Answer:
a) g(x) = f(x) + 3
So g(x) is a vertical translation of f(x), 3 units upwards
b) g(x) = 3x² - 1 + 3
g(x) = 3x² + 2
The graph has shifted 3 units upwards, so has the vertex.
The vertex of f is (0,-1)
Whereas the vertex of g is (0,2)
-1 + 3 = 2
Answer:
(0.084,0.396)
Step-by-step explanation:
The 99% confidence interval for the proportion of customers who use debit card monthly can be constructed as
![p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=p-z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%7D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%3CP%3Cp%2Bz_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%7D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
![p=\frac{x}{n}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7Bx%7D%7Bn%7D)
![p=\frac{12}{50}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B12%7D%7B50%7D)
![p=0.24](https://tex.z-dn.net/?f=p%3D0.24)
![q=1-p=1-0.24=0.76](https://tex.z-dn.net/?f=q%3D1-p%3D1-0.24%3D0.76)
![\frac{\alpha }{2} =\frac{\0.01 }{2}=0.005](https://tex.z-dn.net/?f=%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%3D%5Cfrac%7B%5C0.01%20%7D%7B2%7D%3D0.005)
![p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=p-z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%7D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%3CP%3Cp%2Bz_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%7D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
![0.24-z_{0.005} \sqrt{\frac{0.24*0.76}{50} }](https://tex.z-dn.net/?f=0.24-z_%7B0.005%7D%20%5Csqrt%7B%5Cfrac%7B0.24%2A0.76%7D%7B50%7D%20%7D%20%3CP%3C0.24%2Bz_%7B0.005%7D%20%5Csqrt%7B%5Cfrac%7B0.24%2A0.76%7D%7B50%7D%20%7D)
![0.24-2.58(0.0604)](https://tex.z-dn.net/?f=0.24-2.58%280.0604%29%3CP%3C%200.24%2B2.58%280.0604%29)
![0.24-0.155832](https://tex.z-dn.net/?f=0.24-0.155832%3CP%3C0.24%2B0.155832)
By rounding to three decimal places we get,
![0.084](https://tex.z-dn.net/?f=0.084%3CP%3C0.396)
The 99% confidence interval for the proportion of customers who use debit card monthly is (0.084,0.396).
Answer:
242 cm
Step-by-step explanation:
1. Find the scale factor
A scale factor (SF) is the ratio of two corresponding lengths in similar figures.
SF = actual distance/scale distance
If the scale width is 3.8 cm,
SF = 418 cm/3.8 cm = 110
2. Calculate the actual depth
110 = actual depth/2.2 cm
Actual depth = 110 × 2.2 cm = 242 cm
Answer:
D
Step-by-step explanation:
D represents absolute value, and this is what you use to find the answer to this equation.