A circle has a radius of twenty-one centimeters.
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Answer:
the rate from the plane to the radar station increasing 3 minutes later is 19.81 km/min
Step-by-step explanation:
A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing 3 minutes later?
speed (Δs₁)= change in distance(Δd₁) /(Δt₁)change in time
mathematically,
= Δs₁
= 14 km/min =
and will are to find the speed after passes the radar
=Δs₂ km/min =
to find d₁ and d₂ with respect to angle 45 degree at 4km
sin 45 = opp/hyp = 4/d₁
d₁ = 4/sin45 = 5.66km
tan 45 == opp/adj = 4/d₂
d₂ =4/tan45 = 4km
for three minute increment,
=3 x d₁ x Δs₁ = 3 x d₂ Δs₂
= 3x5.66x14 = 3x 4 xΔs₂
= 237.72 = 12Δs₂
=Δs₂ = 19.81km/min
By formula we know that:
z (x) = (x - m) / [sd / sqrt (n)]
where x is the value we want to know (6.7), m is the mean (5), sd is the standard deviation (7.1) and n is the sample size (29).
Replacing we have:
z (6.7) = (6.7 - 5) / [7.1 / sqrt (29)]
z = 1.289
If we look in the normal distribution table (attached), we have that the probability is 0.8997, therefore:
1 - 0.8897 = 0.1003
So the conditional probability of a herd sample earning at least 6.7 pounds per steer is 10.03%.
Now the hypothesis tells me:
m> 5
The probability is somewhat low, therefore, the most correct thing is to reject the hypothesis even though it is a fact that can occur.
The cardinality of the union between two sets is given by
In fact, if an element is in both A and B, it is counted in both N(A) and N(B), so we're counting it twice. By subtracting the cardinality of the interserction, we're taking back one of these "extra-counted" element, and the count is correct. In your case, the numbers are
This means that the two sets cover, without repetitions, 43 of the 66 elements in the sets. So, there are
elements which are in neither A nor B