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kirza4 [7]
2 years ago
7

Since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year. Predict th

e number of cases that will be reported in 2020 and the trend continues
Mathematics
1 answer:
BaLLatris [955]2 years ago
3 0

Answer:

20,158 cases

Step-by-step explanation:

Let t=0 represent year 2010.

We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.

Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.

We can represent this information in an exponential decay function as:

F(t)=102,390(1-0.15)^t

F(t)=102,390(0.85)^t

To find number of cases in 2020, we will substitute t=10 in our decay function as:

F(10)=102,390(0.85)^{10}

F(10)=102,390(0.1968744043407227)

F(10)=20,157.970260446597\approx 20,158

Therefore, 20,158 cases  will be reported in 2020.

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balandron [24]

Answer:

The approximate percentage of SAT scores that are less than 865 is 16%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 1060, standard deviation of 195.

Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.

865 = 1060 - 195

So 865 is one standard deviation below the mean.

Approximately 68% of the measures are within 1 standard deviation of the mean, so approximately 100 - 68 = 32% are more than 1 standard deviation from the mean. The normal distribution is symmetric, which means that approximately 32/2 = 16% are more than 1 standard deviation below the mean and approximately 16% are more than 1 standard deviation above the mean. So

The approximate percentage of SAT scores that are less than 865 is 16%.

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