Answer:
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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:
Answer:
-2n - 12
Step-by-step explanation:
Combine like terms. Note that each term has one variable (n). Also note that one negative sign and one positive sign results in a negative sign.
-6n + (-12) + 4n = -6n + 4n - 12 = -2n - 12
-2n - 12 is your answer
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Answer:
B. (-7,-3)
Step-by-step explanation:
Given the circle: 
The point (x,y) which lie on the circle are the coordinate which satisfies the given equation of the circle.
We now consider the given options.
<u>Option A (5,12)</u>
When x=5, y=12

<u>Option B (-7,-3)</u>
When x=-7, y=-3

<u>Option C (-6,-10)</u>
When x=-6, y=-10

<u>Option D (6,23)</u>
When x=6, y=23

We can see that only (-7,-3) satisfies the equation of the circle. Thus it is the point which lies on the circle.
The correct option is B.
Total surface area of first box = 2(8 * 6.25) + 2(8 * 10.5) + 2(6.25 * 10.5) = 2(50) + 2(84) + 2(65.625) = 100 + 168 + 131.25 = 399.25 sq. ins
Total surface area of second box = 2(9 * 5.5) + 2(9 * 11.75) + 2(5.5 * 11.75) = 2(49.5) + 2(105.75) + 2(64.625) = 99 + 211.5 + 129.25 = 439.75 sq. ins
Hence, the second box requires more material to make.