What is the relationship

A population has the following characteristics.(a) A total of 25% of the population survives the first year. Of that 25%, 75% su

zaharov [31]

Answer:

After 1st year, the age distribution will be

$x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right]$

After 2nd year, the age distribution will be

$x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right]$

Step-by-step explanation:

A population has the following characteristics.

A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year.

The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.

From the above information, we can construct a transition age matrix.

$A = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right]$

The population now consists of 144 members in each of the three age classes.

From the above information, we can construct the current age matrix.

$x = \left[\begin{array}{ccc}144\\144\\144\end{array}\right]$

How many members will there be in each age class in 1 year?

After 1st year, the age distribution will be

$x_1 = A \cdot x$

$x_1 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}144\\144\\144\end{array}\right]$

The matrix multiplication is possible since the number of columns of first matrix is equal to the number of rows of second matrix.

$x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right]$

After 2nd year, the age distribution will be

$x_2 = A \cdot x_1$

$x_2 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}1584\\36\\108\end{array}\right]$

$x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right]$

4 0

4 years ago

The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 130 gallons and standa

Dmitrij [34]

$\mathbb P(X>154)=\mathbb P\left(\dfrac{X-130}{12}>\dfrac{154-130}{12}\right)=\mathbb P(Z>2)$

Since approximately 95% of any normal distribution falls within two standard deviations of the mean, it follows that 5% falls outside that range, with 2.5% to either side. So $\mathbb P(Z>2)\approx0.025$ .

The actual value is a bit closer to 0.0228, but that's not very far off.

7 0

3 years ago

Expand 6(x-8)= x- (8) = help me

maksim [4K]

Answer:

x = 8

Step-by-step explanation:

6(x-8)= x- (8)

6x - 48=x - 8

6x- 48 + 48 = x - 8 + 48

6x = x + 40

6x - x = x + 40 - x

5x = 40

5x/5 = 40/5

x = 8

Hope it helps! :)

3 0

3 years ago

Change word phrase to expressions or equations<br><br> The sum of p and 45 less than 89

stellarik [79]

Answer:

p + 45 < 89

Step-by-step explanation:

The sum of something is the result of addition so you know that they are adding p and 45 together. They then state that p plus 45 must be less than 89. You can show that by using the less than symbol "<"

If you want to find all of the different values that P could equal then all you have to do is subtract 45 from both sides so the equation would be

p < 44

this means that p can equal anything less than 44 for this statement to be valid. Hope this helped!

5 0

4 years ago

Necesito ayuda con esto

seropon [69]

I hope I helped you^_^

8 0

3 years ago