Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given that
Margin of error = 0.5 years
Standard deviation = 5
At 90% confidence, z = 1.645
We need to find the minimum size of the sample they must take.
So,
![n=(\dfrac{z\sigma}{E})^2\\\\n=(\dfrac{1.645\times 5}{0.5})^2\\\\n=270.6\\\\n\approx 271](https://tex.z-dn.net/?f=n%3D%28%5Cdfrac%7Bz%5Csigma%7D%7BE%7D%29%5E2%5C%5C%5C%5Cn%3D%28%5Cdfrac%7B1.645%5Ctimes%205%7D%7B0.5%7D%29%5E2%5C%5C%5C%5Cn%3D270.6%5C%5C%5C%5Cn%5Capprox%20271)
Hence, Option 'd' is correct.
Answer:
where is the figure and the picture?
Answer:
![\huge\boxed{(2;\ 4)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%282%3B%5C%204%29%7D)
Step-by-step explanation:
We have
![y>-x^2+5](https://tex.z-dn.net/?f=y%3E-x%5E2%2B5)
Put the coordinates of the given points and check the inequality:
For (0; 5) → x = 0; y = 5
![5>-0^2+5\\5>0+5\\5>5\qquad\bold{FALSE}](https://tex.z-dn.net/?f=5%3E-0%5E2%2B5%5C%5C5%3E0%2B5%5C%5C5%3E5%5Cqquad%5Cbold%7BFALSE%7D)
For (2; 4) → x = 2, y = 4
![4>-2^2+5\\4>-4+5\\4>1\qquad\bold{TRUE}](https://tex.z-dn.net/?f=4%3E-2%5E2%2B5%5C%5C4%3E-4%2B5%5C%5C4%3E1%5Cqquad%5Cbold%7BTRUE%7D)
For (1; 3) → x = 1, y = 3
![3>1^2+5\\3>1+5\\3>6\qquad\bold{FALSE}](https://tex.z-dn.net/?f=3%3E1%5E2%2B5%5C%5C3%3E1%2B5%5C%5C3%3E6%5Cqquad%5Cbold%7BFALSE%7D)