What is the result of converting 14 inches into centimeters? Remember that 1 inch = 2.54 centimeters.
2 answers:
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The answer is:
To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.
So, let be the first car speed "x" and the second car speed "y", writing the equations we have:
For the first car:
For the second car:
We know that the speed of the second car is the speed of the first car plus 14 mph, so:
Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles, so, we can calculate the relative speed between them:
If the cars are moving towards each other the relative speed will be:
Then, since we know that they covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we have:
Writing the equation, we have:
We have that the speed of the first car is equal to 41 mph.
Now, for the second car we have that:
Hence, we have that:
Have a nice day!
Answer:
a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.
b) There is a 15.97% probability that x will be between 54 and 55.
c) The 47th percentile of x is .
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.
This means that .
We have to find the standard deviation of the sample, that is:
(a) Is it appropriate to use the normal distribution to find probabilities for x?
We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.
(b) Find the probability that x will be between 54 and 55.
This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.
X = 55
has a pvalue of 0.88877.
X = 54
has a pvalue of 0.72907.
So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.
(c) Find the 47th percentile of x. Round the answer to at least two decimal places.
This is the value of X when Z has a pvalue of 0.47;
This is between and
. So we use
.
The 47th percentile of x is .