Answer:
4th answer
Step-by-step explanation:
g(h(x)) means to put the formula for h(x) into the formula for g( ).
![g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16](https://tex.z-dn.net/?f=g%28h%28x%29%29%3Dg%282x-2%29%3D-3%282x-2%29%5E3-2%282x-2%29%5E2%5C%5C%3D-3%288x%5E3-24x%5E2%2B24x-8%29-2%284x%5E2-8x%2B4%29%5C%5C%3D-24x%5E3%2B72x%5E2-72x%2B24-8x%5E2%2B16x-8%5C%5C%3D-24x%5E3%2B64x%5E2-56x%2B16)
Cubing the binomial 2x - 2 can take some time!
A great time to apply the quadratic formula
for a quadratic equation
Ax^2 + Bx +C =0
then
Step-by-step explanation:
Diameter = 10 inch
Radius = 5 inch
circumference = 2πr = 2× 3.14× 5= 31.4 inch
option A
Answer:
Sample size is ![n=423](https://tex.z-dn.net/?f=n%3D423)
Step-by-step explanation:
Given that,
Margin of error
%
Confidence level
%
Suppose, sample proportion![=0.5](https://tex.z-dn.net/?f=%3D0.5)
i.e. ![\hat{P}=0.5](https://tex.z-dn.net/?f=%5Chat%7BP%7D%3D0.5)
We know that,
Margin of error ![=2^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }](https://tex.z-dn.net/?f=%3D2%5E%2A%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%20%7D)
∴ ![1.64\sqrt{\frac{0.5(0.5)}{n} } \leq 4\%](https://tex.z-dn.net/?f=1.64%5Csqrt%7B%5Cfrac%7B0.5%280.5%29%7D%7Bn%7D%20%7D%20%5Cleq%204%5C%25)
![\Rightarrow 1.64\sqrt{\frac{0.25}{n} } \leq 0.04](https://tex.z-dn.net/?f=%5CRightarrow%201.64%5Csqrt%7B%5Cfrac%7B0.25%7D%7Bn%7D%20%7D%20%5Cleq%200.04)
![\Rightarrow \frac{0.5}{\sqrt{n} } \leq \frac{0.04}{1.64}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B0.5%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5Cleq%20%5Cfrac%7B0.04%7D%7B1.64%7D)
![\Rightarrow \frac{0.5}{\sqrt{n} } \leq 0.0243](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B0.5%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5Cleq%200.0243)
![\Rightarrow \sqrt{n}\geq \frac{0.5}{0.0243}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%7Bn%7D%5Cgeq%20%5Cfrac%7B0.5%7D%7B0.0243%7D)
![\Rightarrow \sqrt{n}\geq 20.57](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%7Bn%7D%5Cgeq%2020.57)
squaring on both side,
∴ ![n=423.1249](https://tex.z-dn.net/?f=n%3D423.1249)
Hence, the sample size is,
![n=423](https://tex.z-dn.net/?f=n%3D423)
Hence, the correct option is ![(b).](https://tex.z-dn.net/?f=%28b%29.)