This is the solution using substitution. Hope this helps!
Pythagorean theorem: Show work please A=16,B=12
1 answer:
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Answer:
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).
Step-by-step explanation:
Our sample size is 96.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
Then, we need to subtract one by the confidence level and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 95 and 0.025 in the t-distribution table, we have .
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
Now, we multiply T and s
For the lower end of the interval, we subtract the mean by M. So
For the upper end of the interval, we add the mean to M. So
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).
Answer:
speed of the boat = 29 mph
Step-by-step explanation:
In order to solve the problem, we need to recall the formula for speed (or velocity "v") of an object as the quotient between the distance (d) covered over the time (t) it takes to cover it:
Now we analyse the two different situations (downstream vs upstream) separately:
Downstream:
Considering that when the boat goes downstream (140 mile trip), it goes with the current, so its velocity (unknown v) couples (adds) to that of the current (6 mph) its total speed would be: v + 6 mph. Therefore we can use this information to write the equation for velocity given above, and solve for time:
Upstream:
In this case, the boat goes against the current, so its speed will be reduced by the current's speed of 6 mph, then its total speed will be: v - 6 mph. Recalling that in this case the boat travels 92 miles in the same time (t) it took it to do the downstream trip, we can write:
Now all we need to do is make these last two equations equal each other since the time used for each trip is the same. We can then solve for the actual speed (unknown v) of the boat: