Answer:
- 5
Step-by-step explanation:
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We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:
![CI(\mu)=\lbrack x-Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}},x+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack](https://tex.z-dn.net/?f=CI%28%5Cmu%29%3D%5Clbrack%20x-Z_%7B1-%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Ccdot%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%7D%2Cx%2BZ_%7B1-%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Ccdot%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%7D%5Crbrack)
Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:
![CI(\mu)=\lbrack30.0-Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}},30.0+Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}}\rbrack](https://tex.z-dn.net/?f=CI%28%5Cmu%29%3D%5Clbrack30.0-Z_%7B0.99%7D%5Ccdot%5Cfrac%7B2.40%7D%7B%5Csqrt%5B%5D%7B28%7D%7D%2C30.0%2BZ_%7B0.99%7D%5Ccdot%5Cfrac%7B2.40%7D%7B%5Csqrt%5B%5D%7B28%7D%7D%5Crbrack)
Where (from tables):

Finally, the interval at 98% confidence level is:
1. Julia's ≤ Rachel's hair
2. 40 < 74
X² + 8x +y² - 2y -64 =0
We see that the equation has x² and y² . Also we see that coefficients in front of x² and y² are equal. So this is an equation of the circle.
(x² + 8x) +(y² - 2y) -64 =0
(x² + 8x) +(y² - 2y) = 64
We need to complete square for x and y groups, that means it should be written in form (a+b)² or (a-b)².
Expressions in parenthesis we will write as a²+/-2ab+b², to write it after as (a+/-b)², because a²+/-2ab+b² = (a+/-b)²
(x² + 2*4x) +(y² - 2*1y) = 64
(x² + 2*4x+4²) +(y² - 2*1y+1²) = 64+4²+1²
(x+4)² + (y-1)²= 81 Sometimes this is called a standard form of the circle.
(x+4)² + (y-1)²= 9² Sometimes it is required to write like this.
And if you are studying circles,ellipses and hyperbolas, the standard form should look like