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Galina-37 [17]
2 years ago
12

A scientist measured the energy of a system and found that it was increasing. The data shown represent the energy taken every bi

llionth of a second. Time (nanoseconds) 0 1 2 3 Energy (Joules) 2.654 6.290 14.909 35.335 Classify the type of growth the scientist observed. 1)linear 2)quadratic 4)exponential 5)logarithmic
Mathematics
2 answers:
Setler [38]2 years ago
5 0

At start ( t = 0 nanoseconds ) :

E ( t = 0 ) = 2.645 J

E ( t = 1 ) = 6.290 J

E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37

Also:

E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37

E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37

E ( t ) = 2.645 * 2.37 ^ t

The answer is 4) exponential growth.

DiKsa [7]2 years ago
3 0

At start ( t = 0 nanoseconds ) :

E ( t = 0 ) = 2.645 J

E ( t = 1 ) = 6.290 J

E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37

Also:

E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37

E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37

Therefore, the formula for calculating the energy of the system is:

E ( t ) = 2.645 * 2.37 ^ t

The answer is 4) exponential growth.


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the time taken by a student to the university has been shown to be normally distributed with mean of 16 minutes and standard dev
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a) 2.84% probability that he is late for his first lecture.

b) 5.112 days

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 16, \sigma = 2.1

a. Find the probability that he is late for his first lecture.

This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So

Z = \frac{X - \mu}{\sigma}

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2.84% probability that he is late for his first lecture.

b. Find the number of days per year he is likely to be late for his first lecture.

Each day, 2.84% probability that he is late for his first lecture.

Out of 180

0.0284*180 = 5.112 days

4 0
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