Answer: The sample mean
Step-by-step explanation:
The confidence interval is given by :-
Sample mean ± Margin of error
Given : The scores on a standardized test are normally distributed. If a random sample of standardized test scores is taken and the confidence interval is (497,537).
i.e. Sample mean - Margin of error = 497 ..(i)
Sample mean + Margin of error=537 ..(ii)
Adding (1) and (2), we get
2 (Sample mean) = 1034
⇒Sample mean = 517
Hence, the sample mean
Answer:
Option C - 52 mph
Step-by-step explanation:
I've attached an image to depict the diagram of movement of both cars.
dy/dt = 50 mph
dx/dt = 20 mph
From the attached image, using pythagoras theorem, we have;
x² + y² = s²
Differentiating with respect to to using implicit differentiation with power rule, we have;
2x(dx/dt) + 2y(dy/dt) = 2s(ds/dt) - - (eq1)
Now, let's find s by pythagoras theorem.
s² = 0.375² + 0.5²
s² = 0.390625
s = √0.390625
s = 0.625
Plugging in all the relevant values into eq 1,we have;
2×0.375(20) + 2×0.5(50) = 2×0.625(ds/dt)
15 + 50 = 1.25(ds/dt)
65 = 1.25(ds/dt)
ds/dt = 65/1.25
ds/dt = 52 mph
