You are putting together a single elimination tournament. You have 4368 people sign up to compete. How many game will have to be
2 answers:
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Answer:
<em>You can chose 3 in 5</em><em> :o</em>
Step-by-step explanation:
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By running in a bearing of 127°, Paul motion is in the south eastern direction.
Correct responses:
a. Please find attached the required diagram created with MS Visio
b. Paul's distance travelled east is approximately 11.98 km
- Paul's distance travelled south is approximately 0.903 km
Given:
The distance Paul runs = 1.5 km
The bearing Paul is running = 127°
a. The bearing of path Paul runs, 127°, is the angle measured in the clockwise direction relative to the northern direction
Please find attached the diagram representing the situation, created with MS Visio.
b. Paul's distance travelled east relative to the starting point is given by the component of Paul's path in the x-axis direction which is found as follows;
- Paul's distance east = 15 km × cos(37°) ≈ <u>11.98 km</u>
Pau's distance travelled in the south direction relative to the starting point
is given by the vertical distance travelled relative to the x-axis, which is
given as follows;
Distance Paul travels south = 1.5 km × sin(37°) ≈ <u>0.903 km</u>
Learn more about bearings in trigonometry here:
Answer:
The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is
Step-by-step explanation:
The main thing we have to take into account in this question is that we are about to find the probability of a <em>sample mean</em>. The distribution for <em>sample means</em> follows a <em>normal distribution</em> with mean and standard deviation
. Mathematically
For values of the sample , no matter the distribution the data come from.
And the variable <em>z</em> follows a <em>standard normal distribution</em>, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically
[1]
That is
We have a variance of 3364. That is, a <em>standard deviation</em> of
The population mean is
The sample size is
The sample mean is
With all this information, we can solve the question
The probability that the mean battery life would be greater than 533.2 minutes
Using equation [1]
With this value of z we can consult a <em>cumulative standard normal table</em> (or use some statistic program) to find the cumulative probability for <em>z</em> (and remember that this variable follows a standard normal distribution).
Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.
Then
However, in the question we are asked for . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have
Thus
Rounding to four decimal places, we have
So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) .