ANSWERx = 5/4
EXPLANATION ![2^x \cdot 2^{x-2} = \sqrt{2}](https://tex.z-dn.net/?f=2%5Ex%20%5Ccdot%202%5E%7Bx-2%7D%20%3D%20%5Csqrt%7B2%7D)
Note that
![\sqrt{a} = a^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
so
![\sqrt{2} = 2^{\frac{1}{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
Note that on the left-hand side, we can use exponent properties for multiplying two powers of the same base together:
![\begin{aligned} 2^x \cdot 2^{x-2} &= \sqrt{2} \\ 2^{x + (x-2)} &= 2^{\frac{1}{2}} \\ 2^{2x - 2} &= 2^{\frac{1}{2}} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A2%5Ex%20%5Ccdot%202%5E%7Bx-2%7D%20%26%3D%20%5Csqrt%7B2%7D%20%5C%5C%0A2%5E%7Bx%20%2B%20%28x-2%29%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%0A2%5E%7B2x%20-%202%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%0A%5Cend%7Baligned%7D)
We can now equate the exponents because both sides of the equation are of the same base with no other terms.
![\begin{aligned} 2^{2x - 2} &= 2^{\frac{1}{2}} \\ 2x - 2 &= \tfrac{1}{2} \\ 2x &= \tfrac{1}{2} + 2 \\ 2x &= \tfrac{5}{2} \\ x &= \tfrac{5}{4} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%0A2%5E%7B2x%20-%202%7D%20%26%3D%202%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%0A2x%20-%202%20%26%3D%20%5Ctfrac%7B1%7D%7B2%7D%20%5C%5C%0A2x%20%26%3D%20%5Ctfrac%7B1%7D%7B2%7D%20%2B%202%20%5C%5C%20%0A2x%20%26%3D%20%5Ctfrac%7B5%7D%7B2%7D%20%5C%5C%0Ax%20%26%3D%20%5Ctfrac%7B5%7D%7B4%7D%0A%5Cend%7Baligned%7D)
The answer is x = 5/4. We can confirm this by using this value in the original equation to get a true statement.
Answer:
c. :)
Step-by-step explanation:
Answer: stratified sampling and judgement sampling
Step-by-step explanation:
Stratified sampling is a probability method that is superior to random sampling because it reduces sampling error. A stratum is a subset of the population that share at least one common characteristic.
While
Judgment sampling is a nonprobability method. The researcher chooses the sample based on judgment. This is usually and extension of convenience sampling. For example, a researcher may decide to draw the entire sample from one "representative" city, even though the population includes all cities. When using this method, the researcher must be confident that the chosen sample is truly representative of the entire population.
Answer:
to figure out the answer / an assignment of values to the variables
Step-by-step explanation: