K, remember
(ab)/(cd)=(a/c)(b/d) or whatever
also
![(ab)^c=(a^c)(b^c)](https://tex.z-dn.net/?f=%28ab%29%5Ec%3D%28a%5Ec%29%28b%5Ec%29)
and
![x^{-m}= \frac{1}{x^m}](https://tex.z-dn.net/?f=x%5E%7B-m%7D%3D%20%5Cfrac%7B1%7D%7Bx%5Em%7D%20)
and
![x^ \frac{m}{n}= \sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%20%5Cfrac%7Bm%7D%7Bn%7D%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%20)
and
![( \frac{x}{y} )^m= \frac{x^m}{y^m}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bx%7D%7By%7D%20%29%5Em%3D%20%5Cfrac%7Bx%5Em%7D%7By%5Em%7D%20)
and
![(x^m)^n=x^{mn}](https://tex.z-dn.net/?f=%28x%5Em%29%5En%3Dx%5E%7Bmn%7D)
and
(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)
so
![( \frac{-7x^ \frac{3}{2} }{5y^4} )^{-2}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B-7x%5E%20%5Cfrac%7B3%7D%7B2%7D%20%7D%7B5y%5E4%7D%20%29%5E%7B-2%7D)
=
![( \frac{-7}{5} )^{-2}( \frac{x^ \frac{3}{2} }{y^4} )^{-2}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B-7%7D%7B5%7D%20%29%5E%7B-2%7D%28%20%5Cfrac%7Bx%5E%20%5Cfrac%7B3%7D%7B2%7D%20%7D%7By%5E4%7D%20%29%5E%7B-2%7D)
=
![( \frac{(-7)^{-2}}{5^{-2}} )( \frac{(x^ \frac{3}{2})^{-2} }{(y^4)^{-2}} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%28-7%29%5E%7B-2%7D%7D%7B5%5E%7B-2%7D%7D%20%29%28%20%5Cfrac%7B%28x%5E%20%5Cfrac%7B3%7D%7B2%7D%29%5E%7B-2%7D%20%7D%7B%28y%5E4%29%5E%7B-2%7D%7D%20%29)
=
![( \frac{ \frac{1}{(-7)^2} }{ \frac{1}{5^2} } )( \frac{x^ \frac{-6}{2} }{y^{-8}} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Cfrac%7B1%7D%7B%28-7%29%5E2%7D%20%7D%7B%20%5Cfrac%7B1%7D%7B5%5E2%7D%20%7D%20%29%28%20%5Cfrac%7Bx%5E%20%5Cfrac%7B-6%7D%7B2%7D%20%7D%7By%5E%7B-8%7D%7D%20%29)
=
![( \frac{ \frac{1}{49} }{ \frac{1}{25} } )( \frac{(x^{-3}) }{\frac{1}{y^8}} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Cfrac%7B1%7D%7B49%7D%20%7D%7B%20%5Cfrac%7B1%7D%7B25%7D%20%7D%20%29%28%20%5Cfrac%7B%28x%5E%7B-3%7D%29%20%7D%7B%5Cfrac%7B1%7D%7By%5E8%7D%7D%20%29)
![( \frac{ \frac{1}{49} }{ \frac{1}{25} } )( \frac{\frac{1}{x^3} }{\frac{1}{y^8}} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Cfrac%7B1%7D%7B49%7D%20%7D%7B%20%5Cfrac%7B1%7D%7B25%7D%20%7D%20%29%28%20%5Cfrac%7B%5Cfrac%7B1%7D%7Bx%5E3%7D%20%7D%7B%5Cfrac%7B1%7D%7By%5E8%7D%7D%20%29)
=
![(\frac{25}{49} )( \frac{y^8}{x^3}](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B25%7D%7B49%7D%20%29%28%20%5Cfrac%7By%5E8%7D%7Bx%5E3%7D%20%20)
=
Answer: The proportion of new car buyers that trade in their old car has statistically significantly decreased.
Step-by-step explanation:
Since we have given that
p = 48% = 0.48
n = 115
x = 46
So, ![\hat{p}=\dfrac{46}{115}=0.40](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B46%7D%7B115%7D%3D0.40)
So, hypothesis would be
![H_0:\ p=\hat{p}\\\\H_a:p](https://tex.z-dn.net/?f=H_0%3A%5C%20p%3D%5Chat%7Bp%7D%5C%5C%5C%5CH_a%3Ap%3C%5Chat%7Bp%7D)
So, test value would be
![z=\dfrac{p-\hat{p}}{\sqrt{\dfrac{p(1-p)}{n}}}\\\z=\dfrac{0.48-0.40}{\sqrt{\dfrac{0.48\times 0.52}{115}}}\\\\z=\dfrac{0.08}{0.0466}\\\\z=1.72](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bp-%5Chat%7Bp%7D%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5C%5C%5Cz%3D%5Cdfrac%7B0.48-0.40%7D%7B%5Csqrt%7B%5Cdfrac%7B0.48%5Ctimes%200.52%7D%7B115%7D%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B0.08%7D%7B0.0466%7D%5C%5C%5C%5Cz%3D1.72)
At 10% level of significance, critical value would be
z= 1.28
Since 1.28 < 1.72
So, we will reject the null hypothesis.
Hence, the proportion of new car buyers that trade in their old car has statistically significantly decreased.
Answer:
20x
Step-by-step explanation:
20 x^3/ x^2
20 x x x
----------------
x x
Cancel the x's
20 x
---------
1
20x