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2 years ago

CALCULUS: Determine which function is a solution to the differential equation y ' − y = 0.

Mathematics

1 answer:

Montano1993 [528]2 years ago

8 0

C: none of these are solutions to the given equation.

• If y(x) = e², then y is constant and y' = 0. Then y' - y = -e² ≠ 0.

• If y(x) = x, then y' = 1, but y' - y = 1 - x ≠ 0.

The actual solution is easy to find, since this equation is separable.

y' - y = 0

dy/dx = y

dy/y = dx

∫ dy/y = ∫ dx

ln|y| = x + C

y = exp(x + C )

y = C exp(x) = C eˣ

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Answer:

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Step-by-step explanation:

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 5,500 and standard deviation 1,000.

This means that $\mu = 5500, \sigma = 1000$

What is the probability that the call center will get between 4,800 and 5,000 calls in a day?

This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So

X = 5000

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

$Z = \frac{5000 - 5500}{1000}$

$Z = -0.5$

$Z = -0.5$ has a p-value of 0.3085.

X = 4800

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

$Z = \frac{4800 - 5500}{1000}$

$Z = -0.7$

$Z = -0.7$ has a p-value of 0.2420.

0.3085 - 0.2420 = 0.0665

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

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Basile [38]

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