Suppose you are researching the eating habits of people your age. What sampling method could you use to find the percentage of s

<span>To determine the quantity of tropical fish a tank can accommodate, calculate the volume by multiplying length, height, and width to obtain cubic centimeters of the aquarium, then divide that result by 10,000. Hence, 60*50*30 results in 90,000 cubic centimeters. Dividing 90,000 by 10,000 yields 9. Therefore, a tank with these measurements can hold 9 tropical fish.</span>

Answer:

After five years beyond the initial 20-year stretch, the population of this small community will be 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The representation of the exponential function is:

p = aeᵏᵗ

where a and k represent constants.

Taking the natural logarithm on both sides:

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We can apply linear regression to model the relationship between In p and t, thereby determining the values of k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

Here m corresponds to k and b is In a

By conducting a linear regression on the transformed linear relationship among In p and t and creating a graph of the variables, we derive the regression equation:

y = 0.151x + 4.584

The first image illustrates the equations needed for estimating the parameters of linear regression.

The second image displays the regression calculations alongside the graph of In p versus t.

By comparing

y = 0.151x + 4.584

to

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

Thus, the exponential relationship between p and t is formulated as:

p = 97.905 e⁰•¹⁵¹ᵗ

In order to forecast the population for 5 years ahead from the 20-year mark, we need to find p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41, which rounds down to 4268.

Hope this assists!!!

Response: Annabelle is employing the statistical concept known as Mode.

Detailed explanation: A central tendency measure, in its most basic sense, is a singular value or measure that effectively represents all elements of a particular data set. As such, one number can serve to essentially represent 99 other numbers in a data set of one hundred figures.

Commonly acknowledged measures of central tendency include mean, median, and mode.

The mode denotes the value that appears most often in a data set. Therefore, the modal value is statistically suitable as a representative of the entire group of values or data points.

If Annabelle measures the sides of 15 right triangles and concludes that the sum of the squares of the two legs is equal to the square of the hypotenuse for any right triangle, she is identifying the most frequently occurring value, and in her analysis, the most common data observed aligns with the Pythagorean Theorem.

This is why Annabelle's assumption is made with confidence.