Answer: B. 105 mph
Step-by-step explanation:
<span>
0.05216228571 is the answer.</span>
<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:
(- 2, 6 )
Step-by-step explanation:
Given the equations
3x + 2y = 6 → (1)
y - x = 6 ( multiply through by 3 to clear the fraction )
2y - 3x = 18 ( add 3x to both sides )
2y = 18 + 3x → (2)
Substitute 2y = 18 + 3x into (1)
3x + 18 + 3x = 6
6x + 18 = 6 ( subtract 18 from both sides )
6x = - 12 ( divide both sides by 6 )
x = - 2
Substitute x = - 2 into (1) and solve for y
3(- 2) + 2y = 6
- 6 + 2y = 6 ( add 6 to both sides )
2y = 12 ( divide both sides by 2 )
y = 6
solution is (- 2, 6 )
