Answer:
It is an unusual result contradicting the national survey.
Step-by-step explanation:
National survey showed 44% of college students who drink.
The professor's survey showed that 96/244 = 39% drink.
The professor's survey deviated from the national survey is 5% (44% - 39%) representing about 0.25% (5% squared) variance.
Standard deviation is the spread of a set of numbers from their mean. In other words, it measures how far an observed value is from the mean. It can be calculated by getting the square root of the variance.
Answer:
![\sf 3^{-3x}=3^{(-4x+6)}](https://tex.z-dn.net/?f=%5Csf%203%5E%7B-3x%7D%3D3%5E%7B%28-4x%2B6%29%7D)
![\sf x=6](https://tex.z-dn.net/?f=%5Csf%20x%3D6)
Step-by-step explanation:
![\sf Given \ equation: \left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}](https://tex.z-dn.net/?f=%5Csf%20Given%20%5C%20equation%3A%20%5Cleft%28%5Cdfrac%7B1%7D%7B27%7D%5Cright%29%5Ex%3D3%5E%7B%28-4x%2B6%29%7D)
![\sf As \ \dfrac{1}{27}=\dfrac{1}{3^3} \ and \ \dfrac{1}{a^b}=a^{-b} \ then \ \dfrac{1}{27}=3^{-3}](https://tex.z-dn.net/?f=%5Csf%20As%20%5C%20%5Cdfrac%7B1%7D%7B27%7D%3D%5Cdfrac%7B1%7D%7B3%5E3%7D%20%5C%20and%20%5C%20%5Cdfrac%7B1%7D%7Ba%5Eb%7D%3Da%5E%7B-b%7D%20%5C%20then%20%5C%20%5Cdfrac%7B1%7D%7B27%7D%3D3%5E%7B-3%7D)
Therefore, we can rewrite the given equation with base 3:
![\implies \sf (3^{-3})^x=3^{(-4x+6)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20%283%5E%7B-3%7D%29%5Ex%3D3%5E%7B%28-4x%2B6%29%7D)
Apply the exponent rule
:
![\implies \sf 3^{-3x}=3^{(-4x+6)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%203%5E%7B-3x%7D%3D3%5E%7B%28-4x%2B6%29%7D)
![\sf If \ a^{f(x)}=a^{g(x)} \ then \ f(x)=g(x)](https://tex.z-dn.net/?f=%5Csf%20If%20%5C%20a%5E%7Bf%28x%29%7D%3Da%5E%7Bg%28x%29%7D%20%5C%20then%20%5C%20f%28x%29%3Dg%28x%29)
![\implies -3x=-4x+6](https://tex.z-dn.net/?f=%5Cimplies%20-3x%3D-4x%2B6)
Add 4x to both sides to solve for x:
![\implies \sf x=6](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20x%3D6)
The answer might be -32 I plugged it into my calculator
7d=84 so d=12 because you have to divide 7 from 84 to see how much each bracelet cost lol