The arc length, radius and the included angle are related as
where
is in radians.
The radius
is given by

Correct choice is (B).
For this there is no exact square root but the closest it get is about 75.33
20 miles per hour
If it can cover 40 mph in 2 hours divide 40 by 2 to get the amount for one hour and 40/2=20mph
A1.) <span>the interval about the mean within which 90% of the data lie = 120 + or - 1.645(10) = 120 + or - 16.45 = 120 - 16.45 to 120 + 16.45 = 103.55 to 136.45
2.) P(100 < X < 140) = P(X < 140) - P(X < 100) = P(z < (140 - 120)/10) - P(z < (100 - 120)/10) = P(z < 2) - P(z < -2) = P(z < 2) - [1 - P(z < 2)] = 2P(z < 2) - 1 = 2(0.97725) - 1 = 1.9545 - 1 = 0.9545 = 95.5%
B1.) </span><span>the interval about the sample mean that has a 1% level of confidence is 500 + or - 2.575(80/√1000) = 500 + or - 7 = 500 - 7 to 500 + 7 = 493 to 507
2.) 2P(z < a) - 1 = 0.90
2P(z < a) = 1.90
P(z < a) = 0.95
a = 1.645
(b - 500)/(80/√1000) = 1.645
b - 500 = 4
b = 500 + 4 = 504
The </span><span>interval about the sample mean such that the probability is 0.90 that the mean number lies within the interval is 496 - 504.</span><span />