Answer:
The sample size is 
Step-by-step explanation:
From the question we are told that
The margin of error is 
From the question we are told the confidence level is 97.5% , hence the level of significance is
=> 
Generally from the normal distribution table the critical value of 
is
Generally we will assume the sample proportion to be 
Generally the sample size is mathematically represented as
![n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7BZ_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%7D%7BE%7D%20%5D%5E2%20%2A%20%5C%5E%20p%20%281%20-%20%5C%5E%20p%20%29%20)
=> ![n = [\frac{2.241}{0.02} ]^2 *0.5 (1 - 0.5 )](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7B2.241%7D%7B0.02%7D%20%5D%5E2%20%2A0.5%20%281%20-%200.5%20%29%20)
=>
Answer:
Step-by-step explanation:
What we know is that A + S = 111. That is, the miles Andre drove plus the miles Scott drove totalled 111 miles. What we also know is that Scott drove quite a bit more than Andre did. Scott drove 7 miles more that ( +7 ) 3 times the number of miles Andrea drove. That looks like this algebraically:
S = 3A + 7
Now we can sub in that value for S to the original equation:
If A + S = 111 and S = 3A + 7, then
A + 3A + 7 = 111 and
4A + 7 = 111 and
4A = 104 so
A = 26 and
S = 3(26) + 7 so
S = 85 miles.
Scott drove 85 miles.
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4900=4200(1+r/2)^(2*4)
Solve for r
R=(4900/4200)^(1/8))-1)*2
R=((4,900÷4,200)^(1÷8)−1)×2
R=0.039*100=3.9%
Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
