Answer: The number of first-year residents she must survey to be 95% confident= 263
Step-by-step explanation:
When population standard deviation (
) is known and margin of error(E) is given, then the minimum sample size (n) is given by :-
, z* = Two-tailed critical value for the given confidence interval.
For 95% confidence level , z* = 1.96
As, = 8.265, E = 1
So, ![n= (\dfrac{1.96\times8.265}{1})^2 =(16.1994)^2\\\\= 262.42056036\approx263\ \ \ [\text{Rounded to the next integer}]](https://tex.z-dn.net/?f=n%3D%20%28%5Cdfrac%7B1.96%5Ctimes8.265%7D%7B1%7D%29%5E2%20%3D%2816.1994%29%5E2%5C%5C%5C%5C%3D%20262.42056036%5Capprox263%5C%20%5C%20%5C%20%5B%5Ctext%7BRounded%20to%20the%20next%20integer%7D%5D)
Hence, the number of first-year residents she must survey to be 95% confident= 263
<span>A postulate becomes a theorem when it is proven by a series of logical steps to a valid outcome. Typically, a postulate is a statement that is presumed to be true without proof, whereas a theorem is a true statement that can be proven</span>
Among the coefficient signs (++-) there is one sign change, so Descarte's rule of signs tells you there is one positive real root. Changing x to -x does not affect the signs, so there is also one negative real root. Then there are two complex roots to bring the total number to 4, the degree of the polynomial.
The factorization is
f(x) = (x^2 +25)(x^2 -4)
Each of these can be factored using the form for factoring the difference of squares.
f(x) = (x -5i)(x +5i)(x -2)(x +2)
There are 2 real roots: ±2.
There are 2 imaginary roots: ±5i.
Answer:
greg, 4 seconds
Step-by-step explanation:
find how long it takes each person to run 2km first.
distance/speed:
- pepper: 2/3 *60(seconds)=40 seconds
- Greg: 2/5 *60= 24 seconds
40-12=28 seconds, pepper will take 28 seconds to finish the race from the time greg starts. greg will win by 4 seconds
