 205.5 + 2.2622\frac{14.2}{\sqrt{10}} = 215.7](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%2B%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20205.5%20%2B%202.2622%5Cfrac%7B14.2%7D%7B%5Csqrt%7B10%7D%7D%20%3D%20215.7)
The 95% confidence interval estimate for the mean number of calories for servings of breakfast cereals is (195.3, 215.7).
More can be learned about the t-distribution at brainly.com/question/16162795
Right triangle
Use Sohcahtoa
Given hypothenuse = 10
Adjacent = x
And angle degree of 52
You can use Cosine
Cos(52) = x/10
0.6156614753 = x/10
x = 6.156614753
Round to nearest tenth
Solution: 6.2
Answer:
Step-by-step explanation:
![\textsf {The slope-intercept form of a line is $y = mx + b$ where m is the slope and b the y-intercept}\\ \\\textsf{Slope is computed using the formula}](https://tex.z-dn.net/?f=%5Ctextsf%20%7BThe%20slope-intercept%20form%20of%20a%20line%20is%20%24y%20%3D%20mx%20%2B%20b%24%20where%20m%20is%20the%20slope%20and%20b%20the%20y-intercept%7D%5C%5C%20%5C%5C%5Ctextsf%7BSlope%20is%20computed%20using%20the%20formula%7D)
![m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%20%7B%28y_%7B2%7D%20-%20y_%7B1%7D%29%7D%20%7B%28x_%7B2%7D%20-%20x_%7B1%7D%29%7D)
![\textsf{Given that the line passes through (4, 0) and (3, 9) we can compute the slope:}](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20that%20the%20line%20passes%20through%20%284%2C%200%29%20and%20%283%2C%209%29%20we%20can%20compute%20the%20slope%3A%7D)
![m = \dfrac{9 - 0}{3 - 4}\\\\m = \dfrac{9}{-1}\\\\m = -9](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7B9%20-%200%7D%7B3%20-%204%7D%5C%5C%5C%5Cm%20%3D%20%5Cdfrac%7B9%7D%7B-1%7D%5C%5C%5C%5Cm%20%3D%20-9)
So the slope of the line is y = -9x + b
We have
y = -9x + b
Add 9x to both sides
y + 9x = -9x + 9x + b
y + 9x = b
switching sides,
b = y + 9x
Plug in the (x, y) values for point (4, 0)
b = 0 + 9(4)
b = 36
So the equation of the line is
![\boxed{y = -9x + 36}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%20-9x%20%2B%2036%7D)