A study is done on the population of a certain fish species in a lake. Suppose that the population size P(t) after t years is given by the following exponential function. P(t)=280(1.29)^t Find the initial population size?
does the function represent growth or decay?
By what percentage does the population change each year?

The three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

To find the magnitude and direction of the translations applied on a triangle, we need to know the coordinates of the vertices of the original triangle and the coordinates of the vertices of the transformed triangle.

Let's say the coordinates of the original triangle are (x1, y1), (x2, y2), and (x3, y3), and the coordinates of the transformed triangle are (x1', y1'), (x2', y2'), and (x3', y3').

The magnitude of the translation can be found by calculating the distance between the corresponding vertices of the original and transformed triangles using the distance formula. For example, the magnitude of the translation from (x1, y1) to (x1', y1') is given by:

sqrt((x1' - x1)^2 + (y1' - y1)^2)

Similarly, we can find the magnitudes of the other two translations.

The direction of the translation can be found by calculating the angle between the line connecting the corresponding vertices of the original and transformed triangles and the x-axis. We can use the arctangent function to find this angle. For example, the direction of the translation from (x1, y1) to (x1', y1') is given by:

tan^-1((y1' - y1)/(x1' - x1))

Similarly, we can find the directions of the other two translations.

Once we have the magnitudes and directions of the translations, we can describe the transformation using vector notation. The vector of the translation is given by:

< magnitude1, direction1 >

< magnitude2, direction2 >

< magnitude3, direction3 >

This represents the three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

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Final answer:

There are 32,768 possible outcomes of 15 football matches.

Explanation:

The number of possibleoutcomes in 15 football matches can be calculated by multiplying the number of outcomes for each match.

Assuming there are only two possible outcomes for each match (win or lose), the number of possible outcomes for one match would be 2. Since there are 15 matches, we can use the formula 2^15 to calculate the total number of possible outcomes.

Using this formula, there are 32,768 possible outcomes of 15 football matches.

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Answer:

He is not correct as the ratios are;

First ratio is 4:5,

Second ratio 11:13

Which are different values

Step-by-step explanation:

The number of correct questions Levi answered = 8 questions

The number of questions in the game = 10

The ratio of correctly answered questions to total number of questions in the first 10 question is given as follows

Correctly answered questions : Total number of questions = 8:10

Which can be simplified as 8:10 = 8/2:10/2 = 4:5

The number of correct questions Levi answered in the next three turns = 3 questions

The total number of questions attempted by Levi becomes 10 + 3 = 13 questions

The total number of correct answers given by Levi = 8 + 3 = 11 correct answers

The new ratio of correctly answered questions to total number of questions is therefore;

New correctly answered questions : Total number of questions = 11:13.

Therefore, the ratios do not remain the same as 4:5 ≠ 11:13.