Answer:
23.52 miles
Step-by-step explanation:
Let us find the number of miles that they would have run.
Kana starts at 9:35 a.m. and runs at an average rate of 7 mph.
Let the time she has spent so far be t.
Speed is given as:
s = d / t
where d = distance and t = time
=> d = s * t
Therefore, for Kana:
d = 7 * t = 7t _____________(1)
Ji-Hun starts at 10:00 am (25 minutes after Hannah) and runs at an average rate of 8 mph.
25 minutes = 25/60 hour = 0.42 hour
So, his time (compared to Kana's) is t - 0.42.
therefore, for Ji-Hun:
d = 8 * (t - 0.42)
=> d = 8t - 3.36 ____________(2)
Equating (1) and (2):
7t = 8t - 3.36
=> 8t - 7t = 3.36
t = 3.36 hours
Therefore, let us find d:
d = 7 * 3.36 = 23.52 miles
So, Ji-Hun will catch up to Kana after 23.52 miles.
Answer:
0.8185 or 81.85%
Step-by-step explanation:
The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.
The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean the z sore is negative. It is given by:

To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.
For 8 inches:

For 12.5 inches:

From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%
The answer to this question:
h=-12
Z for the 5th percentile is about -1.6449