Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as ai
1 answer:
Answer:
(a)
(b) It takes <u>26 seconds</u> to completely fill the balloon.
Step-by-step explanation:
Let the time for which balloon is filled be 't' seconds.
(a)
Given:
Rate of filling (r) = 0.5 ft³/s
Initial volume of hydrogen in the balloon (V₀) = 2 ft³
The filling of hydrogen is a linear function of time.
So, Volume of hydrogen filled in the balloon at any time 't' is given as:
Volume = Initial volume + Rate of fill × time taken
⇒
⇒
Therefore, the linear function 'V' that models the volume of hydrogen in the balloon at any time 't' is
(b)
Given:
Balloon has a capacity of 15 ft³. This means the total volume of hydrogen that can be filled is 15 ft³.
So,
Plugging 'V' value in the above equation and solving for 't', we have:
Therefore, it takes 26 seconds to completely fill the balloon.
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Answer:
Let X the random variable that represent the pulse rates of a population, and for this case we know the distribution for X is given by:
Where and
For this case the z score given by:
And for this case the z score is without units, so the correct answer would be:
The z scores are numbers without units of measurement.
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".
Solution to the problem
Let X the random variable that represent the pulse rates of a population, and for this case we know the distribution for X is given by:
Where and
For this case the z score given by:
And for this case the z score is without units, so the correct answer would be:
The z scores are numbers without units of measurement.