Step-by-step explanation:
perpendicular slope is negative reciprocal. -1/-1 = 1
y - 4 = x +3
y = x + 7
Step-by-step explanation:
![3x + \frac{2}{4} x + 1 = 5x + \frac{1}{3} x + 2 \\ 1.833 x+ 1 = 0 \\ 1.833x = - 1 \\ x = 0.545](https://tex.z-dn.net/?f=3x%20%2B%20%20%5Cfrac%7B2%7D%7B4%7D%20x%20%2B%201%20%3D%205x%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20%2B%202%20%5C%5C%201.833%20x%2B%20%201%20%3D%200%20%5C%5C%201.833x%20%3D%20%20-%201%20%5C%5C%20x%20%3D%200.545)
Answer:
AA SIMILARITY statement
SSS similarity statement is also possible.
Step-by-step explanation:
![In \: \triangle CBA \: and \: \triangle TVU \\ \angle B \cong \angle V... (given) \\\angle A \cong \angle U... (given) \\\therefore \triangle CBA \sim \triangle TVU... (By AA\: Postulate) \\](https://tex.z-dn.net/?f=In%20%5C%3A%20%20%5Ctriangle%20CBA%20%20%5C%3A%20and%20%5C%3A%20%20%5Ctriangle%20TVU%20%5C%5C%20%20%5Cangle%20B%20%5Ccong%20%5Cangle%20V...%20%28given%29%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Cangle%20A%20%5Ccong%20%5Cangle%20U...%20%28given%29%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20%5Ctriangle%20CBA%20%5Csim%20%5Ctriangle%20TVU...%20%28By%20AA%5C%3A%20Postulate%29%20%20%5C%5C%20)
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:
![\begin{gathered} 1-\alpha=0.98 \\ \alpha=0.02 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%201-%5Calpha%3D0.98%20%5C%5C%20%5Calpha%3D0.02%20%5Cend%7Bgathered%7D)
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):
![Z_{0.99}=2.33](https://tex.z-dn.net/?f=Z_%7B0.99%7D%3D2.33)
Finally, the interval at 98% confidence level is:
Answer:
I gotcu
The answer is 30.25
Step-by-step explanation:
5.5 divided by 4 equals 1.375
22 times 1.375 equals 30.25