Answer:
i think its A
Step-by-step explanation:
divide both sides by -2 which makes the y int -3 and A has a negative slope
Answer:
A
The test statistics is ![t = -1.7](https://tex.z-dn.net/?f=t%20%20%3D%20-1.7)
B
The Null and Alternative hypothesis are
and ![H_a : \mu \ne 47.2](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Cmu%20%5Cne%20%2047.2)
Step-by-step explanation:
From the question we are told that
The population mean is ![\mu = 47.2 miles/gallon(MPG)](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%2047.2%20miles%2Fgallon%28MPG%29)
The sample size is ![n = 250 \ van](https://tex.z-dn.net/?f=n%20%3D%20%20250%20%5C%20van)
The sample mean is ![\= x = 47.0](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%2047.0)
The sample standard deviation is ![\sigma = 1.9](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%201.9)
The level of significance is ![\alpha = 0.02](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.02)
Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then
The Null Hypothesis is
![H_o : \mu = 47.2](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20%5Cmu%20%3D%2047.2)
The alternative Hypothesis is
![H_a : \mu \ne 47.2](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Cmu%20%5Cne%20%2047.2)
The test statistics can be mathematically evaluated as
![t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%5C%3D%20x-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
substituting values
![t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%5C%3D%2047-%2047.2%7D%7B%5Cfrac%7B1.9%20%7D%7B%5Csqrt%7B250%7D%20%7D%20%7D)
![t = -1.7](https://tex.z-dn.net/?f=t%20%20%3D%20-1.7)
Answer:
![\boxed{\sf \ \ x = 1 \ \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20%5C%20%5C%20x%20%3D%201%20%5C%20%5C%20%7D)
Step-by-step explanation:
Hello,
First of all we need to take x different from 3 as dividing by 0 is not allowed
then for x real different from 3
![f(x)=0\\\\ \dfrac{x-1}{x-3}=0\\\\ x-1 = 0\\\\ x = 1](https://tex.z-dn.net/?f=f%28x%29%3D0%5C%5C%5C%5C%3C%3D%3E%20%5Cdfrac%7Bx-1%7D%7Bx-3%7D%3D0%5C%5C%5C%5C%3C%3D%3E%20x-1%20%3D%200%5C%5C%5C%5C%3C%3D%3E%20x%20%3D%201)
hope this helps
Answer:
![2 \sqrt{2} + i \sqrt{2}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B2%7D%20%20%2B%20i%20%5Csqrt%7B2%7D%20)
Step-by-step explanation:
The square of a complex number is a complex number. Here, we have:
![{(a + bi)}^{2} = 6 + 8i](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20bi%29%7D%5E%7B2%7D%20%20%3D%206%20%2B%208i)
![{a}^{2} + 2abi - {b}^{2} = 6 + 8i](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%202abi%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%206%20%20%2B%208i)
We then have this system of equations:
![{a}^{2} - {b}^{2} = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%206)
![2ab = 8](https://tex.z-dn.net/?f=2ab%20%3D%208)
Solving this system:
![ab = 4](https://tex.z-dn.net/?f=ab%20%3D%204)
![b = \frac{4}{a}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B4%7D%7Ba%7D%20)
![{a}^{2} - {( \frac{4}{a}) }^{2} = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7B%28%20%5Cfrac%7B4%7D%7Ba%7D%29%20%7D%5E%7B2%7D%20%3D%206%20)
![{a}^{2} - \frac{16}{ {a}^{2} } = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%5Cfrac%7B16%7D%7B%20%7Ba%7D%5E%7B2%7D%20%7D%20%3D%206%20)
![{a}^{4} - 16 = 6{a}^{2}](https://tex.z-dn.net/?f=%20%20%7Ba%7D%5E%7B4%7D%20%20-%2016%20%3D%20%206%7Ba%7D%5E%7B2%7D%20)
![{a}^{4} - 6 {a}^{2} - 16 = 0](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B4%7D%20%20-%206%20%7Ba%7D%5E%7B2%7D%20%20-%2016%20%3D%200)
![( {a}^{2} - 8)( {a}^{2} + 2) = 0](https://tex.z-dn.net/?f=%28%20%7Ba%7D%5E%7B2%7D%20%20-%208%29%28%20%7Ba%7D%5E%7B2%7D%20%20%2B%202%29%20%3D%200)
![{a}^{2} = 8](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%20%3D%208)
![a = 2 \sqrt{2}](https://tex.z-dn.net/?f=%20a%20%3D%202%20%5Csqrt%7B2%7D%20)
![b = \frac{4}{2 \sqrt{2} } = \sqrt{2}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B4%7D%7B2%20%5Csqrt%7B2%7D%20%7D%20%3D%20%20%5Csqrt%7B2%7D%20%20)