<span>n = 5
The formula for the confidence interval (CI) is
CI = m ± z*d/sqrt(n)
where
CI = confidence interval
m = mean
z = z value in standard normal table for desired confidence
n = number of samples
Since we want a 95% confidence interval, we need to divide that in half to get
95/2 = 47.5
Looking up 0.475 in a standard normal table gives us a z value of 1.96
Since we want the margin of error to be ± 0.0001, we want the expression ± z*d/sqrt(n) to also be ± 0.0001. And to simplify things, we can omit the ± and use the formula
0.0001 = z*d/sqrt(n)
Substitute the value z that we looked up, and get
0.0001 = 1.96*d/sqrt(n)
Substitute the standard deviation that we were given and
0.0001 = 1.96*0.001/sqrt(n)
0.0001 = 0.00196/sqrt(n)
Solve for n
0.0001*sqrt(n) = 0.00196
sqrt(n) = 19.6
n = 4.427188724
Since you can't have a fractional value for n, then n should be at least 5 for a 95% confidence interval that the measured mean is within 0.0001 grams of the correct mass.</span>
        
             
        
        
        
Answer:
C
Step-by-step explanation:
 x 105,000,000 = 16,800,000
 x 105,000,000 = 16,800,000
 
        
             
        
        
        
The electrical resistance of a wire varies as its length and inversely as the square of the diameter.
R = (k*L)/(d^2)
where k = proportionality constant
Since the two wires have the same material, their proportionality constant is same.
Equating that
(R1*d1^2)/L1 = (R2*d2^2)/L2
Given that R1 = 10 ohms, d1 = 1.2 mm or 0.0012 m, L1 = 18 m, d2 = 1.5 mm or 0.0015 m, L2 = 27 m, and R2 is unknown.
Therefore
[10*(0.0012^2)]/18 = [R2*(0.0015^2)]/27
R2 = 9.6 ohms 
        
             
        
        
        
Answer:
 
 
and 

Step-by-step explanation:
The standard equation of a circle is  where the coordinate (h,k) is the center of the circle.
 where the coordinate (h,k) is the center of the circle.  
Second Problem:
- We can start with the second problem which uses this info very easily.
- (h,k) in this problem is (-2,15) simply plug these into the equation.  . .
- We can also add the radius 3 and square it so it becomes 9. The equation.
- This simplifies to  . .
First Problem: 
- The first problem takes a different approach it is not in standard form. But we can convert it to standard form by completing the square.
 first subtract 37 from both sides so the equation is now first subtract 37 from both sides so the equation is now . .
 by adding by adding to both the x and y portions of this equation you can complete the squares. to both the x and y portions of this equation you can complete the squares. and and which equals 49 and 4. which equals 49 and 4.
- Add 49 and 4 to both sides and the equation is now: You can simplify the y and x portions of the equations into the perfect squares or factored form You can simplify the y and x portions of the equations into the perfect squares or factored form and and . .
- Finally put the whole thing together.  . .
I hope this helps!
 
        
             
        
        
        
Answer:
20
Step-by-step explanation:
collect like terms and divide both sides