During the Labor Day weekend, Amy and Kathleen each ran in a race. Amy ran in a 5K and completed it in 31 minutes and 15 seconds
2 answers:
Answer:
The relationship is rate is same.
Step-by-step explanation:
Given : During the Labor Day weekend, Amy and Kathleen each ran in a race. Amy ran in a 5K and completed it in 31 minutes and 15 seconds. Kathleen ran in a half-marathon, which is 21.1 kilometers, and completed it in 2 hours, 11 minutes, and 52.5 seconds.
Let d represent distance in kilometers, r represent the rate, and t represent time in minutes.
To find : The proportional relationship ?
Solution :
We know,
1 hour = 60 minutes = 60 × 60 seconds
First we find the rate of both Amy and Kathleen.
Amy ran in a 5 km and completed it in 31 minutes and 15 seconds.
Rate of Amy in km/hr is given by,
Kathleen ran in a half-marathon, which is 21.1 kilometers, and completed it in 2 hours, 11 minutes, and 52.5 seconds.
Rate of Kathleen in km/hr is given by,
Both man ran at the same speed.
Therefore, The relationship is rate is same.
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Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we select a sample of n =100
From the central limit theorem we know that the distribution for the sample mean is given by:
So then the sample mean would be:
And the standard deviation would be:
Yes, $40 is a reasonable amount to pay for the cab fare.
<em><u>Explanation</u></em>
Sheri’s cab fare was $32 and the percentage of gratuity is 20%
So, the amount of gratuity will be:
Thus, <u>the fare of the cab including the gratuity</u> will be:
As Sheri wrote a check to the cab driver for $40 , it means she paying ($40 - $38.40) or <u>$1.60 more to the cab driver</u>. So, the $40 check is a reasonable amount to pay for the cab fare.