Answer:2^7 ≠ 7^2
Step-by-step explanation:
2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2
The only factor is 2
7^2 = 7 * 7
The only factor is 7
Comparing the factors when written as a repeated multiplication,
2^7 and 7^2 have no common factor :
2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128
7^2 = 7 * 7 = 49
Answer:
cool
Step-by-step explanation:
Answer:
0<x<1
Step-by-step explanation:
(x+3)(x−4)<−12
FOIL
x^2 -4x+3x -12 <-12
x^2 -x -12 <-12
Add 12 to each side
x^2 -x -12+12 <-12+12
x^2 -x <0
Factor out an x
x(x-1) <0
Using the zero product property
x(x-1) =0
x=0 x-1=0
x=0 x=1
Check the ranges
x<0
x(x-1) <0
- * - >0
False
0<x<1
x(x-1) <0
+ * - <0
True
x>1
x(x-1) <0
+ * + >0
False
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
