A ball is dropped from a state of rest at time t=0.The distance traveled after t seconds is s(t)=16t^2 ft.
1 answer:
Answer:
i) Δs = 196 - 144 = 52 feet
ii) Δs / Δt = 104 feet/second
iii) Therefore the velocity at t = 3 is v(3) = 96 feet/second
Step-by-step explanation:
a.) i) s =
ii) at 3 seconds the distance traveled
iii) at 3.5 seconds the distance traveled
iv) Δs = 196 - 144 = 52 feet
b) Average velocity over [3, 3.5] = Δs / Δt = 52/(0.5) = 104 feet/second
c) the average velocity over the interval
I) i) [3, 3.01]
ii)
iii) Δs = 144.962 - 144 = 0.962 feet
iv) Average velocity over [3, 3.01] = Δs / Δt = 0.962/(0.01) =
96.2 feet/second
II) i) [3, 3.001]
ii)
iii) Δs = 144.096 - 144 = 0.096 feet
iv) Average velocity over [3, 3.001] = Δs / Δt = 0.096/(0.001) =
96 feet/second
III) i) [3, 3.0001]
ii)
iii) Δs = 144.0096 - 144 = 0.0096 feet
iv) Average velocity over [3, 3.0001] = Δs / Δt = 0.0096/(0.0001) =
96 feet/second
IV) i) [2.9999, 3]
ii)
iii) Δs = 144 - 143.99 = 0.0096 feet
iv) Average velocity over [2.9999, 3] = Δs / Δt = 0.0096/(0.0001) =
96 feet/second
V) i) [2.999, 3]
ii)
iii) Δs = 144 - 143.904 = 0.09598 feet
iv) Average velocity over [2.999, 3] = Δs / Δt = 0.09598/(0.001) =
95.98 feet/second
VI) i) [2.99, 3]
ii)
iii) Δs = 144 - 143.042 = 0.098 feet
iv) Average velocity over [2.99, 3] = Δs / Δt = 0.098/(0.01) =
98 feet/second
Therefore the velocity at t = 3 is v(3) = 96 feet/second
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Answer:
a. The test statistic for this hypothesis would be z=1.71
b. Critical value at α = 0.10: z=1.282
c. Reject H0, the television network should not keep its current lineup.
d. H0: p ≤ 0.50; HA: p > 0.50
Step-by-step explanation:
We have to performa an hypothesis test on a proportion.
The claim is that the proportion of viewers that prefer the new show is bigger than 50% (meaning that most viewers prefer the new show).
The null hypothesis will state that both shows have the same proportion.
Then, the null and alternative hypothesis are:
The sample proportion is p=0.53
The standard error of the proportion is:
Then, the z-statistic can be calculated as:
The critical value for a right tailed test at a significance level of 0.10 is zc=1.282. This value can be looked up in a standard normal distribution table.
As the statistic is bigger than the critical value, it lies in the rejection region. The null hypothesis is rejected. There is evidence to support the claim that the proportion of viewers which support the new show is larger than 0.50.