If g(n) varies inversely with n and g(n) = 8 when n = 3, find the value of n when g(n) = 6.

Mathematics

1 answer:

liraira [26]3 years ago

3 0

Answer: Last option.

Step-by-step explanation:

By definition, Inverse variation equations have this form:

$y=\frac{k}{x}$

Where "k" is the constant of variation.

In this case, it is:

$g(n)=\frac{k}{n}$

Knowing that $g(n) = 8$ when $n = 3$ , we can substitute values into the equation and solve for "k":

$8=\frac{k}{3}\\\\8*3=k\\\\k=24$

Therefore, we can find the value of "n" when $g(n) = 6$ by substiuting this value and the value of "k" into the equation and solving for "n". Then:

$6=\frac{24}{n}\\\\6n=24\\\\n=\frac{24}{6}\\\\n=4$

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The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

KatRina [158]

Answer:

a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

Step-by-step explanation:

Empirical Rule:

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.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean:

$\mu = 47$