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3 years ago

Show that an exponential model fits the data. Then write a recrusive rule that models the data.

Mathematics

1 answer:

Brilliant_brown [7]3 years ago

5 0

Answer:

<u>Exponential function:</u>

f(x) = abˣ

<u>Use the given data to determine the function.</u>

f(0) = ab⁰ = a*1 = a ⇒ a = 0.75

b = 2 as each of the f(n) is twice the previous one in series.

<u>The model is:</u>

f(n) = 0.75*2ⁿ

<u>Recursive rule to reflect this is:</u>

f(0) = 0.75
f(n) = 2*f(n-1)

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3 years ago

Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a s

n200080 [17]

Answer:

Let's assume the following data:

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10 $\sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118$

$r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974$

So then the correlation coefficient would be r =0.974

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

Let's assume the following data

Price in Dollars (X) 26 29 32 38 47

Number of Bids (Y) 12 13 15 16 18

For our case we have this:

n=10 $\sum x = 172, \sum y = 74, \sum xy = 2623, \sum x^2 =6194, \sum y^2 =1118$

$r=\frac{5(2623)-(172)(74)}{\sqrt{[5(6194) -(172)^2][5(1118) -(74)^2]}}=0.974$

So then the correlation coefficient would be r =0.974

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3 years ago

The outer rectangle is 2 feet by 4 feet. There is a semicircle and isosceles triangle within the rectangle. Find the area of the

valina [46]

To find the shaded area in an image first calculate the total area of the figure and then subtract the white area from this total.

<h3>How to find the area of a shaded area?</h3>

Determine the total area of the figure, in this case, the are of the rectangle that contains the triangle and the semicircle.
Calculate the area of the white region.
Substract the non-shaded area to the total area.

<h3>How to find out the area of different shapes?</h3>

Rectangle: side x side = 2 x 4 = 8 square feet
Isosceles triangle = 1/2 base x height
Semicirle = 1/2 (π x r^2)

Note: This question is incomplete because the image of the shaded regions is not provided; due to this, the answer is based on general knowledge.

Learn more about triangles in: brainly.com/question/2773823

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3 years ago

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 ye

sveta [45]

Answer:

13.53% probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ is the mean in the given time interval.

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years.

One earthquake each 100/5 = 20 years.

What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years?

40 years, so $\mu = 40/20 = 2$

This probability is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353$

13.53% probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years

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3 years ago