Express Taxi charges $10 as the starting fare and $2.50 per mile. Speedy Taxi charges $3 per mile with no starting fare. After h
2 answers:
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- At 2 hours, the traveler is 725 miles from home.
- At 3 hours, the distance is constant, at 880 miles. --> TRUE.
- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.
Step-by-step explanation:
The function D(t) is defined as follows:
for
for
for
Where
t is the time in hours
D(t) is the distance covered, in miles, after t hours
Now let's analyze the different statements:
- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get
So, the distance at t = 0 is 125 miles.
- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,
- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:
D(t) = 880
So, not 875 miles.
- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is
D(t) = 880
- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,
Learn more about functions:
Learn more about distance:
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Answer:
The principal amount was $23,393.45
Step-by-step explanation:
The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%
We will calculate Principal amount by this formula
Where A = amount (98,000)
P = Principal amount (P)
r = rate of interest 4.1% (0.041)
n = number of compounding interest monthly (12)
t = time (35 years)
98,000 = P(4.189386)
= 4.189386P = 98,000
P =
P = 23,392.4494 ≈ $23,392.45
The principal amount was $23,393.45
Answer:
a) p-hat (sampling distribution of sample proportions)
b) Symmetric
c) σ=0.058
d) Standard error
e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Step-by-step explanation:
a) This distribution is called the <em>sampling distribution of sample proportions</em> <em>(p-hat)</em>.
b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.
This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.
c) The variability of this distribution, represented by the standard error, is:
d) The formal name is Standard error.
e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:
If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).